id	sid	tid	token	lemma	pos
ap-2101	1	1	acta	acta	PROPN
ap-2101	1	2	polytechnica	polytechnica	PROPN
ap-2101	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2101	1	4	/	/	SYM
ap-2101	1	5	ap.2014.54.0156	ap.2014.54.0156	PROPN
ap-2101	1	6	acta	acta	PROPN
ap-2101	1	7	polytechnica	polytechnica	PROPN
ap-2101	1	8	54(2):156–172	54(2):156–172	PROPN
ap-2101	1	9	,	,	PUNCT
ap-2101	1	10	2014	2014	NUM
ap-2101	1	11	©	©	PROPN
ap-2101	1	12	czech	czech	PROPN
ap-2101	1	13	technical	technical	PROPN
ap-2101	1	14	university	university	PROPN
ap-2101	1	15	in	in	ADP
ap-2101	1	16	prague	prague	PROPN
ap-2101	1	17	,	,	PUNCT
ap-2101	1	18	2014	2014	NUM
ap-2101	1	19	available	available	ADJ
ap-2101	1	20	online	online	ADV
ap-2101	1	21	at	at	ADP
ap-2101	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2101	1	23	exact	exact	ADJ
ap-2101	1	24	renormalization	renormalization	NOUN
ap-2101	1	25	group	group	NOUN
ap-2101	1	26	for	for	ADP
ap-2101	1	27	point	point	NOUN
ap-2101	1	28	interactions	interaction	NOUN
ap-2101	1	29	osman	osman	PROPN
ap-2101	1	30	teoman	teoman	PROPN
ap-2101	1	31	turgut	turgut	PROPN
ap-2101	1	32	,	,	PUNCT
ap-2101	1	33	cem	cem	NOUN
ap-2101	1	34	eröncel∗	eröncel∗	PROPN
ap-2101	1	35	bogazici	bogazici	PROPN
ap-2101	1	36	university	university	PROPN
ap-2101	1	37	,	,	PUNCT
ap-2101	1	38	department	department	NOUN
ap-2101	1	39	of	of	ADP
ap-2101	1	40	physics	physics	PROPN
ap-2101	1	41	,	,	PUNCT
ap-2101	1	42	34342	34342	NUM
ap-2101	1	43	bebek	bebek	PROPN
ap-2101	1	44	,	,	PUNCT
ap-2101	1	45	istanbul	istanbul	PROPN
ap-2101	1	46	∗	∗	NOUN
ap-2101	1	47	corresponding	correspond	VERB
ap-2101	1	48	author	author	NOUN
ap-2101	1	49	:	:	PUNCT
ap-2101	1	50	cem.eroncel@boun.edu.tr	cem.eroncel@boun.edu.tr	PROPN
ap-2101	1	51	abstract	abstract	NOUN
ap-2101	1	52	.	.	PUNCT
ap-2101	2	1	renormalization	renormalization	NOUN
ap-2101	2	2	is	be	AUX
ap-2101	2	3	one	one	NUM
ap-2101	2	4	of	of	ADP
ap-2101	2	5	the	the	DET
ap-2101	2	6	deepest	deep	ADJ
ap-2101	2	7	ideas	idea	NOUN
ap-2101	2	8	in	in	ADP
ap-2101	2	9	physics	physics	NOUN
ap-2101	2	10	,	,	PUNCT
ap-2101	2	11	yet	yet	CCONJ
ap-2101	2	12	its	its	PRON
ap-2101	2	13	exact	exact	ADJ
ap-2101	2	14	implementation	implementation	NOUN
ap-2101	2	15	in	in	ADP
ap-2101	2	16	any	any	DET
ap-2101	2	17	interesting	interesting	ADJ
ap-2101	2	18	problem	problem	NOUN
ap-2101	2	19	is	be	AUX
ap-2101	2	20	usually	usually	ADV
ap-2101	2	21	very	very	ADV
ap-2101	2	22	hard	hard	ADJ
ap-2101	2	23	.	.	PUNCT
ap-2101	3	1	in	in	ADP
ap-2101	3	2	the	the	DET
ap-2101	3	3	present	present	ADJ
ap-2101	3	4	work	work	NOUN
ap-2101	3	5	,	,	PUNCT
ap-2101	3	6	following	follow	VERB
ap-2101	3	7	the	the	DET
ap-2101	3	8	approach	approach	NOUN
ap-2101	3	9	by	by	ADP
ap-2101	3	10	glazek	glazek	PROPN
ap-2101	3	11	and	and	CCONJ
ap-2101	3	12	maslowski	maslowski	ADJ
ap-2101	3	13	in	in	ADP
ap-2101	3	14	the	the	DET
ap-2101	3	15	flat	flat	ADJ
ap-2101	3	16	space	space	NOUN
ap-2101	3	17	,	,	PUNCT
ap-2101	3	18	we	we	PRON
ap-2101	3	19	will	will	AUX
ap-2101	3	20	study	study	VERB
ap-2101	3	21	the	the	DET
ap-2101	3	22	exact	exact	ADJ
ap-2101	3	23	renormalization	renormalization	NOUN
ap-2101	3	24	of	of	ADP
ap-2101	3	25	the	the	DET
ap-2101	3	26	same	same	ADJ
ap-2101	3	27	problem	problem	NOUN
ap-2101	3	28	in	in	ADP
ap-2101	3	29	a	a	DET
ap-2101	3	30	nontrivial	nontrivial	ADJ
ap-2101	3	31	geometric	geometric	ADJ
ap-2101	3	32	setting	setting	NOUN
ap-2101	3	33	,	,	PUNCT
ap-2101	3	34	namely	namely	ADV
ap-2101	3	35	in	in	ADP
ap-2101	3	36	the	the	DET
ap-2101	3	37	two	two	NUM
ap-2101	3	38	dimensional	dimensional	ADJ
ap-2101	3	39	hyperbolic	hyperbolic	ADJ
ap-2101	3	40	space	space	NOUN
ap-2101	3	41	.	.	PUNCT
ap-2101	4	1	delta	delta	NOUN
ap-2101	4	2	function	function	NOUN
ap-2101	4	3	potential	potential	NOUN
ap-2101	4	4	is	be	AUX
ap-2101	4	5	an	an	DET
ap-2101	4	6	asymptotically	asymptotically	ADV
ap-2101	4	7	free	free	ADJ
ap-2101	4	8	quantum	quantum	ADJ
ap-2101	4	9	mechanical	mechanical	ADJ
ap-2101	4	10	problem	problem	NOUN
ap-2101	4	11	which	which	PRON
ap-2101	4	12	makes	make	VERB
ap-2101	4	13	it	it	PRON
ap-2101	4	14	resemble	resemble	VERB
ap-2101	4	15	nonabelian	nonabelian	ADJ
ap-2101	4	16	gauge	gauge	NOUN
ap-2101	4	17	theories	theory	NOUN
ap-2101	4	18	,	,	PUNCT
ap-2101	4	19	yet	yet	CCONJ
ap-2101	4	20	it	it	PRON
ap-2101	4	21	can	can	AUX
ap-2101	4	22	be	be	AUX
ap-2101	4	23	treated	treat	VERB
ap-2101	4	24	exactly	exactly	ADV
ap-2101	4	25	in	in	ADP
ap-2101	4	26	this	this	DET
ap-2101	4	27	nontrivial	nontrivial	ADJ
ap-2101	4	28	geometry	geometry	NOUN
ap-2101	4	29	.	.	PUNCT
ap-2101	5	1	keywords	keyword	NOUN
ap-2101	5	2	:	:	PUNCT
ap-2101	5	3	point	point	VERB
ap-2101	5	4	interactions	interaction	NOUN
ap-2101	5	5	,	,	PUNCT
ap-2101	5	6	exact	exact	ADJ
ap-2101	5	7	renormalization	renormalization	NOUN
ap-2101	5	8	group	group	NOUN
ap-2101	5	9	,	,	PUNCT
ap-2101	5	10	harmonic	harmonic	ADJ
ap-2101	5	11	analysis	analysis	NOUN
ap-2101	5	12	,	,	PUNCT
ap-2101	5	13	hyperbolic	hyperbolic	ADJ
ap-2101	5	14	spaces	space	NOUN
ap-2101	5	15	.	.	PUNCT
ap-2101	6	1	1	1	X
ap-2101	6	2	.	.	X
ap-2101	6	3	introduction	introduction	NOUN
ap-2101	6	4	most	most	ADJ
ap-2101	6	5	problems	problem	NOUN
ap-2101	6	6	of	of	ADP
ap-2101	6	7	deep	deep	ADJ
ap-2101	6	8	significance	significance	NOUN
ap-2101	6	9	in	in	ADP
ap-2101	6	10	the	the	DET
ap-2101	6	11	world	world	NOUN
ap-2101	6	12	of	of	ADP
ap-2101	6	13	interacting	interact	VERB
ap-2101	6	14	many	many	ADJ
ap-2101	6	15	-	-	PUNCT
ap-2101	6	16	particles	particle	NOUN
ap-2101	6	17	are	be	AUX
ap-2101	6	18	formulated	formulate	VERB
ap-2101	6	19	by	by	ADP
ap-2101	6	20	singular	singular	NOUN
ap-2101	6	21	theories	theory	NOUN
ap-2101	6	22	.	.	PUNCT
ap-2101	7	1	typically	typically	ADV
ap-2101	7	2	,	,	PUNCT
ap-2101	7	3	these	these	PRON
ap-2101	7	4	are	be	AUX
ap-2101	7	5	plagued	plague	VERB
ap-2101	7	6	by	by	ADP
ap-2101	7	7	divergences	divergence	NOUN
ap-2101	7	8	,	,	PUNCT
ap-2101	7	9	which	which	PRON
ap-2101	7	10	reflects	reflect	VERB
ap-2101	7	11	our	our	PRON
ap-2101	7	12	ignorance	ignorance	NOUN
ap-2101	7	13	of	of	ADP
ap-2101	7	14	the	the	DET
ap-2101	7	15	physics	physics	NOUN
ap-2101	7	16	beyond	beyond	ADP
ap-2101	7	17	the	the	DET
ap-2101	7	18	scales	scale	NOUN
ap-2101	7	19	defined	define	VERB
ap-2101	7	20	by	by	ADP
ap-2101	7	21	our	our	PRON
ap-2101	7	22	original	original	ADJ
ap-2101	7	23	theory	theory	NOUN
ap-2101	7	24	.	.	PUNCT
ap-2101	8	1	a	a	DET
ap-2101	8	2	deep	deep	ADJ
ap-2101	8	3	insight	insight	NOUN
ap-2101	8	4	into	into	ADP
ap-2101	8	5	this	this	DET
ap-2101	8	6	behavior	behavior	NOUN
ap-2101	8	7	came	come	VERB
ap-2101	8	8	from	from	ADP
ap-2101	8	9	wilson	wilson	PROPN
ap-2101	9	1	[	[	X
ap-2101	9	2	23–28	23–28	NUM
ap-2101	9	3	]	]	PUNCT
ap-2101	9	4	.	.	PUNCT
ap-2101	10	1	he	he	PRON
ap-2101	10	2	argued	argue	VERB
ap-2101	10	3	that	that	SCONJ
ap-2101	10	4	the	the	DET
ap-2101	10	5	physics	physics	NOUN
ap-2101	10	6	beyond	beyond	ADP
ap-2101	10	7	the	the	DET
ap-2101	10	8	scales	scale	NOUN
ap-2101	10	9	of	of	ADP
ap-2101	10	10	interest	interest	NOUN
ap-2101	10	11	should	should	AUX
ap-2101	10	12	be	be	AUX
ap-2101	10	13	incorporated	incorporate	VERB
ap-2101	10	14	into	into	ADP
ap-2101	10	15	lower	low	ADJ
ap-2101	10	16	energies	energy	NOUN
ap-2101	10	17	by	by	ADP
ap-2101	10	18	some	some	DET
ap-2101	10	19	effective	effective	ADJ
ap-2101	10	20	interactions	interaction	NOUN
ap-2101	10	21	.	.	PUNCT
ap-2101	11	1	as	as	SCONJ
ap-2101	11	2	we	we	PRON
ap-2101	11	3	will	will	AUX
ap-2101	11	4	show	show	VERB
ap-2101	11	5	in	in	ADP
ap-2101	11	6	section	section	NOUN
ap-2101	11	7	2.2	2.2	NUM
ap-2101	11	8	,	,	PUNCT
ap-2101	11	9	for	for	ADP
ap-2101	11	10	a	a	DET
ap-2101	11	11	system	system	NOUN
ap-2101	11	12	defined	define	VERB
ap-2101	11	13	by	by	ADP
ap-2101	11	14	a	a	DET
ap-2101	11	15	hamiltonian	hamiltonian	NOUN
ap-2101	11	16	,	,	PUNCT
ap-2101	11	17	if	if	SCONJ
ap-2101	11	18	one	one	PRON
ap-2101	11	19	calculates	calculate	VERB
ap-2101	11	20	the	the	DET
ap-2101	11	21	form	form	NOUN
ap-2101	11	22	of	of	ADP
ap-2101	11	23	the	the	DET
ap-2101	11	24	effective	effective	ADJ
ap-2101	11	25	hamiltonian	hamiltonian	NOUN
ap-2101	11	26	at	at	ADP
ap-2101	11	27	some	some	DET
ap-2101	11	28	energy	energy	NOUN
ap-2101	11	29	scale	scale	NOUN
ap-2101	11	30	λ	λ	NOUN
ap-2101	11	31	specifying	specify	VERB
ap-2101	11	32	the	the	DET
ap-2101	11	33	cutoff	cutoff	NOUN
ap-2101	11	34	,	,	PUNCT
ap-2101	11	35	the	the	DET
ap-2101	11	36	result	result	NOUN
ap-2101	11	37	will	will	AUX
ap-2101	11	38	be	be	AUX
ap-2101	11	39	hλ	hλ	ADP
ap-2101	11	40	eff	eff	PROPN
ap-2101	11	41	=	=	PROPN
ap-2101	11	42	php	php	PROPN
ap-2101	12	1	+	+	NOUN
ap-2101	12	2	xλ	xλ	NOUN
ap-2101	12	3	,	,	PUNCT
ap-2101	12	4	where	where	SCONJ
ap-2101	12	5	php	php	PROPN
ap-2101	12	6	is	be	AUX
ap-2101	12	7	the	the	DET
ap-2101	12	8	projection	projection	NOUN
ap-2101	12	9	of	of	ADP
ap-2101	12	10	the	the	DET
ap-2101	12	11	hamiltonian	hamiltonian	NOUN
ap-2101	12	12	on	on	ADP
ap-2101	12	13	the	the	DET
ap-2101	12	14	subspace	subspace	NOUN
ap-2101	12	15	where	where	SCONJ
ap-2101	12	16	momentum	momentum	NOUN
ap-2101	12	17	eigenvalues	eigenvalue	NOUN
ap-2101	12	18	are	be	AUX
ap-2101	12	19	bounded	bound	VERB
ap-2101	12	20	by	by	ADP
ap-2101	12	21	the	the	DET
ap-2101	12	22	cutoff	cutoff	PROPN
ap-2101	12	23	λ	λ	NOUN
ap-2101	12	24	,	,	PUNCT
ap-2101	12	25	and	and	CCONJ
ap-2101	12	26	the	the	DET
ap-2101	12	27	operator	operator	NOUN
ap-2101	12	28	xλ	xλ	NOUN
ap-2101	12	29	depends	depend	VERB
ap-2101	12	30	on	on	ADP
ap-2101	12	31	higher	high	ADJ
ap-2101	12	32	degrees	degree	NOUN
ap-2101	12	33	of	of	ADP
ap-2101	12	34	freedom	freedom	NOUN
ap-2101	12	35	.	.	PUNCT
ap-2101	13	1	since	since	SCONJ
ap-2101	13	2	the	the	DET
ap-2101	13	3	cutoff	cutoff	NOUN
ap-2101	13	4	is	be	AUX
ap-2101	13	5	totally	totally	ADV
ap-2101	13	6	arbitrary	arbitrary	ADJ
ap-2101	13	7	,	,	PUNCT
ap-2101	13	8	the	the	DET
ap-2101	13	9	effective	effective	ADJ
ap-2101	13	10	hamiltonian	hamiltonian	NOUN
ap-2101	13	11	should	should	AUX
ap-2101	13	12	not	not	PART
ap-2101	13	13	depend	depend	VERB
ap-2101	13	14	on	on	ADP
ap-2101	13	15	it	it	PRON
ap-2101	13	16	.	.	PUNCT
ap-2101	14	1	the	the	DET
ap-2101	14	2	essence	essence	NOUN
ap-2101	14	3	of	of	ADP
ap-2101	14	4	the	the	DET
ap-2101	14	5	wilsonian	wilsonian	ADJ
ap-2101	14	6	renormalization	renormalization	NOUN
ap-2101	14	7	group	group	NOUN
ap-2101	14	8	,	,	PUNCT
ap-2101	14	9	or	or	CCONJ
ap-2101	14	10	the	the	DET
ap-2101	14	11	exact	exact	ADJ
ap-2101	14	12	renormalization	renormalization	NOUN
ap-2101	14	13	group	group	NOUN
ap-2101	14	14	(	(	PUNCT
ap-2101	14	15	erg	erg	PROPN
ap-2101	14	16	)	)	PUNCT
ap-2101	14	17	,	,	PUNCT
ap-2101	14	18	is	be	AUX
ap-2101	14	19	modifying	modify	VERB
ap-2101	14	20	the	the	DET
ap-2101	14	21	parameters	parameter	NOUN
ap-2101	14	22	of	of	ADP
ap-2101	14	23	the	the	DET
ap-2101	14	24	theory	theory	NOUN
ap-2101	14	25	without	without	ADP
ap-2101	14	26	altering	alter	VERB
ap-2101	14	27	the	the	DET
ap-2101	14	28	energy	energy	NOUN
ap-2101	14	29	eigenvalues	eigenvalue	NOUN
ap-2101	14	30	,	,	PUNCT
ap-2101	14	31	so	so	SCONJ
ap-2101	14	32	that	that	SCONJ
ap-2101	14	33	the	the	DET
ap-2101	14	34	effective	effective	ADJ
ap-2101	14	35	hamiltonian	hamiltonian	NOUN
ap-2101	14	36	becomes	become	VERB
ap-2101	14	37	cutoff	cutoff	NOUN
ap-2101	14	38	-	-	PUNCT
ap-2101	14	39	independent	independent	ADJ
ap-2101	14	40	.	.	PUNCT
ap-2101	15	1	this	this	PRON
ap-2101	15	2	is	be	AUX
ap-2101	15	3	done	do	VERB
ap-2101	15	4	as	as	SCONJ
ap-2101	15	5	follows	follow	VERB
ap-2101	15	6	:	:	PUNCT
ap-2101	15	7	we	we	PRON
ap-2101	15	8	start	start	VERB
ap-2101	15	9	by	by	ADP
ap-2101	15	10	specifying	specify	VERB
ap-2101	15	11	the	the	DET
ap-2101	15	12	system	system	NOUN
ap-2101	15	13	at	at	ADP
ap-2101	15	14	some	some	DET
ap-2101	15	15	high	high	ADJ
ap-2101	15	16	energy	energy	NOUN
ap-2101	15	17	scale	scale	NOUN
ap-2101	15	18	λ	λ	PROPN
ap-2101	15	19	,	,	PUNCT
ap-2101	15	20	called	call	VERB
ap-2101	15	21	the	the	DET
ap-2101	15	22	bare	bare	ADJ
ap-2101	15	23	scale	scale	NOUN
ap-2101	15	24	.	.	PUNCT
ap-2101	16	1	then	then	ADV
ap-2101	16	2	we	we	PRON
ap-2101	16	3	introduce	introduce	VERB
ap-2101	16	4	another	another	DET
ap-2101	16	5	scale	scale	NOUN
ap-2101	16	6	λ	λ	PROPN
ap-2101	16	7	,	,	PUNCT
ap-2101	16	8	called	call	VERB
ap-2101	16	9	the	the	DET
ap-2101	16	10	effective	effective	ADJ
ap-2101	16	11	scale	scale	NOUN
ap-2101	16	12	,	,	PUNCT
ap-2101	16	13	such	such	ADJ
ap-2101	16	14	that	that	SCONJ
ap-2101	16	15	1	1	NUM
ap-2101	16	16	�	�	PROPN
ap-2101	16	17	λ	λ	SYM
ap-2101	16	18	�	�	PROPN
ap-2101	16	19	λ	λ	PROPN
ap-2101	16	20	.	.	PUNCT
ap-2101	17	1	the	the	DET
ap-2101	17	2	erg	erg	PROPN
ap-2101	17	3	procedure	procedure	NOUN
ap-2101	17	4	consists	consist	VERB
ap-2101	17	5	of	of	ADP
ap-2101	17	6	integrating	integrate	VERB
ap-2101	17	7	out	out	ADP
ap-2101	17	8	degrees	degree	NOUN
ap-2101	17	9	of	of	ADP
ap-2101	17	10	freedom	freedom	NOUN
ap-2101	17	11	between	between	ADP
ap-2101	17	12	these	these	DET
ap-2101	17	13	two	two	NUM
ap-2101	17	14	scales	scale	NOUN
ap-2101	17	15	.	.	PUNCT
ap-2101	18	1	this	this	PRON
ap-2101	18	2	integrating	integrate	VERB
ap-2101	18	3	out	out	ADP
ap-2101	18	4	procedure	procedure	NOUN
ap-2101	18	5	is	be	AUX
ap-2101	18	6	not	not	PART
ap-2101	18	7	performed	perform	VERB
ap-2101	18	8	in	in	ADP
ap-2101	18	9	a	a	DET
ap-2101	18	10	single	single	ADJ
ap-2101	18	11	step	step	NOUN
ap-2101	18	12	.	.	PUNCT
ap-2101	19	1	in	in	ADP
ap-2101	19	2	each	each	DET
ap-2101	19	3	step	step	NOUN
ap-2101	19	4	one	one	NUM
ap-2101	19	5	integrates	integrate	NOUN
ap-2101	19	6	over	over	ADP
ap-2101	19	7	an	an	DET
ap-2101	19	8	infinitesimal	infinitesimal	ADJ
ap-2101	19	9	mome	mome	NOUN
ap-2101	19	10	!	!	PUNCT
ap-2101	20	1	ntum	ntum	ADJ
ap-2101	20	2	shell	shell	NOUN
ap-2101	20	3	.	.	PUNCT
ap-2101	21	1	this	this	DET
ap-2101	21	2	transformation	transformation	NOUN
ap-2101	21	3	,	,	PUNCT
ap-2101	21	4	which	which	PRON
ap-2101	21	5	is	be	AUX
ap-2101	21	6	called	call	VERB
ap-2101	21	7	a	a	DET
ap-2101	21	8	renormalization	renormalization	NOUN
ap-2101	21	9	group	group	NOUN
ap-2101	21	10	(	(	PUNCT
ap-2101	21	11	rg	rg	NOUN
ap-2101	21	12	)	)	PUNCT
ap-2101	21	13	transformation	transformation	NOUN
ap-2101	21	14	creates	create	VERB
ap-2101	21	15	a	a	DET
ap-2101	21	16	trajectory	trajectory	NOUN
ap-2101	21	17	,	,	PUNCT
ap-2101	21	18	called	call	VERB
ap-2101	21	19	an	an	DET
ap-2101	21	20	rg	rg	PROPN
ap-2101	21	21	trajectory	trajectory	NOUN
ap-2101	21	22	in	in	ADP
ap-2101	21	23	the	the	DET
ap-2101	21	24	space	space	NOUN
ap-2101	21	25	of	of	ADP
ap-2101	21	26	theories	theory	NOUN
ap-2101	21	27	,	,	PUNCT
ap-2101	21	28	or	or	CCONJ
ap-2101	21	29	in	in	ADP
ap-2101	21	30	this	this	DET
ap-2101	21	31	particular	particular	ADJ
ap-2101	21	32	case	case	NOUN
ap-2101	21	33	in	in	ADP
ap-2101	21	34	the	the	DET
ap-2101	21	35	space	space	NOUN
ap-2101	21	36	of	of	ADP
ap-2101	21	37	hamiltonians	hamiltonian	NOUN
ap-2101	21	38	.	.	PUNCT
ap-2101	22	1	the	the	DET
ap-2101	22	2	hamiltonians	hamiltonian	NOUN
ap-2101	22	3	at	at	ADP
ap-2101	22	4	different	different	ADJ
ap-2101	22	5	scales	scale	NOUN
ap-2101	22	6	are	be	AUX
ap-2101	22	7	related	relate	VERB
ap-2101	22	8	by	by	ADP
ap-2101	22	9	the	the	DET
ap-2101	22	10	requirement	requirement	NOUN
ap-2101	22	11	that	that	SCONJ
ap-2101	22	12	the	the	DET
ap-2101	22	13	eigenvalues	eigenvalue	NOUN
ap-2101	22	14	do	do	AUX
ap-2101	22	15	not	not	PART
ap-2101	22	16	change	change	VERB
ap-2101	22	17	as	as	SCONJ
ap-2101	22	18	one	one	NUM
ap-2101	22	19	changes	change	VERB
ap-2101	22	20	the	the	DET
ap-2101	22	21	scale	scale	NOUN
ap-2101	22	22	.	.	PUNCT
ap-2101	23	1	in	in	ADP
ap-2101	23	2	other	other	ADJ
ap-2101	23	3	words	word	NOUN
ap-2101	23	4	the	the	DET
ap-2101	23	5	rg	rg	PROPN
ap-2101	23	6	trajectory	trajectory	NOUN
ap-2101	23	7	is	be	AUX
ap-2101	23	8	determined	determine	VERB
ap-2101	23	9	by	by	ADP
ap-2101	23	10	the	the	DET
ap-2101	23	11	condition	condition	NOUN
ap-2101	23	12	that	that	SCONJ
ap-2101	23	13	all	all	DET
ap-2101	23	14	the	the	DET
ap-2101	23	15	hamiltonians	hamiltonian	NOUN
ap-2101	23	16	on	on	ADP
ap-2101	23	17	this	this	DET
ap-2101	23	18	trajectory	trajectory	NOUN
ap-2101	23	19	give	give	VERB
ap-2101	23	20	the	the	DET
ap-2101	23	21	same	same	ADJ
ap-2101	23	22	set	set	NOUN
ap-2101	23	23	of	of	ADP
ap-2101	23	24	eigenvalues	eigenvalue	NOUN
ap-2101	23	25	as	as	ADP
ap-2101	23	26	the	the	DET
ap-2101	23	27	unrenormalized	unrenormalized	ADJ
ap-2101	23	28	theory	theory	NOUN
ap-2101	23	29	.	.	PUNCT
ap-2101	24	1	there	there	PRON
ap-2101	24	2	is	be	VERB
ap-2101	24	3	no	no	DET
ap-2101	24	4	systematic	systematic	ADJ
ap-2101	24	5	non	non	ADJ
ap-2101	24	6	-	-	ADJ
ap-2101	24	7	perturbative	perturbative	ADJ
ap-2101	24	8	approach	approach	NOUN
ap-2101	24	9	to	to	PART
ap-2101	24	10	implement	implement	VERB
ap-2101	24	11	this	this	DET
ap-2101	24	12	idea	idea	NOUN
ap-2101	24	13	yet	yet	ADV
ap-2101	24	14	,	,	PUNCT
ap-2101	24	15	but	but	CCONJ
ap-2101	24	16	many	many	ADJ
ap-2101	24	17	interesting	interesting	ADJ
ap-2101	24	18	problems	problem	NOUN
ap-2101	24	19	can	can	AUX
ap-2101	24	20	be	be	AUX
ap-2101	24	21	solved	solve	VERB
ap-2101	24	22	by	by	ADP
ap-2101	24	23	means	mean	NOUN
ap-2101	24	24	of	of	ADP
ap-2101	24	25	some	some	DET
ap-2101	24	26	approximation	approximation	NOUN
ap-2101	24	27	method	method	NOUN
ap-2101	24	28	.	.	PUNCT
ap-2101	25	1	the	the	DET
ap-2101	25	2	literature	literature	NOUN
ap-2101	25	3	in	in	ADP
ap-2101	25	4	this	this	DET
ap-2101	25	5	direction	direction	NOUN
ap-2101	25	6	is	be	AUX
ap-2101	25	7	immense	immense	ADJ
ap-2101	25	8	,	,	PUNCT
ap-2101	25	9	and	and	CCONJ
ap-2101	25	10	we	we	PRON
ap-2101	25	11	do	do	AUX
ap-2101	25	12	not	not	PART
ap-2101	25	13	feel	feel	VERB
ap-2101	25	14	competent	competent	ADJ
ap-2101	25	15	enough	enough	ADV
ap-2101	25	16	to	to	PART
ap-2101	25	17	cite	cite	VERB
ap-2101	25	18	all	all	DET
ap-2101	25	19	the	the	DET
ap-2101	25	20	relevant	relevant	ADJ
ap-2101	25	21	works	work	NOUN
ap-2101	25	22	.	.	PUNCT
ap-2101	26	1	we	we	PRON
ap-2101	26	2	will	will	AUX
ap-2101	26	3	mention	mention	VERB
ap-2101	26	4	just	just	ADV
ap-2101	26	5	a	a	DET
ap-2101	26	6	few	few	ADJ
ap-2101	26	7	things	thing	NOUN
ap-2101	26	8	related	relate	VERB
ap-2101	26	9	to	to	ADP
ap-2101	26	10	the	the	DET
ap-2101	26	11	present	present	ADJ
ap-2101	26	12	work	work	NOUN
ap-2101	26	13	.	.	PUNCT
ap-2101	27	1	a	a	DET
ap-2101	27	2	perturbative	perturbative	ADJ
ap-2101	27	3	approach	approach	NOUN
ap-2101	27	4	to	to	ADP
ap-2101	27	5	the	the	DET
ap-2101	27	6	renormalization	renormalization	NOUN
ap-2101	27	7	group	group	NOUN
ap-2101	27	8	for	for	ADP
ap-2101	27	9	effective	effective	ADJ
ap-2101	27	10	hamiltonians	hamiltonian	NOUN
ap-2101	27	11	in	in	ADP
ap-2101	27	12	light	light	ADJ
ap-2101	27	13	-	-	PUNCT
ap-2101	27	14	front	front	NOUN
ap-2101	27	15	field	field	NOUN
ap-2101	27	16	theory	theory	NOUN
ap-2101	27	17	is	be	AUX
ap-2101	27	18	given	give	VERB
ap-2101	27	19	in	in	ADP
ap-2101	27	20	[	[	X
ap-2101	27	21	10	10	NUM
ap-2101	27	22	]	]	PUNCT
ap-2101	27	23	.	.	PUNCT
ap-2101	28	1	another	another	DET
ap-2101	28	2	renormalization	renormalization	NOUN
ap-2101	28	3	procedure	procedure	NOUN
ap-2101	28	4	for	for	ADP
ap-2101	28	5	light	light	ADJ
ap-2101	28	6	-	-	PUNCT
ap-2101	28	7	front	front	NOUN
ap-2101	28	8	hamiltonians	hamiltonian	NOUN
ap-2101	28	9	is	be	AUX
ap-2101	28	10	called	call	VERB
ap-2101	28	11	the	the	DET
ap-2101	28	12	similarity	similarity	NOUN
ap-2101	28	13	renormalization	renormalization	NOUN
ap-2101	28	14	group	group	NOUN
ap-2101	28	15	,	,	PUNCT
ap-2101	28	16	where	where	SCONJ
ap-2101	28	17	the	the	DET
ap-2101	28	18	bare	bare	ADJ
ap-2101	28	19	hamiltonian	hamiltonian	NOUN
ap-2101	28	20	with	with	ADP
ap-2101	28	21	an	an	DET
ap-2101	28	22	arbitrary	arbitrary	ADJ
ap-2101	28	23	large	large	ADJ
ap-2101	28	24	,	,	PUNCT
ap-2101	28	25	but	but	CCONJ
ap-2101	28	26	finite	finite	PROPN
ap-2101	28	27	cutoff	cutoff	NOUN
ap-2101	28	28	,	,	PUNCT
ap-2101	28	29	is	be	AUX
ap-2101	28	30	transformed	transform	VERB
ap-2101	28	31	by	by	ADP
ap-2101	28	32	a	a	DET
ap-2101	28	33	similarity	similarity	NOUN
ap-2101	28	34	transformation	transformation	NOUN
ap-2101	28	35	which	which	PRON
ap-2101	28	36	makes	make	VERB
ap-2101	28	37	the	the	DET
ap-2101	28	38	hamiltonian	hamiltonian	ADJ
ap-2101	28	39	band	band	NOUN
ap-2101	28	40	diagonal	diagonal	ADJ
ap-2101	28	41	[	[	X
ap-2101	28	42	9	9	NUM
ap-2101	28	43	,	,	PUNCT
ap-2101	28	44	11	11	NUM
ap-2101	28	45	]	]	PUNCT
ap-2101	28	46	.	.	PUNCT
ap-2101	29	1	a	a	DET
ap-2101	29	2	pedagogical	pedagogical	ADJ
ap-2101	29	3	treatment	treatment	NOUN
ap-2101	29	4	can	can	AUX
ap-2101	29	5	be	be	AUX
ap-2101	29	6	found	find	VERB
ap-2101	29	7	in	in	ADP
ap-2101	29	8	[	[	X
ap-2101	29	9	7	7	NUM
ap-2101	29	10	]	]	PUNCT
ap-2101	29	11	.	.	PUNCT
ap-2101	30	1	one	one	NUM
ap-2101	30	2	of	of	ADP
ap-2101	30	3	the	the	DET
ap-2101	30	4	main	main	ADJ
ap-2101	30	5	challenges	challenge	NOUN
ap-2101	30	6	is	be	AUX
ap-2101	30	7	to	to	PART
ap-2101	30	8	understand	understand	VERB
ap-2101	30	9	renormalization	renormalization	NOUN
ap-2101	30	10	in	in	ADP
ap-2101	30	11	a	a	DET
ap-2101	30	12	system	system	NOUN
ap-2101	30	13	where	where	SCONJ
ap-2101	30	14	the	the	DET
ap-2101	30	15	interactions	interaction	NOUN
ap-2101	30	16	lead	lead	VERB
ap-2101	30	17	to	to	ADP
ap-2101	30	18	the	the	DET
ap-2101	30	19	appearance	appearance	NOUN
ap-2101	30	20	of	of	ADP
ap-2101	30	21	bound	bind	VERB
ap-2101	30	22	states	state	NOUN
ap-2101	30	23	.	.	PUNCT
ap-2101	31	1	indeed	indeed	ADV
ap-2101	31	2	quantum	quantum	ADJ
ap-2101	31	3	chromodynamics	chromodynamics	NOUN
ap-2101	31	4	is	be	AUX
ap-2101	31	5	the	the	DET
ap-2101	31	6	main	main	ADJ
ap-2101	31	7	example	example	NOUN
ap-2101	31	8	we	we	PRON
ap-2101	31	9	have	have	VERB
ap-2101	31	10	in	in	ADP
ap-2101	31	11	mind	mind	NOUN
ap-2101	31	12	,	,	PUNCT
ap-2101	31	13	where	where	SCONJ
ap-2101	31	14	the	the	DET
ap-2101	31	15	theory	theory	NOUN
ap-2101	31	16	is	be	AUX
ap-2101	31	17	formulated	formulate	VERB
ap-2101	31	18	in	in	ADP
ap-2101	31	19	terms	term	NOUN
ap-2101	31	20	of	of	ADP
ap-2101	31	21	physically	physically	ADV
ap-2101	31	22	unobservable	unobservable	ADJ
ap-2101	31	23	variables	variable	NOUN
ap-2101	31	24	,	,	PUNCT
ap-2101	31	25	in	in	ADP
ap-2101	31	26	ordinary	ordinary	ADJ
ap-2101	31	27	energy	energy	NOUN
ap-2101	31	28	scales	scale	NOUN
ap-2101	31	29	,	,	PUNCT
ap-2101	31	30	and	and	CCONJ
ap-2101	31	31	as	as	ADP
ap-2101	31	32	a	a	DET
ap-2101	31	33	result	result	NOUN
ap-2101	31	34	of	of	ADP
ap-2101	31	35	interactions	interaction	NOUN
ap-2101	31	36	only	only	ADV
ap-2101	31	37	their	their	PRON
ap-2101	31	38	bound	bind	VERB
ap-2101	31	39	states	state	NOUN
ap-2101	31	40	become	become	VERB
ap-2101	31	41	physical	physical	ADJ
ap-2101	31	42	particles	particle	NOUN
ap-2101	31	43	.	.	PUNCT
ap-2101	32	1	since	since	SCONJ
ap-2101	32	2	one	one	NUM
ap-2101	32	3	is	be	AUX
ap-2101	32	4	interested	interested	ADJ
ap-2101	32	5	in	in	ADP
ap-2101	32	6	understanding	understand	VERB
ap-2101	32	7	the	the	DET
ap-2101	32	8	formation	formation	NOUN
ap-2101	32	9	of	of	ADP
ap-2101	32	10	these	these	DET
ap-2101	32	11	bound	bind	VERB
ap-2101	32	12	states	state	NOUN
ap-2101	32	13	and	and	CCONJ
ap-2101	32	14	calculating	calculate	VERB
ap-2101	32	15	the	the	DET
ap-2101	32	16	resulting	result	VERB
ap-2101	32	17	masses	masse	NOUN
ap-2101	32	18	,	,	PUNCT
ap-2101	32	19	in	in	ADP
ap-2101	32	20	principle	principle	NOUN
ap-2101	32	21	,	,	PUNCT
ap-2101	32	22	it	it	PRON
ap-2101	32	23	is	be	AUX
ap-2101	32	24	most	most	ADV
ap-2101	32	25	natural	natural	ADJ
ap-2101	32	26	to	to	PART
ap-2101	32	27	work	work	VERB
ap-2101	32	28	with	with	ADP
ap-2101	32	29	the	the	DET
ap-2101	32	30	hamiltonian	hamiltonian	NOUN
ap-2101	32	31	directly	directly	ADV
ap-2101	32	32	.	.	PUNCT
ap-2101	33	1	of	of	ADP
ap-2101	33	2	course	course	ADV
ap-2101	33	3	this	this	PRON
ap-2101	33	4	is	be	AUX
ap-2101	33	5	a	a	DET
ap-2101	33	6	very	very	ADV
ap-2101	33	7	hard	hard	ADJ
ap-2101	33	8	problem	problem	NOUN
ap-2101	33	9	.	.	PUNCT
ap-2101	34	1	as	as	ADP
ap-2101	34	2	a	a	DET
ap-2101	34	3	result	result	NOUN
ap-2101	34	4	it	it	PRON
ap-2101	34	5	is	be	AUX
ap-2101	34	6	valuable	valuable	ADJ
ap-2101	34	7	and	and	CCONJ
ap-2101	34	8	interesting	interesting	ADJ
ap-2101	34	9	to	to	PART
ap-2101	34	10	learn	learn	VERB
ap-2101	34	11	more	more	ADJ
ap-2101	34	12	about	about	ADP
ap-2101	34	13	renormalization	renormalization	NOUN
ap-2101	34	14	and	and	CCONJ
ap-2101	34	15	its	its	PRON
ap-2101	34	16	non	non	ADJ
ap-2101	34	17	-	-	ADJ
ap-2101	34	18	perturbative	perturbative	ADJ
ap-2101	34	19	aspects	aspect	NOUN
ap-2101	34	20	even	even	ADV
ap-2101	34	21	in	in	ADP
ap-2101	34	22	very	very	ADV
ap-2101	34	23	simple	simple	ADJ
ap-2101	34	24	systems	system	NOUN
ap-2101	34	25	using	use	VERB
ap-2101	34	26	the	the	DET
ap-2101	34	27	hamiltonian	hamiltonian	ADJ
ap-2101	35	1	156	156	NUM
ap-2101	35	2	http://dx.doi.org/10.14311/ap.2014.54.0156	http://dx.doi.org/10.14311/ap.2014.54.0156	DET
ap-2101	35	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2101	35	4	vol	vol	NOUN
ap-2101	35	5	.	.	PUNCT
ap-2101	36	1	54	54	NUM
ap-2101	36	2	no	no	NOUN
ap-2101	36	3	.	.	PUNCT
ap-2101	37	1	2/2014	2/2014	NUM
ap-2101	37	2	exact	exact	ADJ
ap-2101	37	3	renormalization	renormalization	NOUN
ap-2101	37	4	group	group	NOUN
ap-2101	37	5	for	for	ADP
ap-2101	37	6	point	point	NOUN
ap-2101	37	7	interactions	interaction	NOUN
ap-2101	37	8	formalism	formalism	NOUN
ap-2101	37	9	.	.	PUNCT
ap-2101	38	1	this	this	PRON
ap-2101	38	2	has	have	AUX
ap-2101	38	3	been	be	AUX
ap-2101	38	4	done	do	VERB
ap-2101	38	5	by	by	ADP
ap-2101	38	6	glazek	glazek	PROPN
ap-2101	38	7	and	and	CCONJ
ap-2101	38	8	maslowski	maslowski	ADJ
ap-2101	38	9	for	for	ADP
ap-2101	38	10	the	the	DET
ap-2101	38	11	dirac	dirac	NOUN
ap-2101	38	12	-	-	PUNCT
ap-2101	38	13	delta	delta	NOUN
ap-2101	38	14	function	function	NOUN
ap-2101	38	15	in	in	ADP
ap-2101	38	16	two	two	NUM
ap-2101	38	17	dimensions	dimension	NOUN
ap-2101	38	18	[	[	X
ap-2101	38	19	8	8	NUM
ap-2101	38	20	]	]	PUNCT
ap-2101	38	21	.	.	PUNCT
ap-2101	39	1	in	in	ADP
ap-2101	39	2	the	the	DET
ap-2101	39	3	present	present	ADJ
ap-2101	39	4	work	work	NOUN
ap-2101	39	5	,	,	PUNCT
ap-2101	39	6	we	we	PRON
ap-2101	39	7	will	will	AUX
ap-2101	39	8	consider	consider	VERB
ap-2101	39	9	the	the	DET
ap-2101	39	10	same	same	ADJ
ap-2101	39	11	problem	problem	NOUN
ap-2101	39	12	on	on	ADP
ap-2101	39	13	a	a	DET
ap-2101	39	14	nontrivial	nontrivial	ADJ
ap-2101	39	15	manifold	manifold	NOUN
ap-2101	39	16	,	,	PUNCT
ap-2101	39	17	two	two	NUM
ap-2101	39	18	dimensional	dimensional	ADJ
ap-2101	39	19	hy	hy	NOUN
ap-2101	39	20	!	!	PUNCT
ap-2101	39	21	perbolic	perbolic	ADJ
ap-2101	39	22	space	space	NOUN
ap-2101	39	23	.	.	PUNCT
ap-2101	40	1	this	this	PRON
ap-2101	40	2	is	be	AUX
ap-2101	40	3	interesting	interesting	ADJ
ap-2101	40	4	because	because	SCONJ
ap-2101	40	5	the	the	DET
ap-2101	40	6	gauge	gauge	NOUN
ap-2101	40	7	theory	theory	NOUN
ap-2101	40	8	problem	problem	NOUN
ap-2101	40	9	also	also	ADV
ap-2101	40	10	has	have	VERB
ap-2101	40	11	a	a	DET
ap-2101	40	12	nontrivial	nontrivial	ADJ
ap-2101	40	13	geometry	geometry	NOUN
ap-2101	40	14	when	when	SCONJ
ap-2101	40	15	it	it	PRON
ap-2101	40	16	is	be	AUX
ap-2101	40	17	formulated	formulate	VERB
ap-2101	40	18	on	on	ADP
ap-2101	40	19	the	the	DET
ap-2101	40	20	space	space	NOUN
ap-2101	40	21	of	of	ADP
ap-2101	40	22	connections	connection	NOUN
ap-2101	40	23	modulo	modulo	PROPN
ap-2101	40	24	gauge	gauge	VERB
ap-2101	40	25	equivalent	equivalent	ADJ
ap-2101	40	26	configurations	configuration	NOUN
ap-2101	40	27	[	[	X
ap-2101	40	28	19	19	NUM
ap-2101	40	29	]	]	PUNCT
ap-2101	40	30	.	.	PUNCT
ap-2101	41	1	hence	hence	ADV
ap-2101	41	2	,	,	PUNCT
ap-2101	41	3	it	it	PRON
ap-2101	41	4	is	be	AUX
ap-2101	41	5	a	a	DET
ap-2101	41	6	nice	nice	ADJ
ap-2101	41	7	exercise	exercise	NOUN
ap-2101	41	8	to	to	PART
ap-2101	41	9	see	see	VERB
ap-2101	41	10	that	that	DET
ap-2101	41	11	type	type	NOUN
ap-2101	41	12	of	of	ADP
ap-2101	41	13	complications	complication	NOUN
ap-2101	41	14	may	may	AUX
ap-2101	41	15	arise	arise	VERB
ap-2101	41	16	when	when	SCONJ
ap-2101	41	17	the	the	DET
ap-2101	41	18	underlying	underlie	VERB
ap-2101	41	19	geometry	geometry	NOUN
ap-2101	41	20	is	be	AUX
ap-2101	41	21	nontrivial	nontrivial	ADJ
ap-2101	41	22	.	.	PUNCT
ap-2101	42	1	we	we	PRON
ap-2101	42	2	shall	shall	AUX
ap-2101	42	3	start	start	VERB
ap-2101	42	4	by	by	ADP
ap-2101	42	5	reviewing	review	VERB
ap-2101	42	6	point	point	NOUN
ap-2101	42	7	interactions	interaction	NOUN
ap-2101	42	8	on	on	ADP
ap-2101	42	9	the	the	DET
ap-2101	42	10	euclidean	euclidean	ADJ
ap-2101	42	11	plane	plane	NOUN
ap-2101	42	12	and	and	CCONJ
ap-2101	42	13	answer	answer	VERB
ap-2101	42	14	why	why	SCONJ
ap-2101	42	15	this	this	DET
ap-2101	42	16	problem	problem	NOUN
ap-2101	42	17	requires	require	VERB
ap-2101	42	18	renormalization	renormalization	NOUN
ap-2101	42	19	.	.	PUNCT
ap-2101	43	1	following	follow	VERB
ap-2101	43	2	[	[	X
ap-2101	43	3	8	8	NUM
ap-2101	43	4	]	]	PUNCT
ap-2101	43	5	,	,	PUNCT
ap-2101	43	6	we	we	PRON
ap-2101	43	7	will	will	AUX
ap-2101	43	8	review	review	VERB
ap-2101	43	9	the	the	DET
ap-2101	43	10	renormalization	renormalization	NOUN
ap-2101	43	11	of	of	ADP
ap-2101	43	12	point	point	NOUN
ap-2101	43	13	interactions	interaction	NOUN
ap-2101	43	14	in	in	ADP
ap-2101	43	15	the	the	DET
ap-2101	43	16	euclidean	euclidean	ADJ
ap-2101	43	17	plane	plane	NOUN
ap-2101	43	18	using	use	VERB
ap-2101	43	19	the	the	DET
ap-2101	43	20	wilsonian	wilsonian	ADJ
ap-2101	43	21	rg	rg	NOUN
ap-2101	43	22	scheme	scheme	NOUN
ap-2101	43	23	and	and	CCONJ
ap-2101	43	24	derive	derive	VERB
ap-2101	43	25	the	the	DET
ap-2101	43	26	flow	flow	NOUN
ap-2101	43	27	equation	equation	NOUN
ap-2101	43	28	.	.	PUNCT
ap-2101	44	1	as	as	ADP
ap-2101	44	2	an	an	DET
ap-2101	44	3	addendum	addendum	NOUN
ap-2101	44	4	to	to	ADP
ap-2101	44	5	glazek	glazek	PROPN
ap-2101	44	6	and	and	CCONJ
ap-2101	44	7	maslowski	maslowski	ADJ
ap-2101	44	8	,	,	PUNCT
ap-2101	44	9	we	we	PRON
ap-2101	44	10	also	also	ADV
ap-2101	44	11	investigate	investigate	VERB
ap-2101	44	12	the	the	DET
ap-2101	44	13	range	range	NOUN
ap-2101	44	14	of	of	ADP
ap-2101	44	15	renormalizability	renormalizability	NOUN
ap-2101	44	16	using	use	VERB
ap-2101	44	17	the	the	DET
ap-2101	44	18	banach	banach	NOUN
ap-2101	44	19	contraction	contraction	NOUN
ap-2101	44	20	principle	principle	NOUN
ap-2101	44	21	.	.	PUNCT
ap-2101	45	1	in	in	ADP
ap-2101	45	2	the	the	DET
ap-2101	45	3	next	next	ADJ
ap-2101	45	4	section	section	NOUN
ap-2101	45	5	we	we	PRON
ap-2101	45	6	shall	shall	AUX
ap-2101	45	7	analyze	analyze	VERB
ap-2101	45	8	the	the	DET
ap-2101	45	9	same	same	ADJ
ap-2101	45	10	problem	problem	NOUN
ap-2101	45	11	on	on	ADP
ap-2101	45	12	the	the	DET
ap-2101	45	13	hyperbolic	hyperbolic	ADJ
ap-2101	45	14	plane	plane	NOUN
ap-2101	45	15	and	and	CCONJ
ap-2101	45	16	show	show	VERB
ap-2101	45	17	that	that	SCONJ
ap-2101	45	18	the	the	DET
ap-2101	45	19	flow	flow	NOUN
ap-2101	45	20	equation	equation	NOUN
ap-2101	45	21	has	have	VERB
ap-2101	45	22	the	the	DET
ap-2101	45	23	same	same	ADJ
ap-2101	45	24	form	form	NOUN
ap-2101	45	25	.	.	PUNCT
ap-2101	46	1	finally	finally	ADV
ap-2101	46	2	we	we	PRON
ap-2101	46	3	will	will	AUX
ap-2101	46	4	speak	speak	VERB
ap-2101	46	5	about	about	ADP
ap-2101	46	6	a	a	DET
ap-2101	46	7	puzzle	puzzle	NOUN
ap-2101	46	8	where	where	SCONJ
ap-2101	46	9	this	this	DET
ap-2101	46	10	procedure	procedure	NOUN
ap-2101	46	11	fails	fail	VERB
ap-2101	46	12	at	at	ADP
ap-2101	46	13	a	a	DET
ap-2101	46	14	technical	technical	ADJ
ap-2101	46	15	level	level	NOUN
ap-2101	46	16	,	,	PUNCT
ap-2101	46	17	if	if	SCONJ
ap-2101	46	18	one	one	NUM
ap-2101	46	19	studies	study	NOUN
ap-2101	46	20	the	the	DET
ap-2101	46	21	same	same	ADJ
ap-2101	46	22	problem	problem	NOUN
ap-2101	46	23	on	on	ADP
ap-2101	46	24	a	a	DET
ap-2101	46	25	compact	compact	ADJ
ap-2101	46	26	manifold	manifold	NOUN
ap-2101	46	27	,	,	PUNCT
ap-2101	46	28	namely	namely	ADV
ap-2101	46	29	two	two	NUM
ap-2101	46	30	-	-	PUNCT
ap-2101	46	31	dimensional	dimensional	ADJ
ap-2101	46	32	sphere	sphere	NOUN
ap-2101	46	33	,	,	PUNCT
ap-2101	46	34	s2	s2	PROPN
ap-2101	46	35	.	.	PROPN
ap-2101	47	1	2	2	NUM
ap-2101	47	2	.	.	X
ap-2101	47	3	exact	exact	ADJ
ap-2101	47	4	renormalization	renormalization	NOUN
ap-2101	47	5	group	group	NOUN
ap-2101	47	6	on	on	ADP
ap-2101	47	7	the	the	DET
ap-2101	47	8	euclidean	euclidean	ADJ
ap-2101	47	9	plane	plane	NOUN
ap-2101	47	10	2.1	2.1	NUM
ap-2101	47	11	.	.	PUNCT
ap-2101	48	1	formulation	formulation	NOUN
ap-2101	48	2	of	of	ADP
ap-2101	48	3	the	the	DET
ap-2101	48	4	problem	problem	NOUN
ap-2101	48	5	the	the	DET
ap-2101	48	6	schrödinger	schrödinger	ADJ
ap-2101	48	7	equation	equation	NOUN
ap-2101	48	8	for	for	ADP
ap-2101	48	9	the	the	DET
ap-2101	48	10	simplest	simple	ADJ
ap-2101	48	11	type	type	NOUN
ap-2101	48	12	of	of	ADP
ap-2101	48	13	point	point	NOUN
ap-2101	48	14	interaction	interaction	NOUN
ap-2101	48	15	on	on	ADP
ap-2101	48	16	a	a	DET
ap-2101	48	17	d	d	ADJ
ap-2101	48	18	-	-	ADJ
ap-2101	48	19	dimensional	dimensional	ADJ
ap-2101	48	20	euclidean	euclidean	ADJ
ap-2101	48	21	space	space	NOUN
ap-2101	48	22	rd	rd	PROPN
ap-2101	48	23	is	be	AUX
ap-2101	48	24	given	give	VERB
ap-2101	48	25	in	in	ADP
ap-2101	48	26	units	unit	NOUN
ap-2101	48	27	~	~	PUNCT
ap-2101	48	28	=	=	SYM
ap-2101	48	29	1	1	NUM
ap-2101	48	30	and	and	CCONJ
ap-2101	48	31	2	2	NUM
ap-2101	48	32	m	m	NOUN
ap-2101	48	33	=	=	NOUN
ap-2101	48	34	1	1	NUM
ap-2101	48	35	,	,	PUNCT
ap-2101	48	36	as	as	ADP
ap-2101	48	37	(	(	PUNCT
ap-2101	48	38	−∆rd	−∆rd	NOUN
ap-2101	48	39	−	−	PROPN
ap-2101	48	40	gδd(x	gδd(x	NOUN
ap-2101	48	41	)	)	PUNCT
ap-2101	48	42	)	)	PUNCT
ap-2101	48	43	ψ(x	ψ(x	NOUN
ap-2101	48	44	)	)	PUNCT
ap-2101	48	45	=	=	SYM
ap-2101	48	46	eψ(x	eψ(x	NOUN
ap-2101	48	47	)	)	PUNCT
ap-2101	48	48	,	,	PUNCT
ap-2101	48	49	(	(	PUNCT
ap-2101	48	50	2.1	2.1	NUM
ap-2101	48	51	)	)	PUNCT
ap-2101	48	52	where	where	SCONJ
ap-2101	48	53	∆rd	∆rd	NOUN
ap-2101	48	54	is	be	AUX
ap-2101	48	55	the	the	DET
ap-2101	48	56	laplacian	laplacian	ADJ
ap-2101	48	57	operator	operator	NOUN
ap-2101	48	58	on	on	ADP
ap-2101	48	59	rd	rd	PROPN
ap-2101	48	60	and	and	CCONJ
ap-2101	48	61	g	g	PROPN
ap-2101	48	62	is	be	AUX
ap-2101	48	63	real	real	ADJ
ap-2101	48	64	,	,	PUNCT
ap-2101	48	65	positive	positive	ADJ
ap-2101	48	66	parameter	parameter	NOUN
ap-2101	48	67	which	which	PRON
ap-2101	48	68	determines	determine	VERB
ap-2101	48	69	the	the	DET
ap-2101	48	70	strength	strength	NOUN
ap-2101	48	71	of	of	ADP
ap-2101	48	72	the	the	DET
ap-2101	48	73	point	point	NOUN
ap-2101	48	74	interaction	interaction	NOUN
ap-2101	48	75	.	.	PUNCT
ap-2101	49	1	if	if	SCONJ
ap-2101	49	2	we	we	PRON
ap-2101	49	3	parametrize	parametrize	VERB
ap-2101	49	4	the	the	DET
ap-2101	49	5	bound	bound	ADJ
ap-2101	49	6	state	state	NOUN
ap-2101	49	7	energy	energy	NOUN
ap-2101	49	8	by	by	ADP
ap-2101	49	9	e	e	PROPN
ap-2101	49	10	=	=	PROPN
ap-2101	49	11	−ν2	−ν2	PROPN
ap-2101	49	12	,	,	PUNCT
ap-2101	49	13	then	then	ADV
ap-2101	49	14	the	the	DET
ap-2101	49	15	schrödinger	schrödinger	ADJ
ap-2101	49	16	equation	equation	NOUN
ap-2101	49	17	for	for	ADP
ap-2101	49	18	the	the	DET
ap-2101	49	19	bound	bind	VERB
ap-2101	49	20	state	state	NOUN
ap-2101	49	21	of	of	ADP
ap-2101	49	22	the	the	DET
ap-2101	49	23	system	system	NOUN
ap-2101	49	24	becomes	become	VERB
ap-2101	49	25	(	(	PUNCT
ap-2101	49	26	−∆rd	−∆rd	NOUN
ap-2101	49	27	−	−	PROPN
ap-2101	49	28	gδd(x	gδd(x	NOUN
ap-2101	49	29	)	)	PUNCT
ap-2101	49	30	)	)	PUNCT
ap-2101	50	1	φ(x	φ(x	NOUN
ap-2101	50	2	)	)	PUNCT
ap-2101	50	3	=	=	SYM
ap-2101	50	4	−ν2φ(x	−ν2φ(x	PROPN
ap-2101	50	5	)	)	PUNCT
ap-2101	50	6	,	,	PUNCT
ap-2101	50	7	(	(	PUNCT
ap-2101	50	8	2.2	2.2	NUM
ap-2101	50	9	)	)	PUNCT
ap-2101	50	10	where	where	SCONJ
ap-2101	50	11	φ(x	φ(x	NOUN
ap-2101	50	12	)	)	PUNCT
ap-2101	50	13	is	be	AUX
ap-2101	50	14	the	the	DET
ap-2101	50	15	bound	bound	ADJ
ap-2101	50	16	state	state	NOUN
ap-2101	50	17	wavefunction	wavefunction	NOUN
ap-2101	50	18	.	.	PUNCT
ap-2101	51	1	this	this	DET
ap-2101	51	2	expression	expression	NOUN
ap-2101	51	3	can	can	AUX
ap-2101	51	4	be	be	AUX
ap-2101	51	5	expressed	express	VERB
ap-2101	51	6	in	in	ADP
ap-2101	51	7	momentum	momentum	NOUN
ap-2101	51	8	space	space	NOUN
ap-2101	51	9	as	as	ADP
ap-2101	51	10	(	(	PUNCT
ap-2101	51	11	p2	p2	X
ap-2101	51	12	+	+	CCONJ
ap-2101	51	13	ν2)φ̃(p	ν2)φ̃(p	PROPN
ap-2101	51	14	,	,	PUNCT
ap-2101	51	15	ω	ω	NOUN
ap-2101	51	16	)	)	PUNCT
ap-2101	51	17	=	=	SYM
ap-2101	51	18	g	g	PROPN
ap-2101	51	19	(	(	PUNCT
ap-2101	51	20	2π)d	2π)d	PROPN
ap-2101	51	21	∫	∫	PROPN
ap-2101	51	22	sd−1	sd−1	PROPN
ap-2101	51	23	dω	dω	PROPN
ap-2101	51	24	∫	∫	PROPN
ap-2101	51	25	∞	∞	NUM
ap-2101	51	26	0	0	NUM
ap-2101	51	27	dp′	dp′	PROPN
ap-2101	51	28	p′d−1φ̃(p′	p′d−1φ̃(p′	PROPN
ap-2101	51	29	,	,	PUNCT
ap-2101	51	30	ω	ω	NOUN
ap-2101	51	31	)	)	PUNCT
ap-2101	51	32	,	,	PUNCT
ap-2101	51	33	(	(	PUNCT
ap-2101	51	34	2.3	2.3	NUM
ap-2101	51	35	)	)	PUNCT
ap-2101	51	36	where	where	SCONJ
ap-2101	51	37	φ̃(p	φ̃(p	NOUN
ap-2101	51	38	,	,	PUNCT
ap-2101	51	39	ω	ω	NOUN
ap-2101	51	40	)	)	PUNCT
ap-2101	51	41	is	be	AUX
ap-2101	51	42	the	the	DET
ap-2101	51	43	fourier	fourier	ADJ
ap-2101	51	44	transform	transform	NOUN
ap-2101	51	45	of	of	ADP
ap-2101	51	46	φ(x	φ(x	NOUN
ap-2101	51	47	)	)	PUNCT
ap-2101	51	48	.	.	PUNCT
ap-2101	52	1	note	note	VERB
ap-2101	52	2	that	that	SCONJ
ap-2101	52	3	we	we	PRON
ap-2101	52	4	also	also	ADV
ap-2101	52	5	switched	switch	VERB
ap-2101	52	6	to	to	ADP
ap-2101	52	7	spherical	spherical	ADJ
ap-2101	52	8	coordinates	coordinate	NOUN
ap-2101	52	9	in	in	ADP
ap-2101	52	10	momentum	momentum	NOUN
ap-2101	52	11	space	space	NOUN
ap-2101	52	12	,	,	PUNCT
ap-2101	52	13	where	where	SCONJ
ap-2101	52	14	p	p	PROPN
ap-2101	52	15	and	and	CCONJ
ap-2101	52	16	ω	ω	PROPN
ap-2101	52	17	denote	denote	VERB
ap-2101	52	18	the	the	DET
ap-2101	52	19	radial	radial	ADJ
ap-2101	52	20	and	and	CCONJ
ap-2101	52	21	angular	angular	ADJ
ap-2101	52	22	coordinates	coordinate	NOUN
ap-2101	52	23	respectively	respectively	ADV
ap-2101	52	24	.	.	PUNCT
ap-2101	53	1	from	from	ADP
ap-2101	53	2	(	(	PUNCT
ap-2101	53	3	2.3	2.3	NUM
ap-2101	53	4	)	)	PUNCT
ap-2101	53	5	,	,	PUNCT
ap-2101	53	6	g−1	g−1	PROPN
ap-2101	53	7	can	can	AUX
ap-2101	53	8	be	be	AUX
ap-2101	53	9	solved	solve	VERB
ap-2101	53	10	as	as	ADP
ap-2101	53	11	1	1	NUM
ap-2101	53	12	g	g	NOUN
ap-2101	53	13	=	=	PUNCT
ap-2101	53	14	vol	vol	NOUN
ap-2101	53	15	(	(	PUNCT
ap-2101	53	16	sd−1	sd−1	NOUN
ap-2101	53	17	)	)	PUNCT
ap-2101	53	18	(	(	PUNCT
ap-2101	53	19	2π)d	2π)d	NUM
ap-2101	53	20	∫	∫	NOUN
ap-2101	53	21	∞	∞	NUM
ap-2101	53	22	0	0	NUM
ap-2101	53	23	dp′	dp′	PROPN
ap-2101	53	24	p′d−1	p′d−1	PROPN
ap-2101	53	25	p′2	p′2	NOUN
ap-2101	53	26	+	+	CCONJ
ap-2101	53	27	ν2	ν2	NOUN
ap-2101	53	28	,	,	PUNCT
ap-2101	53	29	(	(	PUNCT
ap-2101	53	30	2.4	2.4	NUM
ap-2101	53	31	)	)	PUNCT
ap-2101	53	32	where	where	SCONJ
ap-2101	53	33	vol	vol	NOUN
ap-2101	53	34	(	(	PUNCT
ap-2101	53	35	sd−1	sd−1	NOUN
ap-2101	53	36	)	)	PUNCT
ap-2101	53	37	denotes	denote	VERB
ap-2101	53	38	the	the	DET
ap-2101	53	39	volume	volume	NOUN
ap-2101	53	40	of	of	ADP
ap-2101	53	41	the	the	DET
ap-2101	53	42	unit	unit	NOUN
ap-2101	53	43	sphere	sphere	ADV
ap-2101	53	44	in	in	ADP
ap-2101	53	45	d	d	PROPN
ap-2101	53	46	−	−	PROPN
ap-2101	53	47	1	1	NUM
ap-2101	53	48	dimensions	dimension	NOUN
ap-2101	53	49	.	.	PUNCT
ap-2101	54	1	it	it	PRON
ap-2101	54	2	is	be	AUX
ap-2101	54	3	easy	easy	ADJ
ap-2101	54	4	to	to	PART
ap-2101	54	5	see	see	VERB
ap-2101	54	6	that	that	SCONJ
ap-2101	54	7	the	the	DET
ap-2101	54	8	integral	integral	ADJ
ap-2101	54	9	diverges	diverge	NOUN
ap-2101	54	10	for	for	ADP
ap-2101	54	11	d	d	PRON
ap-2101	54	12	≥	≥	NUM
ap-2101	54	13	2	2	NUM
ap-2101	54	14	,	,	PUNCT
ap-2101	54	15	so	so	ADV
ap-2101	54	16	regularization	regularization	NOUN
ap-2101	54	17	and	and	CCONJ
ap-2101	54	18	renormalization	renormalization	NOUN
ap-2101	54	19	are	be	AUX
ap-2101	54	20	needed	need	VERB
ap-2101	54	21	to	to	PART
ap-2101	54	22	obtain	obtain	VERB
ap-2101	54	23	physical	physical	ADJ
ap-2101	54	24	results	result	NOUN
ap-2101	54	25	.	.	PUNCT
ap-2101	55	1	renormalization	renormalization	NOUN
ap-2101	55	2	of	of	ADP
ap-2101	55	3	point	point	NOUN
ap-2101	55	4	interactions	interaction	NOUN
ap-2101	55	5	has	have	AUX
ap-2101	55	6	been	be	AUX
ap-2101	55	7	studied	study	VERB
ap-2101	55	8	by	by	ADP
ap-2101	55	9	many	many	ADJ
ap-2101	55	10	authors	author	NOUN
ap-2101	55	11	;	;	PUNCT
ap-2101	55	12	in	in	ADP
ap-2101	55	13	position	position	NOUN
ap-2101	55	14	space	space	NOUN
ap-2101	55	15	[	[	X
ap-2101	55	16	12	12	NUM
ap-2101	55	17	,	,	PUNCT
ap-2101	55	18	14	14	NUM
ap-2101	55	19	,	,	PUNCT
ap-2101	55	20	17	17	NUM
ap-2101	55	21	]	]	PUNCT
ap-2101	55	22	,	,	PUNCT
ap-2101	55	23	and	and	CCONJ
ap-2101	55	24	in	in	ADP
ap-2101	55	25	momentum	momentum	NOUN
ap-2101	55	26	space	space	NOUN
ap-2101	55	27	[	[	X
ap-2101	55	28	2	2	NUM
ap-2101	55	29	,	,	PUNCT
ap-2101	55	30	5	5	NUM
ap-2101	55	31	,	,	PUNCT
ap-2101	55	32	6	6	NUM
ap-2101	55	33	,	,	PUNCT
ap-2101	55	34	18	18	NUM
ap-2101	55	35	,	,	PUNCT
ap-2101	55	36	20	20	NUM
ap-2101	55	37	]	]	PUNCT
ap-2101	55	38	.	.	PUNCT
ap-2101	56	1	the	the	DET
ap-2101	56	2	renormalization	renormalization	NOUN
ap-2101	56	3	group	group	NOUN
ap-2101	56	4	equations	equation	NOUN
ap-2101	56	5	were	be	AUX
ap-2101	56	6	derived	derive	VERB
ap-2101	56	7	in	in	ADP
ap-2101	56	8	[	[	X
ap-2101	56	9	1	1	NUM
ap-2101	56	10	,	,	PUNCT
ap-2101	56	11	2	2	NUM
ap-2101	56	12	]	]	PUNCT
ap-2101	56	13	.	.	PUNCT
ap-2101	57	1	instead	instead	ADV
ap-2101	57	2	of	of	ADP
ap-2101	57	3	the	the	DET
ap-2101	57	4	conventional	conventional	ADJ
ap-2101	57	5	approach	approach	NOUN
ap-2101	57	6	,	,	PUNCT
ap-2101	57	7	we	we	PRON
ap-2101	57	8	shall	shall	AUX
ap-2101	57	9	perform	perform	VERB
ap-2101	57	10	the	the	DET
ap-2101	57	11	renormalization	renormalization	NOUN
ap-2101	57	12	using	use	VERB
ap-2101	57	13	the	the	DET
ap-2101	57	14	exact	exact	ADJ
ap-2101	57	15	renormalization	renormalization	NOUN
ap-2101	57	16	group	group	NOUN
ap-2101	57	17	(	(	PUNCT
ap-2101	57	18	erg	erg	NOUN
ap-2101	57	19	)	)	PUNCT
ap-2101	57	20	method	method	NOUN
ap-2101	57	21	.	.	PUNCT
ap-2101	58	1	2.2	2.2	NUM
ap-2101	58	2	.	.	PUNCT
ap-2101	58	3	renormalization	renormalization	NOUN
ap-2101	58	4	of	of	ADP
ap-2101	58	5	hamiltonians	hamiltonian	NOUN
ap-2101	58	6	in	in	ADP
ap-2101	58	7	this	this	DET
ap-2101	58	8	section	section	NOUN
ap-2101	58	9	we	we	PRON
ap-2101	58	10	perform	perform	VERB
ap-2101	58	11	the	the	DET
ap-2101	58	12	renormalization	renormalization	NOUN
ap-2101	58	13	of	of	ADP
ap-2101	58	14	a	a	DET
ap-2101	58	15	point	point	NOUN
ap-2101	58	16	interaction	interaction	NOUN
ap-2101	58	17	on	on	ADP
ap-2101	58	18	the	the	DET
ap-2101	58	19	euclidean	euclidean	ADJ
ap-2101	58	20	plane	plane	NOUN
ap-2101	58	21	,	,	PUNCT
ap-2101	58	22	r2	r2	PROPN
ap-2101	58	23	.	.	PUNCT
ap-2101	59	1	this	this	DET
ap-2101	59	2	part	part	NOUN
ap-2101	59	3	will	will	AUX
ap-2101	59	4	be	be	AUX
ap-2101	59	5	mainly	mainly	ADV
ap-2101	59	6	a	a	DET
ap-2101	59	7	review	review	NOUN
ap-2101	59	8	of	of	ADP
ap-2101	59	9	the	the	DET
ap-2101	59	10	lecture	lecture	NOUN
ap-2101	59	11	notes	note	NOUN
ap-2101	59	12	given	give	VERB
ap-2101	59	13	by	by	ADP
ap-2101	59	14	głazek	głazek	NOUN
ap-2101	59	15	and	and	CCONJ
ap-2101	59	16	maslowski	maslowski	ADJ
ap-2101	59	17	[	[	X
ap-2101	59	18	8	8	NUM
ap-2101	59	19	]	]	PUNCT
ap-2101	59	20	and	and	CCONJ
ap-2101	59	21	we	we	PRON
ap-2101	59	22	include	include	VERB
ap-2101	59	23	it	it	PRON
ap-2101	59	24	for	for	ADP
ap-2101	59	25	the	the	DET
ap-2101	59	26	sake	sake	NOUN
ap-2101	59	27	of	of	ADP
ap-2101	59	28	completeness	completeness	NOUN
ap-2101	59	29	.	.	PUNCT
ap-2101	60	1	however	however	ADV
ap-2101	60	2	our	our	PRON
ap-2101	60	3	approach	approach	NOUN
ap-2101	60	4	will	will	AUX
ap-2101	60	5	be	be	AUX
ap-2101	60	6	slightly	slightly	ADV
ap-2101	60	7	different	different	ADJ
ap-2101	60	8	and	and	CCONJ
ap-2101	60	9	as	as	ADP
ap-2101	60	10	an	an	DET
ap-2101	60	11	addendum	addendum	NOUN
ap-2101	60	12	we	we	PRON
ap-2101	60	13	also	also	ADV
ap-2101	60	14	investigate	investigate	VERB
ap-2101	60	15	the	the	DET
ap-2101	60	16	range	range	NOUN
ap-2101	60	17	of	of	ADP
ap-2101	60	18	renormalizability	renormalizability	NOUN
ap-2101	60	19	using	use	VERB
ap-2101	60	20	the	the	DET
ap-2101	60	21	banach	banach	NOUN
ap-2101	60	22	contraction	contraction	NOUN
ap-2101	60	23	principle	principle	NOUN
ap-2101	60	24	.	.	PUNCT
ap-2101	61	1	before	before	ADP
ap-2101	61	2	any	any	DET
ap-2101	61	3	kind	kind	NOUN
ap-2101	61	4	of	of	ADP
ap-2101	61	5	regularization	regularization	NOUN
ap-2101	61	6	or	or	CCONJ
ap-2101	61	7	renormalization	renormalization	NOUN
ap-2101	61	8	,	,	PUNCT
ap-2101	61	9	the	the	DET
ap-2101	61	10	schrödinger	schrödinger	ADJ
ap-2101	61	11	equation	equation	NOUN
ap-2101	61	12	for	for	ADP
ap-2101	61	13	the	the	DET
ap-2101	61	14	bound	bind	VERB
ap-2101	61	15	state	state	NOUN
ap-2101	61	16	can	can	AUX
ap-2101	61	17	be	be	AUX
ap-2101	61	18	written	write	VERB
ap-2101	61	19	as	as	ADP
ap-2101	61	20	h	h	PROPN
ap-2101	61	21	|φ	|φ	PROPN
ap-2101	61	22	〉	〉	PROPN
ap-2101	61	23	=	=	SYM
ap-2101	61	24	−ν2	−ν2	PROPN
ap-2101	61	25	|φ	|φ	PROPN
ap-2101	61	26	〉	〉	PROPN
ap-2101	61	27	.	.	PUNCT
ap-2101	62	1	(	(	PUNCT
ap-2101	62	2	2.5	2.5	NUM
ap-2101	62	3	)	)	PUNCT
ap-2101	62	4	we	we	PRON
ap-2101	62	5	want	want	VERB
ap-2101	62	6	to	to	PART
ap-2101	62	7	calculate	calculate	VERB
ap-2101	62	8	the	the	DET
ap-2101	62	9	effective	effective	ADJ
ap-2101	62	10	hamiltonian	hamiltonian	NOUN
ap-2101	62	11	hλ	hλ	ADP
ap-2101	62	12	eff	eff	PROPN
ap-2101	62	13	at	at	ADP
ap-2101	62	14	some	some	DET
ap-2101	62	15	energy	energy	NOUN
ap-2101	62	16	scale	scale	NOUN
ap-2101	62	17	λ	λ	NOUN
ap-2101	62	18	,	,	PUNCT
ap-2101	62	19	where	where	SCONJ
ap-2101	62	20	λ	λ	X
ap-2101	62	21	�	�	PROPN
ap-2101	62	22	1	1	NUM
ap-2101	62	23	.	.	PUNCT
ap-2101	63	1	this	this	PRON
ap-2101	63	2	is	be	AUX
ap-2101	63	3	done	do	VERB
ap-2101	63	4	by	by	ADP
ap-2101	63	5	integrating	integrate	VERB
ap-2101	63	6	out	out	ADP
ap-2101	63	7	degrees	degree	NOUN
ap-2101	63	8	of	of	ADP
ap-2101	63	9	freedom	freedom	NOUN
ap-2101	63	10	above	above	ADP
ap-2101	63	11	λ	λ	PROPN
ap-2101	63	12	.	.	PUNCT
ap-2101	64	1	to	to	ADP
ap-2101	64	2	this	this	DET
ap-2101	64	3	end	end	NOUN
ap-2101	64	4	we	we	PRON
ap-2101	64	5	introduce	introduce	VERB
ap-2101	64	6	the	the	DET
ap-2101	64	7	operators	operator	NOUN
ap-2101	64	8	p	p	NOUN
ap-2101	64	9	and	and	CCONJ
ap-2101	64	10	q	q	PROPN
ap-2101	64	11	which	which	PRON
ap-2101	64	12	are	be	AUX
ap-2101	64	13	projections	projection	NOUN
ap-2101	64	14	to	to	ADP
ap-2101	64	15	the	the	DET
ap-2101	64	16	subspaces	subspace	NOUN
ap-2101	64	17	,	,	PUNCT
ap-2101	64	18	where	where	SCONJ
ap-2101	64	19	the	the	DET
ap-2101	64	20	momentum	momentum	NOUN
ap-2101	64	21	eigenvalue	eigenvalue	NOUN
ap-2101	64	22	takes	take	VERB
ap-2101	64	23	the	the	DET
ap-2101	64	24	values	value	NOUN
ap-2101	64	25	0	0	NUM
ap-2101	65	1	≤	≤	NOUN
ap-2101	65	2	p	p	ADJ
ap-2101	65	3	≤	≤	ADJ
ap-2101	65	4	λ	λ	PROPN
ap-2101	65	5	and	and	CCONJ
ap-2101	65	6	p	p	X
ap-2101	65	7	>	>	X
ap-2101	65	8	λ	λ	X
ap-2101	65	9	respectively	respectively	ADV
ap-2101	65	10	.	.	PUNCT
ap-2101	66	1	let	let	VERB
ap-2101	66	2	us	we	PRON
ap-2101	66	3	also	also	ADV
ap-2101	66	4	define	define	VERB
ap-2101	66	5	|φ〉p	|φ〉p	PROPN
ap-2101	66	6	≡	≡	PROPN
ap-2101	66	7	p	p	PROPN
ap-2101	66	8	|φ	|φ	PROPN
ap-2101	66	9	〉	〉	PROPN
ap-2101	66	10	and	and	CCONJ
ap-2101	66	11	|φ〉q	|φ〉q	NOUN
ap-2101	66	12	≡	≡	PROPN
ap-2101	66	13	q	q	PROPN
ap-2101	66	14	|φ	|φ	PROPN
ap-2101	66	15	〉	〉	PROPN
ap-2101	66	16	.	.	PUNCT
ap-2101	67	1	by	by	ADP
ap-2101	67	2	using	use	VERB
ap-2101	67	3	p	p	PROPN
ap-2101	67	4	+	+	NOUN
ap-2101	67	5	q	q	NOUN
ap-2101	67	6	=	=	PUNCT
ap-2101	67	7	i	i	PROPN
ap-2101	67	8	and	and	CCONJ
ap-2101	67	9	pq	pq	INTJ
ap-2101	68	1	=	=	NOUN
ap-2101	68	2	0	0	NUM
ap-2101	68	3	one	one	PRON
ap-2101	68	4	can	can	AUX
ap-2101	68	5	split	split	VERB
ap-2101	68	6	(	(	PUNCT
ap-2101	68	7	2.5	2.5	NUM
ap-2101	68	8	)	)	PUNCT
ap-2101	68	9	as	as	ADP
ap-2101	68	10	php	php	PROPN
ap-2101	68	11	|φ〉p	|φ〉p	NOUN
ap-2101	68	12	+	+	CCONJ
ap-2101	68	13	phq	phq	NOUN
ap-2101	68	14	|φ〉q	|φ〉q	NOUN
ap-2101	68	15	=	=	SYM
ap-2101	68	16	−ν2	−ν2	PROPN
ap-2101	68	17	|φ〉p	|φ〉p	PROPN
ap-2101	68	18	(	(	PUNCT
ap-2101	68	19	2.6	2.6	NUM
ap-2101	68	20	)	)	PUNCT
ap-2101	68	21	qhp	qhp	NOUN
ap-2101	69	1	|φ〉p	|φ〉p	ADJ
ap-2101	69	2	+	+	NOUN
ap-2101	69	3	qhq	qhq	ADJ
ap-2101	69	4	|φ〉q	|φ〉q	NOUN
ap-2101	69	5	=	=	SYM
ap-2101	69	6	−ν2	−ν2	PROPN
ap-2101	69	7	|φ〉q	|φ〉q	NOUN
ap-2101	69	8	.	.	PUNCT
ap-2101	70	1	(	(	PUNCT
ap-2101	70	2	2.7	2.7	NUM
ap-2101	70	3	)	)	PUNCT
ap-2101	70	4	157	157	NUM
ap-2101	70	5	osman	osman	PROPN
ap-2101	70	6	teoman	teoman	PROPN
ap-2101	70	7	turgut	turgut	PROPN
ap-2101	70	8	,	,	PUNCT
ap-2101	70	9	cem	cem	NOUN
ap-2101	70	10	eröncel	eröncel	VERB
ap-2101	70	11	acta	acta	PROPN
ap-2101	70	12	polytechnica	polytechnica	PROPN
ap-2101	70	13	from	from	ADP
ap-2101	70	14	(	(	PUNCT
ap-2101	70	15	2.7	2.7	NUM
ap-2101	70	16	)	)	PUNCT
ap-2101	70	17	we	we	PRON
ap-2101	70	18	find	find	VERB
ap-2101	70	19	|φ〉q	|φ〉q	NOUN
ap-2101	70	20	=	=	SYM
ap-2101	70	21	(	(	PUNCT
ap-2101	70	22	−ν2	−ν2	NOUN
ap-2101	70	23	−qhq)−1qhp	−qhq)−1qhp	PROPN
ap-2101	70	24	|φ〉p	|φ〉p	NOUN
ap-2101	70	25	.	.	PUNCT
ap-2101	71	1	(	(	PUNCT
ap-2101	71	2	2.8	2.8	NUM
ap-2101	71	3	)	)	PUNCT
ap-2101	71	4	if	if	SCONJ
ap-2101	71	5	we	we	PRON
ap-2101	71	6	substitute	substitute	VERB
ap-2101	71	7	this	this	DET
ap-2101	71	8	result	result	NOUN
ap-2101	71	9	back	back	ADV
ap-2101	71	10	into	into	ADP
ap-2101	71	11	(	(	PUNCT
ap-2101	71	12	2.6	2.6	NUM
ap-2101	71	13	)	)	PUNCT
ap-2101	71	14	we	we	PRON
ap-2101	71	15	get	get	VERB
ap-2101	71	16	(	(	PUNCT
ap-2101	71	17	php	php	NOUN
ap-2101	71	18	+	+	CCONJ
ap-2101	71	19	phq(−ν2	phq(−ν2	NOUN
ap-2101	71	20	−qhq)−1qhp	−qhq)−1qhp	NOUN
ap-2101	71	21	)	)	PUNCT
ap-2101	71	22	|φ〉p	|φ〉p	PROPN
ap-2101	71	23	=	=	SYM
ap-2101	71	24	−ν2	−ν2	PROPN
ap-2101	71	25	|φ〉p	|φ〉p	PROPN
ap-2101	71	26	(	(	PUNCT
ap-2101	71	27	2.9	2.9	NUM
ap-2101	71	28	)	)	PUNCT
ap-2101	71	29	and	and	CCONJ
ap-2101	71	30	this	this	PRON
ap-2101	71	31	implies	imply	VERB
ap-2101	71	32	that	that	SCONJ
ap-2101	71	33	the	the	DET
ap-2101	71	34	effective	effective	ADJ
ap-2101	71	35	hamiltonian	hamiltonian	NOUN
ap-2101	71	36	at	at	ADP
ap-2101	71	37	the	the	DET
ap-2101	71	38	scale	scale	NOUN
ap-2101	71	39	λ	λ	NOUN
ap-2101	71	40	is	be	AUX
ap-2101	71	41	given	give	VERB
ap-2101	71	42	by	by	ADP
ap-2101	71	43	hλ	hλ	X
ap-2101	71	44	eff	eff	PROPN
ap-2101	71	45	=	=	PROPN
ap-2101	71	46	php	php	PROPN
ap-2101	71	47	+	+	CCONJ
ap-2101	71	48	phq(−ν2	phq(−ν2	NOUN
ap-2101	71	49	−qhq)−1qhp	−qhq)−1qhp	NOUN
ap-2101	71	50	≡	≡	PROPN
ap-2101	71	51	php	php	NOUN
ap-2101	72	1	+	+	NOUN
ap-2101	73	1	xλ	xλ	NOUN
ap-2101	73	2	.	.	PUNCT
ap-2101	74	1	(	(	PUNCT
ap-2101	74	2	2.10	2.10	NUM
ap-2101	74	3	)	)	PUNCT
ap-2101	74	4	we	we	PRON
ap-2101	74	5	note	note	VERB
ap-2101	74	6	that	that	SCONJ
ap-2101	74	7	,	,	PUNCT
ap-2101	74	8	although	although	SCONJ
ap-2101	74	9	we	we	PRON
ap-2101	74	10	are	be	AUX
ap-2101	74	11	working	work	VERB
ap-2101	74	12	at	at	ADP
ap-2101	74	13	the	the	DET
ap-2101	74	14	scale	scale	NOUN
ap-2101	74	15	λ	λ	NOUN
ap-2101	74	16	,	,	PUNCT
ap-2101	74	17	the	the	DET
ap-2101	74	18	effective	effective	ADJ
ap-2101	74	19	hamiltonian	hamiltonian	NOUN
ap-2101	74	20	contains	contain	VERB
ap-2101	74	21	the	the	DET
ap-2101	74	22	xλ	xλ	PROPN
ap-2101	74	23	term	term	NOUN
ap-2101	74	24	and	and	CCONJ
ap-2101	74	25	this	this	DET
ap-2101	74	26	term	term	NOUN
ap-2101	74	27	,	,	PUNCT
ap-2101	74	28	which	which	PRON
ap-2101	74	29	is	be	AUX
ap-2101	74	30	called	call	VERB
ap-2101	74	31	a	a	DET
ap-2101	74	32	counterterm	counterterm	NOUN
ap-2101	74	33	,	,	PUNCT
ap-2101	74	34	depends	depend	VERB
ap-2101	74	35	on	on	ADP
ap-2101	74	36	the	the	DET
ap-2101	74	37	higher	high	ADJ
ap-2101	74	38	degrees	degree	NOUN
ap-2101	74	39	of	of	ADP
ap-2101	74	40	freedom	freedom	NOUN
ap-2101	74	41	.	.	PUNCT
ap-2101	75	1	and	and	CCONJ
ap-2101	75	2	as	as	SCONJ
ap-2101	75	3	we	we	PRON
ap-2101	75	4	shall	shall	AUX
ap-2101	75	5	see	see	VERB
ap-2101	75	6	now	now	ADV
ap-2101	75	7	,	,	PUNCT
ap-2101	75	8	we	we	PRON
ap-2101	75	9	will	will	AUX
ap-2101	75	10	use	use	VERB
ap-2101	75	11	this	this	DET
ap-2101	75	12	counterterm	counterterm	NOUN
ap-2101	75	13	in	in	ADP
ap-2101	75	14	order	order	NOUN
ap-2101	75	15	to	to	PART
ap-2101	75	16	define	define	VERB
ap-2101	75	17	the	the	DET
ap-2101	75	18	effective	effective	ADJ
ap-2101	75	19	coupling	coupling	NOUN
ap-2101	75	20	constant	constant	ADJ
ap-2101	75	21	at	at	ADP
ap-2101	75	22	the	the	DET
ap-2101	75	23	scale	scale	NOUN
ap-2101	75	24	λ	λ	NOUN
ap-2101	75	25	.	.	PUNCT
ap-2101	76	1	let	let	VERB
ap-2101	76	2	us	we	PRON
ap-2101	76	3	write	write	VERB
ap-2101	76	4	the	the	DET
ap-2101	76	5	hamiltonian	hamiltonian	NOUN
ap-2101	76	6	as	as	ADP
ap-2101	76	7	h	h	NOUN
ap-2101	76	8	=	=	PROPN
ap-2101	76	9	h0	h0	PROPN
ap-2101	77	1	+	+	NOUN
ap-2101	77	2	v	v	ADP
ap-2101	78	1	where	where	SCONJ
ap-2101	78	2	h0	h0	NOUN
ap-2101	78	3	is	be	AUX
ap-2101	78	4	the	the	DET
ap-2101	78	5	free	free	ADJ
ap-2101	78	6	hamiltonian	hamiltonian	NOUN
ap-2101	78	7	and	and	CCONJ
ap-2101	78	8	v	v	NOUN
ap-2101	78	9	denotes	denote	NOUN
ap-2101	78	10	the	the	DET
ap-2101	78	11	point	point	NOUN
ap-2101	78	12	interaction	interaction	NOUN
ap-2101	78	13	,	,	PUNCT
ap-2101	78	14	i.e.	i.e.	X
ap-2101	78	15	〈	〈	PROPN
ap-2101	78	16	x|v	x|v	PROPN
ap-2101	78	17	|φ	|φ	PROPN
ap-2101	78	18	〉	〉	NOUN
ap-2101	78	19	=	=	SYM
ap-2101	78	20	−gδ2(x)φ(x	−gδ2(x)φ(x	NOUN
ap-2101	78	21	)	)	PUNCT
ap-2101	78	22	.	.	PUNCT
ap-2101	79	1	(	(	PUNCT
ap-2101	79	2	2.9	2.9	NUM
ap-2101	79	3	)	)	PUNCT
ap-2101	79	4	can	can	AUX
ap-2101	79	5	be	be	AUX
ap-2101	79	6	written	write	VERB
ap-2101	79	7	in	in	ADP
ap-2101	79	8	momentum	momentum	NOUN
ap-2101	79	9	space	space	NOUN
ap-2101	79	10	as	as	ADP
ap-2101	79	11	(	(	PUNCT
ap-2101	79	12	p2	p2	X
ap-2101	79	13	+	+	X
ap-2101	79	14	ν2)φ̃p(p	ν2)φ̃p(p	NUM
ap-2101	79	15	)	)	PUNCT
ap-2101	80	1	+	+	CCONJ
ap-2101	80	2	∫	∫	PROPN
ap-2101	80	3	rd	rd	PROPN
ap-2101	80	4	ddp′	ddp′	PROPN
ap-2101	80	5	〈	〈	PROPN
ap-2101	80	6	p|	p|	PROPN
ap-2101	80	7	pv	pv	NOUN
ap-2101	80	8	p	p	PROPN
ap-2101	80	9	|p′	|p′	PROPN
ap-2101	80	10	〉	〉	PROPN
ap-2101	80	11	φ̃p(p′	φ̃p(p′	PROPN
ap-2101	80	12	)	)	PUNCT
ap-2101	81	1	+	+	CCONJ
ap-2101	81	2	∫	∫	PROPN
ap-2101	81	3	rd	rd	PROPN
ap-2101	81	4	ddp′	ddp′	PROPN
ap-2101	81	5	〈	〈	PROPN
ap-2101	81	6	p|xλ	p|xλ	NOUN
ap-2101	81	7	|p′	|p′	PROPN
ap-2101	81	8	〉	〉	PROPN
ap-2101	81	9	φ̃p(p′	φ̃p(p′	PROPN
ap-2101	81	10	)	)	PUNCT
ap-2101	81	11	=	=	SYM
ap-2101	81	12	0	0	NUM
ap-2101	81	13	,	,	PUNCT
ap-2101	81	14	(	(	PUNCT
ap-2101	81	15	2.11	2.11	NUM
ap-2101	81	16	)	)	PUNCT
ap-2101	81	17	where	where	SCONJ
ap-2101	81	18	φ̃p(p	φ̃p(p	NOUN
ap-2101	81	19	)	)	PUNCT
ap-2101	81	20	=	=	SYM
ap-2101	82	1	〈	〈	PROPN
ap-2101	82	2	p	p	X
ap-2101	82	3	∣∣	∣∣	NUM
ap-2101	82	4	φ̃p	φ̃p	X
ap-2101	82	5	〉	〉	NOUN
ap-2101	82	6	.	.	PUNCT
ap-2101	82	7	by	by	ADP
ap-2101	82	8	defining	define	VERB
ap-2101	82	9	xλ(p	xλ(p	NOUN
ap-2101	82	10	,	,	PUNCT
ap-2101	82	11	p′	p′	NOUN
ap-2101	82	12	)	)	PUNCT
ap-2101	82	13	≡	≡	PROPN
ap-2101	82	14	(	(	PUNCT
ap-2101	82	15	2π)2	2π)2	NUM
ap-2101	82	16	〈	〈	PROPN
ap-2101	82	17	p|xλ	p|xλ	ADJ
ap-2101	82	18	|p′	|p′	NOUN
ap-2101	82	19	〉	〉	PROPN
ap-2101	82	20	and	and	CCONJ
ap-2101	82	21	using	use	VERB
ap-2101	82	22	〈	〈	PROPN
ap-2101	82	23	p|v	p|v	VERB
ap-2101	82	24	|p′	|p′	PROPN
ap-2101	82	25	〉	〉	PROPN
ap-2101	82	26	=	=	SYM
ap-2101	82	27	∫	∫	PROPN
ap-2101	82	28	r4	r4	PROPN
ap-2101	82	29	d2x	d2x	PROPN
ap-2101	82	30	d2x′	d2x′	PROPN
ap-2101	82	31	〈	〈	PROPN
ap-2101	82	32	p|	p|	NOUN
ap-2101	82	33	x	x	NOUN
ap-2101	82	34	〉	〉	NOUN
ap-2101	82	35	〈	〈	PROPN
ap-2101	82	36	x|v	x|v	PROPN
ap-2101	82	37	|x′	|x′	PROPN
ap-2101	82	38	〉	〉	PROPN
ap-2101	82	39	〈	〈	PROPN
ap-2101	82	40	x′|	x′|	PROPN
ap-2101	82	41	p′	p′	PROPN
ap-2101	82	42	〉	〉	PROPN
ap-2101	82	43	=	=	SYM
ap-2101	82	44	−	−	PROPN
ap-2101	82	45	g	g	NOUN
ap-2101	82	46	(	(	PUNCT
ap-2101	82	47	2π)2	2π)2	NUM
ap-2101	82	48	,	,	PUNCT
ap-2101	82	49	(	(	PUNCT
ap-2101	82	50	2.12	2.12	NUM
ap-2101	82	51	)	)	PUNCT
ap-2101	82	52	we	we	PRON
ap-2101	82	53	get	get	VERB
ap-2101	82	54	(	(	PUNCT
ap-2101	82	55	p2	p2	X
ap-2101	82	56	+	+	CCONJ
ap-2101	82	57	ν2)φ̃p(p)−	ν2)φ̃p(p)−	NOUN
ap-2101	82	58	1	1	NUM
ap-2101	82	59	(	(	PUNCT
ap-2101	82	60	2π)2	2π)2	NUM
ap-2101	82	61	∫	∫	PROPN
ap-2101	82	62	r2	r2	PROPN
ap-2101	82	63	d2p′θλ(p	d2p′θλ(p	PROPN
ap-2101	82	64	)	)	PUNCT
ap-2101	82	65	(	(	PUNCT
ap-2101	82	66	g	g	NOUN
ap-2101	82	67	−	−	PROPN
ap-2101	82	68	xλ(p	xλ(p	PROPN
ap-2101	82	69	,	,	PUNCT
ap-2101	82	70	p′	p′	NOUN
ap-2101	82	71	)	)	PUNCT
ap-2101	82	72	)	)	PUNCT
ap-2101	83	1	φ̃p(p′	φ̃p(p′	X
ap-2101	83	2	)	)	PUNCT
ap-2101	83	3	=	=	SYM
ap-2101	83	4	0	0	NUM
ap-2101	83	5	,	,	PUNCT
ap-2101	83	6	(	(	PUNCT
ap-2101	83	7	2.13	2.13	NUM
ap-2101	83	8	)	)	PUNCT
ap-2101	83	9	where	where	SCONJ
ap-2101	83	10	θλ(p	θλ(p	NOUN
ap-2101	83	11	)	)	PUNCT
ap-2101	83	12	is	be	AUX
ap-2101	83	13	the	the	DET
ap-2101	83	14	step	step	NOUN
ap-2101	83	15	function	function	NOUN
ap-2101	83	16	.	.	PUNCT
ap-2101	84	1	we	we	PRON
ap-2101	84	2	see	see	VERB
ap-2101	84	3	that	that	SCONJ
ap-2101	84	4	the	the	DET
ap-2101	84	5	g	g	PROPN
ap-2101	84	6	−	−	PROPN
ap-2101	84	7	xλ(p	xλ(p	PROPN
ap-2101	84	8	,	,	PUNCT
ap-2101	84	9	p′	p′	NOUN
ap-2101	84	10	)	)	PUNCT
ap-2101	84	11	term	term	NOUN
ap-2101	84	12	plays	play	VERB
ap-2101	84	13	the	the	DET
ap-2101	84	14	role	role	NOUN
ap-2101	84	15	of	of	ADP
ap-2101	84	16	the	the	DET
ap-2101	84	17	effective	effective	ADJ
ap-2101	84	18	coupling	coupling	NOUN
ap-2101	84	19	constant	constant	ADJ
ap-2101	84	20	.	.	PUNCT
ap-2101	85	1	from	from	ADP
ap-2101	85	2	now	now	ADV
ap-2101	85	3	on	on	ADV
ap-2101	85	4	we	we	PRON
ap-2101	85	5	denote	denote	VERB
ap-2101	85	6	it	it	PRON
ap-2101	85	7	by	by	ADP
ap-2101	85	8	gλ(p	gλ(p	NOUN
ap-2101	85	9	,	,	PUNCT
ap-2101	85	10	p′	p′	NOUN
ap-2101	85	11	)	)	PUNCT
ap-2101	85	12	.	.	PUNCT
ap-2101	86	1	the	the	DET
ap-2101	86	2	counterterm	counterterm	NOUN
ap-2101	86	3	xλ(p	xλ(p	PROPN
ap-2101	86	4	,	,	PUNCT
ap-2101	86	5	p′	p′	NUM
ap-2101	86	6	)	)	PUNCT
ap-2101	86	7	acts	act	VERB
ap-2101	86	8	like	like	ADP
ap-2101	86	9	a	a	DET
ap-2101	86	10	correction	correction	NOUN
ap-2101	86	11	to	to	ADP
ap-2101	86	12	the	the	DET
ap-2101	86	13	initial	initial	ADJ
ap-2101	86	14	theory	theory	NOUN
ap-2101	86	15	and	and	CCONJ
ap-2101	86	16	by	by	ADP
ap-2101	86	17	using	use	VERB
ap-2101	86	18	it	it	PRON
ap-2101	86	19	we	we	PRON
ap-2101	86	20	have	have	AUX
ap-2101	86	21	defined	define	VERB
ap-2101	86	22	the	the	DET
ap-2101	86	23	renormalized	renormalize	VERB
ap-2101	86	24	coupling	couple	VERB
ap-2101	86	25	constant	constant	ADJ
ap-2101	86	26	gλ(p	gλ(p	NOUN
ap-2101	86	27	,	,	PUNCT
ap-2101	86	28	p′	p′	NOUN
ap-2101	86	29	)	)	PUNCT
ap-2101	86	30	at	at	ADP
ap-2101	86	31	the	the	DET
ap-2101	86	32	scale	scale	NOUN
ap-2101	86	33	λ	λ	NOUN
ap-2101	86	34	.	.	PROPN
ap-2101	86	35	2.3	2.3	NUM
ap-2101	86	36	.	.	PUNCT
ap-2101	87	1	applying	apply	VERB
ap-2101	87	2	the	the	DET
ap-2101	87	3	erg	erg	NOUN
ap-2101	87	4	procedure	procedure	NOUN
ap-2101	87	5	now	now	ADV
ap-2101	87	6	we	we	PRON
ap-2101	87	7	are	be	AUX
ap-2101	87	8	in	in	ADP
ap-2101	87	9	a	a	DET
ap-2101	87	10	position	position	NOUN
ap-2101	87	11	to	to	PART
ap-2101	87	12	perform	perform	VERB
ap-2101	87	13	the	the	DET
ap-2101	87	14	erg	erg	NOUN
ap-2101	87	15	analysis	analysis	NOUN
ap-2101	87	16	of	of	ADP
ap-2101	87	17	our	our	PRON
ap-2101	87	18	theory	theory	NOUN
ap-2101	87	19	.	.	PUNCT
ap-2101	88	1	since	since	SCONJ
ap-2101	88	2	the	the	DET
ap-2101	88	3	original	original	ADJ
ap-2101	88	4	problem	problem	NOUN
ap-2101	88	5	is	be	AUX
ap-2101	88	6	rotationally	rotationally	ADV
ap-2101	88	7	symmetric	symmetric	ADJ
ap-2101	88	8	,	,	PUNCT
ap-2101	88	9	we	we	PRON
ap-2101	88	10	want	want	VERB
ap-2101	88	11	to	to	PART
ap-2101	88	12	keep	keep	VERB
ap-2101	88	13	the	the	DET
ap-2101	88	14	rotational	rotational	ADJ
ap-2101	88	15	symmetry	symmetry	NOUN
ap-2101	88	16	intact	intact	ADJ
ap-2101	88	17	.	.	PUNCT
ap-2101	89	1	therefore	therefore	ADV
ap-2101	89	2	we	we	PRON
ap-2101	89	3	assume	assume	VERB
ap-2101	89	4	that	that	SCONJ
ap-2101	89	5	the	the	DET
ap-2101	89	6	renormalized	renormalized	ADJ
ap-2101	89	7	coupling	couple	VERB
ap-2101	89	8	constant	constant	ADJ
ap-2101	89	9	gλ	gλ	NOUN
ap-2101	89	10	does	do	AUX
ap-2101	89	11	not	not	PART
ap-2101	89	12	depend	depend	VERB
ap-2101	89	13	on	on	ADP
ap-2101	89	14	ω	ω	PROPN
ap-2101	89	15	.	.	PUNCT
ap-2101	90	1	at	at	ADP
ap-2101	90	2	the	the	DET
ap-2101	90	3	bare	bare	ADJ
ap-2101	90	4	scale	scale	NOUN
ap-2101	90	5	λ	λ	NOUN
ap-2101	90	6	we	we	PRON
ap-2101	90	7	can	can	AUX
ap-2101	90	8	write	write	VERB
ap-2101	90	9	the	the	DET
ap-2101	90	10	following	follow	VERB
ap-2101	90	11	equation	equation	NOUN
ap-2101	90	12	:	:	PUNCT
ap-2101	90	13	(	(	PUNCT
ap-2101	90	14	p2	p2	X
ap-2101	90	15	+	+	CCONJ
ap-2101	90	16	ν2)φ̃(p	ν2)φ̃(p	PROPN
ap-2101	90	17	,	,	PUNCT
ap-2101	90	18	ω	ω	NOUN
ap-2101	90	19	)	)	PUNCT
ap-2101	90	20	=	=	NOUN
ap-2101	90	21	θλ(p	θλ(p	NOUN
ap-2101	90	22	)	)	PUNCT
ap-2101	90	23	(	(	PUNCT
ap-2101	90	24	2π)2	2π)2	NUM
ap-2101	90	25	∫	∫	PROPN
ap-2101	90	26	λ	λ	X
ap-2101	90	27	0	0	NUM
ap-2101	90	28	dp′	dp′	PROPN
ap-2101	90	29	p′gλ(p	p′gλ(p	PROPN
ap-2101	90	30	,	,	PUNCT
ap-2101	90	31	p′)ϑ(p′	p′)ϑ(p′	NOUN
ap-2101	90	32	)	)	PUNCT
ap-2101	90	33	,	,	PUNCT
ap-2101	90	34	(	(	PUNCT
ap-2101	90	35	2.14	2.14	NUM
ap-2101	90	36	)	)	PUNCT
ap-2101	90	37	where	where	SCONJ
ap-2101	90	38	ϑ(p	ϑ(p	PROPN
ap-2101	90	39	)	)	PUNCT
ap-2101	90	40	≡	≡	PROPN
ap-2101	90	41	∫	∫	PROPN
ap-2101	90	42	s1	s1	PROPN
ap-2101	90	43	dω	dω	ADP
ap-2101	90	44	φ̃(p	φ̃(p	PROPN
ap-2101	90	45	,	,	PUNCT
ap-2101	90	46	ω	ω	NOUN
ap-2101	90	47	)	)	PUNCT
ap-2101	90	48	.	.	PUNCT
ap-2101	91	1	(	(	PUNCT
ap-2101	91	2	2.15	2.15	NUM
ap-2101	91	3	)	)	PUNCT
ap-2101	91	4	we	we	PRON
ap-2101	91	5	remark	remark	VERB
ap-2101	91	6	that	that	SCONJ
ap-2101	91	7	we	we	PRON
ap-2101	91	8	have	have	AUX
ap-2101	91	9	switched	switch	VERB
ap-2101	91	10	to	to	ADP
ap-2101	91	11	the	the	DET
ap-2101	91	12	unprojected	unprojected	ADJ
ap-2101	91	13	wavefunction	wavefunction	NOUN
ap-2101	91	14	φ̃(p	φ̃(p	NOUN
ap-2101	91	15	,	,	PUNCT
ap-2101	91	16	ω	ω	NOUN
ap-2101	91	17	)	)	PUNCT
ap-2101	91	18	and	and	CCONJ
ap-2101	91	19	compensate	compensate	VERB
ap-2101	91	20	this	this	DET
ap-2101	91	21	change	change	NOUN
ap-2101	91	22	by	by	ADP
ap-2101	91	23	putting	put	VERB
ap-2101	91	24	the	the	DET
ap-2101	91	25	step	step	NOUN
ap-2101	91	26	function	function	NOUN
ap-2101	91	27	θλ(p	θλ(p	NOUN
ap-2101	91	28	)	)	PUNCT
ap-2101	91	29	in	in	ADP
ap-2101	91	30	front	front	NOUN
ap-2101	91	31	of	of	ADP
ap-2101	91	32	the	the	DET
ap-2101	91	33	integral	integral	ADJ
ap-2101	91	34	,	,	PUNCT
ap-2101	91	35	which	which	PRON
ap-2101	91	36	ensures	ensure	VERB
ap-2101	91	37	that	that	SCONJ
ap-2101	91	38	(	(	PUNCT
ap-2101	91	39	2.14	2.14	NUM
ap-2101	91	40	)	)	PUNCT
ap-2101	91	41	is	be	AUX
ap-2101	91	42	valid	valid	ADJ
ap-2101	91	43	for	for	ADP
ap-2101	91	44	p	p	PROPN
ap-2101	91	45	≤	≤	PROPN
ap-2101	91	46	λ	λ	PROPN
ap-2101	91	47	.	.	PUNCT
ap-2101	92	1	following	follow	VERB
ap-2101	92	2	the	the	DET
ap-2101	92	3	erg	erg	PROPN
ap-2101	92	4	procedure	procedure	NOUN
ap-2101	92	5	,	,	PUNCT
ap-2101	92	6	we	we	PRON
ap-2101	92	7	write	write	VERB
ap-2101	92	8	the	the	DET
ap-2101	92	9	analog	analog	NOUN
ap-2101	92	10	of	of	ADP
ap-2101	92	11	(	(	PUNCT
ap-2101	92	12	2.14	2.14	NUM
ap-2101	92	13	)	)	PUNCT
ap-2101	92	14	at	at	ADP
ap-2101	92	15	the	the	DET
ap-2101	92	16	infinitesimally	infinitesimally	ADV
ap-2101	92	17	lower	low	ADJ
ap-2101	92	18	scale	scale	NOUN
ap-2101	92	19	λ−	λ−	PROPN
ap-2101	92	20	dλ	dλ	NOUN
ap-2101	92	21	.	.	PUNCT
ap-2101	93	1	(	(	PUNCT
ap-2101	93	2	p2	p2	X
ap-2101	93	3	+	+	CCONJ
ap-2101	93	4	ν2)φ̃(p	ν2)φ̃(p	PROPN
ap-2101	93	5	,	,	PUNCT
ap-2101	93	6	ω	ω	NOUN
ap-2101	93	7	)	)	PUNCT
ap-2101	93	8	=	=	SYM
ap-2101	93	9	θλ−dλ(p	θλ−dλ(p	ADJ
ap-2101	93	10	)	)	PUNCT
ap-2101	93	11	(	(	PUNCT
ap-2101	93	12	2π)2	2π)2	NUM
ap-2101	93	13	∫	∫	PROPN
ap-2101	93	14	λ−dλ	λ−dλ	PROPN
ap-2101	93	15	0	0	NUM
ap-2101	93	16	dp′	dp′	PROPN
ap-2101	94	1	p′gλ−dλ(p	p′gλ−dλ(p	PROPN
ap-2101	94	2	,	,	PUNCT
ap-2101	94	3	p′)ϑ(p′	p′)ϑ(p′	NOUN
ap-2101	94	4	)	)	PUNCT
ap-2101	94	5	.	.	PUNCT
ap-2101	95	1	(	(	PUNCT
ap-2101	95	2	2.16	2.16	NUM
ap-2101	95	3	)	)	PUNCT
ap-2101	95	4	we	we	PRON
ap-2101	95	5	can	can	AUX
ap-2101	95	6	rewrite	rewrite	VERB
ap-2101	95	7	(	(	PUNCT
ap-2101	95	8	2.14	2.14	NUM
ap-2101	95	9	)	)	PUNCT
ap-2101	95	10	as	as	ADP
ap-2101	95	11	(	(	PUNCT
ap-2101	95	12	p2	p2	X
ap-2101	95	13	+	+	CCONJ
ap-2101	95	14	ν2)φ̃(p	ν2)φ̃(p	PROPN
ap-2101	95	15	,	,	PUNCT
ap-2101	95	16	ω	ω	NOUN
ap-2101	95	17	)	)	PUNCT
ap-2101	95	18	=	=	NOUN
ap-2101	95	19	θλ(p	θλ(p	NOUN
ap-2101	95	20	)	)	PUNCT
ap-2101	95	21	(	(	PUNCT
ap-2101	95	22	2π)2	2π)2	NUM
ap-2101	95	23	(	(	PUNCT
ap-2101	95	24	∫	∫	PROPN
ap-2101	95	25	λ−dλ	λ−dλ	PROPN
ap-2101	95	26	0	0	NUM
ap-2101	95	27	dp′	dp′	PROPN
ap-2101	95	28	p′gλ(p	p′gλ(p	PROPN
ap-2101	95	29	,	,	PUNCT
ap-2101	95	30	p′)ϑ(p′	p′)ϑ(p′	NOUN
ap-2101	95	31	)	)	PUNCT
ap-2101	96	1	+	+	NUM
ap-2101	96	2	dλ	dλ	NOUN
ap-2101	96	3	λ	λ	NOUN
ap-2101	96	4	gλ(p	gλ(p	NOUN
ap-2101	96	5	,	,	PUNCT
ap-2101	96	6	λ)ϑ(λ	λ)ϑ(λ	ADV
ap-2101	96	7	)	)	PUNCT
ap-2101	96	8	)	)	PUNCT
ap-2101	96	9	.	.	PUNCT
ap-2101	97	1	(	(	PUNCT
ap-2101	97	2	2.17	2.17	NUM
ap-2101	97	3	)	)	PUNCT
ap-2101	97	4	for	for	ADP
ap-2101	97	5	p	p	NOUN
ap-2101	97	6	=	=	PUNCT
ap-2101	97	7	λ	λ	X
ap-2101	97	8	this	this	PRON
ap-2101	97	9	will	will	AUX
ap-2101	97	10	give	give	VERB
ap-2101	97	11	us	we	PRON
ap-2101	97	12	(	(	PUNCT
ap-2101	97	13	λ2	λ2	NOUN
ap-2101	97	14	+	+	CCONJ
ap-2101	97	15	ν2)φ̃(λ	ν2)φ̃(λ	NUM
ap-2101	97	16	,	,	PUNCT
ap-2101	97	17	ω	ω	NOUN
ap-2101	97	18	)	)	PUNCT
ap-2101	97	19	=	=	SYM
ap-2101	97	20	1	1	NUM
ap-2101	97	21	(	(	PUNCT
ap-2101	97	22	2π)2	2π)2	NUM
ap-2101	97	23	(	(	PUNCT
ap-2101	97	24	∫	∫	PROPN
ap-2101	97	25	λ−dλ	λ−dλ	PROPN
ap-2101	97	26	0	0	NUM
ap-2101	97	27	dp′	dp′	PROPN
ap-2101	97	28	p′gλ(λ	p′gλ(λ	PROPN
ap-2101	97	29	,	,	PUNCT
ap-2101	97	30	p′)ϑ(p′	p′)ϑ(p′	NOUN
ap-2101	97	31	)	)	PUNCT
ap-2101	98	1	+	+	NUM
ap-2101	98	2	dλ	dλ	NOUN
ap-2101	98	3	λ	λ	NOUN
ap-2101	98	4	gλ(λ	gλ(λ	PUNCT
ap-2101	98	5	,	,	PUNCT
ap-2101	98	6	λ)ϑ(λ	λ)ϑ(λ	ADV
ap-2101	98	7	)	)	PUNCT
ap-2101	98	8	)	)	PUNCT
ap-2101	98	9	,	,	PUNCT
ap-2101	98	10	(	(	PUNCT
ap-2101	98	11	2.18	2.18	NUM
ap-2101	98	12	)	)	PUNCT
ap-2101	98	13	158	158	NUM
ap-2101	98	14	vol	vol	NOUN
ap-2101	98	15	.	.	PUNCT
ap-2101	99	1	54	54	NUM
ap-2101	99	2	no	no	NOUN
ap-2101	99	3	.	.	PUNCT
ap-2101	100	1	2/2014	2/2014	NUM
ap-2101	100	2	exact	exact	ADJ
ap-2101	100	3	renormalization	renormalization	NOUN
ap-2101	100	4	group	group	NOUN
ap-2101	100	5	for	for	ADP
ap-2101	100	6	point	point	NOUN
ap-2101	100	7	interactions	interaction	NOUN
ap-2101	100	8	and	and	CCONJ
ap-2101	100	9	from	from	ADP
ap-2101	100	10	this	this	PRON
ap-2101	100	11	we	we	PRON
ap-2101	100	12	can	can	AUX
ap-2101	100	13	read	read	VERB
ap-2101	100	14	of	of	ADP
ap-2101	100	15	φ̃(λ	φ̃(λ	PROPN
ap-2101	100	16	,	,	PUNCT
ap-2101	100	17	ω	ω	NOUN
ap-2101	100	18	)	)	PUNCT
ap-2101	100	19	as	as	ADP
ap-2101	100	20	φ̃(λ	φ̃(λ	PROPN
ap-2101	100	21	,	,	PUNCT
ap-2101	100	22	ω	ω	NUM
ap-2101	100	23	)	)	PUNCT
ap-2101	100	24	=	=	SYM
ap-2101	100	25	1	1	NUM
ap-2101	100	26	(	(	PUNCT
ap-2101	100	27	2π)2(λ2	2π)2(λ2	NUM
ap-2101	100	28	+	+	CCONJ
ap-2101	100	29	ν2	ν2	ADJ
ap-2101	100	30	)	)	PUNCT
ap-2101	100	31	∫	∫	PROPN
ap-2101	100	32	λ−dλ	λ−dλ	PROPN
ap-2101	100	33	0	0	NUM
ap-2101	100	34	dp′	dp′	PROPN
ap-2101	100	35	p′gλ(λ	p′gλ(λ	PROPN
ap-2101	100	36	,	,	PUNCT
ap-2101	100	37	p′)ϑ(p′	p′)ϑ(p′	NOUN
ap-2101	100	38	)	)	PUNCT
ap-2101	100	39	,	,	PUNCT
ap-2101	100	40	(	(	PUNCT
ap-2101	100	41	2.19	2.19	NUM
ap-2101	100	42	)	)	PUNCT
ap-2101	100	43	where	where	SCONJ
ap-2101	100	44	we	we	PRON
ap-2101	100	45	have	have	AUX
ap-2101	100	46	ignored	ignore	VERB
ap-2101	100	47	the	the	DET
ap-2101	100	48	term	term	NOUN
ap-2101	100	49	which	which	PRON
ap-2101	100	50	is	be	AUX
ap-2101	100	51	proportional	proportional	ADJ
ap-2101	100	52	to	to	PART
ap-2101	100	53	dλ	dλ	VERB
ap-2101	100	54	.	.	PUNCT
ap-2101	101	1	if	if	SCONJ
ap-2101	101	2	we	we	PRON
ap-2101	101	3	substitute	substitute	VERB
ap-2101	101	4	this	this	DET
ap-2101	101	5	result	result	NOUN
ap-2101	101	6	into	into	ADP
ap-2101	101	7	(	(	PUNCT
ap-2101	101	8	2.15	2.15	NUM
ap-2101	101	9	)	)	PUNCT
ap-2101	101	10	and	and	CCONJ
ap-2101	101	11	perform	perform	VERB
ap-2101	101	12	the	the	DET
ap-2101	101	13	ω	ω	NUM
ap-2101	101	14	integral	integral	ADJ
ap-2101	101	15	we	we	PRON
ap-2101	101	16	find	find	VERB
ap-2101	101	17	ϑ(λ	ϑ(λ	NOUN
ap-2101	101	18	)	)	PUNCT
ap-2101	101	19	=	=	SYM
ap-2101	101	20	1	1	NUM
ap-2101	101	21	(	(	PUNCT
ap-2101	101	22	2π)(λ2	2π)(λ2	NUM
ap-2101	101	23	+	+	NUM
ap-2101	101	24	ν2	ν2	ADJ
ap-2101	101	25	)	)	PUNCT
ap-2101	101	26	∫	∫	PROPN
ap-2101	101	27	λ−dλ	λ−dλ	PROPN
ap-2101	101	28	0	0	NUM
ap-2101	101	29	dp′	dp′	PROPN
ap-2101	101	30	p′gλ(λ	p′gλ(λ	PROPN
ap-2101	101	31	,	,	PUNCT
ap-2101	101	32	p′)ϑ(p′	p′)ϑ(p′	NOUN
ap-2101	101	33	)	)	PUNCT
ap-2101	101	34	.	.	PUNCT
ap-2101	102	1	(	(	PUNCT
ap-2101	102	2	2.20	2.20	NUM
ap-2101	102	3	)	)	PUNCT
ap-2101	102	4	finally	finally	ADV
ap-2101	102	5	we	we	PRON
ap-2101	102	6	put	put	VERB
ap-2101	102	7	this	this	DET
ap-2101	102	8	result	result	NOUN
ap-2101	102	9	into	into	ADP
ap-2101	102	10	(	(	PUNCT
ap-2101	102	11	2.17	2.17	NUM
ap-2101	102	12	)	)	PUNCT
ap-2101	102	13	to	to	PART
ap-2101	102	14	obtain	obtain	VERB
ap-2101	102	15	(	(	PUNCT
ap-2101	102	16	p2	p2	X
ap-2101	102	17	+	+	CCONJ
ap-2101	102	18	ν2)φ̃(p	ν2)φ̃(p	PROPN
ap-2101	102	19	,	,	PUNCT
ap-2101	102	20	ω	ω	NOUN
ap-2101	102	21	)	)	PUNCT
ap-2101	102	22	=	=	NOUN
ap-2101	102	23	θλ(p	θλ(p	NOUN
ap-2101	102	24	)	)	PUNCT
ap-2101	102	25	(	(	PUNCT
ap-2101	102	26	2π)2	2π)2	NUM
ap-2101	102	27	∫	∫	PROPN
ap-2101	102	28	λ−dλ	λ−dλ	PROPN
ap-2101	102	29	0	0	NUM
ap-2101	102	30	dp′	dp′	PROPN
ap-2101	102	31	p′	p′	PROPN
ap-2101	102	32	(	(	PUNCT
ap-2101	102	33	gλ(p	gλ(p	PROPN
ap-2101	102	34	,	,	PUNCT
ap-2101	102	35	p′	p′	NOUN
ap-2101	102	36	)	)	PUNCT
ap-2101	103	1	+	+	NUM
ap-2101	103	2	dλ	dλ	NOUN
ap-2101	103	3	λ	λ	X
ap-2101	103	4	2π(λ2	2π(λ2	NOUN
ap-2101	103	5	+	+	CCONJ
ap-2101	103	6	ν2)gλ(p	ν2)gλ(p	PROPN
ap-2101	103	7	,	,	PUNCT
ap-2101	103	8	λ)gλ(λ	λ)gλ(λ	PROPN
ap-2101	103	9	,	,	PUNCT
ap-2101	103	10	p′	p′	NOUN
ap-2101	103	11	)	)	PUNCT
ap-2101	103	12	)	)	PUNCT
ap-2101	103	13	ϑ(p′	ϑ(p′	PROPN
ap-2101	103	14	)	)	PUNCT
ap-2101	103	15	.	.	PUNCT
ap-2101	104	1	(	(	PUNCT
ap-2101	104	2	2.21	2.21	NUM
ap-2101	104	3	)	)	PUNCT
ap-2101	104	4	clearly	clearly	ADV
ap-2101	104	5	,	,	PUNCT
ap-2101	104	6	we	we	PRON
ap-2101	104	7	can	can	AUX
ap-2101	104	8	replace	replace	VERB
ap-2101	104	9	θλ(p	θλ(p	NOUN
ap-2101	104	10	)	)	PUNCT
ap-2101	104	11	by	by	ADP
ap-2101	104	12	θλ−dλ(p	θλ−dλ(p	PROPN
ap-2101	104	13	)	)	PUNCT
ap-2101	104	14	and	and	CCONJ
ap-2101	104	15	write	write	VERB
ap-2101	104	16	(	(	PUNCT
ap-2101	104	17	p2	p2	X
ap-2101	104	18	+	+	CCONJ
ap-2101	104	19	ν2)φ̃(p	ν2)φ̃(p	PROPN
ap-2101	104	20	,	,	PUNCT
ap-2101	104	21	ω	ω	NOUN
ap-2101	104	22	)	)	PUNCT
ap-2101	104	23	=	=	SYM
ap-2101	104	24	θλ−dλ(p	θλ−dλ(p	ADJ
ap-2101	104	25	)	)	PUNCT
ap-2101	104	26	(	(	PUNCT
ap-2101	104	27	2π)2	2π)2	NUM
ap-2101	104	28	∫	∫	PROPN
ap-2101	104	29	λ−dλ	λ−dλ	PROPN
ap-2101	104	30	0	0	NUM
ap-2101	104	31	dp′	dp′	PROPN
ap-2101	104	32	p′	p′	PROPN
ap-2101	104	33	(	(	PUNCT
ap-2101	104	34	gλ(p	gλ(p	PROPN
ap-2101	104	35	,	,	PUNCT
ap-2101	104	36	p′	p′	NOUN
ap-2101	104	37	)	)	PUNCT
ap-2101	105	1	+	+	NUM
ap-2101	105	2	dλ	dλ	NOUN
ap-2101	105	3	λ	λ	X
ap-2101	105	4	2π(λ2	2π(λ2	NOUN
ap-2101	105	5	+	+	CCONJ
ap-2101	105	6	ν2)gλ(p	ν2)gλ(p	PROPN
ap-2101	105	7	,	,	PUNCT
ap-2101	105	8	λ)gλ(λ	λ)gλ(λ	PROPN
ap-2101	105	9	,	,	PUNCT
ap-2101	105	10	p′	p′	NOUN
ap-2101	105	11	)	)	PUNCT
ap-2101	105	12	)	)	PUNCT
ap-2101	105	13	ϑ(p′	ϑ(p′	PROPN
ap-2101	105	14	)	)	PUNCT
ap-2101	105	15	(	(	PUNCT
ap-2101	105	16	2.22	2.22	NUM
ap-2101	105	17	)	)	PUNCT
ap-2101	105	18	now	now	ADV
ap-2101	105	19	comparing	compare	VERB
ap-2101	105	20	this	this	DET
ap-2101	105	21	equation	equation	NOUN
ap-2101	105	22	with	with	ADP
ap-2101	105	23	(	(	PUNCT
ap-2101	105	24	2.16	2.16	NUM
ap-2101	105	25	)	)	PUNCT
ap-2101	105	26	gives	give	VERB
ap-2101	105	27	us	we	PRON
ap-2101	105	28	an	an	DET
ap-2101	105	29	equation	equation	NOUN
ap-2101	105	30	for	for	ADP
ap-2101	105	31	the	the	DET
ap-2101	105	32	coupling	coupling	NOUN
ap-2101	105	33	constant	constant	ADJ
ap-2101	105	34	gλ−dλ(p	gλ−dλ(p	PROPN
ap-2101	105	35	,	,	PUNCT
ap-2101	105	36	p′	p′	NOUN
ap-2101	105	37	)	)	PUNCT
ap-2101	105	38	=	=	SYM
ap-2101	105	39	gλ(p	gλ(p	NOUN
ap-2101	105	40	,	,	PUNCT
ap-2101	105	41	p′	p′	NOUN
ap-2101	105	42	)	)	PUNCT
ap-2101	106	1	+	+	NUM
ap-2101	106	2	dλ	dλ	NOUN
ap-2101	106	3	λ	λ	X
ap-2101	106	4	2π(λ2	2π(λ2	NOUN
ap-2101	106	5	+	+	CCONJ
ap-2101	106	6	ν2)gλ(p	ν2)gλ(p	PROPN
ap-2101	106	7	,	,	PUNCT
ap-2101	106	8	λ)gλ(λ	λ)gλ(λ	PROPN
ap-2101	106	9	,	,	PUNCT
ap-2101	106	10	p′	p′	NOUN
ap-2101	106	11	)	)	PUNCT
ap-2101	106	12	,	,	PUNCT
ap-2101	106	13	(	(	PUNCT
ap-2101	106	14	2.23	2.23	NUM
ap-2101	106	15	)	)	PUNCT
ap-2101	106	16	which	which	PRON
ap-2101	106	17	can	can	AUX
ap-2101	106	18	be	be	AUX
ap-2101	106	19	put	put	VERB
ap-2101	106	20	into	into	ADP
ap-2101	106	21	differential	differential	ADJ
ap-2101	106	22	form	form	NOUN
ap-2101	106	23	as	as	ADP
ap-2101	106	24	−dgλ(p	−dgλ(p	PROPN
ap-2101	106	25	,	,	PUNCT
ap-2101	106	26	p′	p′	NOUN
ap-2101	106	27	)	)	PUNCT
ap-2101	106	28	dλ	dλ	NOUN
ap-2101	107	1	=	=	SYM
ap-2101	107	2	λ	λ	NOUN
ap-2101	107	3	2π(λ2	2π(λ2	NOUN
ap-2101	107	4	+	+	CCONJ
ap-2101	107	5	ν2)gλ(p	ν2)gλ(p	PROPN
ap-2101	107	6	,	,	PUNCT
ap-2101	107	7	λ)gλ(λ	λ)gλ(λ	PROPN
ap-2101	107	8	,	,	PUNCT
ap-2101	107	9	p′	p′	NOUN
ap-2101	107	10	)	)	PUNCT
ap-2101	107	11	.	.	PUNCT
ap-2101	108	1	(	(	PUNCT
ap-2101	108	2	2.24	2.24	NUM
ap-2101	108	3	)	)	PUNCT
ap-2101	108	4	this	this	DET
ap-2101	108	5	equation	equation	NOUN
ap-2101	108	6	determines	determine	VERB
ap-2101	108	7	the	the	DET
ap-2101	108	8	rg	rg	PROPN
ap-2101	108	9	trajectory	trajectory	NOUN
ap-2101	108	10	of	of	ADP
ap-2101	108	11	the	the	DET
ap-2101	108	12	coupling	coupling	NOUN
ap-2101	108	13	constant	constant	ADJ
ap-2101	108	14	.	.	PUNCT
ap-2101	109	1	to	to	PART
ap-2101	109	2	find	find	VERB
ap-2101	109	3	the	the	DET
ap-2101	109	4	effective	effective	ADJ
ap-2101	109	5	coupling	coupling	NOUN
ap-2101	109	6	at	at	ADP
ap-2101	109	7	the	the	DET
ap-2101	109	8	effective	effective	ADJ
ap-2101	109	9	scale	scale	NOUN
ap-2101	109	10	λ	λ	NOUN
ap-2101	109	11	we	we	PRON
ap-2101	109	12	integrate	integrate	VERB
ap-2101	109	13	this	this	PRON
ap-2101	109	14	from	from	ADP
ap-2101	109	15	λ	λ	PROPN
ap-2101	109	16	to	to	ADP
ap-2101	109	17	λ	λ	PROPN
ap-2101	109	18	and	and	CCONJ
ap-2101	109	19	find	find	VERB
ap-2101	109	20	gλ(p	gλ(p	NOUN
ap-2101	109	21	,	,	PUNCT
ap-2101	109	22	p′	p′	NOUN
ap-2101	109	23	)	)	PUNCT
ap-2101	110	1	=	=	SYM
ap-2101	110	2	gλ(p	gλ(p	NOUN
ap-2101	110	3	,	,	PUNCT
ap-2101	110	4	p′	p′	NOUN
ap-2101	110	5	)	)	PUNCT
ap-2101	111	1	+	+	CCONJ
ap-2101	111	2	1	1	NUM
ap-2101	111	3	2π	2π	NUM
ap-2101	111	4	∫	∫	NOUN
ap-2101	112	1	λ	λ	X
ap-2101	112	2	λ	λ	X
ap-2101	112	3	ds	ds	PROPN
ap-2101	112	4	s	s	NOUN
ap-2101	112	5	s2	s2	NOUN
ap-2101	112	6	+	+	CCONJ
ap-2101	112	7	ν2	ν2	PROPN
ap-2101	112	8	gs(p	gs(p	NOUN
ap-2101	112	9	,	,	PUNCT
ap-2101	112	10	s)gs(s	s)gs(s	NOUN
ap-2101	112	11	,	,	PUNCT
ap-2101	112	12	p	p	NOUN
ap-2101	112	13	′	′	NOUN
ap-2101	112	14	)	)	PUNCT
ap-2101	112	15	(	(	PUNCT
ap-2101	112	16	2.25	2.25	NUM
ap-2101	112	17	)	)	PUNCT
ap-2101	112	18	or	or	CCONJ
ap-2101	112	19	gλ(p	gλ(p	NOUN
ap-2101	112	20	,	,	PUNCT
ap-2101	112	21	p′	p′	NOUN
ap-2101	112	22	)	)	PUNCT
ap-2101	113	1	=	=	SYM
ap-2101	113	2	g	g	PROPN
ap-2101	113	3	−	−	PROPN
ap-2101	113	4	xλ(p	xλ(p	PROPN
ap-2101	113	5	,	,	PUNCT
ap-2101	113	6	p′	p′	NOUN
ap-2101	113	7	)	)	PUNCT
ap-2101	114	1	+	+	CCONJ
ap-2101	114	2	1	1	NUM
ap-2101	114	3	2π	2π	NUM
ap-2101	114	4	∫	∫	NOUN
ap-2101	115	1	λ	λ	X
ap-2101	115	2	λ	λ	X
ap-2101	115	3	ds	ds	PROPN
ap-2101	115	4	s	s	NOUN
ap-2101	115	5	s2	s2	NOUN
ap-2101	115	6	+	+	CCONJ
ap-2101	115	7	ν2	ν2	PROPN
ap-2101	115	8	gs(p	gs(p	NOUN
ap-2101	115	9	,	,	PUNCT
ap-2101	115	10	s)gs(s	s)gs(s	NOUN
ap-2101	115	11	,	,	PUNCT
ap-2101	115	12	p	p	NOUN
ap-2101	115	13	′	′	NOUN
ap-2101	115	14	)	)	PUNCT
ap-2101	115	15	.	.	PUNCT
ap-2101	116	1	(	(	PUNCT
ap-2101	116	2	2.26	2.26	NUM
ap-2101	116	3	)	)	PUNCT
ap-2101	116	4	although	although	SCONJ
ap-2101	116	5	this	this	PRON
ap-2101	116	6	is	be	AUX
ap-2101	116	7	an	an	DET
ap-2101	116	8	ordinary	ordinary	ADJ
ap-2101	116	9	differential	differential	ADJ
ap-2101	116	10	equation	equation	NOUN
ap-2101	116	11	with	with	ADP
ap-2101	116	12	three	three	NUM
ap-2101	116	13	variables	variable	NOUN
ap-2101	116	14	and	and	CCONJ
ap-2101	116	15	we	we	PRON
ap-2101	116	16	have	have	VERB
ap-2101	116	17	one	one	NUM
ap-2101	116	18	initial	initial	ADJ
ap-2101	116	19	condition	condition	NOUN
ap-2101	116	20	,	,	PUNCT
ap-2101	116	21	there	there	PRON
ap-2101	116	22	is	be	VERB
ap-2101	116	23	also	also	ADV
ap-2101	116	24	the	the	DET
ap-2101	116	25	requirement	requirement	NOUN
ap-2101	116	26	that	that	SCONJ
ap-2101	116	27	gλ(p	gλ(p	NOUN
ap-2101	116	28	,	,	PUNCT
ap-2101	116	29	p′	p′	NOUN
ap-2101	116	30	)	)	PUNCT
ap-2101	116	31	should	should	AUX
ap-2101	116	32	not	not	PART
ap-2101	116	33	depend	depend	VERB
ap-2101	116	34	on	on	ADP
ap-2101	116	35	λ	λ	PROPN
ap-2101	116	36	when	when	SCONJ
ap-2101	116	37	we	we	PRON
ap-2101	116	38	take	take	VERB
ap-2101	116	39	the	the	DET
ap-2101	116	40	λ→∞	λ→∞	NUM
ap-2101	116	41	limit	limit	NOUN
ap-2101	116	42	.	.	PUNCT
ap-2101	117	1	this	this	PRON
ap-2101	117	2	can	can	AUX
ap-2101	117	3	be	be	AUX
ap-2101	117	4	satisfied	satisfied	ADJ
ap-2101	117	5	by	by	ADP
ap-2101	117	6	the	the	DET
ap-2101	117	7	appropriate	appropriate	ADJ
ap-2101	117	8	choice	choice	NOUN
ap-2101	117	9	of	of	ADP
ap-2101	117	10	the	the	DET
ap-2101	117	11	counterterm	counterterm	NOUN
ap-2101	117	12	xλ(p	xλ(p	PROPN
ap-2101	117	13	,	,	PUNCT
ap-2101	117	14	p′	p′	NOUN
ap-2101	117	15	)	)	PUNCT
ap-2101	117	16	.	.	PUNCT
ap-2101	118	1	we	we	PRON
ap-2101	118	2	try	try	VERB
ap-2101	118	3	an	an	DET
ap-2101	118	4	iteration	iteration	NOUN
ap-2101	118	5	procedure	procedure	NOUN
ap-2101	118	6	to	to	PART
ap-2101	118	7	obtain	obtain	VERB
ap-2101	118	8	a	a	DET
ap-2101	118	9	solution	solution	NOUN
ap-2101	118	10	.	.	PUNCT
ap-2101	119	1	at	at	ADP
ap-2101	119	2	the	the	DET
ap-2101	119	3	first	first	ADJ
ap-2101	119	4	order	order	NOUN
ap-2101	119	5	we	we	PRON
ap-2101	119	6	choose	choose	VERB
ap-2101	119	7	g	g	PROPN
ap-2101	119	8	(	(	PUNCT
ap-2101	119	9	1	1	NUM
ap-2101	119	10	)	)	PUNCT
ap-2101	119	11	λ	λ	NOUN
ap-2101	119	12	(	(	PUNCT
ap-2101	119	13	p	p	X
ap-2101	119	14	,	,	PUNCT
ap-2101	119	15	p′	p′	NOUN
ap-2101	119	16	)	)	PUNCT
ap-2101	120	1	=	=	SYM
ap-2101	120	2	g	g	NOUN
ap-2101	120	3	so	so	SCONJ
ap-2101	120	4	that	that	SCONJ
ap-2101	120	5	x	x	X
ap-2101	120	6	(	(	PUNCT
ap-2101	120	7	1	1	X
ap-2101	120	8	)	)	PUNCT
ap-2101	120	9	λ	λ	NOUN
ap-2101	120	10	=	=	NOUN
ap-2101	120	11	0	0	PROPN
ap-2101	120	12	.	.	PUNCT
ap-2101	121	1	(	(	PUNCT
ap-2101	121	2	2.27	2.27	NUM
ap-2101	121	3	)	)	PUNCT
ap-2101	121	4	after	after	ADP
ap-2101	121	5	substituting	substitute	VERB
ap-2101	121	6	these	these	DET
ap-2101	121	7	choices	choice	NOUN
ap-2101	121	8	to	to	ADP
ap-2101	121	9	(	(	PUNCT
ap-2101	121	10	2.26	2.26	NUM
ap-2101	121	11	)	)	PUNCT
ap-2101	121	12	we	we	PRON
ap-2101	121	13	get	get	VERB
ap-2101	121	14	g	g	NOUN
ap-2101	121	15	(	(	PUNCT
ap-2101	121	16	2	2	NUM
ap-2101	121	17	)	)	PUNCT
ap-2101	121	18	λ	λ	NOUN
ap-2101	121	19	(	(	PUNCT
ap-2101	121	20	p	p	X
ap-2101	121	21	,	,	PUNCT
ap-2101	121	22	p′	p′	NOUN
ap-2101	121	23	)	)	PUNCT
ap-2101	122	1	=	=	SYM
ap-2101	122	2	g	g	PROPN
ap-2101	122	3	−	−	PROPN
ap-2101	122	4	x(2	x(2	PROPN
ap-2101	122	5	)	)	PUNCT
ap-2101	122	6	λ	λ	PROPN
ap-2101	122	7	(	(	PUNCT
ap-2101	122	8	p	p	X
ap-2101	122	9	,	,	PUNCT
ap-2101	122	10	p′	p′	NOUN
ap-2101	122	11	)	)	PUNCT
ap-2101	123	1	+	+	CCONJ
ap-2101	123	2	g2	g2	PROPN
ap-2101	123	3	2π	2π	NOUN
ap-2101	123	4	∫	∫	INTJ
ap-2101	124	1	λ	λ	X
ap-2101	124	2	λ	λ	X
ap-2101	124	3	ds	ds	PROPN
ap-2101	124	4	s	s	NOUN
ap-2101	124	5	s2	s2	NOUN
ap-2101	124	6	+	+	CCONJ
ap-2101	124	7	ν2	ν2	NOUN
ap-2101	124	8	.	.	PUNCT
ap-2101	125	1	(	(	PUNCT
ap-2101	125	2	2.28	2.28	NUM
ap-2101	125	3	)	)	PUNCT
ap-2101	125	4	the	the	DET
ap-2101	125	5	integral	integral	ADJ
ap-2101	125	6	diverges	diverge	NOUN
ap-2101	125	7	in	in	ADP
ap-2101	125	8	the	the	DET
ap-2101	125	9	λ→∞	λ→∞	NUM
ap-2101	125	10	limit	limit	NOUN
ap-2101	125	11	,	,	PUNCT
ap-2101	125	12	therefore	therefore	ADV
ap-2101	125	13	we	we	PRON
ap-2101	125	14	choose	choose	VERB
ap-2101	125	15	the	the	DET
ap-2101	125	16	counterterm	counterterm	NOUN
ap-2101	125	17	as	as	ADP
ap-2101	125	18	x	x	X
ap-2101	125	19	(	(	PUNCT
ap-2101	125	20	2	2	X
ap-2101	125	21	)	)	PUNCT
ap-2101	125	22	λ	λ	NOUN
ap-2101	125	23	(	(	PUNCT
ap-2101	125	24	p	p	X
ap-2101	125	25	,	,	PUNCT
ap-2101	125	26	p′	p′	NOUN
ap-2101	125	27	)	)	PUNCT
ap-2101	125	28	=	=	PUNCT
ap-2101	126	1	g2	g2	PROPN
ap-2101	126	2	2π	2π	PROPN
ap-2101	126	3	∫	∫	X
ap-2101	126	4	λ	λ	X
ap-2101	126	5	λ0	λ0	NOUN
ap-2101	126	6	ds	ds	NOUN
ap-2101	126	7	s	s	X
ap-2101	126	8	s2	s2	NOUN
ap-2101	126	9	+	+	CCONJ
ap-2101	126	10	ν2	ν2	NOUN
ap-2101	126	11	,	,	PUNCT
ap-2101	126	12	(	(	PUNCT
ap-2101	126	13	2.29	2.29	NUM
ap-2101	126	14	)	)	PUNCT
ap-2101	126	15	where	where	SCONJ
ap-2101	126	16	λ0	λ0	NOUN
ap-2101	126	17	is	be	AUX
ap-2101	126	18	an	an	DET
ap-2101	126	19	another	another	DET
ap-2101	126	20	energy	energy	NOUN
ap-2101	126	21	scale	scale	NOUN
ap-2101	126	22	chosen	choose	VERB
ap-2101	126	23	such	such	ADJ
ap-2101	126	24	that	that	SCONJ
ap-2101	126	25	1	1	NUM
ap-2101	126	26	�	�	NOUN
ap-2101	126	27	λ0	λ0	NOUN
ap-2101	126	28	<	<	X
ap-2101	126	29	λ	λ	X
ap-2101	126	30	�	�	PROPN
ap-2101	126	31	λ	λ	PROPN
ap-2101	126	32	.	.	PUNCT
ap-2101	127	1	now	now	ADV
ap-2101	127	2	the	the	DET
ap-2101	127	3	effective	effective	ADJ
ap-2101	127	4	coupling	coupling	NOUN
ap-2101	127	5	at	at	ADP
ap-2101	127	6	the	the	DET
ap-2101	127	7	second	second	ADJ
ap-2101	127	8	order	order	NOUN
ap-2101	127	9	is	be	AUX
ap-2101	127	10	finite	finite	ADJ
ap-2101	127	11	and	and	CCONJ
ap-2101	127	12	given	give	VERB
ap-2101	127	13	by	by	ADP
ap-2101	127	14	g	g	PROPN
ap-2101	127	15	(	(	PUNCT
ap-2101	127	16	2	2	NUM
ap-2101	127	17	)	)	PUNCT
ap-2101	127	18	λ	λ	NOUN
ap-2101	127	19	(	(	PUNCT
ap-2101	127	20	p	p	X
ap-2101	127	21	,	,	PUNCT
ap-2101	127	22	p′	p′	NOUN
ap-2101	127	23	)	)	PUNCT
ap-2101	128	1	=	=	SYM
ap-2101	129	1	g	g	PROPN
ap-2101	129	2	−	−	PROPN
ap-2101	129	3	g2	g2	PROPN
ap-2101	129	4	2π	2π	PROPN
ap-2101	130	1	∫	∫	X
ap-2101	130	2	λ	λ	X
ap-2101	130	3	λ0	λ0	NOUN
ap-2101	130	4	ds	ds	NOUN
ap-2101	130	5	s	s	X
ap-2101	130	6	s2	s2	NOUN
ap-2101	130	7	+	+	CCONJ
ap-2101	130	8	ν2	ν2	NOUN
ap-2101	130	9	.	.	PUNCT
ap-2101	131	1	(	(	PUNCT
ap-2101	131	2	2.30	2.30	NUM
ap-2101	131	3	)	)	PUNCT
ap-2101	131	4	159	159	NUM
ap-2101	131	5	osman	osman	PROPN
ap-2101	131	6	teoman	teoman	NOUN
ap-2101	131	7	turgut	turgut	PROPN
ap-2101	131	8	,	,	PUNCT
ap-2101	131	9	cem	cem	NOUN
ap-2101	131	10	eröncel	eröncel	VERB
ap-2101	131	11	acta	acta	PROPN
ap-2101	131	12	polytechnica	polytechnica	PROPN
ap-2101	131	13	we	we	PRON
ap-2101	131	14	note	note	VERB
ap-2101	131	15	that	that	SCONJ
ap-2101	131	16	it	it	PRON
ap-2101	131	17	is	be	AUX
ap-2101	131	18	independent	independent	ADJ
ap-2101	131	19	of	of	ADP
ap-2101	131	20	p	p	NOUN
ap-2101	131	21	and	and	CCONJ
ap-2101	131	22	p′.	p′.	NOUN
ap-2101	131	23	if	if	SCONJ
ap-2101	131	24	we	we	PRON
ap-2101	131	25	repeat	repeat	VERB
ap-2101	131	26	this	this	DET
ap-2101	131	27	procedure	procedure	NOUN
ap-2101	131	28	,	,	PUNCT
ap-2101	131	29	then	then	ADV
ap-2101	131	30	by	by	ADP
ap-2101	131	31	induction	induction	NOUN
ap-2101	131	32	it	it	PRON
ap-2101	131	33	is	be	AUX
ap-2101	131	34	straightforward	straightforward	ADJ
ap-2101	131	35	to	to	PART
ap-2101	131	36	see	see	VERB
ap-2101	131	37	that	that	SCONJ
ap-2101	131	38	g(n	g(n	NOUN
ap-2101	131	39	)	)	PUNCT
ap-2101	131	40	λ	λ	PROPN
ap-2101	131	41	and	and	CCONJ
ap-2101	131	42	x(n	x(n	NOUN
ap-2101	131	43	)	)	PUNCT
ap-2101	131	44	λ	λ	NOUN
ap-2101	131	45	are	be	AUX
ap-2101	131	46	independent	independent	ADJ
ap-2101	131	47	of	of	ADP
ap-2101	131	48	p	p	NOUN
ap-2101	131	49	and	and	CCONJ
ap-2101	131	50	p′	p′	NOUN
ap-2101	131	51	for	for	ADP
ap-2101	131	52	all	all	DET
ap-2101	131	53	n.	n.	NOUN
ap-2101	131	54	at	at	ADP
ap-2101	131	55	the	the	DET
ap-2101	131	56	order	order	NOUN
ap-2101	131	57	n+	n+	ADP
ap-2101	131	58	1	1	NUM
ap-2101	131	59	,	,	PUNCT
ap-2101	131	60	the	the	DET
ap-2101	131	61	effective	effective	ADJ
ap-2101	131	62	coupling	coupling	NOUN
ap-2101	131	63	becomes	become	VERB
ap-2101	131	64	g	g	NOUN
ap-2101	131	65	(	(	PUNCT
ap-2101	131	66	n+1	n+1	NOUN
ap-2101	131	67	)	)	PUNCT
ap-2101	131	68	λ	λ	NOUN
ap-2101	131	69	=	=	PUNCT
ap-2101	131	70	g	g	PROPN
ap-2101	131	71	−	−	PROPN
ap-2101	131	72	x(n+1	x(n+1	PUNCT
ap-2101	131	73	)	)	PUNCT
ap-2101	132	1	λ	λ	NOUN
ap-2101	132	2	+	+	NOUN
ap-2101	132	3	1	1	NUM
ap-2101	132	4	2π	2π	NUM
ap-2101	132	5	∫	∫	NOUN
ap-2101	133	1	λ	λ	X
ap-2101	133	2	λ	λ	X
ap-2101	133	3	ds	ds	PROPN
ap-2101	133	4	s	s	NOUN
ap-2101	133	5	s2	s2	NOUN
ap-2101	133	6	+	+	CCONJ
ap-2101	133	7	ν2	ν2	PROPN
ap-2101	133	8	(	(	PUNCT
ap-2101	133	9	g(n	g(n	PROPN
ap-2101	133	10	)	)	PUNCT
ap-2101	133	11	s	s	PART
ap-2101	133	12	)	)	PUNCT
ap-2101	133	13	2	2	NUM
ap-2101	133	14	.	.	PUNCT
ap-2101	134	1	(	(	PUNCT
ap-2101	134	2	2.31	2.31	NUM
ap-2101	134	3	)	)	PUNCT
ap-2101	134	4	we	we	PRON
ap-2101	134	5	choose	choose	VERB
ap-2101	134	6	the	the	DET
ap-2101	134	7	counterterm	counterterm	NOUN
ap-2101	134	8	as	as	ADP
ap-2101	134	9	x	x	X
ap-2101	134	10	(	(	PUNCT
ap-2101	134	11	n+1	n+1	NOUN
ap-2101	134	12	)	)	PUNCT
ap-2101	134	13	λ	λ	NOUN
ap-2101	134	14	=	=	NOUN
ap-2101	134	15	1	1	NUM
ap-2101	134	16	2π	2π	NUM
ap-2101	134	17	∫	∫	NOUN
ap-2101	135	1	λ	λ	X
ap-2101	135	2	λ0	λ0	NOUN
ap-2101	135	3	ds	ds	NOUN
ap-2101	135	4	s	s	X
ap-2101	135	5	s2	s2	NOUN
ap-2101	135	6	+	+	CCONJ
ap-2101	135	7	ν2	ν2	PROPN
ap-2101	135	8	(	(	PUNCT
ap-2101	135	9	g(n	g(n	PROPN
ap-2101	135	10	)	)	PUNCT
ap-2101	135	11	s	s	PART
ap-2101	135	12	)	)	PUNCT
ap-2101	135	13	2	2	NUM
ap-2101	135	14	,	,	PUNCT
ap-2101	135	15	(	(	PUNCT
ap-2101	135	16	2.32	2.32	NUM
ap-2101	135	17	)	)	PUNCT
ap-2101	135	18	hence	hence	ADV
ap-2101	135	19	we	we	PRON
ap-2101	135	20	find	find	VERB
ap-2101	135	21	g	g	PROPN
ap-2101	135	22	(	(	PUNCT
ap-2101	135	23	n+1	n+1	NOUN
ap-2101	135	24	)	)	PUNCT
ap-2101	135	25	λ	λ	NOUN
ap-2101	135	26	=	=	PUNCT
ap-2101	136	1	g	g	NOUN
ap-2101	136	2	−	−	PROPN
ap-2101	136	3	1	1	NUM
ap-2101	136	4	2π	2π	NUM
ap-2101	136	5	∫	∫	NOUN
ap-2101	136	6	λ	λ	X
ap-2101	136	7	λ0	λ0	NOUN
ap-2101	136	8	ds	ds	NOUN
ap-2101	136	9	s	s	X
ap-2101	136	10	s2	s2	NOUN
ap-2101	136	11	+	+	CCONJ
ap-2101	136	12	ν2	ν2	PROPN
ap-2101	136	13	(	(	PUNCT
ap-2101	136	14	g(n	g(n	PROPN
ap-2101	136	15	)	)	PUNCT
ap-2101	136	16	s	s	PART
ap-2101	136	17	)	)	PUNCT
ap-2101	136	18	2	2	NUM
ap-2101	136	19	.	.	PUNCT
ap-2101	137	1	(	(	PUNCT
ap-2101	137	2	2.33	2.33	NUM
ap-2101	137	3	)	)	PUNCT
ap-2101	137	4	it	it	PRON
ap-2101	137	5	is	be	AUX
ap-2101	137	6	not	not	PART
ap-2101	137	7	trivial	trivial	ADJ
ap-2101	137	8	to	to	PART
ap-2101	137	9	conclude	conclude	VERB
ap-2101	137	10	that	that	SCONJ
ap-2101	137	11	this	this	DET
ap-2101	137	12	iteration	iteration	NOUN
ap-2101	137	13	process	process	NOUN
ap-2101	137	14	has	have	VERB
ap-2101	137	15	a	a	DET
ap-2101	137	16	limit	limit	NOUN
ap-2101	137	17	.	.	PUNCT
ap-2101	138	1	we	we	PRON
ap-2101	138	2	shall	shall	AUX
ap-2101	138	3	deal	deal	VERB
ap-2101	138	4	with	with	ADP
ap-2101	138	5	this	this	PRON
ap-2101	138	6	later	later	ADV
ap-2101	138	7	in	in	ADP
ap-2101	138	8	this	this	DET
ap-2101	138	9	section	section	NOUN
ap-2101	138	10	and	and	CCONJ
ap-2101	138	11	for	for	ADP
ap-2101	138	12	now	now	ADV
ap-2101	138	13	we	we	PRON
ap-2101	138	14	assume	assume	VERB
ap-2101	138	15	that	that	SCONJ
ap-2101	138	16	g	g	NOUN
ap-2101	138	17	and	and	CCONJ
ap-2101	138	18	λ0	λ0	NOUN
ap-2101	138	19	are	be	AUX
ap-2101	138	20	chosen	choose	VERB
ap-2101	138	21	such	such	ADJ
ap-2101	138	22	that	that	SCONJ
ap-2101	138	23	the	the	DET
ap-2101	138	24	sequence	sequence	NOUN
ap-2101	138	25	{	{	PUNCT
ap-2101	138	26	g(n	g(n	PROPN
ap-2101	138	27	)	)	PUNCT
ap-2101	138	28	λ	λ	PROPN
ap-2101	138	29	}	}	PUNCT
ap-2101	138	30	∞n=1	∞n=1	PROPN
ap-2101	138	31	has	have	VERB
ap-2101	138	32	a	a	DET
ap-2101	138	33	limit	limit	NOUN
ap-2101	138	34	given	give	VERB
ap-2101	138	35	by	by	ADP
ap-2101	138	36	lim	lim	PROPN
ap-2101	138	37	n→∞	n→∞	NUM
ap-2101	138	38	g	g	PROPN
ap-2101	138	39	(	(	PUNCT
ap-2101	138	40	n+1	n+1	PROPN
ap-2101	138	41	)	)	PUNCT
ap-2101	138	42	λ	λ	NOUN
ap-2101	138	43	=	=	SYM
ap-2101	138	44	gλ	gλ	NOUN
ap-2101	138	45	.	.	PUNCT
ap-2101	139	1	(	(	PUNCT
ap-2101	139	2	2.34	2.34	NUM
ap-2101	139	3	)	)	PUNCT
ap-2101	139	4	after	after	ADP
ap-2101	139	5	taking	take	VERB
ap-2101	139	6	the	the	DET
ap-2101	139	7	limit	limit	NOUN
ap-2101	139	8	we	we	PRON
ap-2101	139	9	can	can	AUX
ap-2101	139	10	write	write	VERB
ap-2101	139	11	for	for	ADP
ap-2101	139	12	the	the	DET
ap-2101	139	13	effective	effective	ADJ
ap-2101	139	14	coupling	couple	VERB
ap-2101	139	15	gλ	gλ	NOUN
ap-2101	139	16	=	=	PUNCT
ap-2101	139	17	g	g	NOUN
ap-2101	139	18	−	−	PROPN
ap-2101	139	19	1	1	NUM
ap-2101	139	20	2π	2π	NUM
ap-2101	139	21	∫	∫	NOUN
ap-2101	139	22	λ	λ	X
ap-2101	139	23	λ0	λ0	NOUN
ap-2101	139	24	ds	ds	NOUN
ap-2101	139	25	s	s	X
ap-2101	139	26	s2	s2	NOUN
ap-2101	139	27	+	+	CCONJ
ap-2101	139	28	ν2	ν2	NOUN
ap-2101	139	29	g	g	PROPN
ap-2101	139	30	2	2	NUM
ap-2101	139	31	s	s	NOUN
ap-2101	139	32	,	,	PUNCT
ap-2101	139	33	(	(	PUNCT
ap-2101	139	34	2.35	2.35	NUM
ap-2101	139	35	)	)	PUNCT
ap-2101	139	36	which	which	PRON
ap-2101	139	37	immediately	immediately	ADV
ap-2101	139	38	implies	imply	VERB
ap-2101	139	39	g	g	PROPN
ap-2101	139	40	=	=	NOUN
ap-2101	139	41	gλ0	gλ0	NOUN
ap-2101	139	42	.	.	PUNCT
ap-2101	140	1	this	this	DET
ap-2101	140	2	equation	equation	NOUN
ap-2101	140	3	can	can	AUX
ap-2101	140	4	be	be	AUX
ap-2101	140	5	put	put	VERB
ap-2101	140	6	into	into	ADP
ap-2101	140	7	the	the	DET
ap-2101	140	8	following	follow	VERB
ap-2101	140	9	form∫	form∫	ADJ
ap-2101	140	10	λ	λ	PROPN
ap-2101	140	11	λ0	λ0	NOUN
ap-2101	140	12	ds	ds	ADJ
ap-2101	140	13	dgs	dgs	NOUN
ap-2101	140	14	ds	ds	NOUN
ap-2101	140	15	=	=	SYM
ap-2101	140	16	−	−	PROPN
ap-2101	140	17	1	1	NUM
ap-2101	140	18	2π	2π	NUM
ap-2101	140	19	∫	∫	NOUN
ap-2101	140	20	λ	λ	X
ap-2101	140	21	λ0	λ0	NOUN
ap-2101	140	22	ds	ds	NOUN
ap-2101	140	23	s	s	X
ap-2101	140	24	s2	s2	NOUN
ap-2101	140	25	+	+	CCONJ
ap-2101	140	26	ν2	ν2	NOUN
ap-2101	140	27	g	g	PROPN
ap-2101	140	28	2	2	NUM
ap-2101	140	29	s	s	NOUN
ap-2101	140	30	,	,	PUNCT
ap-2101	140	31	(	(	PUNCT
ap-2101	140	32	2.36	2.36	NUM
ap-2101	140	33	)	)	PUNCT
ap-2101	140	34	which	which	PRON
ap-2101	140	35	implies	imply	VERB
ap-2101	140	36	dgs	dgs	PROPN
ap-2101	140	37	g2	g2	PROPN
ap-2101	140	38	s	s	PART
ap-2101	140	39	=	=	PUNCT
ap-2101	140	40	−	−	PROPN
ap-2101	140	41	1	1	NUM
ap-2101	140	42	2π	2π	NOUN
ap-2101	140	43	s	s	PART
ap-2101	140	44	ds	ds	ADJ
ap-2101	140	45	s2	s2	NOUN
ap-2101	140	46	+	+	CCONJ
ap-2101	140	47	ν2	ν2	NOUN
ap-2101	140	48	.	.	PUNCT
ap-2101	141	1	(	(	PUNCT
ap-2101	141	2	2.37	2.37	NUM
ap-2101	141	3	)	)	PUNCT
ap-2101	141	4	after	after	ADP
ap-2101	141	5	integrating	integrate	VERB
ap-2101	141	6	this	this	DET
ap-2101	141	7	equation	equation	NOUN
ap-2101	141	8	from	from	ADP
ap-2101	141	9	λ0	λ0	NOUN
ap-2101	141	10	to	to	ADP
ap-2101	141	11	λ	λ	NOUN
ap-2101	141	12	and	and	CCONJ
ap-2101	141	13	solving	solve	VERB
ap-2101	141	14	for	for	ADP
ap-2101	141	15	gλ	gλ	NOUN
ap-2101	141	16	,	,	PUNCT
ap-2101	141	17	we	we	PRON
ap-2101	141	18	obtain	obtain	VERB
ap-2101	141	19	the	the	DET
ap-2101	141	20	final	final	ADJ
ap-2101	141	21	answer	answer	NOUN
ap-2101	141	22	.	.	PUNCT
ap-2101	142	1	gλ	gλ	NOUN
ap-2101	142	2	=	=	PUNCT
ap-2101	142	3	gλ0	gλ0	NOUN
ap-2101	142	4	1	1	NUM
ap-2101	143	1	+	+	CCONJ
ap-2101	143	2	gλ0	gλ0	NOUN
ap-2101	143	3	4π	4π	PRON
ap-2101	143	4	log	log	VERB
ap-2101	143	5	(	(	PUNCT
ap-2101	143	6	λ2+ν2	λ2+ν2	NOUN
ap-2101	143	7	λ2	λ2	NOUN
ap-2101	143	8	0+ν2	0+ν2	NOUN
ap-2101	143	9	)	)	PUNCT
ap-2101	143	10	.	.	PUNCT
ap-2101	144	1	(	(	PUNCT
ap-2101	144	2	2.38	2.38	NUM
ap-2101	144	3	)	)	PUNCT
ap-2101	144	4	this	this	DET
ap-2101	144	5	result	result	NOUN
ap-2101	144	6	is	be	AUX
ap-2101	144	7	in	in	ADP
ap-2101	144	8	agreement	agreement	NOUN
ap-2101	144	9	with	with	ADP
ap-2101	144	10	the	the	DET
ap-2101	144	11	one	one	NOUN
ap-2101	144	12	given	give	VERB
ap-2101	144	13	in	in	ADP
ap-2101	144	14	[	[	X
ap-2101	144	15	1	1	NUM
ap-2101	144	16	]	]	PUNCT
ap-2101	144	17	.	.	PUNCT
ap-2101	145	1	we	we	PRON
ap-2101	145	2	also	also	ADV
ap-2101	145	3	note	note	VERB
ap-2101	145	4	that	that	SCONJ
ap-2101	145	5	as	as	ADP
ap-2101	145	6	λ	λ	PROPN
ap-2101	145	7	→	→	SYM
ap-2101	145	8	∞	∞	PROPN
ap-2101	145	9	,	,	PUNCT
ap-2101	145	10	gλ	gλ	NOUN
ap-2101	145	11	→	→	SYM
ap-2101	145	12	0	0	NUM
ap-2101	145	13	,	,	PUNCT
ap-2101	145	14	so	so	SCONJ
ap-2101	145	15	the	the	DET
ap-2101	145	16	theory	theory	NOUN
ap-2101	145	17	is	be	AUX
ap-2101	145	18	asymptotically	asymptotically	ADV
ap-2101	145	19	free	free	ADJ
ap-2101	145	20	.	.	PUNCT
ap-2101	146	1	2.4	2.4	NUM
ap-2101	146	2	.	.	PUNCT
ap-2101	147	1	estimating	estimate	VERB
ap-2101	147	2	the	the	DET
ap-2101	147	3	range	range	NOUN
ap-2101	147	4	of	of	ADP
ap-2101	147	5	renormalizability	renormalizability	NOUN
ap-2101	147	6	now	now	ADV
ap-2101	147	7	we	we	PRON
ap-2101	147	8	shall	shall	AUX
ap-2101	147	9	try	try	VERB
ap-2101	147	10	to	to	PART
ap-2101	147	11	investigate	investigate	VERB
ap-2101	147	12	under	under	ADP
ap-2101	147	13	which	which	DET
ap-2101	147	14	conditions	condition	NOUN
ap-2101	148	1	the	the	DET
ap-2101	148	2	sequence	sequence	NOUN
ap-2101	148	3	{	{	PUNCT
ap-2101	148	4	g(n	g(n	PROPN
ap-2101	148	5	)	)	PUNCT
ap-2101	148	6	λ	λ	PROPN
ap-2101	148	7	}	}	PUNCT
ap-2101	148	8	∞n=1	∞n=1	PROPN
ap-2101	148	9	has	have	VERB
ap-2101	148	10	a	a	DET
ap-2101	148	11	limit	limit	NOUN
ap-2101	148	12	.	.	PUNCT
ap-2101	149	1	however	however	ADV
ap-2101	149	2	we	we	PRON
ap-2101	149	3	do	do	AUX
ap-2101	149	4	not	not	PART
ap-2101	149	5	have	have	VERB
ap-2101	149	6	a	a	DET
ap-2101	149	7	closed	closed	ADJ
ap-2101	149	8	form	form	NOUN
ap-2101	149	9	expression	expression	NOUN
ap-2101	149	10	for	for	ADP
ap-2101	149	11	g(n	g(n	PROPN
ap-2101	149	12	)	)	PUNCT
ap-2101	149	13	λ	λ	PROPN
ap-2101	149	14	,	,	PUNCT
ap-2101	149	15	(	(	PUNCT
ap-2101	149	16	2.31	2.31	NUM
ap-2101	149	17	)	)	PUNCT
ap-2101	149	18	tells	tell	VERB
ap-2101	149	19	us	we	PRON
ap-2101	149	20	that	that	SCONJ
ap-2101	149	21	g(n	g(n	NOUN
ap-2101	149	22	)	)	PUNCT
ap-2101	149	23	λ	λ	NOUN
ap-2101	149	24	depends	depend	VERB
ap-2101	149	25	on	on	ADP
ap-2101	149	26	g(n−1	g(n−1	PROPN
ap-2101	149	27	)	)	PUNCT
ap-2101	149	28	λ	λ	PROPN
ap-2101	149	29	,	,	PUNCT
ap-2101	149	30	hence	hence	ADV
ap-2101	149	31	we	we	PRON
ap-2101	149	32	could	could	AUX
ap-2101	149	33	not	not	PART
ap-2101	149	34	obtain	obtain	VERB
ap-2101	149	35	a	a	DET
ap-2101	149	36	rigorous	rigorous	ADJ
ap-2101	149	37	result	result	NOUN
ap-2101	149	38	for	for	ADP
ap-2101	149	39	the	the	DET
ap-2101	149	40	convergence	convergence	NOUN
ap-2101	149	41	radius	radius	NOUN
ap-2101	149	42	of	of	ADP
ap-2101	149	43	the	the	DET
ap-2101	149	44	series	series	NOUN
ap-2101	149	45	{	{	PUNCT
ap-2101	149	46	g(n	g(n	PROPN
ap-2101	149	47	)	)	PUNCT
ap-2101	149	48	λ	λ	PROPN
ap-2101	149	49	}	}	PUNCT
ap-2101	149	50	∞n=1	∞n=1	PROPN
ap-2101	149	51	in	in	ADP
ap-2101	149	52	this	this	DET
ap-2101	149	53	way	way	NOUN
ap-2101	149	54	.	.	PUNCT
ap-2101	150	1	an	an	DET
ap-2101	150	2	alternative	alternative	ADJ
ap-2101	150	3	way	way	NOUN
ap-2101	150	4	is	be	AUX
ap-2101	150	5	to	to	PART
ap-2101	150	6	investigate	investigate	VERB
ap-2101	150	7	under	under	ADP
ap-2101	150	8	which	which	DET
ap-2101	150	9	circumstances	circumstance	NOUN
ap-2101	150	10	the	the	DET
ap-2101	150	11	integral	integral	ADJ
ap-2101	150	12	equation	equation	NOUN
ap-2101	150	13	given	give	VERB
ap-2101	150	14	by	by	ADP
ap-2101	150	15	gλ	gλ	NOUN
ap-2101	150	16	=	=	PUNCT
ap-2101	150	17	gλ0	gλ0	NOUN
ap-2101	150	18	−	−	PROPN
ap-2101	150	19	1	1	NUM
ap-2101	150	20	2π	2π	NUM
ap-2101	150	21	∫	∫	NOUN
ap-2101	150	22	λ	λ	X
ap-2101	150	23	λ0	λ0	NOUN
ap-2101	150	24	ds	ds	NOUN
ap-2101	150	25	s	s	X
ap-2101	150	26	s2	s2	NOUN
ap-2101	150	27	+	+	CCONJ
ap-2101	150	28	ν2	ν2	NOUN
ap-2101	150	29	g	g	PROPN
ap-2101	150	30	2	2	NUM
ap-2101	150	31	s	s	PART
ap-2101	150	32	(	(	PUNCT
ap-2101	150	33	2.39	2.39	NUM
ap-2101	150	34	)	)	PUNCT
ap-2101	150	35	has	have	VERB
ap-2101	150	36	a	a	DET
ap-2101	150	37	unique	unique	ADJ
ap-2101	150	38	solution	solution	NOUN
ap-2101	150	39	.	.	PUNCT
ap-2101	151	1	this	this	PRON
ap-2101	151	2	can	can	AUX
ap-2101	151	3	be	be	AUX
ap-2101	151	4	done	do	VERB
ap-2101	151	5	by	by	ADP
ap-2101	151	6	using	use	VERB
ap-2101	151	7	the	the	DET
ap-2101	151	8	theory	theory	NOUN
ap-2101	151	9	of	of	ADP
ap-2101	151	10	ordinary	ordinary	ADJ
ap-2101	151	11	differential	differential	ADJ
ap-2101	151	12	equations	equation	NOUN
ap-2101	151	13	.	.	PUNCT
ap-2101	152	1	we	we	PRON
ap-2101	152	2	begin	begin	VERB
ap-2101	152	3	by	by	ADP
ap-2101	152	4	defining	define	VERB
ap-2101	152	5	a	a	DET
ap-2101	152	6	compact	compact	ADJ
ap-2101	152	7	interval	interval	NOUN
ap-2101	153	1	i	i	PRON
ap-2101	153	2	=	=	PUNCT
ap-2101	154	1	[	[	X
ap-2101	154	2	λ0	λ0	NOUN
ap-2101	154	3	,	,	PUNCT
ap-2101	154	4	λ̃	λ̃	PROPN
ap-2101	154	5	]	]	X
ap-2101	155	1	⊂	⊂	PROPN
ap-2101	155	2	r	r	X
ap-2101	155	3	where	where	SCONJ
ap-2101	155	4	1	1	NUM
ap-2101	155	5	�	�	NOUN
ap-2101	155	6	λ0	λ0	NOUN
ap-2101	155	7	<	<	X
ap-2101	155	8	λ	λ	X
ap-2101	155	9	<	<	X
ap-2101	155	10	λ̃	λ̃	PROPN
ap-2101	155	11	�	�	PROPN
ap-2101	155	12	λ	λ	PROPN
ap-2101	155	13	.	.	PUNCT
ap-2101	156	1	let	let	VERB
ap-2101	156	2	c(i	c(i	NOUN
ap-2101	156	3	)	)	PUNCT
ap-2101	157	1	denote	denote	VERB
ap-2101	157	2	the	the	DET
ap-2101	157	3	space	space	NOUN
ap-2101	157	4	of	of	ADP
ap-2101	157	5	continuous	continuous	ADJ
ap-2101	157	6	functions	function	NOUN
ap-2101	157	7	on	on	ADP
ap-2101	157	8	i.	i.	NOUN
ap-2101	157	9	it	it	PRON
ap-2101	157	10	becomes	become	VERB
ap-2101	157	11	a	a	DET
ap-2101	157	12	vector	vector	NOUN
ap-2101	157	13	space	space	NOUN
ap-2101	157	14	if	if	SCONJ
ap-2101	157	15	the	the	DET
ap-2101	157	16	vector	vector	NOUN
ap-2101	157	17	space	space	NOUN
ap-2101	157	18	operations	operation	NOUN
ap-2101	157	19	are	be	AUX
ap-2101	157	20	defined	define	VERB
ap-2101	157	21	pointwise	pointwise	NOUN
ap-2101	157	22	.	.	PUNCT
ap-2101	158	1	moreover	moreover	ADV
ap-2101	158	2	it	it	PRON
ap-2101	158	3	is	be	AUX
ap-2101	158	4	well	well	ADV
ap-2101	158	5	known	know	VERB
ap-2101	158	6	that	that	SCONJ
ap-2101	158	7	it	it	PRON
ap-2101	158	8	is	be	AUX
ap-2101	158	9	a	a	DET
ap-2101	158	10	banach	banach	NOUN
ap-2101	158	11	space	space	NOUN
ap-2101	158	12	if	if	SCONJ
ap-2101	158	13	we	we	PRON
ap-2101	158	14	define	define	VERB
ap-2101	158	15	a	a	DET
ap-2101	158	16	norm	norm	NOUN
ap-2101	158	17	on	on	ADP
ap-2101	158	18	c(i	c(i	NOUN
ap-2101	158	19	)	)	PUNCT
ap-2101	158	20	by	by	ADP
ap-2101	158	21	‖g‖	‖g‖	ADJ
ap-2101	158	22	=	=	SYM
ap-2101	158	23	sup	sup	NOUN
ap-2101	158	24	s∈i	s∈i	ADJ
ap-2101	158	25	|gs|	|gs|	PROPN
ap-2101	158	26	.	.	PUNCT
ap-2101	159	1	(	(	PUNCT
ap-2101	159	2	2.40	2.40	NUM
ap-2101	159	3	)	)	PUNCT
ap-2101	159	4	160	160	NUM
ap-2101	159	5	vol	vol	NOUN
ap-2101	159	6	.	.	PUNCT
ap-2101	160	1	54	54	NUM
ap-2101	160	2	no	no	NOUN
ap-2101	160	3	.	.	PUNCT
ap-2101	161	1	2/2014	2/2014	NUM
ap-2101	161	2	exact	exact	ADJ
ap-2101	161	3	renormalization	renormalization	NOUN
ap-2101	161	4	group	group	NOUN
ap-2101	161	5	for	for	ADP
ap-2101	161	6	point	point	NOUN
ap-2101	161	7	interactions	interaction	NOUN
ap-2101	161	8	we	we	PRON
ap-2101	161	9	note	note	VERB
ap-2101	161	10	that	that	SCONJ
ap-2101	161	11	we	we	PRON
ap-2101	161	12	use	use	VERB
ap-2101	161	13	g	g	NOUN
ap-2101	161	14	,	,	PUNCT
ap-2101	161	15	h	h	NOUN
ap-2101	161	16	as	as	ADP
ap-2101	161	17	elements	element	NOUN
ap-2101	161	18	of	of	ADP
ap-2101	161	19	c(i	c(i	NOUN
ap-2101	161	20	)	)	PUNCT
ap-2101	161	21	to	to	PART
ap-2101	161	22	avoid	avoid	VERB
ap-2101	161	23	confusion	confusion	NOUN
ap-2101	161	24	with	with	ADP
ap-2101	161	25	the	the	DET
ap-2101	161	26	unrenormalized	unrenormalized	ADJ
ap-2101	161	27	coupling	coupling	NOUN
ap-2101	161	28	constant	constant	ADJ
ap-2101	161	29	g	g	NOUN
ap-2101	161	30	,	,	PUNCT
ap-2101	161	31	that	that	ADV
ap-2101	161	32	is	is	ADV
ap-2101	161	33	,	,	PUNCT
ap-2101	161	34	we	we	PRON
ap-2101	161	35	made	make	VERB
ap-2101	161	36	the	the	DET
ap-2101	161	37	definition	definition	NOUN
ap-2101	161	38	g(s	g(s	NOUN
ap-2101	161	39	)	)	PUNCT
ap-2101	161	40	≡	≡	PROPN
ap-2101	162	1	gs	gs	INTJ
ap-2101	162	2	.	.	PUNCT
ap-2101	163	1	now	now	ADV
ap-2101	163	2	we	we	PRON
ap-2101	163	3	introduce	introduce	VERB
ap-2101	163	4	a	a	DET
ap-2101	163	5	map	map	NOUN
ap-2101	163	6	t	t	NOUN
ap-2101	163	7	:	:	PUNCT
ap-2101	163	8	c(i)→	c(i)→	PROPN
ap-2101	163	9	c(i	c(i	PROPN
ap-2101	163	10	)	)	PUNCT
ap-2101	163	11	defined	define	VERB
ap-2101	163	12	by	by	ADP
ap-2101	163	13	t	t	PROPN
ap-2101	163	14	(	(	PUNCT
ap-2101	163	15	g)(λ	g)(λ	NOUN
ap-2101	163	16	)	)	PUNCT
ap-2101	164	1	=	=	PUNCT
ap-2101	164	2	gλ0	gλ0	NOUN
ap-2101	164	3	−	−	PROPN
ap-2101	164	4	1	1	NUM
ap-2101	164	5	2π	2π	NUM
ap-2101	164	6	∫	∫	NOUN
ap-2101	164	7	λ	λ	X
ap-2101	164	8	λ0	λ0	NOUN
ap-2101	164	9	ds	ds	NOUN
ap-2101	164	10	s	s	X
ap-2101	164	11	s2	s2	NOUN
ap-2101	164	12	+	+	CCONJ
ap-2101	164	13	ν2	ν2	NOUN
ap-2101	164	14	g	g	PROPN
ap-2101	164	15	2	2	NUM
ap-2101	164	16	s	s	NOUN
ap-2101	164	17	.	.	PUNCT
ap-2101	165	1	(	(	PUNCT
ap-2101	165	2	2.41	2.41	NUM
ap-2101	165	3	)	)	PUNCT
ap-2101	165	4	then	then	ADV
ap-2101	165	5	(	(	PUNCT
ap-2101	165	6	2.39	2.39	NUM
ap-2101	165	7	)	)	PUNCT
ap-2101	165	8	can	can	AUX
ap-2101	165	9	be	be	AUX
ap-2101	165	10	expressed	express	VERB
ap-2101	165	11	as	as	ADP
ap-2101	165	12	g	g	PROPN
ap-2101	165	13	=	=	SYM
ap-2101	165	14	tg	tg	PROPN
ap-2101	165	15	,	,	PUNCT
ap-2101	165	16	in	in	ADP
ap-2101	165	17	other	other	ADJ
ap-2101	165	18	words	word	NOUN
ap-2101	165	19	the	the	DET
ap-2101	165	20	solution	solution	NOUN
ap-2101	165	21	of	of	ADP
ap-2101	165	22	(	(	PUNCT
ap-2101	165	23	2.39	2.39	NUM
ap-2101	165	24	)	)	PUNCT
ap-2101	165	25	is	be	AUX
ap-2101	165	26	also	also	ADV
ap-2101	165	27	a	a	DET
ap-2101	165	28	fixed	fix	VERB
ap-2101	165	29	point	point	NOUN
ap-2101	165	30	of	of	ADP
ap-2101	165	31	t	t	PROPN
ap-2101	165	32	.	.	PUNCT
ap-2101	166	1	the	the	DET
ap-2101	166	2	existence	existence	NOUN
ap-2101	166	3	and	and	CCONJ
ap-2101	166	4	uniqueness	uniqueness	NOUN
ap-2101	166	5	of	of	ADP
ap-2101	166	6	a	a	DET
ap-2101	166	7	solution	solution	NOUN
ap-2101	166	8	to	to	ADP
ap-2101	166	9	g	g	PROPN
ap-2101	166	10	=	=	PUNCT
ap-2101	166	11	tg	tg	PROPN
ap-2101	166	12	can	can	AUX
ap-2101	166	13	be	be	AUX
ap-2101	166	14	proved	prove	VERB
ap-2101	166	15	using	use	VERB
ap-2101	166	16	the	the	DET
ap-2101	166	17	contraction	contraction	NOUN
ap-2101	166	18	principle	principle	NOUN
ap-2101	166	19	which	which	PRON
ap-2101	166	20	can	can	AUX
ap-2101	166	21	be	be	AUX
ap-2101	166	22	stated	state	VERB
ap-2101	166	23	as	as	SCONJ
ap-2101	166	24	follows	follow	VERB
ap-2101	166	25	:	:	PUNCT
ap-2101	166	26	let	let	VERB
ap-2101	166	27	d	d	PRON
ap-2101	166	28	be	be	AUX
ap-2101	166	29	a	a	DET
ap-2101	166	30	nonempty	nonempty	ADJ
ap-2101	166	31	closed	close	VERB
ap-2101	166	32	subset	subset	NOUN
ap-2101	166	33	of	of	ADP
ap-2101	166	34	a	a	DET
ap-2101	166	35	banach	banach	NOUN
ap-2101	166	36	space	space	NOUN
ap-2101	166	37	b.	b.	NOUN
ap-2101	166	38	if	if	SCONJ
ap-2101	166	39	a	a	DET
ap-2101	166	40	map	map	NOUN
ap-2101	166	41	t	t	NOUN
ap-2101	166	42	:	:	PUNCT
ap-2101	167	1	d	d	X
ap-2101	167	2	→	→	SYM
ap-2101	167	3	b	b	PROPN
ap-2101	167	4	is	be	AUX
ap-2101	167	5	a	a	DET
ap-2101	167	6	contraction	contraction	NOUN
ap-2101	167	7	and	and	CCONJ
ap-2101	167	8	maps	map	NOUN
ap-2101	167	9	d	d	X
ap-2101	167	10	into	into	ADP
ap-2101	167	11	itself	itself	PRON
ap-2101	167	12	,	,	PUNCT
ap-2101	167	13	i.e.	i.e.	X
ap-2101	167	14	t	t	X
ap-2101	167	15	(	(	PUNCT
ap-2101	167	16	d	d	NOUN
ap-2101	167	17	)	)	PUNCT
ap-2101	167	18	⊆	⊆	NUM
ap-2101	167	19	d	d	NOUN
ap-2101	167	20	,	,	PUNCT
ap-2101	167	21	then	then	ADV
ap-2101	167	22	t	t	PROPN
ap-2101	167	23	has	have	VERB
ap-2101	167	24	exactly	exactly	ADV
ap-2101	167	25	one	one	NUM
ap-2101	167	26	fixed	fix	VERB
ap-2101	167	27	point	point	NOUN
ap-2101	167	28	g	g	NOUN
ap-2101	167	29	which	which	PRON
ap-2101	167	30	is	be	AUX
ap-2101	167	31	in	in	ADP
ap-2101	167	32	d	d	PROPN
ap-2101	167	33	[	[	X
ap-2101	167	34	22	22	NUM
ap-2101	167	35	]	]	PUNCT
ap-2101	167	36	.	.	PUNCT
ap-2101	168	1	t	t	PROPN
ap-2101	168	2	is	be	AUX
ap-2101	168	3	a	a	DET
ap-2101	168	4	contraction	contraction	NOUN
ap-2101	168	5	,	,	PUNCT
ap-2101	168	6	wich	wich	PRON
ap-2101	168	7	means	mean	VERB
ap-2101	168	8	that	that	SCONJ
ap-2101	168	9	there	there	PRON
ap-2101	168	10	exist	exist	VERB
ap-2101	168	11	a	a	DET
ap-2101	168	12	positive	positive	ADJ
ap-2101	168	13	constant	constant	ADJ
ap-2101	168	14	θ	θ	NOUN
ap-2101	168	15	<	<	X
ap-2101	168	16	1	1	NUM
ap-2101	168	17	such	such	ADJ
ap-2101	168	18	that	that	DET
ap-2101	168	19	‖t	‖t	NOUN
ap-2101	168	20	(	(	PUNCT
ap-2101	168	21	g)−	g)−	PROPN
ap-2101	168	22	t	t	PROPN
ap-2101	168	23	(	(	PUNCT
ap-2101	168	24	h)‖	h)‖	NOUN
ap-2101	168	25	≤	≤	PROPN
ap-2101	168	26	θ‖g−	θ‖g−	NUM
ap-2101	168	27	h‖	h‖	ADJ
ap-2101	168	28	for	for	ADP
ap-2101	168	29	g	g	PROPN
ap-2101	168	30	,	,	PUNCT
ap-2101	168	31	h	h	PROPN
ap-2101	168	32	∈	∈	PROPN
ap-2101	168	33	d.	d.	PROPN
ap-2101	168	34	(	(	PUNCT
ap-2101	168	35	2.42	2.42	NUM
ap-2101	168	36	)	)	PUNCT
ap-2101	168	37	if	if	SCONJ
ap-2101	168	38	t	t	PROPN
ap-2101	168	39	is	be	AUX
ap-2101	168	40	a	a	DET
ap-2101	168	41	contraction	contraction	NOUN
ap-2101	168	42	,	,	PUNCT
ap-2101	168	43	then	then	ADV
ap-2101	168	44	the	the	DET
ap-2101	168	45	sequence	sequence	NOUN
ap-2101	168	46	{	{	PUNCT
ap-2101	168	47	g(n)}∞n=1	g(n)}∞n=1	PROPN
ap-2101	168	48	defined	define	VERB
ap-2101	168	49	by	by	ADP
ap-2101	168	50	g(n	g(n	PROPN
ap-2101	168	51	)	)	PUNCT
ap-2101	169	1	=	=	SYM
ap-2101	169	2	t	t	PROPN
ap-2101	169	3	(	(	PUNCT
ap-2101	169	4	g(n−1	g(n−1	PROPN
ap-2101	169	5	)	)	PUNCT
ap-2101	169	6	)	)	PUNCT
ap-2101	169	7	with	with	ADP
ap-2101	169	8	g(1	g(1	NOUN
ap-2101	169	9	)	)	PUNCT
ap-2101	169	10	=	=	SYM
ap-2101	169	11	t	t	PROPN
ap-2101	169	12	(	(	PUNCT
ap-2101	169	13	g0	g0	PROPN
ap-2101	169	14	)	)	PUNCT
ap-2101	169	15	,	,	PUNCT
ap-2101	169	16	(	(	PUNCT
ap-2101	169	17	2.43	2.43	NUM
ap-2101	169	18	)	)	PUNCT
ap-2101	169	19	where	where	SCONJ
ap-2101	169	20	g0	g0	NOUN
ap-2101	169	21	is	be	AUX
ap-2101	169	22	an	an	DET
ap-2101	169	23	arbitrary	arbitrary	ADJ
ap-2101	169	24	element	element	NOUN
ap-2101	169	25	of	of	ADP
ap-2101	169	26	d	d	PROPN
ap-2101	169	27	,	,	PUNCT
ap-2101	169	28	converges	converge	VERB
ap-2101	169	29	to	to	ADP
ap-2101	169	30	the	the	DET
ap-2101	169	31	fixed	fixed	ADJ
ap-2101	169	32	point	point	NOUN
ap-2101	169	33	g	g	PROPN
ap-2101	169	34	,	,	PUNCT
ap-2101	169	35	that	that	PRON
ap-2101	169	36	is	is	ADV
ap-2101	169	37	lim	lim	PROPN
ap-2101	169	38	n→∞	n→∞	NUM
ap-2101	169	39	‖g(n	‖g(n	PRON
ap-2101	169	40	)	)	PUNCT
ap-2101	169	41	−	−	NOUN
ap-2101	169	42	g‖	g‖	NOUN
ap-2101	169	43	=	=	SYM
ap-2101	169	44	0	0	PROPN
ap-2101	169	45	.	.	PUNCT
ap-2101	170	1	(	(	PUNCT
ap-2101	170	2	2.44	2.44	NUM
ap-2101	170	3	)	)	PUNCT
ap-2101	170	4	therefore	therefore	ADV
ap-2101	170	5	to	to	PART
ap-2101	170	6	estimate	estimate	VERB
ap-2101	170	7	the	the	DET
ap-2101	170	8	range	range	NOUN
ap-2101	170	9	of	of	ADP
ap-2101	170	10	renormalizability	renormalizability	NOUN
ap-2101	170	11	of	of	ADP
ap-2101	170	12	our	our	PRON
ap-2101	170	13	theory	theory	NOUN
ap-2101	170	14	,	,	PUNCT
ap-2101	170	15	we	we	PRON
ap-2101	170	16	need	need	VERB
ap-2101	170	17	to	to	PART
ap-2101	170	18	estimate	estimate	VERB
ap-2101	170	19	under	under	ADP
ap-2101	170	20	which	which	PRON
ap-2101	170	21	cases	case	VERB
ap-2101	170	22	the	the	DET
ap-2101	170	23	map	map	NOUN
ap-2101	170	24	t	t	PROPN
ap-2101	170	25	defined	define	VERB
ap-2101	170	26	as	as	ADP
ap-2101	170	27	in	in	ADP
ap-2101	170	28	(	(	PUNCT
ap-2101	170	29	2.41	2.41	NUM
ap-2101	170	30	)	)	PUNCT
ap-2101	170	31	is	be	AUX
ap-2101	170	32	a	a	DET
ap-2101	170	33	contraction	contraction	NOUN
ap-2101	170	34	.	.	PUNCT
ap-2101	171	1	first	first	ADV
ap-2101	171	2	of	of	ADP
ap-2101	171	3	all	all	PRON
ap-2101	171	4	we	we	PRON
ap-2101	171	5	need	need	VERB
ap-2101	171	6	a	a	DET
ap-2101	171	7	closed	closed	ADJ
ap-2101	171	8	subset	subset	NOUN
ap-2101	171	9	of	of	ADP
ap-2101	171	10	c(i	c(i	NOUN
ap-2101	171	11	)	)	PUNCT
ap-2101	171	12	.	.	PUNCT
ap-2101	172	1	from	from	ADP
ap-2101	172	2	(	(	PUNCT
ap-2101	172	3	2.39	2.39	NUM
ap-2101	172	4	)	)	PUNCT
ap-2101	172	5	we	we	PRON
ap-2101	172	6	can	can	AUX
ap-2101	172	7	conclude	conclude	VERB
ap-2101	172	8	that	that	SCONJ
ap-2101	172	9	if	if	SCONJ
ap-2101	172	10	g	g	PROPN
ap-2101	172	11	is	be	AUX
ap-2101	172	12	a	a	DET
ap-2101	172	13	solution	solution	NOUN
ap-2101	172	14	,	,	PUNCT
ap-2101	172	15	then	then	ADV
ap-2101	172	16	it	it	PRON
ap-2101	172	17	should	should	AUX
ap-2101	172	18	be	be	AUX
ap-2101	172	19	monotone	monotone	ADJ
ap-2101	172	20	decreasing	decrease	VERB
ap-2101	172	21	on	on	ADP
ap-2101	172	22	i	i	PRON
ap-2101	172	23	=	=	PUNCT
ap-2101	173	1	[	[	X
ap-2101	173	2	λ0	λ0	NOUN
ap-2101	173	3	,	,	PUNCT
ap-2101	173	4	λ̃	λ̃	PROPN
ap-2101	173	5	]	]	PUNCT
ap-2101	173	6	.	.	PUNCT
ap-2101	174	1	thus	thus	ADV
ap-2101	174	2	it	it	PRON
ap-2101	174	3	is	be	AUX
ap-2101	174	4	natural	natural	ADJ
ap-2101	174	5	to	to	PART
ap-2101	174	6	choose	choose	VERB
ap-2101	174	7	our	our	PRON
ap-2101	174	8	closed	closed	ADJ
ap-2101	174	9	subset	subset	NOUN
ap-2101	174	10	as	as	ADP
ap-2101	174	11	d	d	PROPN
ap-2101	174	12	=	=	PUNCT
ap-2101	174	13	{	{	PUNCT
ap-2101	174	14	g	g	PROPN
ap-2101	174	15	∈	∈	PROPN
ap-2101	174	16	c(a	c(a	PROPN
ap-2101	174	17	)	)	PUNCT
ap-2101	174	18	|	|	ADV
ap-2101	174	19	‖g‖	‖g‖	VERB
ap-2101	174	20	≤	≤	NUM
ap-2101	174	21	gλ0	gλ0	NOUN
ap-2101	174	22	}	}	PUNCT
ap-2101	174	23	.	.	PUNCT
ap-2101	175	1	(	(	PUNCT
ap-2101	175	2	2.45	2.45	NUM
ap-2101	175	3	)	)	PUNCT
ap-2101	175	4	then	then	ADV
ap-2101	175	5	‖t	‖t	NOUN
ap-2101	175	6	(	(	PUNCT
ap-2101	175	7	g)‖	g)‖	NOUN
ap-2101	175	8	=	=	SYM
ap-2101	175	9	sup	sup	NOUN
ap-2101	175	10	λ∈i	λ∈i	NOUN
ap-2101	175	11	|t	|t	VERB
ap-2101	175	12	(	(	PUNCT
ap-2101	175	13	g)(λ)|	g)(λ)|	PROPN
ap-2101	175	14	=	=	PUNCT
ap-2101	175	15	sup	sup	NOUN
ap-2101	175	16	λ∈i	λ∈i	NOUN
ap-2101	175	17	∣∣∣∣gλ0	∣∣∣∣gλ0	NOUN
ap-2101	175	18	−	−	PROPN
ap-2101	175	19	1	1	NUM
ap-2101	175	20	2π	2π	NUM
ap-2101	175	21	∫	∫	NOUN
ap-2101	175	22	λ	λ	X
ap-2101	175	23	λ0	λ0	NOUN
ap-2101	175	24	ds	ds	NOUN
ap-2101	175	25	s	s	X
ap-2101	175	26	s2	s2	NOUN
ap-2101	175	27	+	+	CCONJ
ap-2101	175	28	ν2	ν2	NOUN
ap-2101	175	29	g	g	PROPN
ap-2101	175	30	2	2	NUM
ap-2101	175	31	s	s	NOUN
ap-2101	175	32	∣∣∣∣	∣∣∣∣	NOUN
ap-2101	175	33	=	=	PUNCT
ap-2101	175	34	gλ0	gλ0	NOUN
ap-2101	175	35	,	,	PUNCT
ap-2101	175	36	(	(	PUNCT
ap-2101	175	37	2.46	2.46	NUM
ap-2101	175	38	)	)	PUNCT
ap-2101	175	39	thus	thus	ADV
ap-2101	175	40	t	t	X
ap-2101	175	41	(	(	PUNCT
ap-2101	175	42	d	d	X
ap-2101	175	43	)	)	PUNCT
ap-2101	176	1	⊆	⊆	NUM
ap-2101	176	2	d.	d.	NOUN
ap-2101	176	3	so	so	ADV
ap-2101	176	4	it	it	PRON
ap-2101	176	5	remains	remain	VERB
ap-2101	176	6	to	to	PART
ap-2101	176	7	show	show	VERB
ap-2101	176	8	that	that	SCONJ
ap-2101	176	9	t	t	PROPN
ap-2101	176	10	is	be	AUX
ap-2101	176	11	a	a	DET
ap-2101	176	12	contraction	contraction	NOUN
ap-2101	176	13	.	.	PUNCT
ap-2101	177	1	let	let	VERB
ap-2101	177	2	g	g	NOUN
ap-2101	177	3	,	,	PUNCT
ap-2101	177	4	h	h	PROPN
ap-2101	177	5	∈	∈	PROPN
ap-2101	177	6	d.	d.	PROPN
ap-2101	177	7	then	then	ADV
ap-2101	177	8	we	we	PRON
ap-2101	177	9	have	have	VERB
ap-2101	177	10	the	the	DET
ap-2101	177	11	estimate	estimate	NOUN
ap-2101	177	12	|t	|t	PROPN
ap-2101	177	13	(	(	PUNCT
ap-2101	177	14	g)−	g)−	PROPN
ap-2101	177	15	t	t	PROPN
ap-2101	177	16	(	(	PUNCT
ap-2101	177	17	h)|	h)|	NOUN
ap-2101	177	18	=	=	SYM
ap-2101	177	19	1	1	NUM
ap-2101	177	20	2π	2π	NUM
ap-2101	177	21	∫	∫	NOUN
ap-2101	178	1	λ	λ	X
ap-2101	178	2	λ0	λ0	NOUN
ap-2101	178	3	ds	ds	NOUN
ap-2101	178	4	s	s	X
ap-2101	178	5	s2	s2	NOUN
ap-2101	178	6	+	+	CCONJ
ap-2101	178	7	ν2	ν2	NOUN
ap-2101	178	8	(	(	PUNCT
ap-2101	178	9	(	(	PUNCT
ap-2101	178	10	hs)2	hs)2	NOUN
ap-2101	178	11	−	−	PROPN
ap-2101	178	12	(	(	PUNCT
ap-2101	178	13	gs)2	gs)2	NOUN
ap-2101	178	14	)	)	PUNCT
ap-2101	178	15	≤	≤	NOUN
ap-2101	178	16	1	1	NUM
ap-2101	178	17	2π	2π	NUM
ap-2101	178	18	sup	sup	NOUN
ap-2101	178	19	s∈[λ0,λ	s∈[λ0,λ	NOUN
ap-2101	178	20	]	]	PUNCT
ap-2101	178	21	∣∣(hs)2	∣∣(hs)2	NOUN
ap-2101	178	22	−	−	PROPN
ap-2101	179	1	(	(	PUNCT
ap-2101	179	2	gs)2∣∣	gs)2∣∣	NOUN
ap-2101	179	3	∫	∫	PROPN
ap-2101	179	4	λ	λ	X
ap-2101	179	5	λ0	λ0	NOUN
ap-2101	179	6	ds	ds	NOUN
ap-2101	179	7	s	s	X
ap-2101	179	8	s2	s2	NOUN
ap-2101	179	9	+	+	CCONJ
ap-2101	179	10	ν2	ν2	ADV
ap-2101	179	11	≤	≤	NUM
ap-2101	179	12	1	1	NUM
ap-2101	179	13	2π	2π	NUM
ap-2101	179	14	sup	sup	NOUN
ap-2101	179	15	s∈[λ0,λ	s∈[λ0,λ	NOUN
ap-2101	179	16	]	]	PUNCT
ap-2101	179	17	∣∣(hs)2	∣∣(hs)2	NOUN
ap-2101	179	18	−	−	PROPN
ap-2101	180	1	(	(	PUNCT
ap-2101	180	2	gs)2∣∣	gs)2∣∣	NOUN
ap-2101	180	3	∫	∫	PROPN
ap-2101	180	4	λ	λ	X
ap-2101	180	5	λ0	λ0	NOUN
ap-2101	180	6	ds	ds	NOUN
ap-2101	180	7	1	1	NUM
ap-2101	180	8	s	s	NOUN
ap-2101	180	9	=	=	SYM
ap-2101	180	10	1	1	NUM
ap-2101	180	11	2π	2π	NUM
ap-2101	180	12	sup	sup	NOUN
ap-2101	180	13	s∈[λ0,λ	s∈[λ0,λ	NOUN
ap-2101	180	14	]	]	PUNCT
ap-2101	180	15	|(hs	|(hs	PROPN
ap-2101	180	16	+	+	CCONJ
ap-2101	180	17	gs)(hs	gs)(hs	PROPN
ap-2101	180	18	−	−	PROPN
ap-2101	181	1	gs)|	gs)|	PROPN
ap-2101	181	2	log	log	VERB
ap-2101	181	3	(	(	PUNCT
ap-2101	181	4	λ	λ	X
ap-2101	181	5	λ0	λ0	NOUN
ap-2101	181	6	)	)	PUNCT
ap-2101	181	7	.	.	PUNCT
ap-2101	182	1	(	(	PUNCT
ap-2101	182	2	2.47	2.47	NUM
ap-2101	182	3	)	)	PUNCT
ap-2101	182	4	by	by	ADP
ap-2101	182	5	taking	take	VERB
ap-2101	182	6	the	the	DET
ap-2101	182	7	supremum	supremum	NOUN
ap-2101	182	8	of	of	ADP
ap-2101	182	9	both	both	DET
ap-2101	182	10	sides	side	NOUN
ap-2101	182	11	we	we	PRON
ap-2101	182	12	find	find	VERB
ap-2101	182	13	‖t	‖t	NOUN
ap-2101	182	14	(	(	PUNCT
ap-2101	182	15	g)−	g)−	PROPN
ap-2101	182	16	t	t	PROPN
ap-2101	182	17	(	(	PUNCT
ap-2101	182	18	h)‖	h)‖	NOUN
ap-2101	182	19	≤	≤	NUM
ap-2101	182	20	1	1	NUM
ap-2101	183	1	2π	2π	NUM
ap-2101	183	2	sup	sup	NOUN
ap-2101	183	3	s∈i	s∈i	VERB
ap-2101	183	4	|(hs	|(hs	NUM
ap-2101	184	1	+	+	CCONJ
ap-2101	184	2	gs)(hs	gs)(hs	PROPN
ap-2101	184	3	−	−	PROPN
ap-2101	184	4	gs)|	gs)|	PROPN
ap-2101	184	5	log	log	VERB
ap-2101	184	6	(	(	PUNCT
ap-2101	184	7	λ̃	λ̃	PROPN
ap-2101	184	8	λ0	λ0	NOUN
ap-2101	184	9	)	)	PUNCT
ap-2101	184	10	=	=	SYM
ap-2101	184	11	1	1	NUM
ap-2101	184	12	2π	2π	NUM
ap-2101	184	13	‖g	‖g	VERB
ap-2101	185	1	+	+	CCONJ
ap-2101	185	2	h‖‖g−	h‖‖g−	ADJ
ap-2101	185	3	h‖	h‖	ADJ
ap-2101	185	4	log	log	NOUN
ap-2101	185	5	(	(	PUNCT
ap-2101	185	6	λ̃	λ̃	PROPN
ap-2101	185	7	λ0	λ0	NOUN
ap-2101	185	8	)	)	PUNCT
ap-2101	185	9	≤	≤	NUM
ap-2101	185	10	1	1	NUM
ap-2101	185	11	2π	2π	NOUN
ap-2101	185	12	(	(	PUNCT
ap-2101	185	13	2gλ0)‖g−	2gλ0)‖g−	PROPN
ap-2101	185	14	h‖	h‖	ADJ
ap-2101	185	15	log	log	NOUN
ap-2101	185	16	(	(	PUNCT
ap-2101	185	17	λ̃	λ̃	PROPN
ap-2101	185	18	λ0	λ0	NOUN
ap-2101	185	19	)	)	PUNCT
ap-2101	185	20	.	.	PUNCT
ap-2101	186	1	(	(	PUNCT
ap-2101	186	2	2.48	2.48	NUM
ap-2101	186	3	)	)	PUNCT
ap-2101	186	4	this	this	PRON
ap-2101	186	5	tells	tell	VERB
ap-2101	186	6	us	we	PRON
ap-2101	186	7	that	that	SCONJ
ap-2101	186	8	t	t	PROPN
ap-2101	186	9	is	be	AUX
ap-2101	186	10	a	a	DET
ap-2101	186	11	contraction	contraction	NOUN
ap-2101	186	12	if	if	SCONJ
ap-2101	186	13	gλ0	gλ0	NOUN
ap-2101	186	14	π	π	PROPN
ap-2101	186	15	log	log	INTJ
ap-2101	186	16	(	(	PUNCT
ap-2101	186	17	λ̃	λ̃	PROPN
ap-2101	186	18	λ0	λ0	NOUN
ap-2101	186	19	)	)	PUNCT
ap-2101	186	20	<	<	X
ap-2101	186	21	1	1	X
ap-2101	186	22	.	.	PUNCT
ap-2101	187	1	(	(	PUNCT
ap-2101	187	2	2.49	2.49	NUM
ap-2101	187	3	)	)	PUNCT
ap-2101	187	4	if	if	SCONJ
ap-2101	187	5	we	we	PRON
ap-2101	187	6	interpret	interpret	VERB
ap-2101	187	7	the	the	DET
ap-2101	187	8	interval	interval	NOUN
ap-2101	188	1	i	i	NOUN
ap-2101	188	2	=	=	PUNCT
ap-2101	189	1	[	[	X
ap-2101	189	2	λ0	λ0	NOUN
ap-2101	189	3	,	,	PUNCT
ap-2101	189	4	λ̃	λ̃	PROPN
ap-2101	189	5	]	]	PUNCT
ap-2101	189	6	as	as	ADP
ap-2101	189	7	the	the	DET
ap-2101	189	8	range	range	NOUN
ap-2101	189	9	of	of	ADP
ap-2101	189	10	renormalizability	renormalizability	NOUN
ap-2101	189	11	,	,	PUNCT
ap-2101	189	12	then	then	ADV
ap-2101	189	13	from	from	ADP
ap-2101	189	14	(	(	PUNCT
ap-2101	189	15	2.49	2.49	NUM
ap-2101	189	16	)	)	PUNCT
ap-2101	189	17	we	we	PRON
ap-2101	189	18	can	can	AUX
ap-2101	189	19	see	see	VERB
ap-2101	189	20	that	that	SCONJ
ap-2101	189	21	it	it	PRON
ap-2101	189	22	is	be	AUX
ap-2101	189	23	directly	directly	ADV
ap-2101	189	24	related	relate	VERB
ap-2101	189	25	to	to	ADP
ap-2101	189	26	the	the	DET
ap-2101	189	27	coupling	coupling	NOUN
ap-2101	189	28	at	at	ADP
ap-2101	189	29	the	the	DET
ap-2101	189	30	energy	energy	NOUN
ap-2101	189	31	scale	scale	NOUN
ap-2101	189	32	λ0	λ0	NOUN
ap-2101	189	33	.	.	PUNCT
ap-2101	190	1	for	for	ADP
ap-2101	190	2	a	a	DET
ap-2101	190	3	small	small	ADJ
ap-2101	190	4	coupling	coupling	NOUN
ap-2101	190	5	gλ0	gλ0	PROPN
ap-2101	190	6	�	�	PROPN
ap-2101	190	7	1	1	NUM
ap-2101	190	8	,	,	PUNCT
ap-2101	190	9	we	we	PRON
ap-2101	190	10	can	can	AUX
ap-2101	190	11	shift	shift	VERB
ap-2101	190	12	up	up	ADP
ap-2101	190	13	λ̃	λ̃	PROPN
ap-2101	190	14	considerably	considerably	ADV
ap-2101	190	15	without	without	ADP
ap-2101	190	16	breaking	break	VERB
ap-2101	190	17	the	the	DET
ap-2101	190	18	contraction	contraction	NOUN
ap-2101	190	19	property	property	NOUN
ap-2101	190	20	of	of	ADP
ap-2101	190	21	t	t	PROPN
ap-2101	190	22	.	.	PUNCT
ap-2101	191	1	however	however	ADV
ap-2101	191	2	for	for	ADP
ap-2101	191	3	couplings	coupling	NOUN
ap-2101	191	4	gλ0	gλ0	NOUN
ap-2101	191	5	∼	∼	NOUN
ap-2101	191	6	1	1	NUM
ap-2101	191	7	,	,	PUNCT
ap-2101	191	8	the	the	DET
ap-2101	191	9	range	range	NOUN
ap-2101	191	10	is	be	AUX
ap-2101	191	11	quite	quite	ADV
ap-2101	191	12	small	small	ADJ
ap-2101	191	13	or	or	CCONJ
ap-2101	191	14	we	we	PRON
ap-2101	191	15	may	may	AUX
ap-2101	191	16	not	not	PART
ap-2101	191	17	even	even	ADV
ap-2101	191	18	prove	prove	VERB
ap-2101	191	19	the	the	DET
ap-2101	191	20	existence	existence	NOUN
ap-2101	191	21	of	of	ADP
ap-2101	191	22	a	a	DET
ap-2101	191	23	solution	solution	NOUN
ap-2101	191	24	by	by	ADP
ap-2101	191	25	this	this	DET
ap-2101	191	26	approach	approach	NOUN
ap-2101	191	27	.	.	PUNCT
ap-2101	192	1	161	161	NUM
ap-2101	192	2	osman	osman	PROPN
ap-2101	192	3	teoman	teoman	NOUN
ap-2101	192	4	turgut	turgut	PROPN
ap-2101	192	5	,	,	PUNCT
ap-2101	192	6	cem	cem	NOUN
ap-2101	192	7	eröncel	eröncel	VERB
ap-2101	192	8	acta	acta	PROPN
ap-2101	192	9	polytechnica	polytechnica	PROPN
ap-2101	192	10	2.5	2.5	NUM
ap-2101	192	11	.	.	PUNCT
ap-2101	193	1	bound	bind	VERB
ap-2101	193	2	state	state	NOUN
ap-2101	193	3	solution	solution	NOUN
ap-2101	193	4	we	we	PRON
ap-2101	193	5	can	can	AUX
ap-2101	193	6	check	check	VERB
ap-2101	193	7	that	that	PRON
ap-2101	193	8	with	with	ADP
ap-2101	193	9	the	the	DET
ap-2101	193	10	coupling	coupling	NOUN
ap-2101	193	11	constant	constant	ADJ
ap-2101	193	12	given	give	VERB
ap-2101	193	13	as	as	ADP
ap-2101	193	14	in	in	ADP
ap-2101	193	15	(	(	PUNCT
ap-2101	193	16	2.38	2.38	NUM
ap-2101	193	17	)	)	PUNCT
ap-2101	193	18	we	we	PRON
ap-2101	193	19	get	get	VERB
ap-2101	193	20	a	a	DET
ap-2101	193	21	finite	finite	ADJ
ap-2101	193	22	answer	answer	NOUN
ap-2101	193	23	for	for	ADP
ap-2101	193	24	the	the	DET
ap-2101	193	25	bound	bound	ADJ
ap-2101	193	26	state	state	NOUN
ap-2101	193	27	energy	energy	NOUN
ap-2101	193	28	.	.	PUNCT
ap-2101	194	1	for	for	ADP
ap-2101	194	2	this	this	PRON
ap-2101	194	3	we	we	PRON
ap-2101	194	4	plug	plug	VERB
ap-2101	194	5	(	(	PUNCT
ap-2101	194	6	2.38	2.38	NUM
ap-2101	194	7	)	)	PUNCT
ap-2101	194	8	into	into	ADP
ap-2101	194	9	(	(	PUNCT
ap-2101	194	10	2.14	2.14	NUM
ap-2101	194	11	)	)	PUNCT
ap-2101	194	12	to	to	PART
ap-2101	194	13	find	find	VERB
ap-2101	194	14	(	(	PUNCT
ap-2101	194	15	p2	p2	X
ap-2101	194	16	+	+	CCONJ
ap-2101	194	17	ν2)φ̃(p	ν2)φ̃(p	PROPN
ap-2101	194	18	,	,	PUNCT
ap-2101	194	19	ω	ω	NOUN
ap-2101	194	20	)	)	PUNCT
ap-2101	194	21	=	=	NOUN
ap-2101	194	22	θλ(p	θλ(p	NOUN
ap-2101	194	23	)	)	PUNCT
ap-2101	194	24	(	(	PUNCT
ap-2101	194	25	2π)2	2π)2	NUM
ap-2101	194	26	gλ0	gλ0	NOUN
ap-2101	194	27	1	1	NUM
ap-2101	194	28	+	+	CCONJ
ap-2101	194	29	gλ0	gλ0	NOUN
ap-2101	194	30	4π	4π	PRON
ap-2101	194	31	log	log	VERB
ap-2101	194	32	(	(	PUNCT
ap-2101	194	33	λ2+ν2	λ2+ν2	NOUN
ap-2101	194	34	λ2	λ2	PROPN
ap-2101	194	35	0+ν2	0+ν2	NOUN
ap-2101	194	36	)	)	PUNCT
ap-2101	195	1	∫	∫	PROPN
ap-2101	196	1	λ	λ	X
ap-2101	196	2	0	0	NUM
ap-2101	196	3	dp′	dp′	PROPN
ap-2101	196	4	p′	p′	PROPN
ap-2101	196	5	∫	∫	PROPN
ap-2101	196	6	s1	s1	PROPN
ap-2101	196	7	dω′	dω′	PROPN
ap-2101	196	8	φ̃(p′	φ̃(p′	PROPN
ap-2101	196	9	,	,	PUNCT
ap-2101	196	10	ω′	ω′	NUM
ap-2101	196	11	)	)	PUNCT
ap-2101	196	12	.	.	PUNCT
ap-2101	197	1	(	(	PUNCT
ap-2101	197	2	2.50	2.50	NUM
ap-2101	197	3	)	)	PUNCT
ap-2101	197	4	by	by	ADP
ap-2101	197	5	defining	define	VERB
ap-2101	197	6	n	n	PROPN
ap-2101	197	7	=	=	SYM
ap-2101	197	8	∫	∫	PROPN
ap-2101	197	9	λ	λ	X
ap-2101	197	10	0	0	NUM
ap-2101	197	11	dp′	dp′	PROPN
ap-2101	197	12	p′	p′	PROPN
ap-2101	197	13	∫	∫	PROPN
ap-2101	197	14	s1	s1	PROPN
ap-2101	197	15	dω′	dω′	PROPN
ap-2101	197	16	φ̃(p′	φ̃(p′	PROPN
ap-2101	197	17	,	,	PUNCT
ap-2101	197	18	ω′	ω′	NUM
ap-2101	197	19	)	)	PUNCT
ap-2101	197	20	,	,	PUNCT
ap-2101	197	21	(	(	PUNCT
ap-2101	197	22	2.51	2.51	NUM
ap-2101	197	23	)	)	PUNCT
ap-2101	197	24	we	we	PRON
ap-2101	197	25	obtain	obtain	VERB
ap-2101	197	26	φ̃(p	φ̃(p	NOUN
ap-2101	197	27	,	,	PUNCT
ap-2101	197	28	ω	ω	NOUN
ap-2101	197	29	)	)	PUNCT
ap-2101	197	30	=	=	NOUN
ap-2101	197	31	θλ(p	θλ(p	NOUN
ap-2101	197	32	)	)	PUNCT
ap-2101	197	33	(	(	PUNCT
ap-2101	197	34	2π)2	2π)2	NUM
ap-2101	197	35	gλ0	gλ0	NOUN
ap-2101	197	36	1	1	NUM
ap-2101	197	37	+	+	NUM
ap-2101	197	38	gλ0	gλ0	NOUN
ap-2101	197	39	2π	2π	PROPN
ap-2101	197	40	log	log	VERB
ap-2101	197	41	(	(	PUNCT
ap-2101	197	42	λ	λ	NOUN
ap-2101	197	43	λ0	λ0	NOUN
ap-2101	197	44	)	)	PUNCT
ap-2101	197	45	n	n	NOUN
ap-2101	197	46	p2	p2	NOUN
ap-2101	197	47	+	+	CCONJ
ap-2101	197	48	ν2	ν2	NOUN
ap-2101	197	49	.	.	PUNCT
ap-2101	198	1	(	(	PUNCT
ap-2101	198	2	2.52	2.52	NUM
ap-2101	198	3	)	)	PUNCT
ap-2101	198	4	substituting	substitute	VERB
ap-2101	198	5	this	this	DET
ap-2101	198	6	result	result	NOUN
ap-2101	198	7	into	into	ADP
ap-2101	198	8	(	(	PUNCT
ap-2101	198	9	2.51	2.51	NUM
ap-2101	198	10	)	)	PUNCT
ap-2101	198	11	and	and	CCONJ
ap-2101	198	12	dividing	divide	VERB
ap-2101	198	13	both	both	DET
ap-2101	198	14	sides	side	NOUN
ap-2101	198	15	by	by	ADP
ap-2101	198	16	n	n	X
ap-2101	198	17	gives	give	VERB
ap-2101	198	18	us	we	PRON
ap-2101	198	19	1	1	NUM
ap-2101	198	20	=	=	SYM
ap-2101	198	21	1	1	NUM
ap-2101	198	22	4π	4π	NUM
ap-2101	198	23	gλ0	gλ0	NOUN
ap-2101	198	24	1	1	NUM
ap-2101	199	1	+	+	CCONJ
ap-2101	199	2	gλ0	gλ0	NOUN
ap-2101	199	3	4π	4π	PRON
ap-2101	199	4	log	log	VERB
ap-2101	199	5	(	(	PUNCT
ap-2101	199	6	λ2+ν2	λ2+ν2	NOUN
ap-2101	199	7	λ2	λ2	PROPN
ap-2101	199	8	0+ν2	0+ν2	NOUN
ap-2101	199	9	)	)	PUNCT
ap-2101	199	10	log	log	NOUN
ap-2101	199	11	(	(	PUNCT
ap-2101	199	12	λ2	λ2	NOUN
ap-2101	199	13	+	+	CCONJ
ap-2101	199	14	ν2	ν2	NOUN
ap-2101	199	15	ν2	ν2	NOUN
ap-2101	199	16	)	)	PUNCT
ap-2101	199	17	.	.	PUNCT
ap-2101	200	1	(	(	PUNCT
ap-2101	200	2	2.53	2.53	NUM
ap-2101	200	3	)	)	PUNCT
ap-2101	200	4	from	from	ADP
ap-2101	200	5	this	this	DET
ap-2101	200	6	equation	equation	NOUN
ap-2101	200	7	we	we	PRON
ap-2101	200	8	can	can	AUX
ap-2101	200	9	solve	solve	VERB
ap-2101	200	10	for	for	ADP
ap-2101	200	11	ν2	ν2	NOUN
ap-2101	200	12	in	in	ADP
ap-2101	200	13	the	the	DET
ap-2101	200	14	λ→∞	λ→∞	NUM
ap-2101	200	15	limit	limit	NOUN
ap-2101	200	16	and	and	CCONJ
ap-2101	200	17	find	find	VERB
ap-2101	200	18	eb	eb	PROPN
ap-2101	200	19	=	=	SYM
ap-2101	200	20	lim	lim	PROPN
ap-2101	200	21	λ→∞	λ→∞	NUM
ap-2101	200	22	−ν2	−ν2	NOUN
ap-2101	201	1	=	=	PUNCT
ap-2101	201	2	−λ2	−λ2	NOUN
ap-2101	201	3	0	0	NUM
ap-2101	202	1	e−4π	e−4π	NOUN
ap-2101	202	2	/	/	SYM
ap-2101	202	3	gλ0	gλ0	NOUN
ap-2101	202	4	1−	1−	NUM
ap-2101	202	5	e−4π	e−4π	PROPN
ap-2101	202	6	/	/	SYM
ap-2101	202	7	gλ0	gλ0	NOUN
ap-2101	202	8	,	,	PUNCT
ap-2101	202	9	(	(	PUNCT
ap-2101	202	10	2.54	2.54	NUM
ap-2101	202	11	)	)	PUNCT
ap-2101	202	12	which	which	PRON
ap-2101	202	13	is	be	AUX
ap-2101	202	14	finite	finite	ADJ
ap-2101	202	15	.	.	PUNCT
ap-2101	203	1	3	3	X
ap-2101	203	2	.	.	NOUN
ap-2101	203	3	exact	exact	ADJ
ap-2101	203	4	renormalization	renormalization	NOUN
ap-2101	203	5	group	group	NOUN
ap-2101	203	6	on	on	ADP
ap-2101	203	7	the	the	DET
ap-2101	203	8	hyperbolic	hyperbolic	ADJ
ap-2101	203	9	plane	plane	NOUN
ap-2101	203	10	we	we	PRON
ap-2101	203	11	will	will	AUX
ap-2101	203	12	begin	begin	VERB
ap-2101	203	13	this	this	DET
ap-2101	203	14	section	section	NOUN
ap-2101	203	15	by	by	ADP
ap-2101	203	16	constructing	construct	VERB
ap-2101	203	17	the	the	DET
ap-2101	203	18	spectral	spectral	ADJ
ap-2101	203	19	representation	representation	NOUN
ap-2101	203	20	of	of	ADP
ap-2101	203	21	the	the	DET
ap-2101	203	22	laplacian	laplacian	NOUN
ap-2101	203	23	on	on	ADP
ap-2101	203	24	the	the	DET
ap-2101	203	25	hyperbolic	hyperbolic	ADJ
ap-2101	203	26	plane	plane	NOUN
ap-2101	203	27	h2	h2	NOUN
ap-2101	203	28	.	.	PUNCT
ap-2101	204	1	by	by	ADP
ap-2101	204	2	using	use	VERB
ap-2101	204	3	this	this	DET
ap-2101	204	4	construction	construction	NOUN
ap-2101	204	5	we	we	PRON
ap-2101	204	6	shall	shall	AUX
ap-2101	204	7	perform	perform	VERB
ap-2101	204	8	the	the	DET
ap-2101	204	9	erg	erg	NOUN
ap-2101	204	10	analysis	analysis	NOUN
ap-2101	204	11	of	of	ADP
ap-2101	204	12	a	a	DET
ap-2101	204	13	point	point	NOUN
ap-2101	204	14	interaction	interaction	NOUN
ap-2101	204	15	on	on	ADP
ap-2101	204	16	the	the	DET
ap-2101	204	17	hyperbolic	hyperbolic	ADJ
ap-2101	204	18	plane	plane	NOUN
ap-2101	204	19	.	.	PUNCT
ap-2101	205	1	3.1	3.1	NUM
ap-2101	205	2	.	.	PUNCT
ap-2101	206	1	the	the	DET
ap-2101	206	2	geometry	geometry	NOUN
ap-2101	206	3	and	and	CCONJ
ap-2101	206	4	spectra	spectra	NOUN
ap-2101	206	5	of	of	ADP
ap-2101	206	6	the	the	DET
ap-2101	206	7	hyperbolic	hyperbolic	ADJ
ap-2101	206	8	plane	plane	NOUN
ap-2101	206	9	we	we	PRON
ap-2101	206	10	shall	shall	AUX
ap-2101	206	11	do	do	VERB
ap-2101	206	12	the	the	DET
ap-2101	206	13	construction	construction	NOUN
ap-2101	206	14	by	by	ADP
ap-2101	206	15	using	use	VERB
ap-2101	206	16	ideas	idea	NOUN
ap-2101	206	17	given	give	VERB
ap-2101	206	18	in	in	ADP
ap-2101	206	19	[	[	X
ap-2101	206	20	15	15	NUM
ap-2101	206	21	]	]	PUNCT
ap-2101	206	22	and	and	CCONJ
ap-2101	206	23	[	[	X
ap-2101	206	24	21	21	NUM
ap-2101	206	25	]	]	PUNCT
ap-2101	206	26	.	.	PUNCT
ap-2101	207	1	there	there	PRON
ap-2101	207	2	are	be	VERB
ap-2101	207	3	various	various	ADJ
ap-2101	207	4	models	model	NOUN
ap-2101	207	5	for	for	ADP
ap-2101	207	6	the	the	DET
ap-2101	207	7	hyperbolic	hyperbolic	ADJ
ap-2101	207	8	plane	plane	NOUN
ap-2101	207	9	.	.	PUNCT
ap-2101	208	1	we	we	PRON
ap-2101	208	2	will	will	AUX
ap-2101	208	3	use	use	VERB
ap-2101	208	4	the	the	DET
ap-2101	208	5	upper	upper	ADJ
ap-2101	208	6	half	half	ADJ
ap-2101	208	7	-	-	PUNCT
ap-2101	208	8	plane	plane	NOUN
ap-2101	208	9	model	model	NOUN
ap-2101	208	10	,	,	PUNCT
ap-2101	208	11	where	where	SCONJ
ap-2101	208	12	h2	h2	NOUN
ap-2101	208	13	is	be	AUX
ap-2101	208	14	realized	realize	VERB
ap-2101	208	15	as	as	ADP
ap-2101	208	16	the	the	DET
ap-2101	208	17	set	set	NOUN
ap-2101	208	18	h2	h2	NOUN
ap-2101	208	19	=	=	PUNCT
ap-2101	208	20	{	{	PUNCT
ap-2101	208	21	z	z	NOUN
ap-2101	208	22	=	=	SYM
ap-2101	208	23	(	(	PUNCT
ap-2101	208	24	x	x	X
ap-2101	208	25	,	,	PUNCT
ap-2101	208	26	y	y	NOUN
ap-2101	208	27	)	)	PUNCT
ap-2101	208	28	|	|	ADV
ap-2101	208	29	x	x	SYM
ap-2101	208	30	∈	∈	NOUN
ap-2101	208	31	r	r	NOUN
ap-2101	208	32	,	,	PUNCT
ap-2101	208	33	y	y	PROPN
ap-2101	208	34	∈	∈	PROPN
ap-2101	209	1	[	[	X
ap-2101	209	2	0,∞	0,∞	NOUN
ap-2101	209	3	)	)	PUNCT
ap-2101	209	4	}	}	PUNCT
ap-2101	209	5	,	,	PUNCT
ap-2101	209	6	(	(	PUNCT
ap-2101	209	7	3.1	3.1	NUM
ap-2101	209	8	)	)	PUNCT
ap-2101	209	9	with	with	ADP
ap-2101	209	10	the	the	DET
ap-2101	209	11	riemannian	riemannian	ADJ
ap-2101	209	12	metric	metric	ADJ
ap-2101	209	13	gh2	gh2	NOUN
ap-2101	209	14	given	give	VERB
ap-2101	209	15	by	by	ADP
ap-2101	209	16	gh2	gh2	NOUN
ap-2101	209	17	=	=	SYM
ap-2101	209	18	r2	r2	PROPN
ap-2101	209	19	y2	y2	PROPN
ap-2101	209	20	(	(	PUNCT
ap-2101	209	21	1	1	NUM
ap-2101	209	22	0	0	NUM
ap-2101	209	23	0	0	NUM
ap-2101	209	24	1	1	NUM
ap-2101	209	25	)	)	PUNCT
ap-2101	209	26	,	,	PUNCT
ap-2101	209	27	(	(	PUNCT
ap-2101	209	28	3.2	3.2	NUM
ap-2101	209	29	)	)	PUNCT
ap-2101	209	30	where	where	SCONJ
ap-2101	209	31	−r−2	−r−2	NUM
ap-2101	209	32	is	be	AUX
ap-2101	209	33	the	the	DET
ap-2101	209	34	constant	constant	ADJ
ap-2101	209	35	sectional	sectional	ADJ
ap-2101	209	36	curvature	curvature	NOUN
ap-2101	209	37	.	.	PUNCT
ap-2101	210	1	the	the	DET
ap-2101	210	2	riemannian	riemannian	ADJ
ap-2101	210	3	volume	volume	NOUN
ap-2101	210	4	element	element	NOUN
ap-2101	210	5	is	be	AUX
ap-2101	210	6	given	give	VERB
ap-2101	210	7	by	by	ADP
ap-2101	210	8	dvh2	dvh2	PROPN
ap-2101	210	9	=	=	SYM
ap-2101	210	10	√	√	PROPN
ap-2101	210	11	det	det	PROPN
ap-2101	210	12	gh2	gh2	PROPN
ap-2101	210	13	dx	dx	PROPN
ap-2101	210	14	∧	∧	PROPN
ap-2101	210	15	dy	dy	PROPN
ap-2101	210	16	=	=	SYM
ap-2101	210	17	dx	dx	PROPN
ap-2101	210	18	dy	dy	NOUN
ap-2101	210	19	y2	y2	PROPN
ap-2101	210	20	/	/	SYM
ap-2101	210	21	r2	r2	PROPN
ap-2101	210	22	,	,	PUNCT
ap-2101	210	23	(	(	PUNCT
ap-2101	210	24	3.3	3.3	NUM
ap-2101	210	25	)	)	PUNCT
ap-2101	210	26	and	and	CCONJ
ap-2101	210	27	the	the	DET
ap-2101	210	28	laplacian	laplacian	NOUN
ap-2101	210	29	is	be	AUX
ap-2101	210	30	∆h2	∆h2	NOUN
ap-2101	210	31	=	=	PUNCT
ap-2101	210	32	y2	y2	PROPN
ap-2101	210	33	r2	r2	NOUN
ap-2101	210	34	(	(	PUNCT
ap-2101	210	35	∂2	∂2	NUM
ap-2101	210	36	∂x2	∂x2	NOUN
ap-2101	210	37	+	+	CCONJ
ap-2101	210	38	∂2	∂2	NOUN
ap-2101	210	39	∂y2	∂y2	NOUN
ap-2101	210	40	)	)	PUNCT
ap-2101	210	41	.	.	PUNCT
ap-2101	211	1	(	(	PUNCT
ap-2101	211	2	3.4	3.4	NUM
ap-2101	211	3	)	)	PUNCT
ap-2101	211	4	the	the	DET
ap-2101	211	5	eigenfunctions	eigenfunction	NOUN
ap-2101	211	6	can	can	AUX
ap-2101	211	7	be	be	AUX
ap-2101	211	8	found	find	VERB
ap-2101	211	9	by	by	ADP
ap-2101	211	10	solving	solve	VERB
ap-2101	211	11	the	the	DET
ap-2101	211	12	closed	close	VERB
ap-2101	211	13	eigenvalue	eigenvalue	NOUN
ap-2101	211	14	problem	problem	NOUN
ap-2101	211	15	on	on	ADP
ap-2101	211	16	l2(h2	l2(h2	NOUN
ap-2101	211	17	,	,	PUNCT
ap-2101	211	18	dvh2	dvh2	PROPN
ap-2101	211	19	)	)	PUNCT
ap-2101	211	20	expressed	express	VERB
ap-2101	211	21	by	by	ADP
ap-2101	211	22	(	(	PUNCT
ap-2101	211	23	∆h2	∆h2	NOUN
ap-2101	211	24	+	+	CCONJ
ap-2101	211	25	λ)f(z	λ)f(z	VERB
ap-2101	211	26	)	)	PUNCT
ap-2101	211	27	=	=	SYM
ap-2101	211	28	0	0	NUM
ap-2101	211	29	,	,	PUNCT
ap-2101	211	30	(	(	PUNCT
ap-2101	211	31	3.5	3.5	NUM
ap-2101	211	32	)	)	PUNCT
ap-2101	211	33	where	where	SCONJ
ap-2101	211	34	λ	λ	PROPN
ap-2101	211	35	∈	∈	PROPN
ap-2101	211	36	r.	r.	PROPN
ap-2101	211	37	for	for	ADP
ap-2101	211	38	notational	notational	ADJ
ap-2101	211	39	simplicity	simplicity	NOUN
ap-2101	211	40	,	,	PUNCT
ap-2101	211	41	let	let	VERB
ap-2101	211	42	us	we	PRON
ap-2101	211	43	define	define	VERB
ap-2101	211	44	∆̃h2	∆̃h2	NOUN
ap-2101	211	45	≡	≡	PROPN
ap-2101	211	46	r2∆h2	r2∆h2	NOUN
ap-2101	211	47	and	and	CCONJ
ap-2101	211	48	λ̃	λ̃	PROPN
ap-2101	211	49	≡	≡	PROPN
ap-2101	211	50	r2λ	r2λ	PROPN
ap-2101	211	51	.	.	PUNCT
ap-2101	212	1	then	then	ADV
ap-2101	212	2	(	(	PUNCT
ap-2101	212	3	3.5	3.5	NUM
ap-2101	212	4	)	)	PUNCT
ap-2101	212	5	will	will	AUX
ap-2101	212	6	be	be	AUX
ap-2101	212	7	equivalent	equivalent	ADJ
ap-2101	212	8	to	to	PART
ap-2101	212	9	(	(	PUNCT
ap-2101	212	10	∆̃h2	∆̃h2	VERB
ap-2101	212	11	+	+	CCONJ
ap-2101	212	12	λ̃)f(z	λ̃)f(z	PROPN
ap-2101	212	13	)	)	PUNCT
ap-2101	213	1	=	=	SYM
ap-2101	213	2	0	0	NUM
ap-2101	213	3	,	,	PUNCT
ap-2101	213	4	(	(	PUNCT
ap-2101	213	5	3.6	3.6	NUM
ap-2101	213	6	)	)	PUNCT
ap-2101	213	7	162	162	NUM
ap-2101	213	8	vol	vol	NOUN
ap-2101	213	9	.	.	PUNCT
ap-2101	214	1	54	54	NUM
ap-2101	214	2	no	no	NOUN
ap-2101	214	3	.	.	PUNCT
ap-2101	215	1	2/2014	2/2014	NUM
ap-2101	215	2	exact	exact	ADJ
ap-2101	215	3	renormalization	renormalization	NOUN
ap-2101	215	4	group	group	NOUN
ap-2101	215	5	for	for	ADP
ap-2101	215	6	point	point	NOUN
ap-2101	215	7	interactions	interaction	NOUN
ap-2101	215	8	since	since	SCONJ
ap-2101	215	9	∆̃h2	∆̃h2	NOUN
ap-2101	215	10	is	be	AUX
ap-2101	215	11	separable	separable	ADJ
ap-2101	215	12	in	in	ADP
ap-2101	215	13	(	(	PUNCT
ap-2101	215	14	x	x	NOUN
ap-2101	215	15	,	,	PUNCT
ap-2101	215	16	y	y	NOUN
ap-2101	215	17	)	)	PUNCT
ap-2101	215	18	coordinates	coordinate	NOUN
ap-2101	215	19	we	we	PRON
ap-2101	215	20	can	can	AUX
ap-2101	215	21	use	use	VERB
ap-2101	215	22	separation	separation	NOUN
ap-2101	215	23	of	of	ADP
ap-2101	215	24	variables	variable	NOUN
ap-2101	215	25	.	.	PUNCT
ap-2101	216	1	so	so	ADV
ap-2101	216	2	we	we	PRON
ap-2101	216	3	choose	choose	VERB
ap-2101	216	4	f(z	f(z	NOUN
ap-2101	216	5	)	)	PUNCT
ap-2101	216	6	=	=	SYM
ap-2101	216	7	v(x)w(y	v(x)w(y	NOUN
ap-2101	216	8	)	)	PUNCT
ap-2101	216	9	and	and	CCONJ
ap-2101	216	10	put	put	VERB
ap-2101	216	11	this	this	PRON
ap-2101	216	12	into	into	ADP
ap-2101	216	13	(	(	PUNCT
ap-2101	216	14	3.6	3.6	NUM
ap-2101	216	15	)	)	PUNCT
ap-2101	216	16	to	to	PART
ap-2101	216	17	obtain	obtain	VERB
ap-2101	216	18	∂2v	∂2v	PROPN
ap-2101	216	19	∂x2	∂x2	NOUN
ap-2101	216	20	1	1	NUM
ap-2101	216	21	v(x	v(x	NOUN
ap-2101	216	22	)	)	PUNCT
ap-2101	217	1	+	+	CCONJ
ap-2101	217	2	∂2w	∂2w	VERB
ap-2101	217	3	∂y2	∂y2	ADJ
ap-2101	217	4	1	1	NUM
ap-2101	217	5	w(y	w(y	NOUN
ap-2101	217	6	)	)	PUNCT
ap-2101	217	7	+	+	CCONJ
ap-2101	218	1	λ̃	λ̃	PROPN
ap-2101	218	2	y2	y2	NOUN
ap-2101	218	3	=	=	NOUN
ap-2101	218	4	0	0	PROPN
ap-2101	218	5	.	.	PUNCT
ap-2101	218	6	(	(	PUNCT
ap-2101	218	7	3.7	3.7	NUM
ap-2101	218	8	)	)	PUNCT
ap-2101	218	9	this	this	PRON
ap-2101	218	10	implies	imply	VERB
ap-2101	218	11	that	that	SCONJ
ap-2101	218	12	there	there	PRON
ap-2101	218	13	is	be	VERB
ap-2101	218	14	a	a	DET
ap-2101	218	15	constant	constant	ADJ
ap-2101	218	16	ξ2	ξ2	NOUN
ap-2101	218	17	such	such	ADJ
ap-2101	218	18	that	that	DET
ap-2101	218	19	∂2v	∂2v	PROPN
ap-2101	218	20	∂x2	∂x2	PROPN
ap-2101	218	21	1	1	NUM
ap-2101	218	22	v(x	v(x	NOUN
ap-2101	218	23	)	)	PUNCT
ap-2101	219	1	=	=	SYM
ap-2101	219	2	−ξ2	−ξ2	PROPN
ap-2101	219	3	and	and	CCONJ
ap-2101	219	4	∂2w	∂2w	VERB
ap-2101	219	5	∂y2	∂y2	VERB
ap-2101	219	6	1	1	NUM
ap-2101	219	7	w(y	w(y	NOUN
ap-2101	219	8	)	)	PUNCT
ap-2101	220	1	+	+	CCONJ
ap-2101	220	2	λ̃	λ̃	PROPN
ap-2101	220	3	y2	y2	PROPN
ap-2101	220	4	=	=	SYM
ap-2101	220	5	ξ2	ξ2	PROPN
ap-2101	220	6	.	.	PUNCT
ap-2101	221	1	(	(	PUNCT
ap-2101	221	2	3.8	3.8	NUM
ap-2101	221	3	)	)	PUNCT
ap-2101	221	4	the	the	DET
ap-2101	221	5	x	x	X
ap-2101	221	6	-	-	NOUN
ap-2101	221	7	part	part	NOUN
ap-2101	221	8	can	can	AUX
ap-2101	221	9	be	be	AUX
ap-2101	221	10	solved	solve	VERB
ap-2101	221	11	easily	easily	ADV
ap-2101	221	12	as	as	ADP
ap-2101	221	13	v(x	v(x	NOUN
ap-2101	221	14	)	)	PUNCT
ap-2101	222	1	=	=	SYM
ap-2101	222	2	eiξx	eiξx	PROPN
ap-2101	222	3	.	.	PUNCT
ap-2101	223	1	to	to	PART
ap-2101	223	2	solve	solve	VERB
ap-2101	223	3	the	the	DET
ap-2101	223	4	y	y	NOUN
ap-2101	223	5	-	-	NOUN
ap-2101	223	6	part	part	NOUN
ap-2101	223	7	we	we	PRON
ap-2101	223	8	introduce	introduce	VERB
ap-2101	223	9	a	a	DET
ap-2101	223	10	new	new	ADJ
ap-2101	223	11	function	function	NOUN
ap-2101	223	12	by	by	ADP
ap-2101	223	13	u(y	u(y	PROPN
ap-2101	223	14	)	)	PUNCT
ap-2101	223	15	≡	≡	PROPN
ap-2101	223	16	y−1/2w(y	y−1/2w(y	NOUN
ap-2101	223	17	)	)	PUNCT
ap-2101	223	18	.	.	PUNCT
ap-2101	224	1	after	after	ADP
ap-2101	224	2	substituting	substitute	VERB
ap-2101	224	3	this	this	PRON
ap-2101	224	4	into	into	ADP
ap-2101	224	5	the	the	DET
ap-2101	224	6	y	y	NOUN
ap-2101	224	7	-	-	PUNCT
ap-2101	224	8	part	part	NOUN
ap-2101	224	9	of	of	ADP
ap-2101	224	10	(	(	PUNCT
ap-2101	224	11	3.8	3.8	NUM
ap-2101	224	12	)	)	PUNCT
ap-2101	224	13	and	and	CCONJ
ap-2101	224	14	making	make	VERB
ap-2101	224	15	some	some	DET
ap-2101	224	16	rearrangements	rearrangement	NOUN
ap-2101	224	17	we	we	PRON
ap-2101	224	18	get	get	VERB
ap-2101	224	19	y2	y2	PROPN
ap-2101	224	20	∂	∂	NOUN
ap-2101	224	21	2u	2u	NOUN
ap-2101	224	22	∂y2	∂y2	NOUN
ap-2101	224	23	+	+	CCONJ
ap-2101	224	24	y	y	PROPN
ap-2101	224	25	∂u	∂u	PROPN
ap-2101	224	26	∂y	∂y	PUNCT
ap-2101	225	1	−	−	PROPN
ap-2101	225	2	(	(	PUNCT
ap-2101	225	3	y2ξ2	y2ξ2	ADP
ap-2101	225	4	+	+	NOUN
ap-2101	225	5	1	1	NUM
ap-2101	225	6	4	4	NUM
ap-2101	225	7	−	−	PROPN
ap-2101	225	8	λ̃	λ̃	PROPN
ap-2101	225	9	)	)	PUNCT
ap-2101	225	10	u(y	u(y	X
ap-2101	225	11	)	)	PUNCT
ap-2101	225	12	=	=	SYM
ap-2101	225	13	0	0	X
ap-2101	225	14	.	.	PUNCT
ap-2101	226	1	(	(	PUNCT
ap-2101	226	2	3.9	3.9	NUM
ap-2101	226	3	)	)	PUNCT
ap-2101	226	4	the	the	DET
ap-2101	226	5	eigenvalues	eigenvalue	NOUN
ap-2101	226	6	of	of	ADP
ap-2101	226	7	the	the	DET
ap-2101	226	8	laplacian	laplacian	NOUN
ap-2101	226	9	on	on	ADP
ap-2101	226	10	h2	h2	PROPN
ap-2101	226	11	start	start	VERB
ap-2101	226	12	with	with	ADP
ap-2101	226	13	λ̃0	λ̃0	PROPN
ap-2101	226	14	=	=	NOUN
ap-2101	226	15	1	1	NUM
ap-2101	226	16	4	4	NUM
ap-2101	226	17	[	[	X
ap-2101	226	18	4	4	NUM
ap-2101	226	19	]	]	PUNCT
ap-2101	226	20	.	.	PUNCT
ap-2101	227	1	therefore	therefore	ADV
ap-2101	227	2	1	1	NUM
ap-2101	227	3	4	4	NUM
ap-2101	227	4	−	−	PROPN
ap-2101	227	5	λ̃	λ̃	PROPN
ap-2101	227	6	≤	≤	NUM
ap-2101	227	7	0	0	PUNCT
ap-2101	228	1	so	so	CCONJ
ap-2101	228	2	we	we	PRON
ap-2101	228	3	introduce	introduce	VERB
ap-2101	228	4	a	a	DET
ap-2101	228	5	new	new	ADJ
ap-2101	228	6	variable	variable	NOUN
ap-2101	228	7	τ	τ	PROPN
ap-2101	228	8	∈	∈	PROPN
ap-2101	229	1	[	[	X
ap-2101	229	2	0,∞	0,∞	NOUN
ap-2101	229	3	)	)	PUNCT
ap-2101	229	4	such	such	ADJ
ap-2101	229	5	that	that	SCONJ
ap-2101	229	6	1	1	NUM
ap-2101	229	7	4	4	NUM
ap-2101	229	8	−	−	NOUN
ap-2101	229	9	λ̃	λ̃	PROPN
ap-2101	229	10	=	=	SYM
ap-2101	229	11	(	(	PUNCT
ap-2101	229	12	iτ)2	iτ)2	PROPN
ap-2101	229	13	.	.	PUNCT
ap-2101	230	1	then	then	ADV
ap-2101	230	2	(	(	PUNCT
ap-2101	230	3	3.9	3.9	NUM
ap-2101	230	4	)	)	PUNCT
ap-2101	230	5	becomes	become	VERB
ap-2101	230	6	y2	y2	PROPN
ap-2101	230	7	∂	∂	NUM
ap-2101	230	8	2u	2u	NOUN
ap-2101	230	9	∂y2	∂y2	NOUN
ap-2101	231	1	+	+	CCONJ
ap-2101	231	2	y	y	PROPN
ap-2101	231	3	∂u	∂u	PROPN
ap-2101	231	4	∂y	∂y	PUNCT
ap-2101	231	5	−	−	PROPN
ap-2101	231	6	[	[	PUNCT
ap-2101	231	7	(	(	PUNCT
ap-2101	231	8	yξ)2	yξ)2	PROPN
ap-2101	231	9	+	+	CCONJ
ap-2101	231	10	(	(	PUNCT
ap-2101	231	11	iτ)2]u(y	iτ)2]u(y	PROPN
ap-2101	231	12	)	)	PUNCT
ap-2101	231	13	=	=	PUNCT
ap-2101	231	14	0	0	X
ap-2101	231	15	.	.	PUNCT
ap-2101	232	1	(	(	PUNCT
ap-2101	232	2	3.10	3.10	NUM
ap-2101	232	3	)	)	PUNCT
ap-2101	232	4	there	there	PRON
ap-2101	232	5	are	be	VERB
ap-2101	232	6	two	two	NUM
ap-2101	232	7	linearly	linearly	ADV
ap-2101	232	8	independent	independent	ADJ
ap-2101	232	9	solutions	solution	NOUN
ap-2101	232	10	which	which	PRON
ap-2101	232	11	are	be	AUX
ap-2101	232	12	the	the	DET
ap-2101	232	13	modified	modify	VERB
ap-2101	232	14	bessel	bessel	NOUN
ap-2101	232	15	functions	function	NOUN
ap-2101	232	16	iiτ	iiτ	ADJ
ap-2101	232	17	(	(	PUNCT
ap-2101	232	18	|yξ|	|yξ|	PROPN
ap-2101	232	19	)	)	PUNCT
ap-2101	232	20	and	and	CCONJ
ap-2101	232	21	kiτ	kiτ	INTJ
ap-2101	232	22	(	(	PUNCT
ap-2101	232	23	|yξ|	|yξ|	PROPN
ap-2101	232	24	)	)	PUNCT
ap-2101	232	25	.	.	PUNCT
ap-2101	233	1	since	since	SCONJ
ap-2101	233	2	iiτ	iiτ	PROPN
ap-2101	233	3	(	(	PUNCT
ap-2101	233	4	|yξ|	|yξ|	PROPN
ap-2101	233	5	)	)	PUNCT
ap-2101	233	6	is	be	AUX
ap-2101	233	7	singular	singular	ADJ
ap-2101	233	8	at	at	ADP
ap-2101	233	9	infinity	infinity	NOUN
ap-2101	233	10	,	,	PUNCT
ap-2101	233	11	we	we	PRON
ap-2101	233	12	exclude	exclude	VERB
ap-2101	233	13	it	it	PRON
ap-2101	233	14	from	from	ADP
ap-2101	233	15	our	our	PRON
ap-2101	233	16	solution	solution	NOUN
ap-2101	233	17	space	space	NOUN
ap-2101	233	18	.	.	PUNCT
ap-2101	234	1	moreover	moreover	ADV
ap-2101	234	2	kiτ	kiτ	INTJ
ap-2101	234	3	(	(	PUNCT
ap-2101	234	4	|yξ|	|yξ|	PROPN
ap-2101	234	5	)	)	PUNCT
ap-2101	234	6	has	have	VERB
ap-2101	234	7	a	a	DET
ap-2101	234	8	singularity	singularity	NOUN
ap-2101	234	9	at	at	ADP
ap-2101	234	10	ξ	ξ	X
ap-2101	234	11	=	=	SYM
ap-2101	234	12	0	0	NUM
ap-2101	234	13	given	give	VERB
ap-2101	234	14	by	by	ADP
ap-2101	234	15	[	[	X
ap-2101	234	16	21	21	NUM
ap-2101	234	17	]	]	X
ap-2101	234	18	kiτ	kiτ	X
ap-2101	234	19	(	(	PUNCT
ap-2101	234	20	|yξ|	|yξ|	PROPN
ap-2101	234	21	)	)	PUNCT
ap-2101	234	22	∼	∼	NOUN
ap-2101	234	23	2iτ−1γ(iτ	2iτ−1γ(iτ	NUM
ap-2101	234	24	)	)	PUNCT
ap-2101	234	25	|yξ|−iτ	|yξ|−iτ	VERB
ap-2101	235	1	+	+	CCONJ
ap-2101	236	1	2−iτ−1γ(−iτ	2−iτ−1γ(−iτ	NUM
ap-2101	236	2	)	)	PUNCT
ap-2101	236	3	|yξ|iτ	|yξ|iτ	PUNCT
ap-2101	236	4	as	as	ADP
ap-2101	236	5	ξ	ξ	X
ap-2101	236	6	→	→	SYM
ap-2101	236	7	0	0	NUM
ap-2101	236	8	+	+	NOUN
ap-2101	236	9	.	.	PUNCT
ap-2101	237	1	(	(	PUNCT
ap-2101	237	2	3.11	3.11	NUM
ap-2101	237	3	)	)	PUNCT
ap-2101	237	4	so	so	SCONJ
ap-2101	237	5	we	we	PRON
ap-2101	237	6	choose	choose	VERB
ap-2101	237	7	u(y	u(y	NOUN
ap-2101	237	8	)	)	PUNCT
ap-2101	237	9	=	=	PUNCT
ap-2101	238	1	|ξ|iτ	|ξ|iτ	PROPN
ap-2101	238	2	kiτ	kiτ	X
ap-2101	238	3	(	(	PUNCT
ap-2101	238	4	|yξ|	|yξ|	PROPN
ap-2101	238	5	)	)	PUNCT
ap-2101	238	6	as	as	ADP
ap-2101	238	7	a	a	DET
ap-2101	238	8	solution	solution	NOUN
ap-2101	238	9	to	to	ADP
ap-2101	238	10	(	(	PUNCT
ap-2101	238	11	3.10	3.10	NUM
ap-2101	238	12	)	)	PUNCT
ap-2101	238	13	and	and	CCONJ
ap-2101	238	14	write	write	VERB
ap-2101	238	15	the	the	DET
ap-2101	238	16	eigenfunctions	eigenfunction	NOUN
ap-2101	238	17	of	of	ADP
ap-2101	238	18	∆h2	∆h2	NOUN
ap-2101	238	19	as	as	ADP
ap-2101	238	20	e0(z	e0(z	NOUN
ap-2101	238	21	;	;	PUNCT
ap-2101	238	22	τ	τ	PROPN
ap-2101	238	23	,	,	PUNCT
ap-2101	238	24	ξ	ξ	X
ap-2101	238	25	)	)	PUNCT
ap-2101	238	26	=	=	SYM
ap-2101	238	27	1√	1√	NUM
ap-2101	238	28	2π	2π	NOUN
ap-2101	238	29	eiξx	eiξx	VERB
ap-2101	238	30	√	√	NUM
ap-2101	238	31	y	y	PROPN
ap-2101	238	32	|ξ|iτ	|ξ|iτ	PROPN
ap-2101	238	33	kiτ	kiτ	X
ap-2101	238	34	(	(	PUNCT
ap-2101	238	35	|yξ|	|yξ|	PROPN
ap-2101	238	36	)	)	PUNCT
ap-2101	238	37	,	,	PUNCT
ap-2101	238	38	(	(	PUNCT
ap-2101	238	39	3.12	3.12	NUM
ap-2101	238	40	)	)	PUNCT
ap-2101	238	41	where	where	SCONJ
ap-2101	238	42	we	we	PRON
ap-2101	238	43	have	have	AUX
ap-2101	238	44	put	put	VERB
ap-2101	238	45	an	an	DET
ap-2101	238	46	extra	extra	ADJ
ap-2101	238	47	(	(	PUNCT
ap-2101	238	48	2π)−1/2	2π)−1/2	NOUN
ap-2101	238	49	to	to	PART
ap-2101	238	50	simplify	simplify	VERB
ap-2101	238	51	our	our	PRON
ap-2101	238	52	construction	construction	NOUN
ap-2101	238	53	of	of	ADP
ap-2101	238	54	the	the	DET
ap-2101	238	55	spectral	spectral	ADJ
ap-2101	238	56	representation	representation	NOUN
ap-2101	238	57	.	.	PUNCT
ap-2101	239	1	we	we	PRON
ap-2101	239	2	note	note	VERB
ap-2101	239	3	that	that	SCONJ
ap-2101	239	4	this	this	PRON
ap-2101	239	5	does	do	AUX
ap-2101	239	6	not	not	PART
ap-2101	239	7	alter	alter	VERB
ap-2101	239	8	the	the	DET
ap-2101	239	9	spectrum	spectrum	NOUN
ap-2101	239	10	of	of	ADP
ap-2101	239	11	the	the	DET
ap-2101	239	12	eigenvalues	eigenvalue	NOUN
ap-2101	239	13	.	.	PUNCT
ap-2101	240	1	to	to	PART
ap-2101	240	2	obtain	obtain	VERB
ap-2101	240	3	the	the	DET
ap-2101	240	4	spectral	spectral	ADJ
ap-2101	240	5	representation	representation	NOUN
ap-2101	240	6	of	of	ADP
ap-2101	240	7	∆h2	∆h2	NOUN
ap-2101	240	8	we	we	PRON
ap-2101	240	9	introduce	introduce	VERB
ap-2101	240	10	the	the	DET
ap-2101	240	11	following	follow	VERB
ap-2101	240	12	transform	transform	NOUN
ap-2101	240	13	,	,	PUNCT
ap-2101	240	14	(	(	PUNCT
ap-2101	240	15	kψ)(τ	kψ)(τ	PROPN
ap-2101	240	16	,	,	PUNCT
ap-2101	240	17	ξ	ξ	X
ap-2101	240	18	)	)	PUNCT
ap-2101	240	19	≡	≡	PROPN
ap-2101	240	20	ψ̃(τ	ψ̃(τ	PROPN
ap-2101	240	21	,	,	PUNCT
ap-2101	240	22	ξ	ξ	X
ap-2101	240	23	)	)	PUNCT
ap-2101	240	24	=	=	SYM
ap-2101	240	25	1	1	NUM
ap-2101	240	26	r2	r2	PROPN
ap-2101	240	27	∫	∫	PROPN
ap-2101	240	28	h2	h2	PROPN
ap-2101	240	29	dvh2	dvh2	PROPN
ap-2101	240	30	ψ(z)e0(z	ψ(z)e0(z	PROPN
ap-2101	240	31	;	;	PUNCT
ap-2101	240	32	τ	τ	PROPN
ap-2101	240	33	,	,	PUNCT
ap-2101	240	34	ξ	ξ	X
ap-2101	240	35	)	)	PUNCT
ap-2101	240	36	(	(	PUNCT
ap-2101	240	37	k−1ψ̃)(z	k−1ψ̃)(z	PROPN
ap-2101	240	38	)	)	PUNCT
ap-2101	240	39	=	=	SYM
ap-2101	240	40	2	2	NUM
ap-2101	240	41	π2	π2	NUM
ap-2101	240	42	∫	∫	PROPN
ap-2101	240	43	∞	∞	PROPN
ap-2101	240	44	0	0	NUM
ap-2101	240	45	dτ	dτ	PROPN
ap-2101	240	46	τ	τ	PROPN
ap-2101	240	47	sinh(πτ	sinh(πτ	PROPN
ap-2101	240	48	)	)	PUNCT
ap-2101	240	49	∫	∫	PROPN
ap-2101	240	50	r	r	NOUN
ap-2101	240	51	dξ	dξ	ADP
ap-2101	240	52	ψ̃(τ	ψ̃(τ	PROPN
ap-2101	240	53	,	,	PUNCT
ap-2101	240	54	ξ)e0(z	ξ)e0(z	PROPN
ap-2101	240	55	;	;	PUNCT
ap-2101	240	56	τ	τ	PROPN
ap-2101	240	57	,	,	PUNCT
ap-2101	240	58	ξ	ξ	PROPN
ap-2101	240	59	)	)	PUNCT
ap-2101	240	60	.	.	PUNCT
ap-2101	241	1	(	(	PUNCT
ap-2101	241	2	3.13	3.13	NUM
ap-2101	241	3	)	)	PUNCT
ap-2101	241	4	which	which	PRON
ap-2101	241	5	is	be	AUX
ap-2101	241	6	a	a	DET
ap-2101	241	7	combination	combination	NOUN
ap-2101	241	8	of	of	ADP
ap-2101	241	9	the	the	DET
ap-2101	241	10	fourier	fourier	NOUN
ap-2101	241	11	transform	transform	NOUN
ap-2101	241	12	in	in	ADP
ap-2101	241	13	(	(	PUNCT
ap-2101	241	14	x	x	NOUN
ap-2101	241	15	,	,	PUNCT
ap-2101	241	16	ξ	ξ	NOUN
ap-2101	241	17	)	)	PUNCT
ap-2101	241	18	variables	variable	NOUN
ap-2101	241	19	and	and	CCONJ
ap-2101	241	20	the	the	DET
ap-2101	241	21	kontorovich	kontorovich	NOUN
ap-2101	241	22	-	-	PUNCT
ap-2101	241	23	lebedev	lebedev	NOUN
ap-2101	241	24	transform	transform	NOUN
ap-2101	241	25	in	in	ADP
ap-2101	241	26	(	(	PUNCT
ap-2101	241	27	y	y	PROPN
ap-2101	241	28	,	,	PUNCT
ap-2101	241	29	τ	τ	PROPN
ap-2101	241	30	)	)	PUNCT
ap-2101	241	31	variables	variable	NOUN
ap-2101	242	1	[	[	X
ap-2101	242	2	16	16	NUM
ap-2101	242	3	]	]	PUNCT
ap-2101	242	4	.	.	PUNCT
ap-2101	243	1	the	the	DET
ap-2101	243	2	range	range	NOUN
ap-2101	243	3	of	of	ADP
ap-2101	243	4	k	k	PROPN
ap-2101	243	5	can	can	AUX
ap-2101	243	6	be	be	AUX
ap-2101	243	7	formulated	formulate	VERB
ap-2101	243	8	by	by	ADP
ap-2101	243	9	considering	consider	VERB
ap-2101	243	10	l2(r	l2(r	PROPN
ap-2101	243	11	,	,	PUNCT
ap-2101	243	12	dξ	dξ	PROPN
ap-2101	243	13	)	)	PUNCT
ap-2101	243	14	as	as	SCONJ
ap-2101	243	15	the	the	DET
ap-2101	243	16	hilbert	hilbert	PROPN
ap-2101	243	17	space	space	NOUN
ap-2101	243	18	corresponding	correspond	VERB
ap-2101	243	19	to	to	ADP
ap-2101	243	20	ξ	ξ	PROPN
ap-2101	243	21	,	,	PUNCT
ap-2101	243	22	and	and	CCONJ
ap-2101	243	23	then	then	ADV
ap-2101	243	24	taking	take	VERB
ap-2101	243	25	a	a	DET
ap-2101	243	26	direct	direct	ADJ
ap-2101	243	27	integral	integral	NOUN
ap-2101	243	28	of	of	ADP
ap-2101	243	29	it	it	PRON
ap-2101	243	30	with	with	ADP
ap-2101	243	31	respect	respect	NOUN
ap-2101	243	32	to	to	ADP
ap-2101	243	33	the	the	DET
ap-2101	243	34	measure	measure	NOUN
ap-2101	243	35	space	space	NOUN
ap-2101	243	36	(	(	PUNCT
ap-2101	243	37	0,∞	0,∞	NUM
ap-2101	243	38	)	)	PUNCT
ap-2101	243	39	.	.	PUNCT
ap-2101	244	1	so	so	ADV
ap-2101	244	2	the	the	DET
ap-2101	244	3	map	map	NOUN
ap-2101	244	4	k	k	PROPN
ap-2101	244	5	can	can	AUX
ap-2101	244	6	be	be	AUX
ap-2101	244	7	expressed	express	VERB
ap-2101	244	8	formally	formally	ADV
ap-2101	244	9	as	as	ADP
ap-2101	244	10	k	k	PROPN
ap-2101	244	11	:	:	PUNCT
ap-2101	244	12	l2(h2	l2(h2	NOUN
ap-2101	244	13	,	,	PUNCT
ap-2101	244	14	dvh2)→	dvh2)→	PROPN
ap-2101	244	15	∫	∫	PROPN
ap-2101	244	16	⊕	⊕	PROPN
ap-2101	244	17	(	(	PUNCT
ap-2101	244	18	0,∞	0,∞	NOUN
ap-2101	244	19	)	)	PUNCT
ap-2101	244	20	l2(r	l2(r	PROPN
ap-2101	244	21	,	,	PUNCT
ap-2101	244	22	dξ	dξ	PROPN
ap-2101	244	23	)	)	PUNCT
ap-2101	244	24	.	.	PUNCT
ap-2101	245	1	(	(	PUNCT
ap-2101	245	2	3.14	3.14	NUM
ap-2101	245	3	)	)	PUNCT
ap-2101	245	4	to	to	PART
ap-2101	245	5	prove	prove	VERB
ap-2101	245	6	that	that	SCONJ
ap-2101	245	7	k	k	PROPN
ap-2101	245	8	provides	provide	VERB
ap-2101	245	9	a	a	DET
ap-2101	245	10	spectral	spectral	ADJ
ap-2101	245	11	representation	representation	NOUN
ap-2101	245	12	of	of	ADP
ap-2101	245	13	∆h2	∆h2	NOUN
ap-2101	245	14	,	,	PUNCT
ap-2101	245	15	we	we	PRON
ap-2101	245	16	need	need	VERB
ap-2101	245	17	two	two	NUM
ap-2101	245	18	identities	identity	NOUN
ap-2101	245	19	involving	involve	VERB
ap-2101	245	20	modified	modify	VERB
ap-2101	245	21	bessel	bessel	NOUN
ap-2101	245	22	functions	function	NOUN
ap-2101	245	23	which	which	PRON
ap-2101	245	24	are	be	AUX
ap-2101	245	25	given	give	VERB
ap-2101	245	26	by	by	ADP
ap-2101	245	27	[	[	X
ap-2101	245	28	15	15	NUM
ap-2101	245	29	]	]	SYM
ap-2101	245	30	2	2	NUM
ap-2101	245	31	π2	π2	NUM
ap-2101	245	32	∫	∫	PROPN
ap-2101	245	33	∞	∞	PROPN
ap-2101	245	34	0	0	NUM
ap-2101	245	35	dτ	dτ	NOUN
ap-2101	245	36	τ	τ	X
ap-2101	245	37	sinh(πτ)kiτ	sinh(πτ)kiτ	X
ap-2101	245	38	(	(	PUNCT
ap-2101	245	39	u)kiτ	u)kiτ	PROPN
ap-2101	245	40	(	(	PUNCT
ap-2101	245	41	v	v	NOUN
ap-2101	245	42	)	)	PUNCT
ap-2101	245	43	=	=	SYM
ap-2101	245	44	vδ(u−	vδ(u−	X
ap-2101	245	45	v	v	NOUN
ap-2101	245	46	)	)	PUNCT
ap-2101	245	47	,	,	PUNCT
ap-2101	245	48	(	(	PUNCT
ap-2101	245	49	3.15	3.15	NUM
ap-2101	245	50	)	)	PUNCT
ap-2101	245	51	and	and	CCONJ
ap-2101	246	1	2	2	NUM
ap-2101	246	2	π2	π2	NUM
ap-2101	246	3	∫	∫	PROPN
ap-2101	246	4	∞	∞	NOUN
ap-2101	246	5	0	0	NUM
ap-2101	246	6	du	du	PROPN
ap-2101	246	7	u	u	PROPN
ap-2101	246	8	kiτ	kiτ	NOUN
ap-2101	246	9	(	(	PUNCT
ap-2101	246	10	u)kiτ	u)kiτ	PROPN
ap-2101	246	11	′(u	′(u	NOUN
ap-2101	246	12	)	)	PUNCT
ap-2101	246	13	=	=	PUNCT
ap-2101	247	1	δ(τ	δ(τ	PROPN
ap-2101	247	2	−	−	PROPN
ap-2101	248	1	τ	τ	PROPN
ap-2101	248	2	′)√	′)√	PROPN
ap-2101	248	3	ττ	ττ	NOUN
ap-2101	248	4	′	′	NOUN
ap-2101	248	5	√	√	NUM
ap-2101	248	6	sinh(πτ	sinh(πτ	NOUN
ap-2101	248	7	)	)	PUNCT
ap-2101	248	8	sinh(πτ	sinh(πτ	NOUN
ap-2101	248	9	′	′	NOUN
ap-2101	248	10	)	)	PUNCT
ap-2101	248	11	.	.	PUNCT
ap-2101	249	1	(	(	PUNCT
ap-2101	249	2	3.16	3.16	NUM
ap-2101	249	3	)	)	PUNCT
ap-2101	249	4	163	163	NUM
ap-2101	249	5	osman	osman	PROPN
ap-2101	249	6	teoman	teoman	NOUN
ap-2101	249	7	turgut	turgut	PROPN
ap-2101	249	8	,	,	PUNCT
ap-2101	249	9	cem	cem	NOUN
ap-2101	249	10	eröncel	eröncel	VERB
ap-2101	249	11	acta	acta	PROPN
ap-2101	249	12	polytechnica	polytechnica	PROPN
ap-2101	249	13	moreover	moreover	ADV
ap-2101	249	14	we	we	PRON
ap-2101	249	15	shall	shall	AUX
ap-2101	249	16	also	also	ADV
ap-2101	249	17	use	use	VERB
ap-2101	249	18	the	the	DET
ap-2101	249	19	property	property	NOUN
ap-2101	249	20	kiτ	kiτ	NOUN
ap-2101	249	21	(	(	PUNCT
ap-2101	249	22	u	u	NOUN
ap-2101	249	23	)	)	PUNCT
ap-2101	249	24	=	=	PUNCT
ap-2101	249	25	k−iτ	k−iτ	X
ap-2101	249	26	(	(	PUNCT
ap-2101	249	27	u	u	NOUN
ap-2101	249	28	)	)	PUNCT
ap-2101	249	29	.	.	PUNCT
ap-2101	250	1	using	use	VERB
ap-2101	250	2	(	(	PUNCT
ap-2101	250	3	3.16	3.16	NUM
ap-2101	250	4	)	)	PUNCT
ap-2101	250	5	one	one	NOUN
ap-2101	250	6	can	can	AUX
ap-2101	250	7	show	show	VERB
ap-2101	250	8	that	that	SCONJ
ap-2101	250	9	k	k	PROPN
ap-2101	250	10	diagonalizes	diagonalize	VERB
ap-2101	250	11	the	the	DET
ap-2101	250	12	laplacian	laplacian	NOUN
ap-2101	250	13	,	,	PUNCT
ap-2101	250	14	that	that	PRON
ap-2101	250	15	is	be	AUX
ap-2101	250	16	for	for	ADP
ap-2101	250	17	all	all	DET
ap-2101	250	18	ψ̃	ψ̃	PROPN
ap-2101	250	19	∈	∈	PROPN
ap-2101	250	20	∫	∫	PROPN
ap-2101	250	21	⊕	⊕	PROPN
ap-2101	250	22	(	(	PUNCT
ap-2101	250	23	0,∞	0,∞	NUM
ap-2101	250	24	)	)	PUNCT
ap-2101	250	25	l	l	NOUN
ap-2101	250	26	2(r	2(r	NUM
ap-2101	250	27	,	,	PUNCT
ap-2101	250	28	dξ	dξ	PROPN
ap-2101	250	29	)	)	PUNCT
ap-2101	250	30	we	we	PRON
ap-2101	250	31	have	have	VERB
ap-2101	250	32	−(k∆̃h2k−1ψ̃)(τ	−(k∆̃h2k−1ψ̃)(τ	NOUN
ap-2101	250	33	,	,	PUNCT
ap-2101	250	34	ξ	ξ	X
ap-2101	250	35	)	)	PUNCT
ap-2101	251	1	=	=	NOUN
ap-2101	251	2	(	(	PUNCT
ap-2101	251	3	τ2	τ2	NOUN
ap-2101	251	4	+	+	NOUN
ap-2101	251	5	1	1	NUM
ap-2101	251	6	4	4	NUM
ap-2101	251	7	)	)	PUNCT
ap-2101	252	1	ψ̃(τ	ψ̃(τ	PROPN
ap-2101	252	2	,	,	PUNCT
ap-2101	252	3	ξ	ξ	NOUN
ap-2101	252	4	)	)	PUNCT
ap-2101	252	5	,	,	PUNCT
ap-2101	252	6	(	(	PUNCT
ap-2101	252	7	3.17	3.17	NUM
ap-2101	252	8	)	)	PUNCT
ap-2101	252	9	and	and	CCONJ
ap-2101	252	10	therefore	therefore	ADV
ap-2101	252	11	−(k∆h2k−1ψ̃)(τ	−(k∆h2k−1ψ̃)(τ	PROPN
ap-2101	252	12	,	,	PUNCT
ap-2101	252	13	ξ	ξ	X
ap-2101	252	14	)	)	PUNCT
ap-2101	252	15	=	=	SYM
ap-2101	252	16	1	1	NUM
ap-2101	252	17	r2	r2	NOUN
ap-2101	252	18	(	(	PUNCT
ap-2101	252	19	τ2	τ2	NOUN
ap-2101	252	20	+	+	NOUN
ap-2101	252	21	1	1	NUM
ap-2101	252	22	4	4	NUM
ap-2101	252	23	)	)	PUNCT
ap-2101	252	24	ψ̃(τ	ψ̃(τ	PROPN
ap-2101	252	25	,	,	PUNCT
ap-2101	252	26	ξ	ξ	NOUN
ap-2101	252	27	)	)	PUNCT
ap-2101	252	28	,	,	PUNCT
ap-2101	252	29	(	(	PUNCT
ap-2101	252	30	3.18	3.18	NUM
ap-2101	252	31	)	)	PUNCT
ap-2101	252	32	so	so	SCONJ
ap-2101	252	33	the	the	DET
ap-2101	252	34	spectrum	spectrum	NOUN
ap-2101	252	35	of	of	ADP
ap-2101	252	36	∆h2	∆h2	NOUN
ap-2101	252	37	is	be	AUX
ap-2101	252	38	given	give	VERB
ap-2101	252	39	by	by	ADP
ap-2101	252	40	σ(∆h2	σ(∆h2	ADJ
ap-2101	252	41	)	)	PUNCT
ap-2101	253	1	=	=	PUNCT
ap-2101	253	2	[	[	PUNCT
ap-2101	253	3	1	1	NUM
ap-2101	253	4	4r2	4r2	NUM
ap-2101	253	5	,	,	PUNCT
ap-2101	253	6	∞	∞	PROPN
ap-2101	253	7	)	)	PUNCT
ap-2101	253	8	.	.	PUNCT
ap-2101	254	1	(	(	PUNCT
ap-2101	254	2	3.19	3.19	NUM
ap-2101	254	3	)	)	PUNCT
ap-2101	254	4	by	by	ADP
ap-2101	254	5	using	use	VERB
ap-2101	254	6	(	(	PUNCT
ap-2101	254	7	3.15	3.15	NUM
ap-2101	254	8	)	)	PUNCT
ap-2101	254	9	it	it	PRON
ap-2101	254	10	is	be	AUX
ap-2101	254	11	straightforward	straightforward	ADJ
ap-2101	254	12	to	to	PART
ap-2101	254	13	show	show	VERB
ap-2101	254	14	that	that	SCONJ
ap-2101	254	15	k	k	PROPN
ap-2101	254	16	is	be	AUX
ap-2101	254	17	an	an	DET
ap-2101	254	18	isomorphism	isomorphism	NOUN
ap-2101	254	19	,	,	PUNCT
ap-2101	254	20	i.e.	i.e.	X
ap-2101	254	21	for	for	ADP
ap-2101	254	22	all	all	PRON
ap-2101	254	23	ψ	ψ	PRON
ap-2101	254	24	∈	∈	NOUN
ap-2101	254	25	l2(h2	l2(h2	NOUN
ap-2101	254	26	,	,	PUNCT
ap-2101	254	27	dvh2	dvh2	PROPN
ap-2101	254	28	)	)	PUNCT
ap-2101	254	29	we	we	PRON
ap-2101	254	30	have	have	VERB
ap-2101	254	31	(	(	PUNCT
ap-2101	254	32	k−1kψ)(z	k−1kψ)(z	INTJ
ap-2101	254	33	)	)	PUNCT
ap-2101	254	34	=	=	SYM
ap-2101	254	35	ψ(z	ψ(z	PROPN
ap-2101	254	36	)	)	PUNCT
ap-2101	254	37	.	.	PUNCT
ap-2101	255	1	(	(	PUNCT
ap-2101	255	2	3.20	3.20	NUM
ap-2101	255	3	)	)	PUNCT
ap-2101	255	4	therefore	therefore	ADV
ap-2101	255	5	,	,	PUNCT
ap-2101	255	6	the	the	DET
ap-2101	255	7	transformation	transformation	NOUN
ap-2101	255	8	k	k	PROPN
ap-2101	255	9	with	with	ADP
ap-2101	255	10	the	the	DET
ap-2101	255	11	eigenfunctions	eigenfunction	NOUN
ap-2101	255	12	given	give	VERB
ap-2101	255	13	as	as	ADP
ap-2101	255	14	in	in	ADP
ap-2101	255	15	(	(	PUNCT
ap-2101	255	16	3.12	3.12	NUM
ap-2101	255	17	)	)	PUNCT
ap-2101	255	18	provide	provide	VERB
ap-2101	255	19	a	a	DET
ap-2101	255	20	complete	complete	ADJ
ap-2101	255	21	spectral	spectral	ADJ
ap-2101	255	22	representation	representation	NOUN
ap-2101	255	23	of	of	ADP
ap-2101	255	24	∆h2	∆h2	NOUN
ap-2101	255	25	.	.	PUNCT
ap-2101	256	1	3.2	3.2	NUM
ap-2101	256	2	.	.	PUNCT
ap-2101	256	3	formulation	formulation	NOUN
ap-2101	256	4	of	of	ADP
ap-2101	256	5	the	the	DET
ap-2101	256	6	problem	problem	NOUN
ap-2101	256	7	as	as	ADP
ap-2101	256	8	in	in	ADP
ap-2101	256	9	the	the	DET
ap-2101	256	10	flat	flat	ADJ
ap-2101	256	11	case	case	NOUN
ap-2101	256	12	we	we	PRON
ap-2101	256	13	consider	consider	VERB
ap-2101	256	14	a	a	DET
ap-2101	256	15	particle	particle	NOUN
ap-2101	256	16	of	of	ADP
ap-2101	256	17	mass	mass	NOUN
ap-2101	256	18	m	m	AUX
ap-2101	256	19	interacting	interact	VERB
ap-2101	256	20	with	with	ADP
ap-2101	256	21	a	a	DET
ap-2101	256	22	dirac	dirac	NOUN
ap-2101	256	23	-	-	PUNCT
ap-2101	256	24	delta	delta	NOUN
ap-2101	256	25	potential	potential	NOUN
ap-2101	256	26	on	on	ADP
ap-2101	256	27	the	the	DET
ap-2101	256	28	hyperbolic	hyperbolic	ADJ
ap-2101	256	29	plane	plane	NOUN
ap-2101	256	30	h2	h2	NOUN
ap-2101	256	31	.	.	PUNCT
ap-2101	257	1	let	let	VERB
ap-2101	257	2	z0	z0	PROPN
ap-2101	257	3	=	=	SYM
ap-2101	257	4	(	(	PUNCT
ap-2101	257	5	x0	x0	PROPN
ap-2101	257	6	,	,	PUNCT
ap-2101	257	7	y0	y0	PROPN
ap-2101	257	8	)	)	PUNCT
ap-2101	257	9	,	,	PUNCT
ap-2101	257	10	y0	y0	PROPN
ap-2101	257	11	6=	6=	SYM
ap-2101	257	12	0	0	NUM
ap-2101	257	13	denote	denote	VERB
ap-2101	257	14	the	the	DET
ap-2101	257	15	location	location	NOUN
ap-2101	257	16	of	of	ADP
ap-2101	257	17	the	the	DET
ap-2101	257	18	dirac	dirac	NOUN
ap-2101	257	19	-	-	PUNCT
ap-2101	257	20	delta	delta	NOUN
ap-2101	257	21	potential	potential	NOUN
ap-2101	257	22	.	.	PUNCT
ap-2101	258	1	the	the	DET
ap-2101	258	2	corresponding	correspond	VERB
ap-2101	258	3	schrödinger	schrödinger	ADJ
ap-2101	258	4	equation	equation	NOUN
ap-2101	258	5	for	for	ADP
ap-2101	258	6	the	the	DET
ap-2101	258	7	bound	bind	VERB
ap-2101	258	8	state	state	NOUN
ap-2101	258	9	is	be	AUX
ap-2101	258	10	written	write	VERB
ap-2101	258	11	in	in	ADP
ap-2101	258	12	coordinates	coordinate	NOUN
ap-2101	258	13	~	~	PUNCT
ap-2101	259	1	=	=	SYM
ap-2101	259	2	1	1	NUM
ap-2101	259	3	,	,	PUNCT
ap-2101	259	4	2	2	NUM
ap-2101	259	5	m	m	NOUN
ap-2101	259	6	=	=	NOUN
ap-2101	259	7	1	1	NUM
ap-2101	259	8	as	as	ADP
ap-2101	259	9	(	(	PUNCT
ap-2101	259	10	−∆h2	−∆h2	NOUN
ap-2101	259	11	−	−	NOUN
ap-2101	259	12	gδh2(z	gδh2(z	NOUN
ap-2101	259	13	,	,	PUNCT
ap-2101	259	14	z0))φ(z	z0))φ(z	NOUN
ap-2101	259	15	)	)	PUNCT
ap-2101	259	16	=	=	SYM
ap-2101	259	17	−ν2φ(z	−ν2φ(z	NOUN
ap-2101	259	18	)	)	PUNCT
ap-2101	259	19	.	.	PUNCT
ap-2101	260	1	(	(	PUNCT
ap-2101	260	2	3.21	3.21	NUM
ap-2101	260	3	)	)	PUNCT
ap-2101	260	4	on	on	ADP
ap-2101	260	5	a	a	DET
ap-2101	260	6	riemannian	riemannian	ADJ
ap-2101	260	7	manifold	manifold	NOUN
ap-2101	260	8	(	(	PUNCT
ap-2101	260	9	m	m	PROPN
ap-2101	260	10	,	,	PUNCT
ap-2101	260	11	g	g	NOUN
ap-2101	260	12	)	)	PUNCT
ap-2101	260	13	the	the	DET
ap-2101	260	14	dirac	dirac	PROPN
ap-2101	260	15	delta	delta	NOUN
ap-2101	260	16	function	function	NOUN
ap-2101	260	17	δg(z	δg(z	NUM
ap-2101	260	18	,	,	PUNCT
ap-2101	260	19	z0	z0	PROPN
ap-2101	260	20	)	)	PUNCT
ap-2101	260	21	is	be	AUX
ap-2101	260	22	defined	define	VERB
ap-2101	260	23	such	such	ADJ
ap-2101	260	24	that∫	that∫	NOUN
ap-2101	260	25	m	m	NOUN
ap-2101	260	26	dvg(z	dvg(z	PROPN
ap-2101	260	27	)	)	PUNCT
ap-2101	260	28	δg(z	δg(z	NUM
ap-2101	260	29	,	,	PUNCT
ap-2101	260	30	z0	z0	PROPN
ap-2101	260	31	)	)	PUNCT
ap-2101	260	32	=	=	NOUN
ap-2101	260	33	1	1	NUM
ap-2101	260	34	for	for	ADP
ap-2101	260	35	all	all	DET
ap-2101	260	36	z0	z0	PROPN
ap-2101	260	37	∈m	∈m	NOUN
ap-2101	260	38	.	.	PUNCT
ap-2101	261	1	(	(	PUNCT
ap-2101	261	2	3.22	3.22	NUM
ap-2101	261	3	)	)	PUNCT
ap-2101	261	4	thus	thus	ADV
ap-2101	261	5	δh2(z	δh2(z	PROPN
ap-2101	261	6	,	,	PUNCT
ap-2101	261	7	z0	z0	PROPN
ap-2101	261	8	)	)	PUNCT
ap-2101	261	9	is	be	AUX
ap-2101	261	10	given	give	VERB
ap-2101	261	11	by	by	ADP
ap-2101	261	12	δh2(z	δh2(z	PROPN
ap-2101	261	13	,	,	PUNCT
ap-2101	261	14	z0	z0	PROPN
ap-2101	261	15	)	)	PUNCT
ap-2101	261	16	=	=	PUNCT
ap-2101	261	17	y2	y2	NOUN
ap-2101	261	18	r2	r2	PROPN
ap-2101	261	19	δ(x	δ(x	PROPN
ap-2101	261	20	,	,	PUNCT
ap-2101	261	21	x0)δ(y	x0)δ(y	PROPN
ap-2101	261	22	,	,	PUNCT
ap-2101	261	23	y0	y0	NOUN
ap-2101	261	24	)	)	PUNCT
ap-2101	261	25	.	.	PUNCT
ap-2101	262	1	(	(	PUNCT
ap-2101	262	2	3.23	3.23	NUM
ap-2101	262	3	)	)	PUNCT
ap-2101	262	4	since	since	SCONJ
ap-2101	262	5	k	k	PROPN
ap-2101	262	6	is	be	AUX
ap-2101	262	7	an	an	DET
ap-2101	262	8	isomorphism	isomorphism	NOUN
ap-2101	262	9	we	we	PRON
ap-2101	262	10	can	can	AUX
ap-2101	262	11	write	write	VERB
ap-2101	262	12	(	(	PUNCT
ap-2101	262	13	3.21	3.21	NUM
ap-2101	262	14	)	)	PUNCT
ap-2101	262	15	as	as	ADP
ap-2101	262	16	−k∆h2k−1φ̃(τ	−k∆h2k−1φ̃(τ	PROPN
ap-2101	262	17	,	,	PUNCT
ap-2101	262	18	ξ)−	ξ)−	PROPN
ap-2101	262	19	gkδh2(z	gkδh2(z	NOUN
ap-2101	262	20	,	,	PUNCT
ap-2101	262	21	z0)k−1φ̃(τ	z0)k−1φ̃(τ	PROPN
ap-2101	262	22	,	,	PUNCT
ap-2101	262	23	ξ	ξ	X
ap-2101	262	24	)	)	PUNCT
ap-2101	262	25	=	=	SYM
ap-2101	262	26	−ν2φ̃(τ	−ν2φ̃(τ	PROPN
ap-2101	262	27	,	,	PUNCT
ap-2101	262	28	ξ	ξ	NOUN
ap-2101	262	29	)	)	PUNCT
ap-2101	262	30	.	.	PUNCT
ap-2101	263	1	(	(	PUNCT
ap-2101	263	2	3.24	3.24	NUM
ap-2101	263	3	)	)	PUNCT
ap-2101	263	4	the	the	DET
ap-2101	263	5	first	first	ADJ
ap-2101	263	6	term	term	NOUN
ap-2101	263	7	can	can	AUX
ap-2101	263	8	be	be	AUX
ap-2101	263	9	read	read	VERB
ap-2101	263	10	directly	directly	ADV
ap-2101	263	11	from	from	ADP
ap-2101	263	12	(	(	PUNCT
ap-2101	263	13	3.17	3.17	NUM
ap-2101	263	14	)	)	PUNCT
ap-2101	263	15	,	,	PUNCT
ap-2101	263	16	which	which	PRON
ap-2101	263	17	is	be	AUX
ap-2101	263	18	−k∆h2k−1φ̃(τ	−k∆h2k−1φ̃(τ	PROPN
ap-2101	263	19	,	,	PUNCT
ap-2101	263	20	ξ	ξ	NOUN
ap-2101	263	21	)	)	PUNCT
ap-2101	263	22	=	=	SYM
ap-2101	263	23	1	1	NUM
ap-2101	263	24	r2	r2	NOUN
ap-2101	263	25	(	(	PUNCT
ap-2101	263	26	τ2	τ2	NOUN
ap-2101	263	27	+	+	NOUN
ap-2101	263	28	1	1	NUM
ap-2101	263	29	4	4	NUM
ap-2101	263	30	)	)	PUNCT
ap-2101	263	31	φ̃(τ	φ̃(τ	NOUN
ap-2101	263	32	,	,	PUNCT
ap-2101	263	33	ξ	ξ	NOUN
ap-2101	263	34	)	)	PUNCT
ap-2101	263	35	.	.	PUNCT
ap-2101	264	1	(	(	PUNCT
ap-2101	264	2	3.25	3.25	NUM
ap-2101	264	3	)	)	PUNCT
ap-2101	264	4	the	the	DET
ap-2101	264	5	second	second	ADJ
ap-2101	264	6	term	term	NOUN
ap-2101	264	7	can	can	AUX
ap-2101	264	8	be	be	AUX
ap-2101	264	9	easily	easily	ADV
ap-2101	264	10	calculated	calculate	VERB
ap-2101	264	11	using	use	VERB
ap-2101	264	12	δh2(z	δh2(z	NOUN
ap-2101	264	13	,	,	PUNCT
ap-2101	264	14	z0	z0	PROPN
ap-2101	264	15	)	)	PUNCT
ap-2101	264	16	.	.	PUNCT
ap-2101	265	1	the	the	DET
ap-2101	265	2	result	result	NOUN
ap-2101	265	3	is	be	AUX
ap-2101	265	4	gkδh2(z	gkδh2(z	NOUN
ap-2101	265	5	,	,	PUNCT
ap-2101	265	6	z0)k−1φ̃(τ	z0)k−1φ̃(τ	PROPN
ap-2101	265	7	,	,	PUNCT
ap-2101	265	8	ξ	ξ	X
ap-2101	265	9	)	)	PUNCT
ap-2101	265	10	=	=	SYM
ap-2101	266	1	2	2	NUM
ap-2101	266	2	g	g	NOUN
ap-2101	266	3	π2r2	π2r2	X
ap-2101	266	4	∫	∫	PROPN
ap-2101	266	5	∞	∞	PROPN
ap-2101	266	6	0	0	NUM
ap-2101	266	7	dτ	dτ	NOUN
ap-2101	267	1	′	′	NUM
ap-2101	267	2	τ	τ	PROPN
ap-2101	267	3	′	′	NUM
ap-2101	267	4	sinh(πτ	sinh(πτ	PROPN
ap-2101	267	5	′	′	NOUN
ap-2101	267	6	)	)	PUNCT
ap-2101	267	7	∫	∫	PROPN
ap-2101	267	8	r	r	NOUN
ap-2101	267	9	dξ′e0(z0	dξ′e0(z0	PROPN
ap-2101	267	10	,	,	PUNCT
ap-2101	267	11	τ	τ	X
ap-2101	267	12	,	,	PUNCT
ap-2101	267	13	ξ)e0(z0	ξ)e0(z0	PROPN
ap-2101	267	14	,	,	PUNCT
ap-2101	267	15	τ	τ	PROPN
ap-2101	267	16	′	′	NUM
ap-2101	267	17	,	,	PUNCT
ap-2101	267	18	ξ′)φ̃(τ	ξ′)φ̃(τ	PROPN
ap-2101	267	19	′	′	NOUN
ap-2101	267	20	,	,	PUNCT
ap-2101	267	21	ξ′	ξ′	NOUN
ap-2101	267	22	)	)	PUNCT
ap-2101	267	23	.	.	PUNCT
ap-2101	268	1	(	(	PUNCT
ap-2101	268	2	3.26	3.26	NUM
ap-2101	268	3	)	)	PUNCT
ap-2101	268	4	if	if	SCONJ
ap-2101	268	5	we	we	PRON
ap-2101	268	6	put	put	VERB
ap-2101	268	7	(	(	PUNCT
ap-2101	268	8	3.25	3.25	NUM
ap-2101	268	9	)	)	PUNCT
ap-2101	268	10	and	and	CCONJ
ap-2101	268	11	(	(	PUNCT
ap-2101	268	12	3.26	3.26	NUM
ap-2101	268	13	)	)	PUNCT
ap-2101	268	14	into	into	ADP
ap-2101	268	15	(	(	PUNCT
ap-2101	268	16	3.21	3.21	NUM
ap-2101	268	17	)	)	PUNCT
ap-2101	268	18	and	and	CCONJ
ap-2101	268	19	rearrange	rearrange	VERB
ap-2101	268	20	the	the	DET
ap-2101	268	21	terms	term	NOUN
ap-2101	268	22	we	we	PRON
ap-2101	268	23	obtain	obtain	VERB
ap-2101	268	24	(	(	PUNCT
ap-2101	268	25	τ2	τ2	NOUN
ap-2101	268	26	+	+	CCONJ
ap-2101	268	27	a2	a2	PROPN
ap-2101	268	28	)	)	PUNCT
ap-2101	268	29	φ̃(τ	φ̃(τ	PROPN
ap-2101	268	30	,	,	PUNCT
ap-2101	268	31	ξ	ξ	NOUN
ap-2101	268	32	)	)	PUNCT
ap-2101	268	33	=	=	SYM
ap-2101	268	34	2	2	NUM
ap-2101	268	35	g	g	NOUN
ap-2101	268	36	π2	π2	ADJ
ap-2101	268	37	∫	∫	PROPN
ap-2101	268	38	∞	∞	PROPN
ap-2101	268	39	0	0	NUM
ap-2101	269	1	dτ	dτ	NOUN
ap-2101	270	1	′	′	NUM
ap-2101	270	2	τ	τ	PROPN
ap-2101	270	3	′	′	NUM
ap-2101	270	4	sinh(πτ	sinh(πτ	PROPN
ap-2101	270	5	′	′	NOUN
ap-2101	270	6	)	)	PUNCT
ap-2101	270	7	∫	∫	PROPN
ap-2101	270	8	r	r	NOUN
ap-2101	270	9	dξ′e0(z0	dξ′e0(z0	PROPN
ap-2101	270	10	,	,	PUNCT
ap-2101	270	11	τ	τ	X
ap-2101	270	12	,	,	PUNCT
ap-2101	270	13	ξ)e0(z0	ξ)e0(z0	PROPN
ap-2101	270	14	,	,	PUNCT
ap-2101	270	15	τ	τ	PROPN
ap-2101	270	16	′	′	NUM
ap-2101	270	17	,	,	PUNCT
ap-2101	270	18	ξ′)φ̃(τ	ξ′)φ̃(τ	PROPN
ap-2101	270	19	′	′	NOUN
ap-2101	270	20	,	,	PUNCT
ap-2101	270	21	ξ′	ξ′	NOUN
ap-2101	270	22	)	)	PUNCT
ap-2101	270	23	,	,	PUNCT
ap-2101	270	24	(	(	PUNCT
ap-2101	270	25	3.27	3.27	NUM
ap-2101	270	26	)	)	PUNCT
ap-2101	270	27	where	where	SCONJ
ap-2101	270	28	we	we	PRON
ap-2101	270	29	made	make	VERB
ap-2101	270	30	the	the	DET
ap-2101	270	31	definition	definition	NOUN
ap-2101	270	32	a2	a2	PROPN
ap-2101	270	33	≡	≡	PROPN
ap-2101	270	34	1	1	NUM
ap-2101	270	35	4	4	NUM
ap-2101	270	36	+	+	CCONJ
ap-2101	270	37	ν2r2	ν2r2	VERB
ap-2101	270	38	.	.	PUNCT
ap-2101	271	1	our	our	PRON
ap-2101	271	2	next	next	ADJ
ap-2101	271	3	goal	goal	NOUN
ap-2101	271	4	is	be	AUX
ap-2101	271	5	to	to	PART
ap-2101	271	6	determine	determine	VERB
ap-2101	271	7	the	the	DET
ap-2101	271	8	type	type	NOUN
ap-2101	271	9	and	and	CCONJ
ap-2101	271	10	the	the	DET
ap-2101	271	11	cause	cause	NOUN
ap-2101	271	12	of	of	ADP
ap-2101	271	13	the	the	DET
ap-2101	271	14	divergence	divergence	NOUN
ap-2101	271	15	.	.	PUNCT
ap-2101	272	1	to	to	ADP
ap-2101	272	2	this	this	DET
ap-2101	272	3	end	end	NOUN
ap-2101	272	4	we	we	PRON
ap-2101	272	5	make	make	VERB
ap-2101	272	6	an	an	DET
ap-2101	272	7	attempt	attempt	NOUN
ap-2101	272	8	to	to	PART
ap-2101	272	9	solve	solve	VERB
ap-2101	272	10	(	(	PUNCT
ap-2101	272	11	3.27	3.27	NUM
ap-2101	272	12	)	)	PUNCT
ap-2101	272	13	.	.	PUNCT
ap-2101	273	1	we	we	PRON
ap-2101	273	2	define	define	VERB
ap-2101	273	3	n	n	DET
ap-2101	273	4	≡	≡	PROPN
ap-2101	273	5	∫	∫	PROPN
ap-2101	273	6	∞	∞	PROPN
ap-2101	273	7	0	0	NUM
ap-2101	274	1	dτ	dτ	NOUN
ap-2101	275	1	′	′	NUM
ap-2101	275	2	τ	τ	PROPN
ap-2101	275	3	′	′	NUM
ap-2101	275	4	sinh(πτ	sinh(πτ	PROPN
ap-2101	275	5	′	′	NOUN
ap-2101	275	6	)	)	PUNCT
ap-2101	275	7	∫	∫	PROPN
ap-2101	275	8	r	r	NOUN
ap-2101	275	9	dξ′e0(z0	dξ′e0(z0	PROPN
ap-2101	275	10	,	,	PUNCT
ap-2101	275	11	τ	τ	PROPN
ap-2101	275	12	′	′	NUM
ap-2101	275	13	,	,	PUNCT
ap-2101	275	14	ξ′)φ̃(τ	ξ′)φ̃(τ	PROPN
ap-2101	275	15	′	′	NOUN
ap-2101	275	16	,	,	PUNCT
ap-2101	275	17	ξ′	ξ′	NOUN
ap-2101	275	18	)	)	PUNCT
ap-2101	275	19	.	.	PUNCT
ap-2101	276	1	(	(	PUNCT
ap-2101	276	2	3.28	3.28	NUM
ap-2101	276	3	)	)	PUNCT
ap-2101	276	4	164	164	NUM
ap-2101	276	5	vol	vol	NOUN
ap-2101	276	6	.	.	PUNCT
ap-2101	277	1	54	54	NUM
ap-2101	277	2	no	no	NOUN
ap-2101	277	3	.	.	PUNCT
ap-2101	278	1	2/2014	2/2014	NUM
ap-2101	278	2	exact	exact	ADJ
ap-2101	278	3	renormalization	renormalization	NOUN
ap-2101	278	4	group	group	NOUN
ap-2101	278	5	for	for	ADP
ap-2101	278	6	point	point	NOUN
ap-2101	278	7	interactions	interaction	NOUN
ap-2101	278	8	then	then	ADV
ap-2101	278	9	φ̃(τ	φ̃(τ	NOUN
ap-2101	278	10	,	,	PUNCT
ap-2101	278	11	ξ	ξ	X
ap-2101	278	12	)	)	PUNCT
ap-2101	278	13	becomes	become	VERB
ap-2101	278	14	φ̃(τ	φ̃(τ	NOUN
ap-2101	278	15	,	,	PUNCT
ap-2101	278	16	ξ	ξ	NOUN
ap-2101	278	17	)	)	PUNCT
ap-2101	278	18	=	=	SYM
ap-2101	278	19	2	2	NUM
ap-2101	278	20	g	g	NOUN
ap-2101	278	21	π2ne0(z0	π2ne0(z0	NOUN
ap-2101	278	22	,	,	PUNCT
ap-2101	278	23	τ	τ	PROPN
ap-2101	278	24	,	,	PUNCT
ap-2101	278	25	ξ	ξ	X
ap-2101	278	26	)	)	PUNCT
ap-2101	278	27	(	(	PUNCT
ap-2101	278	28	τ2	τ2	NOUN
ap-2101	278	29	+	+	NOUN
ap-2101	278	30	a2)−1	a2)−1	NOUN
ap-2101	278	31	.	.	PUNCT
ap-2101	279	1	(	(	PUNCT
ap-2101	279	2	3.29	3.29	NUM
ap-2101	279	3	)	)	PUNCT
ap-2101	279	4	we	we	PRON
ap-2101	279	5	put	put	VERB
ap-2101	279	6	this	this	DET
ap-2101	279	7	result	result	NOUN
ap-2101	279	8	back	back	ADV
ap-2101	279	9	into	into	ADP
ap-2101	279	10	(	(	PUNCT
ap-2101	279	11	3.28	3.28	NUM
ap-2101	279	12	)	)	PUNCT
ap-2101	279	13	and	and	CCONJ
ap-2101	279	14	find	find	VERB
ap-2101	279	15	1	1	NUM
ap-2101	279	16	g	g	NOUN
ap-2101	279	17	=	=	SYM
ap-2101	279	18	2	2	NUM
ap-2101	280	1	π2	π2	NUM
ap-2101	280	2	∫	∫	PROPN
ap-2101	280	3	∞	∞	PROPN
ap-2101	280	4	0	0	NUM
ap-2101	280	5	dτ	dτ	NOUN
ap-2101	281	1	′	′	NUM
ap-2101	281	2	τ	τ	PROPN
ap-2101	281	3	′	′	NUM
ap-2101	281	4	sinh(πτ	sinh(πτ	PROPN
ap-2101	281	5	′	′	NOUN
ap-2101	281	6	)	)	PUNCT
ap-2101	281	7	(	(	PUNCT
ap-2101	281	8	τ	τ	X
ap-2101	281	9	′2	′2	X
ap-2101	281	10	+	+	NUM
ap-2101	281	11	a2)−1	a2)−1	ADJ
ap-2101	281	12	∫	∫	PROPN
ap-2101	281	13	r	r	NOUN
ap-2101	281	14	dξ′e0(z0	dξ′e0(z0	PROPN
ap-2101	281	15	,	,	PUNCT
ap-2101	281	16	τ	τ	PROPN
ap-2101	281	17	′	′	NUM
ap-2101	281	18	,	,	PUNCT
ap-2101	281	19	ξ′)e0(z0	ξ′)e0(z0	X
ap-2101	281	20	,	,	PUNCT
ap-2101	281	21	τ	τ	PROPN
ap-2101	281	22	′	′	NUM
ap-2101	281	23	,	,	PUNCT
ap-2101	281	24	ξ′	ξ′	NOUN
ap-2101	281	25	)	)	PUNCT
ap-2101	281	26	.	.	PUNCT
ap-2101	282	1	(	(	PUNCT
ap-2101	282	2	3.30	3.30	NUM
ap-2101	282	3	)	)	PUNCT
ap-2101	282	4	let	let	VERB
ap-2101	282	5	us	we	PRON
ap-2101	282	6	denote	denote	VERB
ap-2101	282	7	the	the	DET
ap-2101	282	8	ξ	ξ	NOUN
ap-2101	282	9	-	-	NOUN
ap-2101	282	10	integral	integral	ADJ
ap-2101	282	11	by	by	ADP
ap-2101	282	12	υ(τ	υ(τ	PROPN
ap-2101	282	13	′	′	NUM
ap-2101	282	14	)	)	PUNCT
ap-2101	282	15	.	.	PUNCT
ap-2101	283	1	using	use	VERB
ap-2101	283	2	the	the	DET
ap-2101	283	3	explicit	explicit	ADJ
ap-2101	283	4	form	form	NOUN
ap-2101	283	5	of	of	ADP
ap-2101	283	6	the	the	DET
ap-2101	283	7	eigenfunctions	eigenfunction	NOUN
ap-2101	283	8	as	as	SCONJ
ap-2101	283	9	given	give	VERB
ap-2101	283	10	in	in	ADP
ap-2101	283	11	(	(	PUNCT
ap-2101	283	12	3.12	3.12	NUM
ap-2101	283	13	)	)	PUNCT
ap-2101	283	14	we	we	PRON
ap-2101	283	15	can	can	AUX
ap-2101	283	16	write	write	VERB
ap-2101	283	17	υ(τ	υ(τ	PROPN
ap-2101	283	18	′	′	NUM
ap-2101	283	19	)	)	PUNCT
ap-2101	283	20	as	as	ADP
ap-2101	283	21	υ(τ	υ(τ	PROPN
ap-2101	283	22	′	′	NUM
ap-2101	283	23	)	)	PUNCT
ap-2101	284	1	=	=	SYM
ap-2101	285	1	y0	y0	NOUN
ap-2101	285	2	2π	2π	NUM
ap-2101	285	3	∫	∫	NOUN
ap-2101	285	4	r	r	NOUN
ap-2101	285	5	dξ′kiτ	dξ′kiτ	PUNCT
ap-2101	285	6	′(y0	′(y0	NUM
ap-2101	285	7	|ξ|)k−iτ	|ξ|)k−iτ	NOUN
ap-2101	285	8	′(y0	′(y0	NUM
ap-2101	285	9	|ξ|	|ξ|	PROPN
ap-2101	285	10	)	)	PUNCT
ap-2101	285	11	=	=	PUNCT
ap-2101	286	1	y0	y0	NOUN
ap-2101	286	2	π	π	NOUN
ap-2101	286	3	∫	∫	PROPN
ap-2101	286	4	∞	∞	NOUN
ap-2101	286	5	0	0	PUNCT
ap-2101	287	1	dξ′kiτ	dξ′kiτ	ADJ
ap-2101	287	2	′(y0ξ)kiτ	′(y0ξ)kiτ	NUM
ap-2101	287	3	′(y0ξ	′(y0ξ	NOUN
ap-2101	287	4	)	)	PUNCT
ap-2101	287	5	(	(	PUNCT
ap-2101	287	6	3.31	3.31	NUM
ap-2101	287	7	)	)	PUNCT
ap-2101	287	8	to	to	PART
ap-2101	287	9	evaluate	evaluate	VERB
ap-2101	287	10	the	the	DET
ap-2101	287	11	integral	integral	ADJ
ap-2101	287	12	we	we	PRON
ap-2101	287	13	will	will	AUX
ap-2101	287	14	use	use	VERB
ap-2101	287	15	the	the	DET
ap-2101	287	16	following	follow	VERB
ap-2101	287	17	integral	integral	ADJ
ap-2101	287	18	representation	representation	NOUN
ap-2101	287	19	of	of	ADP
ap-2101	287	20	the	the	DET
ap-2101	287	21	modified	modify	VERB
ap-2101	287	22	bessel	bessel	NOUN
ap-2101	287	23	functions	function	NOUN
ap-2101	287	24	[	[	X
ap-2101	287	25	3	3	NUM
ap-2101	287	26	]	]	X
ap-2101	287	27	:	:	PUNCT
ap-2101	287	28	kν(z	kν(z	X
ap-2101	287	29	)	)	PUNCT
ap-2101	288	1	=	=	SYM
ap-2101	288	2	∫	∫	PROPN
ap-2101	289	1	∞	∞	NUM
ap-2101	289	2	0	0	NUM
ap-2101	289	3	du	du	PROPN
ap-2101	289	4	e−z	e−z	PROPN
ap-2101	289	5	coshu	coshu	PROPN
ap-2101	289	6	cosh(νu	cosh(νu	PROPN
ap-2101	289	7	)	)	PUNCT
ap-2101	289	8	,	,	PUNCT
ap-2101	289	9	re	re	VERB
ap-2101	289	10	z	z	NOUN
ap-2101	289	11	>	>	X
ap-2101	289	12	0	0	PUNCT
ap-2101	289	13	(	(	PUNCT
ap-2101	289	14	3.32	3.32	NUM
ap-2101	289	15	)	)	PUNCT
ap-2101	289	16	therefore	therefore	ADV
ap-2101	289	17	υ(τ	υ(τ	PROPN
ap-2101	289	18	′	′	NOUN
ap-2101	289	19	)	)	PUNCT
ap-2101	289	20	becomes	become	VERB
ap-2101	289	21	υ(τ	υ(τ	PROPN
ap-2101	289	22	′	′	NUM
ap-2101	289	23	)	)	PUNCT
ap-2101	290	1	=	=	SYM
ap-2101	290	2	y0	y0	NOUN
ap-2101	290	3	π	π	NOUN
ap-2101	290	4	∫	∫	PROPN
ap-2101	290	5	∞	∞	NUM
ap-2101	290	6	0	0	NUM
ap-2101	291	1	dξ	dξ	PROPN
ap-2101	291	2	∫	∫	PROPN
ap-2101	292	1	∞	∞	PROPN
ap-2101	292	2	0	0	NUM
ap-2101	292	3	du	du	PROPN
ap-2101	292	4	∫	∫	PROPN
ap-2101	292	5	∞	∞	PROPN
ap-2101	292	6	0	0	NUM
ap-2101	293	1	dv	dv	PROPN
ap-2101	293	2	e−y0ξ(coshu+cosh	e−y0ξ(coshu+cosh	PROPN
ap-2101	293	3	v	v	NOUN
ap-2101	293	4	)	)	PUNCT
ap-2101	293	5	cosh(iτ	cosh(iτ	PROPN
ap-2101	293	6	′u	′u	NOUN
ap-2101	293	7	)	)	PUNCT
ap-2101	293	8	cosh(iτ	cosh(iτ	PROPN
ap-2101	293	9	′v	′v	PROPN
ap-2101	293	10	)	)	PUNCT
ap-2101	293	11	=	=	SYM
ap-2101	294	1	y0	y0	NOUN
ap-2101	294	2	π	π	NOUN
ap-2101	294	3	∫	∫	PROPN
ap-2101	294	4	∞	∞	NUM
ap-2101	294	5	0	0	NUM
ap-2101	294	6	du	du	PROPN
ap-2101	294	7	∫	∫	PROPN
ap-2101	294	8	∞	∞	PROPN
ap-2101	294	9	0	0	PROPN
ap-2101	295	1	dv	dv	PROPN
ap-2101	295	2	cos(τ	cos(τ	PROPN
ap-2101	295	3	′u	′u	PROPN
ap-2101	295	4	)	)	PUNCT
ap-2101	295	5	cos(τ	cos(τ	PROPN
ap-2101	295	6	′v	′v	PROPN
ap-2101	295	7	)	)	PUNCT
ap-2101	295	8	∫	∫	PROPN
ap-2101	296	1	∞	∞	PROPN
ap-2101	296	2	0	0	NUM
ap-2101	297	1	dξ	dξ	PROPN
ap-2101	297	2	e−y0ξ(coshu+cosh	e−y0ξ(coshu+cosh	PROPN
ap-2101	297	3	v	v	NOUN
ap-2101	297	4	)	)	PUNCT
ap-2101	297	5	=	=	SYM
ap-2101	298	1	1	1	NUM
ap-2101	298	2	π	π	NOUN
ap-2101	298	3	∫	∫	PROPN
ap-2101	298	4	∞	∞	NUM
ap-2101	298	5	0	0	NUM
ap-2101	298	6	du	du	PROPN
ap-2101	298	7	cos(τ	cos(τ	PROPN
ap-2101	298	8	′u	′u	PROPN
ap-2101	298	9	)	)	PUNCT
ap-2101	298	10	∫	∫	PROPN
ap-2101	298	11	∞	∞	PROPN
ap-2101	298	12	0	0	NUM
ap-2101	298	13	dv	dv	PROPN
ap-2101	298	14	cos(τ	cos(τ	PROPN
ap-2101	298	15	′v	′v	PROPN
ap-2101	298	16	)	)	PUNCT
ap-2101	298	17	cosh	cosh	PROPN
ap-2101	298	18	u+	u+	PUNCT
ap-2101	298	19	cosh	cosh	NOUN
ap-2101	298	20	v	v	NOUN
ap-2101	298	21	.	.	PUNCT
ap-2101	299	1	(	(	PUNCT
ap-2101	299	2	3.33	3.33	NUM
ap-2101	299	3	)	)	PUNCT
ap-2101	299	4	the	the	DET
ap-2101	299	5	dv	dv	PROPN
ap-2101	299	6	integral	integral	PROPN
ap-2101	299	7	can	can	AUX
ap-2101	299	8	be	be	AUX
ap-2101	299	9	evaluated	evaluate	VERB
ap-2101	299	10	using	use	VERB
ap-2101	299	11	the	the	DET
ap-2101	299	12	definite	definite	ADJ
ap-2101	299	13	integral	integral	ADJ
ap-2101	300	1	[	[	X
ap-2101	300	2	13]∫	13]∫	NUM
ap-2101	300	3	∞	∞	NUM
ap-2101	300	4	0	0	PUNCT
ap-2101	300	5	cos(ax)dx	cos(ax)dx	NOUN
ap-2101	300	6	b	b	PROPN
ap-2101	300	7	cosh(βx	cosh(βx	PROPN
ap-2101	300	8	)	)	PUNCT
ap-2101	301	1	+	+	PUNCT
ap-2101	301	2	c	c	NOUN
ap-2101	301	3	=	=	SYM
ap-2101	301	4	π	π	X
ap-2101	301	5	sin	sin	NOUN
ap-2101	301	6	(	(	PUNCT
ap-2101	301	7	a	a	PRON
ap-2101	301	8	β	β	X
ap-2101	301	9	cosh−1	cosh−1	X
ap-2101	301	10	(	(	PUNCT
ap-2101	301	11	c	c	NOUN
ap-2101	301	12	b	b	PROPN
ap-2101	301	13	)	)	PUNCT
ap-2101	301	14	)	)	PUNCT
ap-2101	301	15	β	β	X
ap-2101	301	16	√	√	PROPN
ap-2101	301	17	c2	c2	PROPN
ap-2101	301	18	−	−	PROPN
ap-2101	301	19	b2	b2	NOUN
ap-2101	301	20	sinh	sinh	NOUN
ap-2101	301	21	(	(	PUNCT
ap-2101	301	22	aπ	aπ	NOUN
ap-2101	301	23	β	β	NOUN
ap-2101	301	24	)	)	PUNCT
ap-2101	301	25	,	,	PUNCT
ap-2101	301	26	for	for	ADP
ap-2101	301	27	c	c	PROPN
ap-2101	301	28	>	>	X
ap-2101	301	29	b	b	X
ap-2101	301	30	>	>	X
ap-2101	301	31	0	0	NUM
ap-2101	301	32	.	.	PUNCT
ap-2101	301	33	(	(	PUNCT
ap-2101	301	34	3.34	3.34	NUM
ap-2101	301	35	)	)	PUNCT
ap-2101	301	36	in	in	ADP
ap-2101	301	37	our	our	PRON
ap-2101	301	38	case	case	NOUN
ap-2101	301	39	a	a	PRON
ap-2101	301	40	=	=	SYM
ap-2101	301	41	τ	τ	PROPN
ap-2101	301	42	′	′	NUM
ap-2101	301	43	,	,	PUNCT
ap-2101	301	44	b	b	NOUN
ap-2101	301	45	=	=	SYM
ap-2101	301	46	1	1	NUM
ap-2101	301	47	,	,	PUNCT
ap-2101	301	48	β	β	X
ap-2101	301	49	=	=	SYM
ap-2101	301	50	1	1	NUM
ap-2101	301	51	,	,	PUNCT
ap-2101	301	52	c	c	NOUN
ap-2101	301	53	=	=	SYM
ap-2101	301	54	cosh	cosh	PROPN
ap-2101	301	55	u	u	NOUN
ap-2101	301	56	and	and	CCONJ
ap-2101	301	57	cosh	cosh	PROPN
ap-2101	301	58	u	u	PROPN
ap-2101	301	59	≥	≥	NUM
ap-2101	301	60	1	1	NUM
ap-2101	301	61	>	>	SYM
ap-2101	301	62	0	0	NUM
ap-2101	301	63	,	,	PUNCT
ap-2101	301	64	for	for	ADP
ap-2101	301	65	all	all	DET
ap-2101	301	66	u	u	NOUN
ap-2101	301	67	∈	∈	PROPN
ap-2101	301	68	[	[	X
ap-2101	301	69	0,∞	0,∞	NOUN
ap-2101	301	70	)	)	PUNCT
ap-2101	301	71	so	so	SCONJ
ap-2101	301	72	we	we	PRON
ap-2101	301	73	can	can	AUX
ap-2101	301	74	use	use	VERB
ap-2101	301	75	(	(	PUNCT
ap-2101	301	76	3.34	3.34	NUM
ap-2101	301	77	)	)	PUNCT
ap-2101	301	78	.	.	PUNCT
ap-2101	302	1	hence	hence	ADV
ap-2101	302	2	dv	dv	PROPN
ap-2101	302	3	integral	integral	PROPN
ap-2101	302	4	becomes∫	becomes∫	VERB
ap-2101	302	5	∞	∞	PROPN
ap-2101	302	6	0	0	NUM
ap-2101	303	1	dv	dv	PROPN
ap-2101	303	2	cos(τ	cos(τ	PROPN
ap-2101	303	3	′v	′v	PROPN
ap-2101	303	4	)	)	PUNCT
ap-2101	303	5	cosh	cosh	PROPN
ap-2101	303	6	u+	u+	PRON
ap-2101	303	7	cosh	cosh	NOUN
ap-2101	303	8	v	v	NOUN
ap-2101	303	9	=	=	SYM
ap-2101	303	10	π	π	X
ap-2101	303	11	sin	sin	NOUN
ap-2101	303	12	(	(	PUNCT
ap-2101	303	13	τ	τ	PROPN
ap-2101	303	14	′	′	NUM
ap-2101	303	15	cosh−1(cosh	cosh−1(cosh	PROPN
ap-2101	303	16	u	u	NOUN
ap-2101	303	17	)	)	PUNCT
ap-2101	303	18	)	)	PUNCT
ap-2101	303	19	√	√	NUM
ap-2101	303	20	cosh2−1	cosh2−1	VERB
ap-2101	303	21	sinh(τ	sinh(τ	PROPN
ap-2101	303	22	′π	′π	PROPN
ap-2101	303	23	)	)	PUNCT
ap-2101	304	1	=	=	PUNCT
ap-2101	304	2	π	π	PROPN
ap-2101	304	3	sin(τ	sin(τ	PROPN
ap-2101	304	4	′u	′u	PROPN
ap-2101	304	5	)	)	PUNCT
ap-2101	304	6	sinh(u	sinh(u	NOUN
ap-2101	304	7	)	)	PUNCT
ap-2101	304	8	sinh(τ	sinh(τ	PROPN
ap-2101	304	9	′π	′π	PROPN
ap-2101	304	10	)	)	PUNCT
ap-2101	304	11	.	.	PUNCT
ap-2101	305	1	(	(	PUNCT
ap-2101	305	2	3.35	3.35	NUM
ap-2101	305	3	)	)	PUNCT
ap-2101	305	4	then	then	ADV
ap-2101	305	5	we	we	PRON
ap-2101	305	6	have	have	VERB
ap-2101	305	7	υ(τ	υ(τ	NOUN
ap-2101	305	8	′	′	NUM
ap-2101	305	9	)	)	PUNCT
ap-2101	306	1	=	=	SYM
ap-2101	306	2	1	1	NUM
ap-2101	306	3	sinh(τ	sinh(τ	NUM
ap-2101	306	4	′π	′π	PROPN
ap-2101	306	5	)	)	PUNCT
ap-2101	306	6	∫	∫	PROPN
ap-2101	307	1	∞	∞	PROPN
ap-2101	307	2	0	0	NUM
ap-2101	307	3	du	du	PROPN
ap-2101	307	4	cos(τ	cos(τ	PROPN
ap-2101	307	5	′u	′u	PROPN
ap-2101	307	6	)	)	PUNCT
ap-2101	307	7	sin(τ	sin(τ	PROPN
ap-2101	307	8	′u	′u	NOUN
ap-2101	307	9	)	)	PUNCT
ap-2101	307	10	sinh	sinh	NOUN
ap-2101	307	11	u	u	NOUN
ap-2101	307	12	.	.	PUNCT
ap-2101	308	1	(	(	PUNCT
ap-2101	308	2	3.36	3.36	NUM
ap-2101	308	3	)	)	PUNCT
ap-2101	308	4	finally	finally	ADV
ap-2101	308	5	we	we	PRON
ap-2101	308	6	will	will	AUX
ap-2101	308	7	use	use	VERB
ap-2101	308	8	[	[	PUNCT
ap-2101	308	9	13	13	NUM
ap-2101	308	10	]	]	PUNCT
ap-2101	308	11	∫	∫	PROPN
ap-2101	309	1	∞	∞	NUM
ap-2101	309	2	0	0	NUM
ap-2101	309	3	dx	dx	PROPN
ap-2101	309	4	sin(αx	sin(αx	NOUN
ap-2101	309	5	)	)	PUNCT
ap-2101	309	6	cos(βx	cos(βx	NOUN
ap-2101	309	7	)	)	PUNCT
ap-2101	309	8	sinh(γx	sinh(γx	NOUN
ap-2101	309	9	)	)	PUNCT
ap-2101	309	10	=	=	PUNCT
ap-2101	310	1	π	π	X
ap-2101	310	2	sinh	sinh	NOUN
ap-2101	310	3	(	(	PUNCT
ap-2101	310	4	πa	πa	ADP
ap-2101	310	5	γ	γ	PROPN
ap-2101	310	6	)	)	PUNCT
ap-2101	310	7	2γ	2γ	NOUN
ap-2101	310	8	(	(	PUNCT
ap-2101	310	9	cosh	cosh	NOUN
ap-2101	310	10	(	(	PUNCT
ap-2101	310	11	απ	απ	NOUN
ap-2101	310	12	γ	γ	PROPN
ap-2101	310	13	)	)	PUNCT
ap-2101	310	14	+	+	CCONJ
ap-2101	311	1	cosh	cosh	NOUN
ap-2101	311	2	(	(	PUNCT
ap-2101	311	3	βπ	βπ	NOUN
ap-2101	311	4	γ	γ	PROPN
ap-2101	311	5	)	)	PUNCT
ap-2101	311	6	)	)	PUNCT
ap-2101	311	7	(	(	PUNCT
ap-2101	311	8	3.37	3.37	NUM
ap-2101	311	9	)	)	PUNCT
ap-2101	311	10	for	for	ADP
ap-2101	311	11	i	i	PRON
ap-2101	311	12	m	m	PROPN
ap-2101	311	13	(	(	PUNCT
ap-2101	311	14	α+	α+	X
ap-2101	311	15	β	β	X
ap-2101	311	16	)	)	PUNCT
ap-2101	311	17	<	<	X
ap-2101	311	18	re	re	X
ap-2101	311	19	γ	γ	X
ap-2101	311	20	.	.	PROPN
ap-2101	311	21	in	in	ADP
ap-2101	311	22	our	our	PRON
ap-2101	311	23	case	case	NOUN
ap-2101	311	24	α	α	NOUN
ap-2101	311	25	=	=	PUNCT
ap-2101	311	26	β	β	X
ap-2101	311	27	=	=	SYM
ap-2101	311	28	τ	τ	PROPN
ap-2101	311	29	′	′	NUM
ap-2101	311	30	,	,	PUNCT
ap-2101	311	31	γ	γ	NOUN
ap-2101	311	32	=	=	SYM
ap-2101	311	33	1	1	NUM
ap-2101	311	34	and	and	CCONJ
ap-2101	311	35	τ	τ	NUM
ap-2101	311	36	′	′	NUM
ap-2101	311	37	∈	∈	PROPN
ap-2101	311	38	r	r	NOUN
ap-2101	311	39	,	,	PUNCT
ap-2101	311	40	therefore	therefore	ADV
ap-2101	311	41	i	i	PRON
ap-2101	311	42	m	m	VERB
ap-2101	311	43	(	(	PUNCT
ap-2101	311	44	α+	α+	X
ap-2101	311	45	β	β	X
ap-2101	311	46	)	)	PUNCT
ap-2101	311	47	=	=	SYM
ap-2101	311	48	0	0	PUNCT
ap-2101	311	49	<	<	X
ap-2101	311	50	1	1	X
ap-2101	311	51	.	.	PUNCT
ap-2101	312	1	thus∫	thus∫	NOUN
ap-2101	312	2	∞	∞	NUM
ap-2101	312	3	0	0	NUM
ap-2101	312	4	du	du	PROPN
ap-2101	312	5	cos(τ	cos(τ	PROPN
ap-2101	312	6	′u	′u	PROPN
ap-2101	312	7	)	)	PUNCT
ap-2101	312	8	sin(τ	sin(τ	PROPN
ap-2101	312	9	′u	′u	NOUN
ap-2101	312	10	)	)	PUNCT
ap-2101	312	11	sinh	sinh	NOUN
ap-2101	312	12	u	u	NOUN
ap-2101	312	13	=	=	PROPN
ap-2101	312	14	π	π	PROPN
ap-2101	312	15	sinh(πτ	sinh(πτ	PROPN
ap-2101	312	16	′	′	NUM
ap-2101	312	17	)	)	PUNCT
ap-2101	312	18	2	2	NUM
ap-2101	312	19	(	(	PUNCT
ap-2101	312	20	cosh(πτ	cosh(πτ	NOUN
ap-2101	312	21	′	′	NUM
ap-2101	312	22	)	)	PUNCT
ap-2101	313	1	+	+	CCONJ
ap-2101	313	2	cosh(πτ	cosh(πτ	NOUN
ap-2101	313	3	′	′	NUM
ap-2101	313	4	)	)	PUNCT
ap-2101	313	5	)	)	PUNCT
ap-2101	314	1	=	=	PUNCT
ap-2101	315	1	π	π	X
ap-2101	315	2	4	4	NUM
ap-2101	315	3	tanh(πτ	tanh(πτ	NUM
ap-2101	315	4	′	′	NUM
ap-2101	315	5	)	)	PUNCT
ap-2101	315	6	,	,	PUNCT
ap-2101	315	7	(	(	PUNCT
ap-2101	315	8	3.38	3.38	NUM
ap-2101	315	9	)	)	PUNCT
ap-2101	315	10	and	and	CCONJ
ap-2101	315	11	υ(τ	υ(τ	PROPN
ap-2101	315	12	′	′	NOUN
ap-2101	315	13	)	)	PUNCT
ap-2101	315	14	becomes	become	VERB
ap-2101	315	15	υ(τ	υ(τ	PROPN
ap-2101	315	16	′	′	NUM
ap-2101	315	17	)	)	PUNCT
ap-2101	316	1	=	=	SYM
ap-2101	316	2	∫	∫	PROPN
ap-2101	316	3	r	r	NOUN
ap-2101	316	4	dξ′e0(z0	dξ′e0(z0	PROPN
ap-2101	316	5	,	,	PUNCT
ap-2101	316	6	τ	τ	PROPN
ap-2101	316	7	′	′	NUM
ap-2101	316	8	,	,	PUNCT
ap-2101	316	9	ξ′)e0(z0	ξ′)e0(z0	X
ap-2101	316	10	,	,	PUNCT
ap-2101	316	11	τ	τ	PROPN
ap-2101	316	12	′	′	NUM
ap-2101	316	13	,	,	PUNCT
ap-2101	316	14	ξ′	ξ′	NOUN
ap-2101	316	15	)	)	PUNCT
ap-2101	316	16	=	=	PUNCT
ap-2101	317	1	π	π	X
ap-2101	317	2	4	4	NUM
ap-2101	317	3	tanh(πτ	tanh(πτ	NUM
ap-2101	317	4	′	′	NUM
ap-2101	317	5	)	)	PUNCT
ap-2101	317	6	sinh(πτ	sinh(πτ	NOUN
ap-2101	317	7	′	′	NOUN
ap-2101	317	8	)	)	PUNCT
ap-2101	317	9	.	.	PUNCT
ap-2101	318	1	(	(	PUNCT
ap-2101	318	2	3.39	3.39	NUM
ap-2101	318	3	)	)	PUNCT
ap-2101	318	4	finally	finally	ADV
ap-2101	318	5	we	we	PRON
ap-2101	318	6	put	put	VERB
ap-2101	318	7	this	this	DET
ap-2101	318	8	result	result	NOUN
ap-2101	318	9	into	into	ADP
ap-2101	318	10	(	(	PUNCT
ap-2101	318	11	3.30	3.30	NUM
ap-2101	318	12	)	)	PUNCT
ap-2101	318	13	and	and	CCONJ
ap-2101	318	14	obtain	obtain	VERB
ap-2101	318	15	1	1	NUM
ap-2101	318	16	g	g	NOUN
ap-2101	318	17	=	=	SYM
ap-2101	318	18	1	1	NUM
ap-2101	318	19	2π	2π	NUM
ap-2101	318	20	∫	∫	PROPN
ap-2101	319	1	∞	∞	NUM
ap-2101	319	2	0	0	NUM
ap-2101	319	3	dτ	dτ	NOUN
ap-2101	320	1	′	′	NUM
ap-2101	320	2	τ	τ	PROPN
ap-2101	320	3	′	′	NUM
ap-2101	320	4	tanh(πτ	tanh(πτ	NOUN
ap-2101	320	5	′	′	NUM
ap-2101	320	6	)	)	PUNCT
ap-2101	320	7	(	(	PUNCT
ap-2101	320	8	τ	τ	X
ap-2101	320	9	′2	′2	X
ap-2101	320	10	+	+	X
ap-2101	320	11	a2)−1	a2)−1	NOUN
ap-2101	320	12	.	.	PUNCT
ap-2101	321	1	(	(	PUNCT
ap-2101	321	2	3.40	3.40	NUM
ap-2101	321	3	)	)	PUNCT
ap-2101	321	4	for	for	ADP
ap-2101	321	5	large	large	ADJ
ap-2101	321	6	values	value	NOUN
ap-2101	321	7	of	of	ADP
ap-2101	321	8	τ	τ	PROPN
ap-2101	321	9	′	′	NUM
ap-2101	321	10	,	,	PUNCT
ap-2101	321	11	tanh(πτ	tanh(πτ	NOUN
ap-2101	321	12	′	′	NUM
ap-2101	321	13	)	)	PUNCT
ap-2101	322	1	≈	≈	PROPN
ap-2101	322	2	1	1	NUM
ap-2101	322	3	and	and	CCONJ
ap-2101	322	4	the	the	DET
ap-2101	322	5	integrand	integrand	NOUN
ap-2101	322	6	behaves	behave	VERB
ap-2101	322	7	as	as	ADP
ap-2101	322	8	1	1	NUM
ap-2101	322	9	/	/	SYM
ap-2101	322	10	τ	τ	PROPN
ap-2101	322	11	′	′	NUM
ap-2101	323	1	so	so	ADV
ap-2101	323	2	,	,	PUNCT
ap-2101	323	3	as	as	ADP
ap-2101	323	4	in	in	ADP
ap-2101	323	5	the	the	DET
ap-2101	323	6	flat	flat	ADJ
ap-2101	323	7	case	case	NOUN
ap-2101	323	8	,	,	PUNCT
ap-2101	323	9	we	we	PRON
ap-2101	323	10	face	face	VERB
ap-2101	323	11	with	with	ADP
ap-2101	323	12	a	a	DET
ap-2101	323	13	logarithmic	logarithmic	ADJ
ap-2101	323	14	divergence	divergence	NOUN
ap-2101	323	15	.	.	PUNCT
ap-2101	324	1	this	this	DET
ap-2101	324	2	analysis	analysis	NOUN
ap-2101	324	3	also	also	ADV
ap-2101	324	4	shows	show	VERB
ap-2101	324	5	us	we	PRON
ap-2101	324	6	that	that	SCONJ
ap-2101	324	7	there	there	PRON
ap-2101	324	8	is	be	VERB
ap-2101	324	9	no	no	DET
ap-2101	324	10	divergence	divergence	NOUN
ap-2101	324	11	in	in	ADP
ap-2101	324	12	the	the	DET
ap-2101	324	13	ξ	ξ	PROPN
ap-2101	324	14	term	term	NOUN
ap-2101	324	15	.	.	PUNCT
ap-2101	325	1	therefore	therefore	ADV
ap-2101	325	2	we	we	PRON
ap-2101	325	3	only	only	ADV
ap-2101	325	4	need	need	VERB
ap-2101	325	5	to	to	PART
ap-2101	325	6	concern	concern	VERB
ap-2101	325	7	ourselves	ourselves	PRON
ap-2101	325	8	with	with	ADP
ap-2101	325	9	the	the	DET
ap-2101	325	10	renormalization	renormalization	NOUN
ap-2101	325	11	of	of	ADP
ap-2101	325	12	τ	τ	PROPN
ap-2101	325	13	.	.	PUNCT
ap-2101	326	1	165	165	NUM
ap-2101	326	2	osman	osman	PROPN
ap-2101	326	3	teoman	teoman	NOUN
ap-2101	326	4	turgut	turgut	PROPN
ap-2101	326	5	,	,	PUNCT
ap-2101	326	6	cem	cem	NOUN
ap-2101	326	7	eröncel	eröncel	VERB
ap-2101	326	8	acta	acta	PROPN
ap-2101	326	9	polytechnica	polytechnica	PROPN
ap-2101	326	10	3.3	3.3	NUM
ap-2101	326	11	.	.	PUNCT
ap-2101	327	1	applying	apply	VERB
ap-2101	327	2	the	the	DET
ap-2101	327	3	erg	erg	NOUN
ap-2101	327	4	procedure	procedure	NOUN
ap-2101	327	5	we	we	PRON
ap-2101	327	6	start	start	VERB
ap-2101	327	7	by	by	ADP
ap-2101	327	8	writing	write	VERB
ap-2101	327	9	the	the	DET
ap-2101	327	10	eigenvalue	eigenvalue	ADJ
ap-2101	327	11	equation	equation	NOUN
ap-2101	327	12	at	at	ADP
ap-2101	327	13	the	the	DET
ap-2101	327	14	bare	bare	ADJ
ap-2101	327	15	scale	scale	NOUN
ap-2101	327	16	λ	λ	NOUN
ap-2101	327	17	.	.	PUNCT
ap-2101	328	1	(	(	PUNCT
ap-2101	328	2	τ2	τ2	NOUN
ap-2101	328	3	+	+	CCONJ
ap-2101	328	4	a2	a2	PROPN
ap-2101	328	5	)	)	PUNCT
ap-2101	328	6	φ̃(τ	φ̃(τ	PROPN
ap-2101	328	7	,	,	PUNCT
ap-2101	328	8	ξ	ξ	NOUN
ap-2101	328	9	)	)	PUNCT
ap-2101	328	10	=	=	SYM
ap-2101	328	11	2	2	NUM
ap-2101	328	12	π2	π2	ADJ
ap-2101	328	13	θλ(τ	θλ(τ	NOUN
ap-2101	328	14	)	)	PUNCT
ap-2101	328	15	∫	∫	PROPN
ap-2101	329	1	λ	λ	X
ap-2101	329	2	0	0	NUM
ap-2101	329	3	dτ	dτ	NOUN
ap-2101	329	4	′	′	NUM
ap-2101	329	5	gλ(τ	gλ(τ	NOUN
ap-2101	329	6	,	,	PUNCT
ap-2101	329	7	τ	τ	PROPN
ap-2101	329	8	′)τ	′)τ	PROPN
ap-2101	329	9	′	′	NUM
ap-2101	329	10	sinh(πτ	sinh(πτ	NOUN
ap-2101	329	11	′)ϑ(τ	′)ϑ(τ	ADJ
ap-2101	329	12	,	,	PUNCT
ap-2101	329	13	τ	τ	PROPN
ap-2101	329	14	′	′	NUM
ap-2101	329	15	;	;	PUNCT
ap-2101	329	16	ξ	ξ	X
ap-2101	329	17	)	)	PUNCT
ap-2101	329	18	,	,	PUNCT
ap-2101	329	19	(	(	PUNCT
ap-2101	329	20	3.41	3.41	NUM
ap-2101	329	21	)	)	PUNCT
ap-2101	329	22	where	where	SCONJ
ap-2101	329	23	gλ(τ	gλ(τ	NOUN
ap-2101	329	24	,	,	PUNCT
ap-2101	329	25	τ	τ	PROPN
ap-2101	329	26	′	′	NUM
ap-2101	329	27	)	)	PUNCT
ap-2101	330	1	=	=	NOUN
ap-2101	331	1	g	g	NOUN
ap-2101	331	2	−	−	PROPN
ap-2101	331	3	xλ(τ	xλ(τ	PROPN
ap-2101	331	4	,	,	PUNCT
ap-2101	331	5	τ	τ	PROPN
ap-2101	331	6	′	′	NUM
ap-2101	331	7	)	)	PUNCT
ap-2101	331	8	and	and	CCONJ
ap-2101	331	9	ϑ(τ	ϑ(τ	PROPN
ap-2101	331	10	,	,	PUNCT
ap-2101	331	11	τ	τ	PROPN
ap-2101	331	12	′	′	NUM
ap-2101	331	13	;	;	PUNCT
ap-2101	331	14	ξ	ξ	X
ap-2101	331	15	)	)	PUNCT
ap-2101	331	16	≡	≡	PROPN
ap-2101	331	17	∫	∫	PROPN
ap-2101	331	18	r	r	NOUN
ap-2101	331	19	dξ′e0(z0	dξ′e0(z0	PROPN
ap-2101	331	20	,	,	PUNCT
ap-2101	331	21	τ	τ	X
ap-2101	331	22	,	,	PUNCT
ap-2101	331	23	ξ)e0(z0	ξ)e0(z0	PROPN
ap-2101	331	24	,	,	PUNCT
ap-2101	331	25	τ	τ	PROPN
ap-2101	331	26	′	′	NUM
ap-2101	331	27	,	,	PUNCT
ap-2101	331	28	ξ′)φ̃(τ	ξ′)φ̃(τ	PROPN
ap-2101	331	29	′	′	NOUN
ap-2101	331	30	,	,	PUNCT
ap-2101	331	31	ξ′	ξ′	NOUN
ap-2101	331	32	)	)	PUNCT
ap-2101	331	33	.	.	PUNCT
ap-2101	332	1	(	(	PUNCT
ap-2101	332	2	3.42	3.42	NUM
ap-2101	332	3	)	)	PUNCT
ap-2101	332	4	at	at	ADP
ap-2101	332	5	an	an	DET
ap-2101	332	6	infinitesimally	infinitesimally	ADV
ap-2101	332	7	lower	low	ADJ
ap-2101	332	8	scale	scale	NOUN
ap-2101	332	9	λ−	λ−	PROPN
ap-2101	332	10	dλ	dλ	NOUN
ap-2101	332	11	we	we	PRON
ap-2101	332	12	write	write	VERB
ap-2101	332	13	(	(	PUNCT
ap-2101	332	14	τ2	τ2	PROPN
ap-2101	332	15	+	+	CCONJ
ap-2101	332	16	a2	a2	PROPN
ap-2101	332	17	)	)	PUNCT
ap-2101	332	18	φ̃(τ	φ̃(τ	PROPN
ap-2101	332	19	,	,	PUNCT
ap-2101	332	20	ξ	ξ	NOUN
ap-2101	332	21	)	)	PUNCT
ap-2101	332	22	=	=	SYM
ap-2101	332	23	2	2	NUM
ap-2101	332	24	π2	π2	NUM
ap-2101	332	25	θλ−dλ(τ	θλ−dλ(τ	NOUN
ap-2101	332	26	)	)	PUNCT
ap-2101	332	27	∫	∫	PROPN
ap-2101	333	1	λ−dλ	λ−dλ	PROPN
ap-2101	333	2	0	0	NUM
ap-2101	333	3	dτ	dτ	NOUN
ap-2101	333	4	′	′	NUM
ap-2101	333	5	gλ−dλ(τ	gλ−dλ(τ	NOUN
ap-2101	333	6	,	,	PUNCT
ap-2101	333	7	τ	τ	PROPN
ap-2101	333	8	′)τ	′)τ	PROPN
ap-2101	333	9	′	′	NUM
ap-2101	333	10	sinh(πτ	sinh(πτ	NOUN
ap-2101	333	11	′)ϑ(τ	′)ϑ(τ	ADJ
ap-2101	333	12	,	,	PUNCT
ap-2101	333	13	τ	τ	PROPN
ap-2101	333	14	′	′	NUM
ap-2101	333	15	;	;	PUNCT
ap-2101	333	16	ξ	ξ	X
ap-2101	333	17	)	)	PUNCT
ap-2101	333	18	.	.	PUNCT
ap-2101	334	1	(	(	PUNCT
ap-2101	334	2	3.43	3.43	NUM
ap-2101	334	3	)	)	PUNCT
ap-2101	334	4	we	we	PRON
ap-2101	334	5	can	can	AUX
ap-2101	334	6	rewrite	rewrite	VERB
ap-2101	334	7	(	(	PUNCT
ap-2101	334	8	3.41	3.41	NUM
ap-2101	334	9	)	)	PUNCT
ap-2101	334	10	as	as	ADP
ap-2101	334	11	(	(	PUNCT
ap-2101	334	12	τ2	τ2	PROPN
ap-2101	334	13	+	+	CCONJ
ap-2101	334	14	a2	a2	NOUN
ap-2101	334	15	)	)	PUNCT
ap-2101	334	16	φ̃(τ	φ̃(τ	PROPN
ap-2101	334	17	,	,	PUNCT
ap-2101	334	18	ξ	ξ	NOUN
ap-2101	334	19	)	)	PUNCT
ap-2101	334	20	=	=	SYM
ap-2101	334	21	2	2	NUM
ap-2101	334	22	π2	π2	ADJ
ap-2101	334	23	θλ(τ	θλ(τ	NOUN
ap-2101	334	24	)	)	PUNCT
ap-2101	334	25	(	(	PUNCT
ap-2101	334	26	∫	∫	PROPN
ap-2101	334	27	λ−dλ	λ−dλ	PROPN
ap-2101	334	28	0	0	NUM
ap-2101	334	29	dτ	dτ	NOUN
ap-2101	334	30	′	′	NUM
ap-2101	334	31	gλ(τ	gλ(τ	NOUN
ap-2101	334	32	,	,	PUNCT
ap-2101	334	33	τ	τ	PROPN
ap-2101	334	34	′)τ	′)τ	PROPN
ap-2101	334	35	′	′	NUM
ap-2101	334	36	sinh(πτ	sinh(πτ	NOUN
ap-2101	334	37	′)ϑ(τ	′)ϑ(τ	ADJ
ap-2101	334	38	,	,	PUNCT
ap-2101	334	39	τ	τ	PROPN
ap-2101	334	40	′	′	NUM
ap-2101	334	41	;	;	PUNCT
ap-2101	334	42	ξ	ξ	X
ap-2101	334	43	)	)	PUNCT
ap-2101	335	1	+	+	NUM
ap-2101	335	2	dλ	dλ	NOUN
ap-2101	335	3	gλ(τ	gλ(τ	NOUN
ap-2101	335	4	,	,	PUNCT
ap-2101	335	5	λ)λ	λ)λ	X
ap-2101	335	6	sinh(πλ)ϑ(τ	sinh(πλ)ϑ(τ	NOUN
ap-2101	335	7	,	,	PUNCT
ap-2101	335	8	λ	λ	PROPN
ap-2101	335	9	;	;	PUNCT
ap-2101	335	10	ξ	ξ	NUM
ap-2101	335	11	)	)	PUNCT
ap-2101	335	12	)	)	PUNCT
ap-2101	335	13	,	,	PUNCT
ap-2101	335	14	(	(	PUNCT
ap-2101	335	15	3.44	3.44	NUM
ap-2101	335	16	)	)	PUNCT
ap-2101	335	17	and	and	CCONJ
ap-2101	335	18	for	for	ADP
ap-2101	335	19	τ	τ	PROPN
ap-2101	335	20	=	=	SYM
ap-2101	335	21	λ	λ	X
ap-2101	335	22	we	we	PRON
ap-2101	335	23	obtain	obtain	VERB
ap-2101	335	24	(	(	PUNCT
ap-2101	335	25	λ2	λ2	NOUN
ap-2101	335	26	+	+	CCONJ
ap-2101	335	27	a2	a2	PROPN
ap-2101	335	28	)	)	PUNCT
ap-2101	335	29	φ̃(λ	φ̃(λ	PROPN
ap-2101	335	30	,	,	PUNCT
ap-2101	335	31	ξ	ξ	X
ap-2101	335	32	)	)	PUNCT
ap-2101	335	33	=	=	SYM
ap-2101	335	34	2	2	NUM
ap-2101	335	35	π2	π2	NOUN
ap-2101	335	36	(	(	PUNCT
ap-2101	335	37	∫	∫	PROPN
ap-2101	335	38	λ−dλ	λ−dλ	PROPN
ap-2101	335	39	0	0	NUM
ap-2101	335	40	dτ	dτ	PROPN
ap-2101	335	41	′	′	NUM
ap-2101	335	42	gλ(λ	gλ(λ	PROPN
ap-2101	335	43	,	,	PUNCT
ap-2101	335	44	τ	τ	PROPN
ap-2101	335	45	′)τ	′)τ	PART
ap-2101	335	46	′	′	NUM
ap-2101	335	47	sinh(πτ	sinh(πτ	NOUN
ap-2101	335	48	′)ϑ(λ	′)ϑ(λ	NOUN
ap-2101	335	49	,	,	PUNCT
ap-2101	335	50	τ	τ	PROPN
ap-2101	335	51	′	′	NUM
ap-2101	335	52	;	;	PUNCT
ap-2101	335	53	ξ	ξ	X
ap-2101	335	54	)	)	PUNCT
ap-2101	335	55	+	+	CCONJ
ap-2101	335	56	dλ	dλ	NOUN
ap-2101	335	57	gλ(λ	gλ(λ	PUNCT
ap-2101	335	58	,	,	PUNCT
ap-2101	335	59	λ)λ	λ)λ	X
ap-2101	335	60	sinh(πλ)ϑ(λ	sinh(πλ)ϑ(λ	PROPN
ap-2101	335	61	,	,	PUNCT
ap-2101	335	62	λ	λ	PROPN
ap-2101	335	63	;	;	PUNCT
ap-2101	335	64	ξ	ξ	X
ap-2101	335	65	)	)	PUNCT
ap-2101	335	66	)	)	PUNCT
ap-2101	335	67	.	.	PUNCT
ap-2101	336	1	(	(	PUNCT
ap-2101	336	2	3.45	3.45	NUM
ap-2101	336	3	)	)	PUNCT
ap-2101	336	4	then	then	ADV
ap-2101	336	5	φ̃(λ	φ̃(λ	PROPN
ap-2101	336	6	,	,	PUNCT
ap-2101	336	7	ξ	ξ	X
ap-2101	336	8	)	)	PUNCT
ap-2101	336	9	becomes	become	VERB
ap-2101	336	10	φ̃(λ	φ̃(λ	PROPN
ap-2101	336	11	,	,	PUNCT
ap-2101	336	12	ξ	ξ	X
ap-2101	336	13	)	)	PUNCT
ap-2101	336	14	=	=	SYM
ap-2101	336	15	2	2	NUM
ap-2101	336	16	π2	π2	NOUN
ap-2101	336	17	(	(	PUNCT
ap-2101	336	18	λ2	λ2	NOUN
ap-2101	336	19	+	+	CCONJ
ap-2101	336	20	a2)−1	a2)−1	ADJ
ap-2101	336	21	∫	∫	PROPN
ap-2101	336	22	λ−dλ	λ−dλ	PROPN
ap-2101	336	23	0	0	NUM
ap-2101	336	24	dτ	dτ	PROPN
ap-2101	337	1	′	′	NUM
ap-2101	337	2	gλ(λ	gλ(λ	PROPN
ap-2101	337	3	,	,	PUNCT
ap-2101	337	4	τ	τ	PROPN
ap-2101	337	5	′)τ	′)τ	PART
ap-2101	338	1	′	′	NUM
ap-2101	338	2	sinh(πτ	sinh(πτ	NOUN
ap-2101	338	3	′)ϑ(λ	′)ϑ(λ	NOUN
ap-2101	338	4	,	,	PUNCT
ap-2101	338	5	τ	τ	PROPN
ap-2101	338	6	′	′	NUM
ap-2101	338	7	;	;	PUNCT
ap-2101	338	8	ξ	ξ	X
ap-2101	338	9	)	)	PUNCT
ap-2101	338	10	,	,	PUNCT
ap-2101	338	11	(	(	PUNCT
ap-2101	338	12	3.46	3.46	NUM
ap-2101	338	13	)	)	PUNCT
ap-2101	338	14	where	where	SCONJ
ap-2101	338	15	we	we	PRON
ap-2101	338	16	have	have	AUX
ap-2101	338	17	again	again	ADV
ap-2101	338	18	ignored	ignore	VERB
ap-2101	338	19	the	the	DET
ap-2101	338	20	term	term	NOUN
ap-2101	338	21	proportional	proportional	ADJ
ap-2101	338	22	to	to	PART
ap-2101	338	23	dλ	dλ	VERB
ap-2101	338	24	.	.	PUNCT
ap-2101	339	1	from	from	ADP
ap-2101	339	2	this	this	DET
ap-2101	339	3	result	result	NOUN
ap-2101	339	4	we	we	PRON
ap-2101	339	5	can	can	AUX
ap-2101	339	6	find	find	VERB
ap-2101	339	7	ϑ(τ	ϑ(τ	PROPN
ap-2101	339	8	,	,	PUNCT
ap-2101	339	9	λ	λ	PROPN
ap-2101	339	10	;	;	PUNCT
ap-2101	339	11	ξ	ξ	X
ap-2101	339	12	)	)	PUNCT
ap-2101	339	13	as	as	ADP
ap-2101	339	14	ϑ(τ	ϑ(τ	PROPN
ap-2101	339	15	,	,	PUNCT
ap-2101	339	16	λ	λ	PROPN
ap-2101	339	17	;	;	PUNCT
ap-2101	339	18	ξ	ξ	X
ap-2101	339	19	)	)	PUNCT
ap-2101	339	20	=	=	SYM
ap-2101	339	21	2	2	NUM
ap-2101	339	22	π2	π2	NOUN
ap-2101	339	23	(	(	PUNCT
ap-2101	339	24	λ2	λ2	NOUN
ap-2101	339	25	+	+	CCONJ
ap-2101	339	26	a2)−1	a2)−1	ADJ
ap-2101	339	27	∫	∫	PROPN
ap-2101	339	28	λ−dλ	λ−dλ	PROPN
ap-2101	339	29	0	0	NUM
ap-2101	339	30	dτ	dτ	PROPN
ap-2101	340	1	′	′	NUM
ap-2101	340	2	gλ(λ	gλ(λ	PROPN
ap-2101	340	3	,	,	PUNCT
ap-2101	340	4	τ	τ	PROPN
ap-2101	340	5	′)τ	′)τ	PROPN
ap-2101	340	6	′	′	NUM
ap-2101	340	7	sinh(πτ	sinh(πτ	NOUN
ap-2101	340	8	′	′	NOUN
ap-2101	340	9	)	)	PUNCT
ap-2101	340	10	∫	∫	PROPN
ap-2101	340	11	r	r	NOUN
ap-2101	340	12	dξ′e0(z0	dξ′e0(z0	PROPN
ap-2101	340	13	,	,	PUNCT
ap-2101	340	14	τ	τ	PROPN
ap-2101	340	15	,	,	PUNCT
ap-2101	340	16	ξ)e0(z0,λ	ξ)e0(z0,λ	PROPN
ap-2101	340	17	,	,	PUNCT
ap-2101	340	18	ξ′)ϑ(λ	ξ′)ϑ(λ	PROPN
ap-2101	340	19	,	,	PUNCT
ap-2101	340	20	τ	τ	PROPN
ap-2101	340	21	′	′	NUM
ap-2101	340	22	;	;	PUNCT
ap-2101	340	23	ξ′	ξ′	NUM
ap-2101	340	24	)	)	PUNCT
ap-2101	340	25	.	.	PUNCT
ap-2101	341	1	(	(	PUNCT
ap-2101	341	2	3.47	3.47	NUM
ap-2101	341	3	)	)	PUNCT
ap-2101	341	4	by	by	ADP
ap-2101	341	5	putting	put	VERB
ap-2101	341	6	the	the	DET
ap-2101	341	7	explicit	explicit	ADJ
ap-2101	341	8	expression	expression	NOUN
ap-2101	341	9	for	for	ADP
ap-2101	341	10	ϑ(λ	ϑ(λ	NOUN
ap-2101	341	11	,	,	PUNCT
ap-2101	341	12	τ	τ	PROPN
ap-2101	341	13	′	′	NUM
ap-2101	341	14	;	;	PUNCT
ap-2101	341	15	ξ′	ξ′	NUM
ap-2101	341	16	)	)	PUNCT
ap-2101	341	17	we	we	PRON
ap-2101	341	18	get	get	VERB
ap-2101	341	19	ϑ(τ	ϑ(τ	PROPN
ap-2101	341	20	,	,	PUNCT
ap-2101	341	21	λ	λ	PROPN
ap-2101	341	22	;	;	PUNCT
ap-2101	341	23	ξ	ξ	X
ap-2101	341	24	)	)	PUNCT
ap-2101	341	25	=	=	SYM
ap-2101	341	26	2	2	NUM
ap-2101	341	27	π2	π2	NOUN
ap-2101	341	28	(	(	PUNCT
ap-2101	341	29	λ2	λ2	NOUN
ap-2101	341	30	+	+	CCONJ
ap-2101	341	31	a2)−1	a2)−1	ADJ
ap-2101	341	32	∫	∫	PROPN
ap-2101	341	33	λ−dλ	λ−dλ	PROPN
ap-2101	341	34	0	0	NUM
ap-2101	341	35	dτ	dτ	PROPN
ap-2101	342	1	′	′	NUM
ap-2101	342	2	gλ(λ	gλ(λ	PROPN
ap-2101	342	3	,	,	PUNCT
ap-2101	342	4	τ	τ	PROPN
ap-2101	342	5	′)τ	′)τ	PROPN
ap-2101	342	6	′	′	NUM
ap-2101	342	7	sinh(πτ	sinh(πτ	NOUN
ap-2101	342	8	′	′	NOUN
ap-2101	342	9	)	)	PUNCT
ap-2101	342	10	×	×	NOUN
ap-2101	342	11	∫	∫	NOUN
ap-2101	342	12	r	r	NOUN
ap-2101	342	13	dξ′e0(z0	dξ′e0(z0	PROPN
ap-2101	342	14	,	,	PUNCT
ap-2101	342	15	τ	τ	PROPN
ap-2101	342	16	,	,	PUNCT
ap-2101	342	17	ξ)e0(z0,λ	ξ)e0(z0,λ	NOUN
ap-2101	342	18	,	,	PUNCT
ap-2101	342	19	ξ′	ξ′	NOUN
ap-2101	342	20	)	)	PUNCT
ap-2101	343	1	∫	∫	NOUN
ap-2101	344	1	r	r	NOUN
ap-2101	344	2	dξ′′e0(z0,λ	dξ′′e0(z0,λ	NOUN
ap-2101	344	3	,	,	PUNCT
ap-2101	344	4	ξ′)e0(z0	ξ′)e0(z0	NUM
ap-2101	344	5	,	,	PUNCT
ap-2101	344	6	τ	τ	PROPN
ap-2101	344	7	′	′	NUM
ap-2101	344	8	,	,	PUNCT
ap-2101	344	9	ξ′′)φ̃(τ	ξ′′)φ̃(τ	PROPN
ap-2101	344	10	′	′	NOUN
ap-2101	344	11	,	,	PUNCT
ap-2101	344	12	ξ′′	ξ′′	NOUN
ap-2101	344	13	)	)	PUNCT
ap-2101	345	1	=	=	SYM
ap-2101	345	2	2	2	NUM
ap-2101	345	3	π2	π2	NOUN
ap-2101	345	4	(	(	PUNCT
ap-2101	345	5	λ2	λ2	NOUN
ap-2101	345	6	+	+	CCONJ
ap-2101	345	7	a2)−1	a2)−1	ADJ
ap-2101	345	8	∫	∫	PROPN
ap-2101	345	9	λ−dλ	λ−dλ	PROPN
ap-2101	345	10	0	0	NUM
ap-2101	345	11	dτ	dτ	PROPN
ap-2101	346	1	′	′	NUM
ap-2101	346	2	gλ(λ	gλ(λ	PROPN
ap-2101	346	3	,	,	PUNCT
ap-2101	346	4	τ	τ	PROPN
ap-2101	346	5	′)τ	′)τ	PROPN
ap-2101	346	6	′	′	NUM
ap-2101	346	7	sinh(πτ	sinh(πτ	NOUN
ap-2101	346	8	′	′	NOUN
ap-2101	346	9	)	)	PUNCT
ap-2101	347	1	×	×	NOUN
ap-2101	347	2	∫	∫	NOUN
ap-2101	347	3	r	r	NOUN
ap-2101	347	4	dξ′e0(z0,λ	dξ′e0(z0,λ	NOUN
ap-2101	347	5	,	,	PUNCT
ap-2101	347	6	ξ′)e0(z0,λ	ξ′)e0(z0,λ	NOUN
ap-2101	347	7	,	,	PUNCT
ap-2101	347	8	ξ′	ξ′	NOUN
ap-2101	347	9	)	)	PUNCT
ap-2101	347	10	∫	∫	NOUN
ap-2101	347	11	r	r	NOUN
ap-2101	347	12	dξ′′e0(z0	dξ′′e0(z0	PROPN
ap-2101	347	13	,	,	PUNCT
ap-2101	347	14	τ	τ	X
ap-2101	347	15	,	,	PUNCT
ap-2101	347	16	ξ)e0(z0	ξ)e0(z0	PROPN
ap-2101	347	17	,	,	PUNCT
ap-2101	347	18	τ	τ	PROPN
ap-2101	347	19	′	′	NUM
ap-2101	347	20	,	,	PUNCT
ap-2101	347	21	ξ′′)φ̃(τ	ξ′′)φ̃(τ	PROPN
ap-2101	347	22	′	′	NOUN
ap-2101	347	23	,	,	PUNCT
ap-2101	347	24	ξ′′	ξ′′	NOUN
ap-2101	347	25	)	)	PUNCT
ap-2101	347	26	=	=	SYM
ap-2101	347	27	1	1	NUM
ap-2101	347	28	2π	2π	NOUN
ap-2101	347	29	(	(	PUNCT
ap-2101	347	30	λ2	λ2	NOUN
ap-2101	347	31	+	+	CCONJ
ap-2101	347	32	a2)−1	a2)−1	ADJ
ap-2101	347	33	tanh(πλ	tanh(πλ	NOUN
ap-2101	347	34	)	)	PUNCT
ap-2101	347	35	sinh(πλ	sinh(πλ	PROPN
ap-2101	347	36	)	)	PUNCT
ap-2101	347	37	∫	∫	PROPN
ap-2101	347	38	λ−dλ	λ−dλ	PROPN
ap-2101	347	39	0	0	NUM
ap-2101	347	40	dτ	dτ	PROPN
ap-2101	348	1	′	′	NUM
ap-2101	348	2	gλ(λ	gλ(λ	PROPN
ap-2101	348	3	,	,	PUNCT
ap-2101	348	4	τ	τ	PROPN
ap-2101	348	5	′)τ	′)τ	PROPN
ap-2101	348	6	′	′	NUM
ap-2101	348	7	sinh(πτ	sinh(πτ	NOUN
ap-2101	348	8	′)ϑ(τ	′)ϑ(τ	ADJ
ap-2101	348	9	,	,	PUNCT
ap-2101	348	10	τ	τ	PROPN
ap-2101	348	11	′	′	NUM
ap-2101	348	12	;	;	PUNCT
ap-2101	348	13	ξ	ξ	X
ap-2101	348	14	)	)	PUNCT
ap-2101	348	15	.	.	PUNCT
ap-2101	349	1	(	(	PUNCT
ap-2101	349	2	3.48	3.48	NUM
ap-2101	349	3	)	)	PUNCT
ap-2101	349	4	if	if	SCONJ
ap-2101	349	5	we	we	PRON
ap-2101	349	6	put	put	VERB
ap-2101	349	7	this	this	DET
ap-2101	349	8	result	result	NOUN
ap-2101	349	9	back	back	ADV
ap-2101	349	10	into	into	ADP
ap-2101	349	11	(	(	PUNCT
ap-2101	349	12	3.44	3.44	NUM
ap-2101	349	13	)	)	PUNCT
ap-2101	349	14	we	we	PRON
ap-2101	349	15	find	find	VERB
ap-2101	349	16	(	(	PUNCT
ap-2101	349	17	τ2	τ2	NOUN
ap-2101	349	18	+	+	CCONJ
ap-2101	349	19	a2	a2	PROPN
ap-2101	349	20	)	)	PUNCT
ap-2101	349	21	φ̃(τ	φ̃(τ	PROPN
ap-2101	349	22	,	,	PUNCT
ap-2101	349	23	ξ	ξ	NOUN
ap-2101	349	24	)	)	PUNCT
ap-2101	349	25	=	=	SYM
ap-2101	349	26	2θλ(τ	2θλ(τ	PROPN
ap-2101	349	27	)	)	PUNCT
ap-2101	349	28	π2	π2	ADJ
ap-2101	349	29	∫	∫	PROPN
ap-2101	349	30	λ−dλ	λ−dλ	PROPN
ap-2101	349	31	0	0	PROPN
ap-2101	350	1	dτ	dτ	INTJ
ap-2101	350	2	′τ	′τ	INTJ
ap-2101	350	3	′	′	NUM
ap-2101	350	4	sinh(πτ	sinh(πτ	NOUN
ap-2101	350	5	′)ϑ(τ	′)ϑ(τ	ADJ
ap-2101	350	6	,	,	PUNCT
ap-2101	350	7	τ	τ	PROPN
ap-2101	350	8	′	′	NUM
ap-2101	350	9	;	;	PUNCT
ap-2101	350	10	ξ	ξ	X
ap-2101	350	11	)	)	PUNCT
ap-2101	350	12	(	(	PUNCT
ap-2101	350	13	gλ(τ	gλ(τ	NOUN
ap-2101	350	14	,	,	PUNCT
ap-2101	350	15	τ	τ	PROPN
ap-2101	350	16	′	′	NUM
ap-2101	350	17	)	)	PUNCT
ap-2101	351	1	+	+	CCONJ
ap-2101	351	2	λ	λ	X
ap-2101	351	3	tanh(πλ	tanh(πλ	NOUN
ap-2101	351	4	)	)	PUNCT
ap-2101	351	5	2π(λ2	2π(λ2	NOUN
ap-2101	352	1	+	+	CCONJ
ap-2101	352	2	a2)gλ(λ	a2)gλ(λ	PROPN
ap-2101	352	3	,	,	PUNCT
ap-2101	352	4	τ	τ	PROPN
ap-2101	352	5	′)gλ(τ	′)gλ(τ	PROPN
ap-2101	352	6	,	,	PUNCT
ap-2101	352	7	λ	λ	NOUN
ap-2101	352	8	)	)	PUNCT
ap-2101	352	9	)	)	PUNCT
ap-2101	352	10	.	.	PUNCT
ap-2101	353	1	(	(	PUNCT
ap-2101	353	2	3.49	3.49	NUM
ap-2101	353	3	)	)	PUNCT
ap-2101	353	4	by	by	ADP
ap-2101	353	5	comparing	compare	VERB
ap-2101	353	6	this	this	PRON
ap-2101	353	7	with	with	ADP
ap-2101	353	8	(	(	PUNCT
ap-2101	353	9	3.43	3.43	NUM
ap-2101	353	10	)	)	PUNCT
ap-2101	353	11	we	we	PRON
ap-2101	353	12	arrive	arrive	VERB
ap-2101	353	13	at	at	ADP
ap-2101	353	14	an	an	DET
ap-2101	353	15	equation	equation	NOUN
ap-2101	353	16	for	for	ADP
ap-2101	353	17	the	the	DET
ap-2101	353	18	coupling	couple	VERB
ap-2101	353	19	constant	constant	ADJ
ap-2101	353	20	gλ−dλ(τ	gλ−dλ(τ	NOUN
ap-2101	353	21	,	,	PUNCT
ap-2101	353	22	τ	τ	PROPN
ap-2101	353	23	′	′	NUM
ap-2101	353	24	)	)	PUNCT
ap-2101	354	1	=	=	PUNCT
ap-2101	354	2	gλ(τ	gλ(τ	NOUN
ap-2101	354	3	,	,	PUNCT
ap-2101	354	4	τ	τ	PROPN
ap-2101	354	5	′	′	NUM
ap-2101	354	6	)	)	PUNCT
ap-2101	354	7	+	+	CCONJ
ap-2101	354	8	λ	λ	X
ap-2101	354	9	tanh(πλ	tanh(πλ	NOUN
ap-2101	354	10	)	)	PUNCT
ap-2101	354	11	2π(λ2	2π(λ2	NOUN
ap-2101	354	12	+	+	CCONJ
ap-2101	354	13	a2)gλ(λ	a2)gλ(λ	PROPN
ap-2101	354	14	,	,	PUNCT
ap-2101	354	15	τ	τ	PROPN
ap-2101	354	16	′)gλ(τ	′)gλ(τ	PROPN
ap-2101	354	17	,	,	PUNCT
ap-2101	354	18	λ	λ	NOUN
ap-2101	354	19	)	)	PUNCT
ap-2101	354	20	,	,	PUNCT
ap-2101	354	21	(	(	PUNCT
ap-2101	354	22	3.50	3.50	NUM
ap-2101	354	23	)	)	PUNCT
ap-2101	354	24	which	which	PRON
ap-2101	354	25	can	can	AUX
ap-2101	354	26	be	be	AUX
ap-2101	354	27	put	put	VERB
ap-2101	354	28	into	into	ADP
ap-2101	354	29	differential	differential	ADJ
ap-2101	354	30	form	form	NOUN
ap-2101	354	31	as	as	ADP
ap-2101	354	32	−dgλ(τ	−dgλ(τ	PROPN
ap-2101	354	33	,	,	PUNCT
ap-2101	354	34	τ	τ	PROPN
ap-2101	354	35	′	′	NUM
ap-2101	354	36	)	)	PUNCT
ap-2101	354	37	dλ	dλ	NOUN
ap-2101	354	38	=	=	SYM
ap-2101	354	39	λ	λ	PROPN
ap-2101	354	40	tanh(πλ	tanh(πλ	NOUN
ap-2101	354	41	)	)	PUNCT
ap-2101	354	42	2π(λ2	2π(λ2	NOUN
ap-2101	354	43	+	+	CCONJ
ap-2101	354	44	a2)gλ(λ	a2)gλ(λ	PROPN
ap-2101	354	45	,	,	PUNCT
ap-2101	354	46	τ	τ	PROPN
ap-2101	354	47	′)gλ(τ	′)gλ(τ	PROPN
ap-2101	354	48	,	,	PUNCT
ap-2101	354	49	λ	λ	NOUN
ap-2101	354	50	)	)	PUNCT
ap-2101	354	51	,	,	PUNCT
ap-2101	354	52	(	(	PUNCT
ap-2101	354	53	3.51	3.51	NUM
ap-2101	354	54	)	)	PUNCT
ap-2101	354	55	166	166	NUM
ap-2101	354	56	vol	vol	NOUN
ap-2101	354	57	.	.	PUNCT
ap-2101	355	1	54	54	NUM
ap-2101	355	2	no	no	NOUN
ap-2101	355	3	.	.	PUNCT
ap-2101	356	1	2/2014	2/2014	NUM
ap-2101	356	2	exact	exact	ADJ
ap-2101	356	3	renormalization	renormalization	NOUN
ap-2101	356	4	group	group	NOUN
ap-2101	356	5	for	for	ADP
ap-2101	356	6	point	point	NOUN
ap-2101	356	7	interactions	interaction	NOUN
ap-2101	356	8	and	and	CCONJ
ap-2101	356	9	by	by	ADP
ap-2101	356	10	integrating	integrate	VERB
ap-2101	356	11	from	from	ADP
ap-2101	356	12	λ	λ	PROPN
ap-2101	356	13	to	to	ADP
ap-2101	356	14	λ	λ	X
ap-2101	356	15	we	we	PRON
ap-2101	356	16	find	find	VERB
ap-2101	356	17	gλ(τ	gλ(τ	NOUN
ap-2101	356	18	,	,	PUNCT
ap-2101	356	19	τ	τ	PROPN
ap-2101	356	20	′	′	NUM
ap-2101	356	21	)	)	PUNCT
ap-2101	356	22	=	=	NOUN
ap-2101	357	1	g	g	NOUN
ap-2101	357	2	−	−	PROPN
ap-2101	357	3	xλ(τ	xλ(τ	PROPN
ap-2101	357	4	,	,	PUNCT
ap-2101	357	5	τ	τ	PROPN
ap-2101	357	6	′	′	NUM
ap-2101	357	7	)	)	PUNCT
ap-2101	358	1	+	+	CCONJ
ap-2101	358	2	1	1	NUM
ap-2101	358	3	2π	2π	NUM
ap-2101	358	4	∫	∫	NOUN
ap-2101	359	1	λ	λ	X
ap-2101	359	2	λ	λ	X
ap-2101	359	3	ds	ds	PROPN
ap-2101	359	4	s	s	NOUN
ap-2101	359	5	s2	s2	NOUN
ap-2101	359	6	+	+	CCONJ
ap-2101	359	7	a2	a2	PROPN
ap-2101	359	8	tanh(πs)gs(s	tanh(πs)gs(s	PROPN
ap-2101	359	9	,	,	PUNCT
ap-2101	359	10	τ	τ	PROPN
ap-2101	359	11	′)gs(τ	′)gs(τ	PROPN
ap-2101	359	12	,	,	PUNCT
ap-2101	359	13	s	s	PROPN
ap-2101	359	14	)	)	PUNCT
ap-2101	359	15	.	.	PUNCT
ap-2101	360	1	(	(	PUNCT
ap-2101	360	2	3.52	3.52	NUM
ap-2101	360	3	)	)	PUNCT
ap-2101	360	4	to	to	PART
ap-2101	360	5	obtain	obtain	VERB
ap-2101	360	6	a	a	DET
ap-2101	360	7	solution	solution	NOUN
ap-2101	360	8	we	we	PRON
ap-2101	360	9	shall	shall	AUX
ap-2101	360	10	use	use	VERB
ap-2101	360	11	the	the	DET
ap-2101	360	12	same	same	ADJ
ap-2101	360	13	procedure	procedure	NOUN
ap-2101	360	14	we	we	PRON
ap-2101	360	15	used	use	VERB
ap-2101	360	16	in	in	ADP
ap-2101	360	17	the	the	DET
ap-2101	360	18	flat	flat	ADJ
ap-2101	360	19	case	case	NOUN
ap-2101	360	20	.	.	PUNCT
ap-2101	361	1	we	we	PRON
ap-2101	361	2	begin	begin	VERB
ap-2101	361	3	with	with	ADP
ap-2101	361	4	g	g	PROPN
ap-2101	361	5	(	(	PUNCT
ap-2101	361	6	1	1	NUM
ap-2101	361	7	)	)	PUNCT
ap-2101	361	8	λ	λ	NOUN
ap-2101	361	9	(	(	PUNCT
ap-2101	361	10	τ	τ	PROPN
ap-2101	361	11	,	,	PUNCT
ap-2101	361	12	τ	τ	PROPN
ap-2101	361	13	′	′	NUM
ap-2101	361	14	)	)	PUNCT
ap-2101	361	15	=	=	NOUN
ap-2101	361	16	g	g	NOUN
ap-2101	362	1	so	so	SCONJ
ap-2101	362	2	that	that	SCONJ
ap-2101	362	3	x	x	X
ap-2101	362	4	(	(	PUNCT
ap-2101	362	5	1	1	X
ap-2101	362	6	)	)	PUNCT
ap-2101	362	7	λ	λ	NOUN
ap-2101	362	8	(	(	PUNCT
ap-2101	362	9	τ	τ	PROPN
ap-2101	362	10	,	,	PUNCT
ap-2101	362	11	τ	τ	PROPN
ap-2101	362	12	′	′	NUM
ap-2101	362	13	)	)	PUNCT
ap-2101	362	14	=	=	SYM
ap-2101	363	1	0	0	X
ap-2101	363	2	.	.	PUNCT
ap-2101	364	1	(	(	PUNCT
ap-2101	364	2	3.53	3.53	NUM
ap-2101	364	3	)	)	PUNCT
ap-2101	364	4	then	then	ADV
ap-2101	364	5	g(2	g(2	PROPN
ap-2101	364	6	)	)	PUNCT
ap-2101	364	7	λ	λ	NOUN
ap-2101	364	8	becomes	become	VERB
ap-2101	364	9	g	g	NOUN
ap-2101	364	10	(	(	PUNCT
ap-2101	364	11	2	2	NUM
ap-2101	364	12	)	)	PUNCT
ap-2101	364	13	λ	λ	NOUN
ap-2101	364	14	=	=	SYM
ap-2101	364	15	g	g	PROPN
ap-2101	364	16	−	−	PROPN
ap-2101	364	17	x(2	x(2	PROPN
ap-2101	364	18	)	)	PUNCT
ap-2101	364	19	λ	λ	PROPN
ap-2101	364	20	(	(	PUNCT
ap-2101	364	21	τ	τ	PROPN
ap-2101	364	22	,	,	PUNCT
ap-2101	364	23	τ	τ	PROPN
ap-2101	364	24	′	′	NUM
ap-2101	364	25	)	)	PUNCT
ap-2101	365	1	+	+	CCONJ
ap-2101	365	2	g2	g2	PROPN
ap-2101	365	3	2π	2π	NOUN
ap-2101	365	4	∫	∫	INTJ
ap-2101	366	1	λ	λ	X
ap-2101	366	2	λ	λ	X
ap-2101	366	3	ds	ds	NOUN
ap-2101	366	4	s	s	NOUN
ap-2101	366	5	tanh(πs	tanh(πs	ADJ
ap-2101	366	6	)	)	PUNCT
ap-2101	366	7	s2	s2	NOUN
ap-2101	366	8	+	+	NUM
ap-2101	366	9	a2	a2	PROPN
ap-2101	366	10	.	.	PUNCT
ap-2101	367	1	(	(	PUNCT
ap-2101	367	2	3.54	3.54	NUM
ap-2101	367	3	)	)	PUNCT
ap-2101	367	4	we	we	PRON
ap-2101	367	5	choose	choose	VERB
ap-2101	367	6	the	the	DET
ap-2101	367	7	counterterm	counterterm	NOUN
ap-2101	367	8	as	as	ADP
ap-2101	367	9	x	x	X
ap-2101	367	10	(	(	PUNCT
ap-2101	367	11	2	2	X
ap-2101	367	12	)	)	PUNCT
ap-2101	367	13	λ	λ	NOUN
ap-2101	367	14	(	(	PUNCT
ap-2101	367	15	τ	τ	PROPN
ap-2101	367	16	,	,	PUNCT
ap-2101	367	17	τ	τ	PROPN
ap-2101	367	18	′	′	NUM
ap-2101	367	19	)	)	PUNCT
ap-2101	367	20	=	=	PUNCT
ap-2101	368	1	g2	g2	PROPN
ap-2101	368	2	2π	2π	PROPN
ap-2101	368	3	∫	∫	X
ap-2101	369	1	λ	λ	X
ap-2101	369	2	λ0	λ0	NOUN
ap-2101	369	3	ds	ds	NOUN
ap-2101	369	4	s	s	X
ap-2101	369	5	tanh(πs	tanh(πs	NOUN
ap-2101	369	6	)	)	PUNCT
ap-2101	369	7	s2	s2	NOUN
ap-2101	369	8	+	+	NUM
ap-2101	369	9	a2	a2	PROPN
ap-2101	369	10	,	,	PUNCT
ap-2101	369	11	(	(	PUNCT
ap-2101	369	12	3.55	3.55	NUM
ap-2101	369	13	)	)	PUNCT
ap-2101	369	14	so	so	SCONJ
ap-2101	369	15	that	that	SCONJ
ap-2101	369	16	the	the	DET
ap-2101	369	17	effective	effective	ADJ
ap-2101	369	18	coupling	coupling	NOUN
ap-2101	369	19	at	at	ADP
ap-2101	369	20	the	the	DET
ap-2101	369	21	second	second	ADJ
ap-2101	369	22	order	order	NOUN
ap-2101	369	23	is	be	AUX
ap-2101	369	24	now	now	ADV
ap-2101	369	25	finite	finite	ADJ
ap-2101	369	26	and	and	CCONJ
ap-2101	369	27	given	give	VERB
ap-2101	369	28	by	by	ADP
ap-2101	369	29	g	g	PROPN
ap-2101	369	30	(	(	PUNCT
ap-2101	369	31	2	2	NUM
ap-2101	369	32	)	)	PUNCT
ap-2101	369	33	λ	λ	NOUN
ap-2101	369	34	(	(	PUNCT
ap-2101	369	35	τ	τ	PROPN
ap-2101	369	36	,	,	PUNCT
ap-2101	369	37	τ	τ	PROPN
ap-2101	369	38	′	′	NUM
ap-2101	369	39	)	)	PUNCT
ap-2101	369	40	=	=	NOUN
ap-2101	370	1	g	g	PROPN
ap-2101	370	2	−	−	PROPN
ap-2101	370	3	g2	g2	PROPN
ap-2101	370	4	2π	2π	PROPN
ap-2101	371	1	∫	∫	X
ap-2101	371	2	λ	λ	X
ap-2101	371	3	λ0	λ0	NOUN
ap-2101	371	4	ds	ds	NOUN
ap-2101	371	5	s	s	X
ap-2101	371	6	tanh(πs	tanh(πs	NOUN
ap-2101	371	7	)	)	PUNCT
ap-2101	371	8	s2	s2	NOUN
ap-2101	371	9	+	+	NUM
ap-2101	371	10	a2	a2	PROPN
ap-2101	371	11	.	.	PUNCT
ap-2101	372	1	(	(	PUNCT
ap-2101	372	2	3.56	3.56	NUM
ap-2101	372	3	)	)	PUNCT
ap-2101	372	4	just	just	ADV
ap-2101	372	5	like	like	ADP
ap-2101	372	6	the	the	DET
ap-2101	372	7	flat	flat	ADJ
ap-2101	372	8	case	case	NOUN
ap-2101	372	9	,	,	PUNCT
ap-2101	372	10	g(n	g(n	PROPN
ap-2101	372	11	)	)	PUNCT
ap-2101	372	12	λ	λ	PROPN
ap-2101	372	13	(	(	PUNCT
ap-2101	372	14	τ	τ	PROPN
ap-2101	372	15	,	,	PUNCT
ap-2101	372	16	τ	τ	PROPN
ap-2101	372	17	′	′	NUM
ap-2101	372	18	)	)	PUNCT
ap-2101	372	19	is	be	AUX
ap-2101	372	20	independent	independent	ADJ
ap-2101	372	21	of	of	ADP
ap-2101	372	22	τ	τ	PROPN
ap-2101	372	23	and	and	CCONJ
ap-2101	372	24	τ	τ	PROPN
ap-2101	372	25	′	′	NUM
ap-2101	372	26	for	for	ADP
ap-2101	372	27	all	all	DET
ap-2101	372	28	n.	n.	NOUN
ap-2101	372	29	at	at	ADP
ap-2101	372	30	the	the	DET
ap-2101	372	31	order	order	NOUN
ap-2101	372	32	n+	n+	ADP
ap-2101	372	33	1	1	NUM
ap-2101	372	34	,	,	PUNCT
ap-2101	372	35	the	the	DET
ap-2101	372	36	effective	effective	ADJ
ap-2101	372	37	coupling	coupling	NOUN
ap-2101	372	38	becomes	become	VERB
ap-2101	372	39	g	g	NOUN
ap-2101	372	40	(	(	PUNCT
ap-2101	372	41	n+1	n+1	NOUN
ap-2101	372	42	)	)	PUNCT
ap-2101	372	43	λ	λ	NOUN
ap-2101	372	44	=	=	PUNCT
ap-2101	372	45	g	g	PROPN
ap-2101	372	46	−	−	PROPN
ap-2101	372	47	x(n+1	x(n+1	PUNCT
ap-2101	372	48	)	)	PUNCT
ap-2101	373	1	λ	λ	NOUN
ap-2101	373	2	+	+	NOUN
ap-2101	373	3	1	1	NUM
ap-2101	373	4	2π	2π	NUM
ap-2101	373	5	∫	∫	NOUN
ap-2101	374	1	λ	λ	X
ap-2101	374	2	λ	λ	X
ap-2101	374	3	ds	ds	NOUN
ap-2101	374	4	s	s	NOUN
ap-2101	374	5	tanh(πs	tanh(πs	ADJ
ap-2101	374	6	)	)	PUNCT
ap-2101	374	7	s2	s2	NOUN
ap-2101	374	8	+	+	NUM
ap-2101	374	9	a2	a2	PROPN
ap-2101	374	10	(	(	PUNCT
ap-2101	374	11	g(n	g(n	PROPN
ap-2101	374	12	)	)	PUNCT
ap-2101	374	13	s	s	PART
ap-2101	374	14	)	)	PUNCT
ap-2101	374	15	2	2	NUM
ap-2101	374	16	.	.	PUNCT
ap-2101	375	1	(	(	PUNCT
ap-2101	375	2	3.57	3.57	NUM
ap-2101	375	3	)	)	PUNCT
ap-2101	375	4	by	by	ADP
ap-2101	375	5	choosing	choose	VERB
ap-2101	375	6	the	the	DET
ap-2101	375	7	counterterm	counterterm	NOUN
ap-2101	375	8	as	as	ADP
ap-2101	375	9	x	x	X
ap-2101	375	10	(	(	PUNCT
ap-2101	375	11	n+1	n+1	NOUN
ap-2101	375	12	)	)	PUNCT
ap-2101	375	13	λ	λ	NOUN
ap-2101	375	14	=	=	NOUN
ap-2101	376	1	1	1	NUM
ap-2101	376	2	2π	2π	NUM
ap-2101	376	3	∫	∫	NOUN
ap-2101	376	4	λ	λ	X
ap-2101	376	5	λ0	λ0	NOUN
ap-2101	376	6	ds	ds	NOUN
ap-2101	376	7	s	s	X
ap-2101	376	8	tanh(πs	tanh(πs	NOUN
ap-2101	376	9	)	)	PUNCT
ap-2101	376	10	s2	s2	NOUN
ap-2101	376	11	+	+	NUM
ap-2101	376	12	a2	a2	PROPN
ap-2101	376	13	(	(	PUNCT
ap-2101	376	14	g(n	g(n	PROPN
ap-2101	376	15	)	)	PUNCT
ap-2101	376	16	s	s	PART
ap-2101	376	17	)	)	PUNCT
ap-2101	376	18	2	2	NUM
ap-2101	376	19	,	,	PUNCT
ap-2101	376	20	(	(	PUNCT
ap-2101	376	21	3.58	3.58	NUM
ap-2101	376	22	)	)	PUNCT
ap-2101	376	23	we	we	PRON
ap-2101	376	24	find	find	VERB
ap-2101	376	25	g	g	PROPN
ap-2101	376	26	(	(	PUNCT
ap-2101	376	27	n+1	n+1	NOUN
ap-2101	376	28	)	)	PUNCT
ap-2101	376	29	λ	λ	NOUN
ap-2101	376	30	=	=	PUNCT
ap-2101	376	31	g	g	NOUN
ap-2101	376	32	−	−	PROPN
ap-2101	376	33	1	1	NUM
ap-2101	376	34	2π	2π	NUM
ap-2101	377	1	∫	∫	NOUN
ap-2101	377	2	λ	λ	X
ap-2101	377	3	λ0	λ0	NOUN
ap-2101	377	4	ds	ds	NOUN
ap-2101	377	5	s	s	X
ap-2101	377	6	tanh(πs	tanh(πs	NOUN
ap-2101	377	7	)	)	PUNCT
ap-2101	377	8	s2	s2	NOUN
ap-2101	377	9	+	+	NUM
ap-2101	377	10	a2	a2	PROPN
ap-2101	377	11	(	(	PUNCT
ap-2101	377	12	g(n	g(n	PROPN
ap-2101	377	13	)	)	PUNCT
ap-2101	377	14	s	s	PART
ap-2101	377	15	)	)	PUNCT
ap-2101	377	16	2	2	NUM
ap-2101	377	17	.	.	PUNCT
ap-2101	378	1	(	(	PUNCT
ap-2101	378	2	3.59	3.59	NUM
ap-2101	378	3	)	)	PUNCT
ap-2101	378	4	if	if	SCONJ
ap-2101	378	5	we	we	PRON
ap-2101	378	6	assume	assume	VERB
ap-2101	378	7	the	the	DET
ap-2101	378	8	existence	existence	NOUN
ap-2101	378	9	of	of	ADP
ap-2101	378	10	lim	lim	PROPN
ap-2101	378	11	n→∞	n→∞	PRON
ap-2101	378	12	g	g	PROPN
ap-2101	378	13	(	(	PUNCT
ap-2101	378	14	n+1	n+1	PROPN
ap-2101	378	15	)	)	PUNCT
ap-2101	378	16	λ	λ	NOUN
ap-2101	378	17	=	=	SYM
ap-2101	378	18	gλ	gλ	NOUN
ap-2101	378	19	,	,	PUNCT
ap-2101	378	20	we	we	PRON
ap-2101	378	21	can	can	AUX
ap-2101	378	22	write	write	VERB
ap-2101	378	23	for	for	ADP
ap-2101	378	24	the	the	DET
ap-2101	378	25	effective	effective	ADJ
ap-2101	378	26	coupling	couple	VERB
ap-2101	378	27	gλ	gλ	NOUN
ap-2101	378	28	=	=	PUNCT
ap-2101	379	1	g	g	NOUN
ap-2101	379	2	−	−	PROPN
ap-2101	379	3	1	1	NUM
ap-2101	379	4	2π	2π	NUM
ap-2101	379	5	∫	∫	NOUN
ap-2101	379	6	λ	λ	X
ap-2101	379	7	λ0	λ0	NOUN
ap-2101	379	8	ds	ds	NOUN
ap-2101	379	9	s	s	X
ap-2101	379	10	tanh(πs	tanh(πs	NOUN
ap-2101	379	11	)	)	PUNCT
ap-2101	379	12	s2	s2	NOUN
ap-2101	379	13	+	+	CCONJ
ap-2101	379	14	a2	a2	PROPN
ap-2101	379	15	g2	g2	PROPN
ap-2101	379	16	s	s	PART
ap-2101	379	17	,	,	PUNCT
ap-2101	379	18	(	(	PUNCT
ap-2101	379	19	3.60	3.60	NUM
ap-2101	379	20	)	)	PUNCT
ap-2101	379	21	which	which	PRON
ap-2101	379	22	again	again	ADV
ap-2101	379	23	implies	imply	VERB
ap-2101	379	24	g	g	PROPN
ap-2101	379	25	=	=	SYM
ap-2101	379	26	gλ0	gλ0	NOUN
ap-2101	379	27	.	.	PUNCT
ap-2101	380	1	this	this	DET
ap-2101	380	2	expression	expression	NOUN
ap-2101	380	3	can	can	AUX
ap-2101	380	4	be	be	AUX
ap-2101	380	5	put	put	VERB
ap-2101	380	6	into	into	ADP
ap-2101	380	7	the	the	DET
ap-2101	380	8	following	follow	VERB
ap-2101	380	9	form	form	NOUN
ap-2101	380	10	−	−	PROPN
ap-2101	380	11	∫	∫	PROPN
ap-2101	380	12	λ	λ	PROPN
ap-2101	380	13	λ0	λ0	NOUN
ap-2101	380	14	dgs	dgs	PROPN
ap-2101	380	15	dgs	dgs	PROPN
ap-2101	380	16	g2	g2	PROPN
ap-2101	380	17	s	s	PART
ap-2101	380	18	=	=	SYM
ap-2101	380	19	1	1	NUM
ap-2101	380	20	2π	2π	NUM
ap-2101	380	21	∫	∫	NOUN
ap-2101	380	22	λ	λ	X
ap-2101	380	23	λ0	λ0	NOUN
ap-2101	380	24	ds	ds	NOUN
ap-2101	380	25	s	s	X
ap-2101	380	26	tanh(πs	tanh(πs	NOUN
ap-2101	380	27	)	)	PUNCT
ap-2101	380	28	s2	s2	NOUN
ap-2101	380	29	+	+	NUM
ap-2101	380	30	a2	a2	PROPN
ap-2101	380	31	.	.	PUNCT
ap-2101	381	1	(	(	PUNCT
ap-2101	381	2	3.61	3.61	NUM
ap-2101	381	3	)	)	PUNCT
ap-2101	381	4	by	by	ADP
ap-2101	381	5	evaluating	evaluate	VERB
ap-2101	381	6	the	the	DET
ap-2101	381	7	integral	integral	NOUN
ap-2101	381	8	on	on	ADP
ap-2101	381	9	the	the	DET
ap-2101	381	10	lhs	lhs	PROPN
ap-2101	381	11	and	and	CCONJ
ap-2101	381	12	expressing	express	VERB
ap-2101	381	13	tanh(πs	tanh(πs	NOUN
ap-2101	381	14	)	)	PUNCT
ap-2101	381	15	as	as	ADV
ap-2101	381	16	tanh(πs	tanh(πs	ADV
ap-2101	381	17	)	)	PUNCT
ap-2101	381	18	=	=	SYM
ap-2101	382	1	1−	1−	NUM
ap-2101	382	2	2	2	NUM
ap-2101	382	3	e2πs	e2πs	PUNCT
ap-2101	382	4	+	+	CCONJ
ap-2101	382	5	1	1	NUM
ap-2101	382	6	,	,	PUNCT
ap-2101	382	7	we	we	PRON
ap-2101	382	8	obtain	obtain	VERB
ap-2101	382	9	1	1	NUM
ap-2101	382	10	gλ	gλ	NOUN
ap-2101	382	11	=	=	SYM
ap-2101	382	12	1	1	NUM
ap-2101	382	13	gλ0	gλ0	NOUN
ap-2101	382	14	+	+	CCONJ
ap-2101	382	15	1	1	NUM
ap-2101	382	16	2π	2π	NUM
ap-2101	382	17	∫	∫	NOUN
ap-2101	382	18	λ	λ	X
ap-2101	382	19	λ0	λ0	NOUN
ap-2101	382	20	ds	ds	NOUN
ap-2101	382	21	s	s	X
ap-2101	382	22	s2	s2	NOUN
ap-2101	382	23	+	+	CCONJ
ap-2101	382	24	a2	a2	PROPN
ap-2101	382	25	−	−	PROPN
ap-2101	383	1	1	1	NUM
ap-2101	383	2	2π	2π	NUM
ap-2101	383	3	∫	∫	NOUN
ap-2101	383	4	λ	λ	X
ap-2101	383	5	λ0	λ0	NOUN
ap-2101	383	6	ds	ds	NOUN
ap-2101	383	7	s	s	X
ap-2101	383	8	s2	s2	NOUN
ap-2101	383	9	+	+	CCONJ
ap-2101	383	10	a2	a2	PROPN
ap-2101	383	11	2	2	NUM
ap-2101	383	12	e2πs	e2πs	PUNCT
ap-2101	383	13	+	+	CCONJ
ap-2101	383	14	1	1	NUM
ap-2101	383	15	.	.	PUNCT
ap-2101	384	1	(	(	PUNCT
ap-2101	384	2	3.62	3.62	NUM
ap-2101	384	3	)	)	PUNCT
ap-2101	384	4	167	167	NUM
ap-2101	384	5	osman	osman	PROPN
ap-2101	384	6	teoman	teoman	NOUN
ap-2101	384	7	turgut	turgut	PROPN
ap-2101	384	8	,	,	PUNCT
ap-2101	384	9	cem	cem	NOUN
ap-2101	384	10	eröncel	eröncel	VERB
ap-2101	384	11	acta	acta	PROPN
ap-2101	384	12	polytechnica	polytechnica	PROPN
ap-2101	384	13	let	let	VERB
ap-2101	384	14	us	we	PRON
ap-2101	384	15	define	define	VERB
ap-2101	384	16	function	function	NOUN
ap-2101	384	17	α(s	α(s	PROPN
ap-2101	384	18	)	)	PUNCT
ap-2101	384	19	by	by	ADP
ap-2101	384	20	α−1(s	α−1(s	PROPN
ap-2101	384	21	)	)	PUNCT
ap-2101	384	22	≡	≡	PROPN
ap-2101	384	23	1	1	NUM
ap-2101	384	24	2π	2π	NUM
ap-2101	384	25	∫	∫	PROPN
ap-2101	384	26	s	s	PART
ap-2101	384	27	0	0	NUM
ap-2101	384	28	ds′	ds′	PROPN
ap-2101	384	29	s′	s′	ADJ
ap-2101	384	30	s′2	s′2	NOUN
ap-2101	384	31	+	+	CCONJ
ap-2101	384	32	a2	a2	PROPN
ap-2101	384	33	2	2	NUM
ap-2101	384	34	e2πs′	e2πs′	NUM
ap-2101	384	35	+	+	X
ap-2101	384	36	1	1	NUM
ap-2101	384	37	.	.	PUNCT
ap-2101	385	1	(	(	PUNCT
ap-2101	385	2	3.63	3.63	NUM
ap-2101	385	3	)	)	PUNCT
ap-2101	385	4	then	then	ADV
ap-2101	385	5	(	(	PUNCT
ap-2101	385	6	3.62	3.62	NUM
ap-2101	385	7	)	)	PUNCT
ap-2101	385	8	becomes	become	VERB
ap-2101	385	9	1	1	NUM
ap-2101	385	10	gλ	gλ	NOUN
ap-2101	385	11	=	=	SYM
ap-2101	385	12	1	1	NUM
ap-2101	385	13	gλ0	gλ0	NOUN
ap-2101	385	14	+	+	CCONJ
ap-2101	385	15	1	1	NUM
ap-2101	385	16	2π	2π	NUM
ap-2101	386	1	∫	∫	NOUN
ap-2101	386	2	λ	λ	X
ap-2101	386	3	λ0	λ0	NOUN
ap-2101	386	4	ds	ds	NOUN
ap-2101	386	5	s	s	X
ap-2101	386	6	s2	s2	NOUN
ap-2101	386	7	+	+	CCONJ
ap-2101	386	8	a2	a2	PROPN
ap-2101	386	9	−	−	PROPN
ap-2101	386	10	1	1	NUM
ap-2101	386	11	α(λ	α(λ	PROPN
ap-2101	386	12	)	)	PUNCT
ap-2101	387	1	+	+	CCONJ
ap-2101	387	2	1	1	NUM
ap-2101	387	3	α(λ0	α(λ0	NOUN
ap-2101	387	4	)	)	PUNCT
ap-2101	387	5	.	.	PUNCT
ap-2101	388	1	(	(	PUNCT
ap-2101	388	2	3.64	3.64	NUM
ap-2101	388	3	)	)	PUNCT
ap-2101	388	4	by	by	ADP
ap-2101	388	5	redefining	redefine	VERB
ap-2101	388	6	the	the	DET
ap-2101	388	7	coupling	coupling	NOUN
ap-2101	388	8	constant	constant	ADJ
ap-2101	388	9	by	by	ADP
ap-2101	388	10	g̃−1	g̃−1	PROPN
ap-2101	388	11	s	s	PART
ap-2101	388	12	≡	≡	PROPN
ap-2101	388	13	g−1	g−1	PROPN
ap-2101	388	14	s	s	PROPN
ap-2101	388	15	+	+	NUM
ap-2101	388	16	α−1	α−1	PROPN
ap-2101	388	17	s	s	PART
ap-2101	388	18	and	and	CCONJ
ap-2101	388	19	evaluating	evaluate	VERB
ap-2101	388	20	the	the	DET
ap-2101	388	21	integral	integral	ADJ
ap-2101	388	22	in	in	ADP
ap-2101	388	23	(	(	PUNCT
ap-2101	388	24	3.64	3.64	NUM
ap-2101	388	25	)	)	PUNCT
ap-2101	388	26	we	we	PRON
ap-2101	388	27	obtain	obtain	VERB
ap-2101	388	28	1	1	NUM
ap-2101	388	29	g̃λ	g̃λ	ADJ
ap-2101	388	30	=	=	SYM
ap-2101	388	31	1	1	NUM
ap-2101	388	32	g̃λ0	g̃λ0	NOUN
ap-2101	388	33	+	+	CCONJ
ap-2101	388	34	1	1	NUM
ap-2101	388	35	4π	4π	NUM
ap-2101	388	36	log	log	VERB
ap-2101	388	37	(	(	PUNCT
ap-2101	388	38	λ2	λ2	NOUN
ap-2101	388	39	+	+	NUM
ap-2101	388	40	a2	a2	PROPN
ap-2101	388	41	λ2	λ2	NOUN
ap-2101	388	42	0	0	NUM
ap-2101	388	43	+	+	NUM
ap-2101	388	44	a2	a2	PROPN
ap-2101	388	45	)	)	PUNCT
ap-2101	388	46	,	,	PUNCT
ap-2101	388	47	(	(	PUNCT
ap-2101	388	48	3.65	3.65	NUM
ap-2101	388	49	)	)	PUNCT
ap-2101	388	50	which	which	PRON
ap-2101	388	51	can	can	AUX
ap-2101	388	52	be	be	AUX
ap-2101	388	53	solved	solve	VERB
ap-2101	388	54	as	as	ADP
ap-2101	388	55	g̃λ	g̃λ	VERB
ap-2101	388	56	=	=	SYM
ap-2101	388	57	g̃λ0	g̃λ0	NOUN
ap-2101	388	58	1	1	NUM
ap-2101	389	1	+	+	CCONJ
ap-2101	389	2	g̃λ0	g̃λ0	PROPN
ap-2101	389	3	4π	4π	NUM
ap-2101	389	4	log	log	VERB
ap-2101	389	5	(	(	PUNCT
ap-2101	389	6	λ2+a2	λ2+a2	NOUN
ap-2101	389	7	λ2	λ2	NOUN
ap-2101	389	8	0+a2	0+a2	NOUN
ap-2101	389	9	)	)	PUNCT
ap-2101	389	10	.	.	PUNCT
ap-2101	390	1	(	(	PUNCT
ap-2101	390	2	3.66	3.66	X
ap-2101	390	3	)	)	PUNCT
ap-2101	390	4	we	we	PRON
ap-2101	390	5	see	see	VERB
ap-2101	390	6	that	that	SCONJ
ap-2101	390	7	by	by	ADP
ap-2101	390	8	slightly	slightly	ADV
ap-2101	390	9	modifying	modify	VERB
ap-2101	390	10	the	the	DET
ap-2101	390	11	coupling	coupling	NOUN
ap-2101	390	12	constant	constant	ADJ
ap-2101	390	13	we	we	PRON
ap-2101	390	14	can	can	AUX
ap-2101	390	15	obtain	obtain	VERB
ap-2101	390	16	the	the	DET
ap-2101	390	17	same	same	ADJ
ap-2101	390	18	solution	solution	NOUN
ap-2101	390	19	as	as	ADP
ap-2101	390	20	for	for	ADP
ap-2101	390	21	the	the	DET
ap-2101	390	22	flat	flat	ADJ
ap-2101	390	23	case	case	NOUN
ap-2101	390	24	.	.	PUNCT
ap-2101	391	1	to	to	PART
ap-2101	391	2	show	show	VERB
ap-2101	391	3	that	that	SCONJ
ap-2101	391	4	this	this	DET
ap-2101	391	5	modification	modification	NOUN
ap-2101	391	6	brings	bring	VERB
ap-2101	391	7	no	no	DET
ap-2101	391	8	problems	problem	NOUN
ap-2101	391	9	at	at	ADP
ap-2101	391	10	high	high	ADJ
ap-2101	391	11	energies	energy	NOUN
ap-2101	391	12	let	let	VERB
ap-2101	391	13	us	we	PRON
ap-2101	391	14	try	try	VERB
ap-2101	391	15	to	to	PART
ap-2101	391	16	estimate	estimate	VERB
ap-2101	391	17	α−1(λ	α−1(λ	NOUN
ap-2101	391	18	)	)	PUNCT
ap-2101	391	19	.	.	PUNCT
ap-2101	392	1	α−1(λ	α−1(λ	NOUN
ap-2101	392	2	)	)	PUNCT
ap-2101	392	3	=	=	SYM
ap-2101	393	1	1	1	NUM
ap-2101	393	2	2π	2π	NUM
ap-2101	393	3	∫	∫	PROPN
ap-2101	393	4	λ	λ	X
ap-2101	393	5	0	0	NUM
ap-2101	393	6	ds	ds	PROPN
ap-2101	393	7	s	s	NOUN
ap-2101	393	8	s2	s2	NOUN
ap-2101	393	9	+	+	CCONJ
ap-2101	393	10	a2	a2	PROPN
ap-2101	393	11	2	2	NUM
ap-2101	393	12	e2πs	e2πs	NOUN
ap-2101	393	13	+	+	CCONJ
ap-2101	393	14	1	1	NUM
ap-2101	393	15	≤	≤	NUM
ap-2101	393	16	1	1	NUM
ap-2101	393	17	π	π	NOUN
ap-2101	393	18	∫	∫	PROPN
ap-2101	393	19	λ	λ	X
ap-2101	393	20	0	0	NUM
ap-2101	393	21	ds	ds	PROPN
ap-2101	393	22	se−2πs	se−2πs	NUM
ap-2101	393	23	s2	s2	PROPN
ap-2101	393	24	+	+	CCONJ
ap-2101	393	25	a2	a2	PROPN
ap-2101	393	26	.	.	PUNCT
ap-2101	394	1	(	(	PUNCT
ap-2101	394	2	3.67	3.67	NUM
ap-2101	394	3	)	)	PUNCT
ap-2101	394	4	using	use	VERB
ap-2101	394	5	cauchy	cauchy	PROPN
ap-2101	394	6	-	-	PUNCT
ap-2101	394	7	schwartz	schwartz	PROPN
ap-2101	394	8	inequality	inequality	NOUN
ap-2101	394	9	we	we	PRON
ap-2101	394	10	find	find	VERB
ap-2101	394	11	α−1(λ	α−1(λ	NOUN
ap-2101	394	12	)	)	PUNCT
ap-2101	394	13	≤	≤	NOUN
ap-2101	395	1	1	1	NUM
ap-2101	395	2	π	π	PROPN
ap-2101	395	3	[	[	X
ap-2101	395	4	∫	∫	X
ap-2101	395	5	λ	λ	X
ap-2101	395	6	0	0	NUM
ap-2101	395	7	ds	ds	PROPN
ap-2101	395	8	s2	s2	NOUN
ap-2101	395	9	(	(	PUNCT
ap-2101	395	10	s2	s2	NOUN
ap-2101	395	11	+	+	CCONJ
ap-2101	395	12	a2)2	a2)2	DET
ap-2101	395	13	]	]	SYM
ap-2101	395	14	1/2	1/2	NUM
ap-2101	395	15	[	[	X
ap-2101	395	16	∫	∫	X
ap-2101	395	17	λ	λ	X
ap-2101	395	18	0	0	NUM
ap-2101	395	19	ds	ds	PROPN
ap-2101	395	20	e−4πs	e−4πs	NOUN
ap-2101	395	21	]	]	PUNCT
ap-2101	395	22	1/2	1/2	NUM
ap-2101	395	23	=	=	SYM
ap-2101	395	24	1	1	NUM
ap-2101	395	25	π	π	NOUN
ap-2101	395	26	[	[	PUNCT
ap-2101	395	27	1	1	NUM
ap-2101	395	28	2	2	NUM
ap-2101	395	29	(	(	PUNCT
ap-2101	395	30	tan−1	tan−1	PROPN
ap-2101	395	31	(	(	PUNCT
ap-2101	395	32	λ	λ	X
ap-2101	395	33	a	a	NOUN
ap-2101	395	34	)	)	PUNCT
ap-2101	395	35	a	a	DET
ap-2101	395	36	−	−	NOUN
ap-2101	395	37	λ	λ	X
ap-2101	395	38	λ2	λ2	NOUN
ap-2101	395	39	+	+	NUM
ap-2101	395	40	a2	a2	PROPN
ap-2101	395	41	)	)	PUNCT
ap-2101	395	42	]	]	PUNCT
ap-2101	396	1	1/2	1/2	NUM
ap-2101	396	2	[	[	PUNCT
ap-2101	396	3	1	1	NUM
ap-2101	396	4	4π	4π	NUM
ap-2101	396	5	(	(	PUNCT
ap-2101	396	6	1−	1−	NUM
ap-2101	396	7	e−4πλ)]1/2	e−4πλ)]1/2	PROPN
ap-2101	396	8	.	.	PUNCT
ap-2101	397	1	(	(	PUNCT
ap-2101	397	2	3.68	3.68	NUM
ap-2101	397	3	)	)	PUNCT
ap-2101	397	4	we	we	PRON
ap-2101	397	5	see	see	VERB
ap-2101	397	6	that	that	PRON
ap-2101	397	7	for	for	ADP
ap-2101	397	8	high	high	ADJ
ap-2101	397	9	energies	energy	NOUN
ap-2101	397	10	λ	λ	X
ap-2101	397	11	�	�	PROPN
ap-2101	397	12	1	1	NUM
ap-2101	397	13	,	,	PUNCT
ap-2101	397	14	this	this	DET
ap-2101	397	15	correction	correction	NOUN
ap-2101	397	16	term	term	NOUN
ap-2101	397	17	behaves	behave	VERB
ap-2101	397	18	like	like	ADP
ap-2101	397	19	a	a	DET
ap-2101	397	20	constant	constant	ADJ
ap-2101	397	21	.	.	PUNCT
ap-2101	398	1	3.4	3.4	NUM
ap-2101	398	2	.	.	PUNCT
ap-2101	398	3	estimating	estimate	VERB
ap-2101	398	4	the	the	DET
ap-2101	398	5	range	range	NOUN
ap-2101	398	6	of	of	ADP
ap-2101	398	7	renormalizability	renormalizability	NOUN
ap-2101	398	8	the	the	DET
ap-2101	398	9	conditions	condition	NOUN
ap-2101	398	10	under	under	ADP
ap-2101	398	11	which	which	PRON
ap-2101	398	12	the	the	DET
ap-2101	398	13	sequence	sequence	NOUN
ap-2101	398	14	{	{	PUNCT
ap-2101	398	15	g(n	g(n	PROPN
ap-2101	398	16	)	)	PUNCT
ap-2101	398	17	λ	λ	PROPN
ap-2101	398	18	}	}	PUNCT
ap-2101	398	19	has	have	VERB
ap-2101	398	20	a	a	DET
ap-2101	398	21	limit	limit	NOUN
ap-2101	398	22	is	be	AUX
ap-2101	398	23	investigated	investigate	VERB
ap-2101	398	24	in	in	ADP
ap-2101	398	25	an	an	DET
ap-2101	398	26	identical	identical	ADJ
ap-2101	398	27	manner	manner	NOUN
ap-2101	398	28	to	to	ADP
ap-2101	398	29	the	the	DET
ap-2101	398	30	one	one	NOUN
ap-2101	398	31	presented	present	VERB
ap-2101	398	32	in	in	ADP
ap-2101	398	33	the	the	DET
ap-2101	398	34	flat	flat	ADJ
ap-2101	398	35	case	case	NOUN
ap-2101	398	36	in	in	ADP
ap-2101	398	37	section	section	NOUN
ap-2101	398	38	2.4	2.4	NUM
ap-2101	398	39	.	.	PUNCT
ap-2101	399	1	in	in	ADP
ap-2101	399	2	this	this	DET
ap-2101	399	3	case	case	NOUN
ap-2101	399	4	we	we	PRON
ap-2101	399	5	define	define	VERB
ap-2101	399	6	the	the	DET
ap-2101	399	7	map	map	NOUN
ap-2101	399	8	t	t	NOUN
ap-2101	399	9	:	:	PUNCT
ap-2101	399	10	c(i)→	c(i)→	PROPN
ap-2101	399	11	c(i	c(i	PROPN
ap-2101	399	12	)	)	PUNCT
ap-2101	399	13	as	as	ADP
ap-2101	399	14	t	t	PROPN
ap-2101	399	15	(	(	PUNCT
ap-2101	399	16	g)(λ	g)(λ	NOUN
ap-2101	399	17	)	)	PUNCT
ap-2101	400	1	=	=	PUNCT
ap-2101	400	2	gλ0	gλ0	NOUN
ap-2101	400	3	−	−	PROPN
ap-2101	400	4	1	1	NUM
ap-2101	400	5	2π	2π	NUM
ap-2101	400	6	∫	∫	NOUN
ap-2101	400	7	λ	λ	X
ap-2101	400	8	λ0	λ0	NOUN
ap-2101	400	9	ds	ds	NOUN
ap-2101	400	10	s	s	X
ap-2101	400	11	tanh(πs	tanh(πs	NOUN
ap-2101	400	12	)	)	PUNCT
ap-2101	400	13	s2	s2	NOUN
ap-2101	400	14	+	+	CCONJ
ap-2101	400	15	a2	a2	PROPN
ap-2101	400	16	g2	g2	PROPN
ap-2101	400	17	s	s	PART
ap-2101	400	18	.	.	PUNCT
ap-2101	401	1	(	(	PUNCT
ap-2101	401	2	3.69	3.69	NUM
ap-2101	401	3	)	)	PUNCT
ap-2101	401	4	then	then	ADV
ap-2101	401	5	we	we	PRON
ap-2101	401	6	have	have	VERB
ap-2101	401	7	the	the	DET
ap-2101	401	8	estimate	estimate	NOUN
ap-2101	401	9	|t	|t	PROPN
ap-2101	401	10	(	(	PUNCT
ap-2101	401	11	g)−	g)−	PROPN
ap-2101	401	12	t	t	PROPN
ap-2101	401	13	(	(	PUNCT
ap-2101	401	14	h)|	h)|	NOUN
ap-2101	401	15	=	=	SYM
ap-2101	401	16	1	1	NUM
ap-2101	401	17	2π	2π	NUM
ap-2101	401	18	∫	∫	NOUN
ap-2101	402	1	λ	λ	X
ap-2101	402	2	λ0	λ0	NOUN
ap-2101	402	3	ds	ds	NOUN
ap-2101	402	4	s	s	X
ap-2101	402	5	tanh(πs	tanh(πs	NOUN
ap-2101	402	6	)	)	PUNCT
ap-2101	402	7	s2	s2	NOUN
ap-2101	402	8	+	+	CCONJ
ap-2101	402	9	ν2	ν2	NOUN
ap-2101	402	10	(	(	PUNCT
ap-2101	402	11	(	(	PUNCT
ap-2101	402	12	hs)2	hs)2	NOUN
ap-2101	402	13	−	−	PROPN
ap-2101	402	14	(	(	PUNCT
ap-2101	402	15	gs)2	gs)2	NOUN
ap-2101	402	16	)	)	PUNCT
ap-2101	402	17	≤	≤	NOUN
ap-2101	402	18	1	1	NUM
ap-2101	402	19	2π	2π	NUM
ap-2101	402	20	sup	sup	NOUN
ap-2101	402	21	s∈[λ0,λ	s∈[λ0,λ	NOUN
ap-2101	402	22	]	]	PUNCT
ap-2101	402	23	∣∣(hs)2	∣∣(hs)2	NOUN
ap-2101	402	24	−	−	PROPN
ap-2101	403	1	(	(	PUNCT
ap-2101	403	2	gs)2∣∣	gs)2∣∣	NOUN
ap-2101	403	3	∫	∫	PROPN
ap-2101	403	4	λ	λ	X
ap-2101	403	5	λ0	λ0	NOUN
ap-2101	403	6	ds	ds	NOUN
ap-2101	403	7	s	s	X
ap-2101	403	8	tanh(πs	tanh(πs	NOUN
ap-2101	403	9	)	)	PUNCT
ap-2101	403	10	s2	s2	NOUN
ap-2101	403	11	+	+	CCONJ
ap-2101	403	12	ν2	ν2	ADJ
ap-2101	403	13	≤	≤	NUM
ap-2101	403	14	1	1	NUM
ap-2101	403	15	2π	2π	NUM
ap-2101	403	16	sup	sup	NOUN
ap-2101	403	17	s∈[λ0,λ	s∈[λ0,λ	NOUN
ap-2101	403	18	]	]	PUNCT
ap-2101	403	19	∣∣(hs)2	∣∣(hs)2	NOUN
ap-2101	403	20	−	−	PROPN
ap-2101	404	1	(	(	PUNCT
ap-2101	404	2	gs)2∣∣	gs)2∣∣	NOUN
ap-2101	404	3	∫	∫	PROPN
ap-2101	404	4	λ	λ	X
ap-2101	404	5	λ0	λ0	NOUN
ap-2101	404	6	ds	ds	NOUN
ap-2101	404	7	1	1	NUM
ap-2101	404	8	s	s	NOUN
ap-2101	404	9	=	=	SYM
ap-2101	404	10	1	1	NUM
ap-2101	404	11	2π	2π	NUM
ap-2101	404	12	sup	sup	NOUN
ap-2101	404	13	s∈[λ0,λ	s∈[λ0,λ	NOUN
ap-2101	404	14	]	]	PUNCT
ap-2101	404	15	|(hs	|(hs	PROPN
ap-2101	404	16	+	+	CCONJ
ap-2101	404	17	gs)(hs	gs)(hs	PROPN
ap-2101	404	18	−	−	PROPN
ap-2101	405	1	gs)|	gs)|	PROPN
ap-2101	405	2	log	log	VERB
ap-2101	405	3	(	(	PUNCT
ap-2101	405	4	λ	λ	X
ap-2101	405	5	λ0	λ0	NOUN
ap-2101	405	6	)	)	PUNCT
ap-2101	405	7	.	.	PUNCT
ap-2101	406	1	(	(	PUNCT
ap-2101	406	2	3.70	3.70	NUM
ap-2101	406	3	)	)	PUNCT
ap-2101	406	4	as	as	ADP
ap-2101	406	5	in	in	ADP
ap-2101	406	6	the	the	DET
ap-2101	406	7	flat	flat	ADJ
ap-2101	406	8	case	case	NOUN
ap-2101	406	9	,	,	PUNCT
ap-2101	406	10	t	t	PROPN
ap-2101	406	11	is	be	AUX
ap-2101	406	12	a	a	DET
ap-2101	406	13	contraction	contraction	NOUN
ap-2101	406	14	if	if	SCONJ
ap-2101	406	15	gλ0	gλ0	NOUN
ap-2101	406	16	π	π	PROPN
ap-2101	406	17	log	log	INTJ
ap-2101	406	18	(	(	PUNCT
ap-2101	406	19	λ̃	λ̃	PROPN
ap-2101	406	20	λ0	λ0	NOUN
ap-2101	406	21	)	)	PUNCT
ap-2101	406	22	<	<	X
ap-2101	406	23	1	1	X
ap-2101	406	24	.	.	PUNCT
ap-2101	407	1	(	(	PUNCT
ap-2101	407	2	3.71	3.71	NUM
ap-2101	407	3	)	)	PUNCT
ap-2101	407	4	3.5	3.5	NUM
ap-2101	407	5	.	.	PUNCT
ap-2101	408	1	bound	bind	VERB
ap-2101	408	2	state	state	NOUN
ap-2101	408	3	solution	solution	NOUN
ap-2101	408	4	to	to	PART
ap-2101	408	5	find	find	VERB
ap-2101	408	6	the	the	DET
ap-2101	408	7	bound	bound	ADJ
ap-2101	408	8	state	state	NOUN
ap-2101	408	9	energy	energy	NOUN
ap-2101	408	10	we	we	PRON
ap-2101	408	11	rewrite	rewrite	VERB
ap-2101	408	12	(	(	PUNCT
ap-2101	408	13	3.40	3.40	NUM
ap-2101	408	14	)	)	PUNCT
ap-2101	408	15	in	in	ADP
ap-2101	408	16	terms	term	NOUN
ap-2101	408	17	of	of	ADP
ap-2101	408	18	renormalized	renormalized	ADJ
ap-2101	408	19	coupling	coupling	NOUN
ap-2101	408	20	.	.	PUNCT
ap-2101	409	1	1	1	NUM
ap-2101	409	2	gλ	gλ	NOUN
ap-2101	409	3	=	=	SYM
ap-2101	409	4	1	1	NUM
ap-2101	409	5	2π	2π	NUM
ap-2101	409	6	∫	∫	PROPN
ap-2101	409	7	λ	λ	X
ap-2101	409	8	0	0	NUM
ap-2101	409	9	dτ	dτ	NOUN
ap-2101	409	10	′	′	NUM
ap-2101	409	11	τ	τ	PROPN
ap-2101	409	12	′	′	NUM
ap-2101	409	13	tanh(πτ	tanh(πτ	NOUN
ap-2101	409	14	′	′	NUM
ap-2101	409	15	)	)	PUNCT
ap-2101	409	16	(	(	PUNCT
ap-2101	409	17	τ	τ	X
ap-2101	409	18	′2	′2	X
ap-2101	409	19	+	+	NUM
ap-2101	409	20	a2)−1	a2)−1	X
ap-2101	409	21	,	,	PUNCT
ap-2101	409	22	(	(	PUNCT
ap-2101	409	23	3.72	3.72	NUM
ap-2101	409	24	)	)	PUNCT
ap-2101	409	25	168	168	NUM
ap-2101	409	26	vol	vol	NOUN
ap-2101	409	27	.	.	PUNCT
ap-2101	409	28	54	54	NUM
ap-2101	410	1	no	no	NOUN
ap-2101	410	2	.	.	PUNCT
ap-2101	411	1	2/2014	2/2014	NUM
ap-2101	411	2	exact	exact	ADJ
ap-2101	411	3	renormalization	renormalization	NOUN
ap-2101	411	4	group	group	NOUN
ap-2101	411	5	for	for	ADP
ap-2101	411	6	point	point	NOUN
ap-2101	411	7	interactions	interaction	NOUN
ap-2101	411	8	where	where	SCONJ
ap-2101	411	9	1	1	NUM
ap-2101	411	10	gλ	gλ	NOUN
ap-2101	411	11	=	=	SYM
ap-2101	411	12	1	1	NUM
ap-2101	411	13	g̃λ	g̃λ	NOUN
ap-2101	411	14	−	−	PROPN
ap-2101	411	15	1	1	NUM
ap-2101	411	16	α(λ	α(λ	PROPN
ap-2101	411	17	)	)	PUNCT
ap-2101	411	18	=	=	SYM
ap-2101	411	19	1	1	NUM
ap-2101	411	20	g̃λ0	g̃λ0	NOUN
ap-2101	411	21	+	+	CCONJ
ap-2101	411	22	1	1	NUM
ap-2101	411	23	4π	4π	NUM
ap-2101	411	24	log	log	VERB
ap-2101	411	25	(	(	PUNCT
ap-2101	411	26	λ2	λ2	NOUN
ap-2101	411	27	+	+	NUM
ap-2101	411	28	a2	a2	PROPN
ap-2101	411	29	λ2	λ2	NOUN
ap-2101	411	30	0	0	NUM
ap-2101	411	31	+	+	NUM
ap-2101	411	32	a2	a2	PROPN
ap-2101	411	33	)	)	PUNCT
ap-2101	411	34	−	−	PROPN
ap-2101	412	1	1	1	NUM
ap-2101	412	2	2π	2π	NUM
ap-2101	412	3	∫	∫	PROPN
ap-2101	412	4	λ	λ	X
ap-2101	412	5	0	0	NUM
ap-2101	412	6	ds	ds	PROPN
ap-2101	412	7	s	s	NOUN
ap-2101	412	8	s2	s2	NOUN
ap-2101	412	9	+	+	CCONJ
ap-2101	412	10	a2	a2	PROPN
ap-2101	412	11	2	2	NUM
ap-2101	412	12	e2πs	e2πs	PUNCT
ap-2101	412	13	+	+	CCONJ
ap-2101	412	14	1	1	NUM
ap-2101	412	15	.	.	PUNCT
ap-2101	413	1	(	(	PUNCT
ap-2101	413	2	3.73	3.73	NUM
ap-2101	413	3	)	)	PUNCT
ap-2101	413	4	thus	thus	ADV
ap-2101	413	5	(	(	PUNCT
ap-2101	413	6	3.72	3.72	NUM
ap-2101	413	7	)	)	PUNCT
ap-2101	413	8	becomes	become	VERB
ap-2101	413	9	1	1	NUM
ap-2101	413	10	g̃λ0	g̃λ0	NOUN
ap-2101	413	11	+	+	CCONJ
ap-2101	413	12	1	1	NUM
ap-2101	413	13	4π	4π	NUM
ap-2101	413	14	log	log	VERB
ap-2101	413	15	(	(	PUNCT
ap-2101	413	16	λ2	λ2	NOUN
ap-2101	413	17	+	+	NUM
ap-2101	413	18	a2	a2	PROPN
ap-2101	413	19	λ2	λ2	NOUN
ap-2101	413	20	0	0	NUM
ap-2101	413	21	+	+	NUM
ap-2101	413	22	a2	a2	PROPN
ap-2101	413	23	)	)	PUNCT
ap-2101	413	24	−	−	PROPN
ap-2101	414	1	1	1	NUM
ap-2101	414	2	2π	2π	NUM
ap-2101	414	3	∫	∫	PROPN
ap-2101	414	4	λ	λ	X
ap-2101	414	5	0	0	NUM
ap-2101	414	6	ds	ds	PROPN
ap-2101	414	7	s	s	NOUN
ap-2101	414	8	s2	s2	NOUN
ap-2101	414	9	+	+	CCONJ
ap-2101	414	10	a2	a2	PROPN
ap-2101	414	11	2	2	NUM
ap-2101	414	12	e2πs	e2πs	PUNCT
ap-2101	414	13	+	+	CCONJ
ap-2101	414	14	1	1	NUM
ap-2101	414	15	=	=	SYM
ap-2101	414	16	1	1	NUM
ap-2101	414	17	2π	2π	NUM
ap-2101	414	18	∫	∫	PROPN
ap-2101	414	19	λ	λ	X
ap-2101	414	20	0	0	NUM
ap-2101	414	21	dτ	dτ	NOUN
ap-2101	415	1	′	′	NUM
ap-2101	415	2	τ	τ	PROPN
ap-2101	415	3	′	′	NUM
ap-2101	415	4	τ	τ	X
ap-2101	415	5	′2	′2	X
ap-2101	415	6	+	+	NUM
ap-2101	415	7	a2	a2	PROPN
ap-2101	415	8	−	−	PROPN
ap-2101	415	9	1	1	NUM
ap-2101	415	10	2π	2π	NUM
ap-2101	415	11	∫	∫	PROPN
ap-2101	416	1	λ	λ	X
ap-2101	416	2	0	0	NUM
ap-2101	416	3	dτ	dτ	NOUN
ap-2101	417	1	′	′	NUM
ap-2101	417	2	τ	τ	PROPN
ap-2101	417	3	′	′	NUM
ap-2101	417	4	τ	τ	X
ap-2101	417	5	′2	′2	X
ap-2101	417	6	+	+	CCONJ
ap-2101	417	7	a2	a2	PROPN
ap-2101	417	8	2	2	NUM
ap-2101	417	9	e2πτ	e2πτ	NOUN
ap-2101	417	10	′	′	NUM
ap-2101	418	1	+	+	CCONJ
ap-2101	418	2	1	1	NUM
ap-2101	418	3	.	.	PUNCT
ap-2101	419	1	(	(	PUNCT
ap-2101	419	2	3.74	3.74	NUM
ap-2101	419	3	)	)	PUNCT
ap-2101	419	4	the	the	DET
ap-2101	419	5	integrals	integral	NOUN
ap-2101	419	6	on	on	ADP
ap-2101	419	7	both	both	DET
ap-2101	419	8	sides	side	NOUN
ap-2101	419	9	vanish	vanish	VERB
ap-2101	419	10	so	so	SCONJ
ap-2101	419	11	we	we	PRON
ap-2101	419	12	are	be	AUX
ap-2101	419	13	left	leave	VERB
ap-2101	419	14	with	with	ADP
ap-2101	419	15	1	1	NUM
ap-2101	419	16	g̃λ0	g̃λ0	NOUN
ap-2101	419	17	+	+	CCONJ
ap-2101	419	18	1	1	NUM
ap-2101	419	19	4π	4π	NUM
ap-2101	419	20	log	log	VERB
ap-2101	419	21	(	(	PUNCT
ap-2101	419	22	λ2	λ2	NOUN
ap-2101	419	23	+	+	NUM
ap-2101	419	24	a2	a2	PROPN
ap-2101	419	25	λ2	λ2	NOUN
ap-2101	419	26	0	0	NUM
ap-2101	419	27	+	+	NUM
ap-2101	419	28	a2	a2	NOUN
ap-2101	419	29	)	)	PUNCT
ap-2101	419	30	=	=	SYM
ap-2101	420	1	1	1	NUM
ap-2101	420	2	4π	4π	NUM
ap-2101	420	3	log	log	VERB
ap-2101	420	4	(	(	PUNCT
ap-2101	420	5	λ2	λ2	NOUN
ap-2101	420	6	+	+	NUM
ap-2101	420	7	a2	a2	PROPN
ap-2101	420	8	a2	a2	PROPN
ap-2101	420	9	)	)	PUNCT
ap-2101	420	10	,	,	PUNCT
ap-2101	420	11	(	(	PUNCT
ap-2101	420	12	3.75	3.75	NUM
ap-2101	420	13	)	)	PUNCT
ap-2101	420	14	with	with	ADP
ap-2101	420	15	the	the	DET
ap-2101	420	16	solution	solution	NOUN
ap-2101	420	17	in	in	ADP
ap-2101	420	18	the	the	DET
ap-2101	420	19	λ→∞	λ→∞	NUM
ap-2101	420	20	limit	limit	NOUN
ap-2101	420	21	lim	lim	NOUN
ap-2101	420	22	λ→∞	λ→∞	PUNCT
ap-2101	420	23	−ν2r2	−ν2r2	SYM
ap-2101	420	24	=	=	SYM
ap-2101	420	25	−λ2	−λ2	NOUN
ap-2101	420	26	0	0	NUM
ap-2101	420	27	e−4π	e−4π	PROPN
ap-2101	420	28	/	/	SYM
ap-2101	420	29	g̃λ0	g̃λ0	PROPN
ap-2101	420	30	1−	1−	NUM
ap-2101	420	31	e−4π	e−4π	PROPN
ap-2101	420	32	/	/	SYM
ap-2101	420	33	g̃λ0	g̃λ0	PROPN
ap-2101	420	34	+	+	CCONJ
ap-2101	420	35	1	1	NUM
ap-2101	420	36	4	4	NUM
ap-2101	420	37	.	.	PUNCT
ap-2101	421	1	(	(	PUNCT
ap-2101	421	2	3.76	3.76	NUM
ap-2101	421	3	)	)	PUNCT
ap-2101	421	4	4	4	NUM
ap-2101	421	5	.	.	PUNCT
ap-2101	421	6	exact	exact	ADJ
ap-2101	421	7	renormalization	renormalization	NOUN
ap-2101	421	8	group	group	NOUN
ap-2101	421	9	on	on	ADP
ap-2101	421	10	the	the	DET
ap-2101	421	11	sphere	sphere	NOUN
ap-2101	421	12	4.1	4.1	NUM
ap-2101	421	13	.	.	PUNCT
ap-2101	422	1	formulation	formulation	NOUN
ap-2101	422	2	of	of	ADP
ap-2101	422	3	the	the	DET
ap-2101	422	4	problem	problem	NOUN
ap-2101	422	5	considering	consider	VERB
ap-2101	422	6	the	the	DET
ap-2101	422	7	same	same	ADJ
ap-2101	422	8	problems	problem	NOUN
ap-2101	422	9	as	as	ADP
ap-2101	422	10	in	in	ADP
ap-2101	422	11	the	the	DET
ap-2101	422	12	previous	previous	ADJ
ap-2101	422	13	sections	section	NOUN
ap-2101	422	14	we	we	PRON
ap-2101	422	15	write	write	VERB
ap-2101	422	16	the	the	DET
ap-2101	422	17	eigenvalue	eigenvalue	ADJ
ap-2101	422	18	equation	equation	NOUN
ap-2101	422	19	for	for	ADP
ap-2101	422	20	the	the	DET
ap-2101	422	21	bound	bind	VERB
ap-2101	422	22	state	state	NOUN
ap-2101	422	23	as	as	ADP
ap-2101	422	24	(	(	PUNCT
ap-2101	422	25	−∆s2	−∆s2	X
ap-2101	422	26	+	+	CCONJ
ap-2101	422	27	ν2)φ(ω	ν2)φ(ω	NOUN
ap-2101	422	28	)	)	PUNCT
ap-2101	422	29	=	=	SYM
ap-2101	422	30	gδs2(ω	gδs2(ω	X
ap-2101	422	31	,	,	PUNCT
ap-2101	422	32	ω0)φ(ω	ω0)φ(ω	NUM
ap-2101	422	33	)	)	PUNCT
ap-2101	422	34	,	,	PUNCT
ap-2101	422	35	(	(	PUNCT
ap-2101	422	36	4.1	4.1	NUM
ap-2101	422	37	)	)	PUNCT
ap-2101	422	38	where	where	SCONJ
ap-2101	422	39	ω0	ω0	PROPN
ap-2101	422	40	∈	∈	PROPN
ap-2101	422	41	s2	s2	NOUN
ap-2101	422	42	is	be	AUX
ap-2101	422	43	the	the	DET
ap-2101	422	44	location	location	NOUN
ap-2101	422	45	of	of	ADP
ap-2101	422	46	the	the	DET
ap-2101	422	47	dirac	dirac	NOUN
ap-2101	422	48	-	-	PUNCT
ap-2101	422	49	delta	delta	NOUN
ap-2101	422	50	potential	potential	NOUN
ap-2101	422	51	.	.	PUNCT
ap-2101	423	1	since	since	SCONJ
ap-2101	423	2	the	the	DET
ap-2101	423	3	spherical	spherical	ADJ
ap-2101	423	4	harmonics	harmonic	NOUN
ap-2101	423	5	y	y	PROPN
ap-2101	423	6	ml	ml	PROPN
ap-2101	423	7	(	(	PUNCT
ap-2101	423	8	ω	ω	NOUN
ap-2101	423	9	)	)	PUNCT
ap-2101	423	10	form	form	NOUN
ap-2101	423	11	a	a	DET
ap-2101	423	12	complete	complete	ADJ
ap-2101	423	13	set	set	NOUN
ap-2101	423	14	,	,	PUNCT
ap-2101	423	15	we	we	PRON
ap-2101	423	16	can	can	AUX
ap-2101	423	17	expand	expand	VERB
ap-2101	423	18	φ(ω	φ(ω	PRON
ap-2101	423	19	)	)	PUNCT
ap-2101	423	20	in	in	ADP
ap-2101	423	21	terms	term	NOUN
ap-2101	423	22	of	of	ADP
ap-2101	423	23	them	they	PRON
ap-2101	423	24	and	and	CCONJ
ap-2101	423	25	using	use	VERB
ap-2101	423	26	the	the	DET
ap-2101	423	27	eigenvalue	eigenvalue	PROPN
ap-2101	423	28	relation	relation	NOUN
ap-2101	423	29	−∆s2y	−∆s2y	PROPN
ap-2101	423	30	ml	ml	PROPN
ap-2101	423	31	(	(	PUNCT
ap-2101	423	32	ω	ω	NOUN
ap-2101	423	33	)	)	PUNCT
ap-2101	423	34	=	=	SYM
ap-2101	424	1	r−2l(l	r−2l(l	ADJ
ap-2101	424	2	+	+	NUM
ap-2101	424	3	1)y	1)y	NUM
ap-2101	424	4	ml	ml	X
ap-2101	424	5	(	(	PUNCT
ap-2101	424	6	ω	ω	NOUN
ap-2101	424	7	)	)	PUNCT
ap-2101	424	8	,	,	PUNCT
ap-2101	424	9	we	we	PRON
ap-2101	424	10	find	find	VERB
ap-2101	424	11	∞∑	∞∑	NUM
ap-2101	424	12	l=0	l=0	PROPN
ap-2101	424	13	l∑	l∑	PUNCT
ap-2101	425	1	m=−l	m=−l	PROPN
ap-2101	425	2	cml	cml	PROPN
ap-2101	425	3	[	[	PUNCT
ap-2101	425	4	r−2l(l	r−2l(l	ADJ
ap-2101	425	5	+	+	NUM
ap-2101	425	6	1	1	NUM
ap-2101	425	7	)	)	PUNCT
ap-2101	425	8	+	+	CCONJ
ap-2101	425	9	ν2]y	ν2]y	ADJ
ap-2101	425	10	ml	ml	PROPN
ap-2101	425	11	(	(	PUNCT
ap-2101	425	12	ω	ω	NOUN
ap-2101	425	13	)	)	PUNCT
ap-2101	425	14	=	=	SYM
ap-2101	425	15	gδs2(ω	gδs2(ω	X
ap-2101	425	16	,	,	PUNCT
ap-2101	425	17	ω0	ω0	NOUN
ap-2101	425	18	)	)	PUNCT
ap-2101	425	19	∞∑	∞∑	NUM
ap-2101	425	20	l=0	l=0	PROPN
ap-2101	425	21	l∑	l∑	PUNCT
ap-2101	426	1	m=−l	m=−l	PROPN
ap-2101	426	2	cml	cml	PROPN
ap-2101	426	3	y	y	PROPN
ap-2101	426	4	m	m	PROPN
ap-2101	426	5	l	l	NOUN
ap-2101	426	6	(	(	PUNCT
ap-2101	426	7	ω	ω	NOUN
ap-2101	426	8	)	)	PUNCT
ap-2101	426	9	.	.	PUNCT
ap-2101	427	1	(	(	PUNCT
ap-2101	427	2	4.2	4.2	NUM
ap-2101	427	3	)	)	PUNCT
ap-2101	427	4	now	now	ADV
ap-2101	427	5	if	if	SCONJ
ap-2101	427	6	we	we	PRON
ap-2101	427	7	multiply	multiply	VERB
ap-2101	427	8	both	both	DET
ap-2101	427	9	sides	side	NOUN
ap-2101	427	10	by	by	ADP
ap-2101	427	11	y	y	PROPN
ap-2101	427	12	m′l′	m′l′	PROPN
ap-2101	427	13	(	(	PUNCT
ap-2101	427	14	ω	ω	NOUN
ap-2101	427	15	)	)	PUNCT
ap-2101	427	16	and	and	CCONJ
ap-2101	427	17	integrate	integrate	VERB
ap-2101	427	18	over	over	ADP
ap-2101	427	19	r−2	r−2	PROPN
ap-2101	427	20	∫	∫	NOUN
ap-2101	427	21	s2	s2	PROPN
ap-2101	427	22	dvs2	dvs2	NOUN
ap-2101	427	23	we	we	PRON
ap-2101	427	24	obtain	obtain	VERB
ap-2101	427	25	cml	cml	PROPN
ap-2101	427	26	[	[	PUNCT
ap-2101	427	27	l(l	l(l	NOUN
ap-2101	427	28	+	+	CCONJ
ap-2101	427	29	1	1	NUM
ap-2101	427	30	)	)	PUNCT
ap-2101	427	31	+	+	CCONJ
ap-2101	427	32	ν2r2	ν2r2	X
ap-2101	427	33	]	]	X
ap-2101	427	34	=	=	SYM
ap-2101	427	35	g	g	PROPN
ap-2101	427	36	∞∑	∞∑	PROPN
ap-2101	427	37	l′=0	l′=0	PROPN
ap-2101	427	38	l′∑	l′∑	NOUN
ap-2101	427	39	m′=−l′	m′=−l′	NOUN
ap-2101	427	40	cm	cm	PROPN
ap-2101	427	41	′	′	NUM
ap-2101	428	1	l′	l′	PROPN
ap-2101	429	1	y	y	PROPN
ap-2101	429	2	m	m	VERB
ap-2101	429	3	l	l	NOUN
ap-2101	429	4	(	(	PUNCT
ap-2101	429	5	ω0)y	ω0)y	PROPN
ap-2101	429	6	m	m	PROPN
ap-2101	429	7	′	′	NOUN
ap-2101	429	8	l′	l′	NOUN
ap-2101	429	9	(	(	PUNCT
ap-2101	429	10	ω0	ω0	PROPN
ap-2101	429	11	)	)	PUNCT
ap-2101	429	12	,	,	PUNCT
ap-2101	429	13	(	(	PUNCT
ap-2101	429	14	4.3	4.3	NUM
ap-2101	429	15	)	)	PUNCT
ap-2101	429	16	where	where	SCONJ
ap-2101	429	17	we	we	PRON
ap-2101	429	18	have	have	AUX
ap-2101	429	19	also	also	ADV
ap-2101	429	20	used	use	VERB
ap-2101	429	21	the	the	DET
ap-2101	429	22	orthogonality	orthogonality	NOUN
ap-2101	429	23	relation	relation	NOUN
ap-2101	429	24	of	of	ADP
ap-2101	429	25	the	the	DET
ap-2101	429	26	spherical	spherical	ADJ
ap-2101	429	27	harmonics	harmonic	NOUN
ap-2101	429	28	.	.	PUNCT
ap-2101	430	1	the	the	DET
ap-2101	430	2	next	next	ADJ
ap-2101	430	3	step	step	NOUN
ap-2101	430	4	is	be	AUX
ap-2101	430	5	to	to	PART
ap-2101	430	6	determine	determine	VERB
ap-2101	430	7	the	the	DET
ap-2101	430	8	type	type	NOUN
ap-2101	430	9	of	of	ADP
ap-2101	430	10	divergence	divergence	NOUN
ap-2101	430	11	.	.	PUNCT
ap-2101	431	1	for	for	ADP
ap-2101	431	2	this	this	PRON
ap-2101	431	3	we	we	PRON
ap-2101	431	4	define	define	VERB
ap-2101	431	5	n	n	NOUN
ap-2101	431	6	=	=	SYM
ap-2101	431	7	∞∑	∞∑	NUM
ap-2101	431	8	l′=0	l′=0	PROPN
ap-2101	431	9	l′∑	l′∑	NOUN
ap-2101	431	10	m′=−l′	m′=−l′	NOUN
ap-2101	431	11	cm	cm	PROPN
ap-2101	431	12	′	′	NUM
ap-2101	431	13	l′	l′	PROPN
ap-2101	432	1	y	y	PROPN
ap-2101	432	2	m′	m′	NOUN
ap-2101	432	3	l′	l′	NOUN
ap-2101	432	4	(	(	PUNCT
ap-2101	432	5	ω0	ω0	PROPN
ap-2101	432	6	)	)	PUNCT
ap-2101	432	7	,	,	PUNCT
ap-2101	432	8	(	(	PUNCT
ap-2101	432	9	4.4	4.4	NUM
ap-2101	432	10	)	)	PUNCT
ap-2101	432	11	so	so	SCONJ
ap-2101	432	12	that	that	SCONJ
ap-2101	432	13	cml	cml	PROPN
ap-2101	432	14	is	be	AUX
ap-2101	432	15	given	give	VERB
ap-2101	432	16	by	by	ADP
ap-2101	432	17	cml	cml	PROPN
ap-2101	432	18	=	=	SYM
ap-2101	432	19	n	n	PROPN
ap-2101	432	20	gy	gy	VERB
ap-2101	432	21	ml	ml	PROPN
ap-2101	432	22	(	(	PUNCT
ap-2101	432	23	ω0	ω0	NOUN
ap-2101	432	24	)	)	PUNCT
ap-2101	433	1	l(l	l(l	NOUN
ap-2101	433	2	+	+	CCONJ
ap-2101	433	3	1	1	X
ap-2101	433	4	)	)	PUNCT
ap-2101	433	5	+	+	NUM
ap-2101	433	6	ν2r2	ν2r2	X
ap-2101	433	7	.	.	PUNCT
ap-2101	434	1	(	(	PUNCT
ap-2101	434	2	4.5	4.5	NUM
ap-2101	434	3	)	)	PUNCT
ap-2101	434	4	by	by	ADP
ap-2101	434	5	plugging	plug	VERB
ap-2101	434	6	this	this	DET
ap-2101	434	7	result	result	NOUN
ap-2101	434	8	into	into	ADP
ap-2101	434	9	(	(	PUNCT
ap-2101	434	10	4.4	4.4	NUM
ap-2101	434	11	)	)	PUNCT
ap-2101	434	12	we	we	PRON
ap-2101	434	13	find	find	VERB
ap-2101	434	14	g−1	g−1	ADJ
ap-2101	434	15	as	as	ADP
ap-2101	434	16	1	1	NUM
ap-2101	434	17	g	g	NOUN
ap-2101	435	1	=	=	SYM
ap-2101	435	2	1	1	NUM
ap-2101	435	3	4π	4π	NUM
ap-2101	435	4	∞∑	∞∑	NUM
ap-2101	435	5	l′=0	l′=0	NOUN
ap-2101	435	6	2l′	2l′	NUM
ap-2101	435	7	+	+	SYM
ap-2101	435	8	1	1	NUM
ap-2101	435	9	l′(l′	l′(l′	NOUN
ap-2101	435	10	+	+	X
ap-2101	435	11	1	1	X
ap-2101	435	12	)	)	PUNCT
ap-2101	435	13	+	+	CCONJ
ap-2101	435	14	ν2r2	ν2r2	NOUN
ap-2101	435	15	,	,	PUNCT
ap-2101	435	16	(	(	PUNCT
ap-2101	435	17	4.6	4.6	NUM
ap-2101	435	18	)	)	PUNCT
ap-2101	435	19	where	where	SCONJ
ap-2101	435	20	we	we	PRON
ap-2101	435	21	have	have	AUX
ap-2101	435	22	used	use	VERB
ap-2101	435	23	l′∑	l′∑	PROPN
ap-2101	435	24	m′=−l′	m′=−l′	PROPN
ap-2101	435	25	y	y	PROPN
ap-2101	435	26	m	m	PROPN
ap-2101	435	27	′	′	NOUN
ap-2101	435	28	l′	l′	NOUN
ap-2101	435	29	(	(	PUNCT
ap-2101	435	30	ω0)y	ω0)y	PROPN
ap-2101	435	31	m	m	PROPN
ap-2101	435	32	′	′	NOUN
ap-2101	435	33	l′	l′	NOUN
ap-2101	435	34	(	(	PUNCT
ap-2101	435	35	ω0	ω0	X
ap-2101	435	36	)	)	PUNCT
ap-2101	435	37	=	=	SYM
ap-2101	435	38	2l′	2l′	NUM
ap-2101	436	1	+	+	CCONJ
ap-2101	436	2	1	1	NUM
ap-2101	436	3	4π	4π	NUM
ap-2101	436	4	.	.	PUNCT
ap-2101	437	1	(	(	PUNCT
ap-2101	437	2	4.7	4.7	NUM
ap-2101	437	3	)	)	PUNCT
ap-2101	437	4	by	by	ADP
ap-2101	437	5	using	use	VERB
ap-2101	437	6	the	the	DET
ap-2101	437	7	maclaurin	maclaurin	NOUN
ap-2101	437	8	-	-	PUNCT
ap-2101	437	9	cauchy	cauchy	ADJ
ap-2101	437	10	integral	integral	ADJ
ap-2101	437	11	test	test	NOUN
ap-2101	437	12	we	we	PRON
ap-2101	437	13	can	can	AUX
ap-2101	437	14	see	see	VERB
ap-2101	437	15	that	that	SCONJ
ap-2101	437	16	the	the	DET
ap-2101	437	17	l′	l′	NUM
ap-2101	437	18	sum	sum	NOUN
ap-2101	437	19	in	in	ADP
ap-2101	437	20	(	(	PUNCT
ap-2101	437	21	4.6	4.6	NUM
ap-2101	437	22	)	)	PUNCT
ap-2101	437	23	is	be	AUX
ap-2101	437	24	logarithmically	logarithmically	ADV
ap-2101	437	25	divergent	divergent	ADJ
ap-2101	437	26	and	and	CCONJ
ap-2101	437	27	the	the	DET
ap-2101	437	28	divergence	divergence	NOUN
ap-2101	437	29	is	be	AUX
ap-2101	437	30	caused	cause	VERB
ap-2101	437	31	by	by	ADP
ap-2101	437	32	the	the	DET
ap-2101	437	33	large	large	ADJ
ap-2101	437	34	l′	l′	NOUN
ap-2101	437	35	values	value	NOUN
ap-2101	437	36	.	.	PUNCT
ap-2101	438	1	169	169	NUM
ap-2101	438	2	osman	osman	PROPN
ap-2101	438	3	teoman	teoman	PROPN
ap-2101	438	4	turgut	turgut	PROPN
ap-2101	438	5	,	,	PUNCT
ap-2101	438	6	cem	cem	NOUN
ap-2101	438	7	eröncel	eröncel	VERB
ap-2101	438	8	acta	acta	PROPN
ap-2101	438	9	polytechnica	polytechnica	PROPN
ap-2101	438	10	4.2	4.2	NUM
ap-2101	438	11	.	.	PUNCT
ap-2101	439	1	applying	apply	VERB
ap-2101	439	2	the	the	DET
ap-2101	439	3	erg	erg	NOUN
ap-2101	439	4	procedure	procedure	NOUN
ap-2101	439	5	we	we	PRON
ap-2101	439	6	begin	begin	VERB
ap-2101	439	7	by	by	ADP
ap-2101	439	8	writing	write	VERB
ap-2101	439	9	the	the	DET
ap-2101	439	10	eigenvalue	eigenvalue	ADJ
ap-2101	439	11	equation	equation	NOUN
ap-2101	439	12	at	at	ADP
ap-2101	439	13	the	the	DET
ap-2101	439	14	bare	bare	ADJ
ap-2101	439	15	scale	scale	NOUN
ap-2101	439	16	λ	λ	PROPN
ap-2101	439	17	.	.	PUNCT
ap-2101	439	18	cml	cml	PROPN
ap-2101	439	19	[	[	PUNCT
ap-2101	439	20	l(l	l(l	NOUN
ap-2101	439	21	+	+	CCONJ
ap-2101	439	22	1	1	NUM
ap-2101	439	23	)	)	PUNCT
ap-2101	439	24	+	+	CCONJ
ap-2101	439	25	ν2r2	ν2r2	X
ap-2101	439	26	]	]	X
ap-2101	439	27	=	=	SYM
ap-2101	439	28	θλ(l	θλ(l	X
ap-2101	439	29	)	)	PUNCT
ap-2101	440	1	λ∑	λ∑	PROPN
ap-2101	440	2	l′=0	l′=0	PROPN
ap-2101	440	3	gλ(l	gλ(l	PROPN
ap-2101	440	4	,	,	PUNCT
ap-2101	440	5	l′)ϑ(l	l′)ϑ(l	PROPN
ap-2101	440	6	,	,	PUNCT
ap-2101	440	7	l′;m	l′;m	PROPN
ap-2101	440	8	)	)	PUNCT
ap-2101	440	9	,	,	PUNCT
ap-2101	440	10	(	(	PUNCT
ap-2101	440	11	4.8	4.8	NUM
ap-2101	440	12	)	)	PUNCT
ap-2101	440	13	where	where	SCONJ
ap-2101	440	14	ϑ(l	ϑ(l	NOUN
ap-2101	440	15	,	,	PUNCT
ap-2101	440	16	l′;m	l′;m	PROPN
ap-2101	440	17	)	)	PUNCT
ap-2101	440	18	≡	≡	PROPN
ap-2101	440	19	l′∑	l′∑	PROPN
ap-2101	440	20	m′=−l′	m′=−l′	PROPN
ap-2101	440	21	cm	cm	PROPN
ap-2101	440	22	′	′	NUM
ap-2101	440	23	l′	l′	PROPN
ap-2101	441	1	y	y	PROPN
ap-2101	441	2	m	m	VERB
ap-2101	441	3	l	l	NOUN
ap-2101	441	4	(	(	PUNCT
ap-2101	441	5	ω0)y	ω0)y	PROPN
ap-2101	441	6	m	m	PROPN
ap-2101	441	7	′	′	NOUN
ap-2101	441	8	l′	l′	NOUN
ap-2101	441	9	(	(	PUNCT
ap-2101	441	10	ω0	ω0	PROPN
ap-2101	441	11	)	)	PUNCT
ap-2101	441	12	.	.	PUNCT
ap-2101	442	1	(	(	PUNCT
ap-2101	442	2	4.9	4.9	NUM
ap-2101	442	3	)	)	PUNCT
ap-2101	442	4	since	since	SCONJ
ap-2101	442	5	the	the	DET
ap-2101	442	6	eigenvalue	eigenvalue	PROPN
ap-2101	442	7	spectrum	spectrum	NOUN
ap-2101	442	8	is	be	AUX
ap-2101	442	9	discrete	discrete	ADJ
ap-2101	442	10	,	,	PUNCT
ap-2101	442	11	we	we	PRON
ap-2101	442	12	take	take	VERB
ap-2101	442	13	the	the	DET
ap-2101	442	14	second	second	ADJ
ap-2101	442	15	cutoff	cutoff	NOUN
ap-2101	442	16	as	as	ADP
ap-2101	442	17	λ−	λ−	PROPN
ap-2101	442	18	1	1	NUM
ap-2101	442	19	instead	instead	ADV
ap-2101	442	20	of	of	ADP
ap-2101	442	21	λ−	λ−	PROPN
ap-2101	442	22	dλ	dλ	NOUN
ap-2101	442	23	.	.	PUNCT
ap-2101	443	1	we	we	PRON
ap-2101	443	2	write	write	VERB
ap-2101	443	3	cml	cml	PROPN
ap-2101	443	4	[	[	PUNCT
ap-2101	443	5	l(l	l(l	NOUN
ap-2101	443	6	+	+	CCONJ
ap-2101	443	7	1	1	NUM
ap-2101	443	8	)	)	PUNCT
ap-2101	443	9	+	+	CCONJ
ap-2101	443	10	ν2r2	ν2r2	X
ap-2101	443	11	]	]	X
ap-2101	443	12	=	=	SYM
ap-2101	443	13	θλ−1(l	θλ−1(l	NOUN
ap-2101	443	14	)	)	PUNCT
ap-2101	443	15	λ−1∑	λ−1∑	NUM
ap-2101	443	16	l′=0	l′=0	NOUN
ap-2101	443	17	gλ−1(l	gλ−1(l	NOUN
ap-2101	443	18	,	,	PUNCT
ap-2101	443	19	l′)ϑ(l	l′)ϑ(l	PROPN
ap-2101	443	20	,	,	PUNCT
ap-2101	443	21	l′;m	l′;m	PROPN
ap-2101	443	22	)	)	PUNCT
ap-2101	443	23	.	.	PUNCT
ap-2101	444	1	(	(	PUNCT
ap-2101	444	2	4.10	4.10	NUM
ap-2101	444	3	)	)	PUNCT
ap-2101	444	4	we	we	PRON
ap-2101	444	5	rewrite	rewrite	VERB
ap-2101	444	6	(	(	PUNCT
ap-2101	444	7	4.8	4.8	NUM
ap-2101	444	8	)	)	PUNCT
ap-2101	444	9	as	as	ADP
ap-2101	444	10	cml	cml	PROPN
ap-2101	444	11	[	[	PUNCT
ap-2101	444	12	l(l	l(l	NOUN
ap-2101	444	13	+	+	CCONJ
ap-2101	444	14	1	1	NUM
ap-2101	444	15	)	)	PUNCT
ap-2101	444	16	+	+	CCONJ
ap-2101	444	17	ν2r2	ν2r2	X
ap-2101	444	18	]	]	X
ap-2101	444	19	=	=	SYM
ap-2101	444	20	θλ(l	θλ(l	X
ap-2101	444	21	)	)	PUNCT
ap-2101	444	22	(	(	PUNCT
ap-2101	444	23	λ−1∑	λ−1∑	X
ap-2101	444	24	l′=0	l′=0	PROPN
ap-2101	444	25	gλ(l	gλ(l	NOUN
ap-2101	444	26	,	,	PUNCT
ap-2101	444	27	l′)ϑ(l	l′)ϑ(l	PROPN
ap-2101	444	28	,	,	PUNCT
ap-2101	444	29	l′;m	l′;m	PROPN
ap-2101	444	30	)	)	PUNCT
ap-2101	444	31	+	+	CCONJ
ap-2101	445	1	gλ(l	gλ(l	NOUN
ap-2101	445	2	,	,	PUNCT
ap-2101	445	3	λ)ϑ(l	λ)ϑ(l	X
ap-2101	445	4	,	,	PUNCT
ap-2101	445	5	λ;m	λ;m	PROPN
ap-2101	445	6	)	)	PUNCT
ap-2101	445	7	)	)	PUNCT
ap-2101	445	8	,	,	PUNCT
ap-2101	445	9	(	(	PUNCT
ap-2101	445	10	4.11	4.11	NUM
ap-2101	445	11	)	)	PUNCT
ap-2101	445	12	so	so	SCONJ
ap-2101	445	13	that	that	SCONJ
ap-2101	445	14	by	by	ADP
ap-2101	445	15	substituting	substitute	VERB
ap-2101	445	16	l	l	NOUN
ap-2101	445	17	=	=	PUNCT
ap-2101	445	18	λ	λ	X
ap-2101	445	19	we	we	PRON
ap-2101	445	20	get	get	VERB
ap-2101	445	21	an	an	DET
ap-2101	445	22	expression	expression	NOUN
ap-2101	445	23	for	for	ADP
ap-2101	445	24	cmλ	cmλ	NOUN
ap-2101	445	25	:	:	PUNCT
ap-2101	445	26	cmλ	cmλ	NOUN
ap-2101	445	27	=	=	NOUN
ap-2101	445	28	1	1	NUM
ap-2101	446	1	λ(λ	λ(λ	X
ap-2101	446	2	+	+	NUM
ap-2101	446	3	1	1	X
ap-2101	446	4	)	)	PUNCT
ap-2101	446	5	+	+	CCONJ
ap-2101	446	6	ν2r2	ν2r2	X
ap-2101	446	7	(	(	PUNCT
ap-2101	446	8	λ−1∑	λ−1∑	X
ap-2101	446	9	l′=0	l′=0	NOUN
ap-2101	446	10	gλ(λ	gλ(λ	NUM
ap-2101	446	11	,	,	PUNCT
ap-2101	446	12	l′)ϑ(λ	l′)ϑ(λ	PROPN
ap-2101	446	13	,	,	PUNCT
ap-2101	446	14	l′;m	l′;m	PROPN
ap-2101	446	15	)	)	PUNCT
ap-2101	446	16	+	+	CCONJ
ap-2101	446	17	gλ(λ	gλ(λ	NOUN
ap-2101	446	18	,	,	PUNCT
ap-2101	446	19	λ)ϑ(λ	λ)ϑ(λ	ADV
ap-2101	446	20	,	,	PUNCT
ap-2101	446	21	λ;m	λ;m	PROPN
ap-2101	446	22	)	)	PUNCT
ap-2101	446	23	)	)	PUNCT
ap-2101	446	24	.	.	PUNCT
ap-2101	447	1	(	(	PUNCT
ap-2101	447	2	4.12	4.12	NUM
ap-2101	447	3	)	)	PUNCT
ap-2101	447	4	we	we	PRON
ap-2101	447	5	note	note	VERB
ap-2101	447	6	that	that	SCONJ
ap-2101	447	7	due	due	ADP
ap-2101	447	8	to	to	ADP
ap-2101	447	9	the	the	DET
ap-2101	447	10	discrete	discrete	ADJ
ap-2101	447	11	spectrum	spectrum	NOUN
ap-2101	447	12	we	we	PRON
ap-2101	447	13	could	could	AUX
ap-2101	447	14	not	not	PART
ap-2101	447	15	ignore	ignore	VERB
ap-2101	447	16	the	the	DET
ap-2101	447	17	second	second	ADJ
ap-2101	447	18	term	term	NOUN
ap-2101	447	19	.	.	PUNCT
ap-2101	448	1	using	use	VERB
ap-2101	448	2	(	(	PUNCT
ap-2101	448	3	4.9	4.9	NUM
ap-2101	448	4	)	)	PUNCT
ap-2101	448	5	and	and	CCONJ
ap-2101	448	6	(	(	PUNCT
ap-2101	448	7	4.12	4.12	NUM
ap-2101	448	8	)	)	PUNCT
ap-2101	448	9	we	we	PRON
ap-2101	448	10	can	can	AUX
ap-2101	448	11	write	write	VERB
ap-2101	448	12	ϑ(l	ϑ(l	NOUN
ap-2101	448	13	,	,	PUNCT
ap-2101	448	14	λ;m	λ;m	NUM
ap-2101	448	15	)	)	PUNCT
ap-2101	448	16	=	=	SYM
ap-2101	449	1	λ∑	λ∑	PUNCT
ap-2101	449	2	m′=−λ	m′=−λ	NOUN
ap-2101	449	3	cm	cm	NOUN
ap-2101	449	4	′	′	NUM
ap-2101	450	1	λ	λ	INTJ
ap-2101	450	2	y	y	NOUN
ap-2101	450	3	m	m	VERB
ap-2101	450	4	′	′	NUM
ap-2101	451	1	λ	λ	X
ap-2101	451	2	(	(	PUNCT
ap-2101	451	3	ω0)y	ω0)y	PROPN
ap-2101	451	4	ml	ml	PROPN
ap-2101	451	5	(	(	PUNCT
ap-2101	451	6	ω0	ω0	PROPN
ap-2101	451	7	)	)	PUNCT
ap-2101	451	8	=	=	SYM
ap-2101	452	1	λ∑	λ∑	PUNCT
ap-2101	452	2	m′=−λ	m′=−λ	PROPN
ap-2101	452	3	y	y	PROPN
ap-2101	452	4	m	m	VERB
ap-2101	452	5	′	′	NUM
ap-2101	453	1	λ	λ	X
ap-2101	453	2	(	(	PUNCT
ap-2101	453	3	ω0)y	ω0)y	PROPN
ap-2101	453	4	ml	ml	PROPN
ap-2101	453	5	(	(	PUNCT
ap-2101	453	6	ω0	ω0	PROPN
ap-2101	453	7	)	)	PUNCT
ap-2101	453	8	λ(λ	λ(λ	PROPN
ap-2101	454	1	+	+	CCONJ
ap-2101	454	2	1	1	X
ap-2101	454	3	)	)	PUNCT
ap-2101	454	4	+	+	CCONJ
ap-2101	454	5	ν2r2	ν2r2	X
ap-2101	454	6	(	(	PUNCT
ap-2101	454	7	λ−1∑	λ−1∑	X
ap-2101	454	8	l′=0	l′=0	NOUN
ap-2101	454	9	gλ(λ	gλ(λ	NUM
ap-2101	454	10	,	,	PUNCT
ap-2101	454	11	l′)ϑ(λ	l′)ϑ(λ	PROPN
ap-2101	454	12	,	,	PUNCT
ap-2101	454	13	l′;m	l′;m	PROPN
ap-2101	454	14	)	)	PUNCT
ap-2101	454	15	+	+	CCONJ
ap-2101	454	16	gλ(λ	gλ(λ	NOUN
ap-2101	454	17	,	,	PUNCT
ap-2101	454	18	λ)ϑ(λ	λ)ϑ(λ	ADV
ap-2101	454	19	,	,	PUNCT
ap-2101	454	20	λ;m	λ;m	PUNCT
ap-2101	454	21	)	)	PUNCT
ap-2101	454	22	+	+	CCONJ
ap-2101	454	23	gλ(λ	gλ(λ	NUM
ap-2101	454	24	,	,	PUNCT
ap-2101	454	25	λ	λ	NOUN
ap-2101	454	26	)	)	PUNCT
ap-2101	454	27	λ∑	λ∑	PROPN
ap-2101	455	1	m′=−λ	m′=−λ	NOUN
ap-2101	455	2	y	y	PROPN
ap-2101	455	3	m	m	VERB
ap-2101	455	4	′	′	NUM
ap-2101	455	5	λ	λ	X
ap-2101	455	6	(	(	PUNCT
ap-2101	455	7	ω0)y	ω0)y	PROPN
ap-2101	455	8	ml	ml	X
ap-2101	455	9	(	(	PUNCT
ap-2101	455	10	ω0)ϑ(λ	ω0)ϑ(λ	NOUN
ap-2101	455	11	,	,	PUNCT
ap-2101	455	12	λ;m′	λ;m′	NOUN
ap-2101	455	13	)	)	PUNCT
ap-2101	455	14	)	)	PUNCT
ap-2101	455	15	.	.	PUNCT
ap-2101	456	1	(	(	PUNCT
ap-2101	456	2	4.13	4.13	NUM
ap-2101	456	3	)	)	PUNCT
ap-2101	456	4	by	by	ADP
ap-2101	456	5	putting	put	VERB
ap-2101	456	6	explicit	explicit	ADJ
ap-2101	456	7	expressions	expression	NOUN
ap-2101	456	8	for	for	ADP
ap-2101	456	9	ϑ(λ	ϑ(λ	NOUN
ap-2101	456	10	,	,	PUNCT
ap-2101	456	11	l′;m′	l′;m′	NOUN
ap-2101	456	12	)	)	PUNCT
ap-2101	456	13	and	and	CCONJ
ap-2101	456	14	ϑ(λ	ϑ(λ	PROPN
ap-2101	456	15	,	,	PUNCT
ap-2101	456	16	λ;m′	λ;m′	NOUN
ap-2101	456	17	)	)	PUNCT
ap-2101	456	18	we	we	PRON
ap-2101	456	19	get	get	VERB
ap-2101	456	20	ϑ(l	ϑ(l	ADP
ap-2101	456	21	,	,	PUNCT
ap-2101	456	22	λ;m	λ;m	NUM
ap-2101	456	23	)	)	PUNCT
ap-2101	456	24	=	=	SYM
ap-2101	457	1	1	1	NUM
ap-2101	457	2	λ(λ	λ(λ	X
ap-2101	457	3	+	+	NUM
ap-2101	457	4	1	1	X
ap-2101	457	5	)	)	PUNCT
ap-2101	457	6	+	+	CCONJ
ap-2101	457	7	ν2r2	ν2r2	X
ap-2101	457	8	(	(	PUNCT
ap-2101	457	9	λ−1∑	λ−1∑	X
ap-2101	457	10	l′=0	l′=0	NOUN
ap-2101	457	11	gλ(λ	gλ(λ	NUM
ap-2101	457	12	,	,	PUNCT
ap-2101	457	13	l′	l′	NUM
ap-2101	457	14	)	)	PUNCT
ap-2101	458	1	λ∑	λ∑	X
ap-2101	459	1	m′=−λ	m′=−λ	NOUN
ap-2101	459	2	y	y	PROPN
ap-2101	459	3	m	m	VERB
ap-2101	459	4	′	′	NUM
ap-2101	459	5	λ	λ	X
ap-2101	459	6	(	(	PUNCT
ap-2101	459	7	ω0)y	ω0)y	PROPN
ap-2101	459	8	m′λ	m′λ	PROPN
ap-2101	459	9	(	(	PUNCT
ap-2101	459	10	ω0	ω0	PROPN
ap-2101	459	11	)	)	PUNCT
ap-2101	459	12	l′∑	l′∑	PROPN
ap-2101	459	13	m′′=−l′	m′′=−l′	PROPN
ap-2101	459	14	cm	cm	PROPN
ap-2101	459	15	′′	′′	PROPN
ap-2101	459	16	l′	l′	VERB
ap-2101	459	17	y	y	PROPN
ap-2101	459	18	m	m	PROPN
ap-2101	459	19	′′	′′	PROPN
ap-2101	459	20	l′	l′	NOUN
ap-2101	459	21	(	(	PUNCT
ap-2101	459	22	ω0)y	ω0)y	PROPN
ap-2101	459	23	ml	ml	PROPN
ap-2101	459	24	(	(	PUNCT
ap-2101	459	25	ω0	ω0	PROPN
ap-2101	459	26	)	)	PUNCT
ap-2101	459	27	+	+	CCONJ
ap-2101	459	28	gλ(λ	gλ(λ	NUM
ap-2101	459	29	,	,	PUNCT
ap-2101	459	30	λ	λ	NOUN
ap-2101	459	31	)	)	PUNCT
ap-2101	459	32	λ∑	λ∑	PROPN
ap-2101	460	1	m′=−λ	m′=−λ	NOUN
ap-2101	460	2	y	y	PROPN
ap-2101	460	3	m	m	VERB
ap-2101	460	4	′	′	NUM
ap-2101	460	5	λ	λ	X
ap-2101	460	6	(	(	PUNCT
ap-2101	460	7	ω0)y	ω0)y	PROPN
ap-2101	460	8	m′λ	m′λ	X
ap-2101	460	9	(	(	PUNCT
ap-2101	460	10	ω0	ω0	PROPN
ap-2101	460	11	)	)	PUNCT
ap-2101	460	12	λ∑	λ∑	X
ap-2101	460	13	m′′=−λ	m′′=−λ	PROPN
ap-2101	460	14	cm	cm	PROPN
ap-2101	461	1	′′	′′	PROPN
ap-2101	461	2	λ	λ	PROPN
ap-2101	461	3	y	y	NOUN
ap-2101	461	4	m	m	PROPN
ap-2101	461	5	′′	′′	ADJ
ap-2101	461	6	λ	λ	PROPN
ap-2101	461	7	(	(	PUNCT
ap-2101	461	8	ω0)y	ω0)y	PROPN
ap-2101	461	9	ml	ml	PROPN
ap-2101	461	10	(	(	PUNCT
ap-2101	461	11	ω0	ω0	PROPN
ap-2101	461	12	)	)	PUNCT
ap-2101	461	13	)	)	PUNCT
ap-2101	462	1	=	=	SYM
ap-2101	462	2	1	1	NUM
ap-2101	462	3	4π	4π	NUM
ap-2101	462	4	2λ	2λ	NOUN
ap-2101	463	1	+	+	CCONJ
ap-2101	463	2	1	1	NUM
ap-2101	463	3	λ(λ	λ(λ	NOUN
ap-2101	463	4	+	+	NUM
ap-2101	463	5	1	1	X
ap-2101	463	6	)	)	PUNCT
ap-2101	463	7	+	+	CCONJ
ap-2101	463	8	ν2r2	ν2r2	X
ap-2101	463	9	(	(	PUNCT
ap-2101	463	10	λ−1∑	λ−1∑	X
ap-2101	463	11	l′=0	l′=0	NOUN
ap-2101	463	12	gλ(λ	gλ(λ	NUM
ap-2101	463	13	,	,	PUNCT
ap-2101	463	14	l′)ϑ(l	l′)ϑ(l	PROPN
ap-2101	463	15	,	,	PUNCT
ap-2101	463	16	l′;m	l′;m	PROPN
ap-2101	463	17	)	)	PUNCT
ap-2101	463	18	+	+	CCONJ
ap-2101	463	19	gλ(λ	gλ(λ	NOUN
ap-2101	463	20	,	,	PUNCT
ap-2101	463	21	λ)ϑ(l	λ)ϑ(l	NOUN
ap-2101	463	22	,	,	PUNCT
ap-2101	463	23	λ;m	λ;m	PROPN
ap-2101	463	24	)	)	PUNCT
ap-2101	463	25	)	)	PUNCT
ap-2101	463	26	.	.	PUNCT
ap-2101	464	1	(	(	PUNCT
ap-2101	464	2	4.14	4.14	NUM
ap-2101	464	3	)	)	PUNCT
ap-2101	464	4	from	from	ADP
ap-2101	464	5	this	this	PRON
ap-2101	464	6	,	,	PUNCT
ap-2101	464	7	ϑ(l	ϑ(l	PRON
ap-2101	464	8	,	,	PUNCT
ap-2101	464	9	λ;m	λ;m	NUM
ap-2101	464	10	)	)	PUNCT
ap-2101	464	11	can	can	AUX
ap-2101	464	12	be	be	AUX
ap-2101	464	13	solved	solve	VERB
ap-2101	464	14	as	as	ADP
ap-2101	464	15	ϑ(l	ϑ(l	NOUN
ap-2101	464	16	,	,	PUNCT
ap-2101	464	17	λ;m	λ;m	NUM
ap-2101	464	18	)	)	PUNCT
ap-2101	464	19	=	=	PRON
ap-2101	465	1	(	(	PUNCT
ap-2101	465	2	4πλ(λ	4πλ(λ	NUM
ap-2101	465	3	+	+	CCONJ
ap-2101	465	4	1	1	X
ap-2101	465	5	)	)	PUNCT
ap-2101	466	1	+	+	CCONJ
ap-2101	466	2	ν2r2	ν2r2	NOUN
ap-2101	466	3	2λ	2λ	NUM
ap-2101	466	4	+	+	CCONJ
ap-2101	466	5	1	1	NUM
ap-2101	466	6	−	−	NOUN
ap-2101	466	7	gλ(λ	gλ(λ	PUNCT
ap-2101	466	8	,	,	PUNCT
ap-2101	466	9	λ	λ	NOUN
ap-2101	466	10	)	)	PUNCT
ap-2101	466	11	)	)	PUNCT
ap-2101	466	12	−1	−1	NOUN
ap-2101	466	13	λ−1∑	λ−1∑	X
ap-2101	466	14	l′=0	l′=0	NOUN
ap-2101	466	15	gλ(λ	gλ(λ	NUM
ap-2101	466	16	,	,	PUNCT
ap-2101	466	17	l′)ϑ(l	l′)ϑ(l	PROPN
ap-2101	466	18	,	,	PUNCT
ap-2101	466	19	l′;m	l′;m	PROPN
ap-2101	466	20	)	)	PUNCT
ap-2101	466	21	.	.	PUNCT
ap-2101	467	1	(	(	PUNCT
ap-2101	467	2	4.15	4.15	NUM
ap-2101	467	3	)	)	PUNCT
ap-2101	467	4	by	by	ADP
ap-2101	467	5	putting	put	VERB
ap-2101	467	6	this	this	DET
ap-2101	467	7	result	result	NOUN
ap-2101	467	8	back	back	ADV
ap-2101	467	9	into	into	ADP
ap-2101	467	10	(	(	PUNCT
ap-2101	467	11	4.11	4.11	NUM
ap-2101	467	12	)	)	PUNCT
ap-2101	467	13	we	we	PRON
ap-2101	467	14	get	get	VERB
ap-2101	467	15	cml	cml	PROPN
ap-2101	468	1	[	[	X
ap-2101	468	2	l(l	l(l	NOUN
ap-2101	468	3	+	+	CCONJ
ap-2101	468	4	1	1	NUM
ap-2101	468	5	)	)	PUNCT
ap-2101	468	6	+	+	CCONJ
ap-2101	468	7	ν2r2	ν2r2	X
ap-2101	468	8	]	]	X
ap-2101	468	9	=	=	SYM
ap-2101	468	10	θλ(l	θλ(l	X
ap-2101	468	11	)	)	PUNCT
ap-2101	468	12	λ−1∑	λ−1∑	PROPN
ap-2101	468	13	l′=0	l′=0	PROPN
ap-2101	468	14	[	[	PUNCT
ap-2101	468	15	gλ(l	gλ(l	NOUN
ap-2101	468	16	,	,	PUNCT
ap-2101	468	17	l′	l′	NUM
ap-2101	468	18	)	)	PUNCT
ap-2101	469	1	+	+	CCONJ
ap-2101	469	2	(	(	PUNCT
ap-2101	469	3	4πλ(λ	4πλ(λ	NUM
ap-2101	469	4	+	+	NOUN
ap-2101	469	5	1)−m	1)−m	NUM
ap-2101	469	6	2λ	2λ	NOUN
ap-2101	469	7	+	+	CCONJ
ap-2101	469	8	1	1	NUM
ap-2101	469	9	−	−	NOUN
ap-2101	469	10	gλ(λ	gλ(λ	PUNCT
ap-2101	469	11	,	,	PUNCT
ap-2101	469	12	λ	λ	NOUN
ap-2101	469	13	)	)	PUNCT
ap-2101	469	14	)	)	PUNCT
ap-2101	469	15	−1	−1	NOUN
ap-2101	469	16	×	×	NOUN
ap-2101	469	17	gλ(l	gλ(l	NOUN
ap-2101	469	18	,	,	PUNCT
ap-2101	469	19	λ)gλ(λ	λ)gλ(λ	PROPN
ap-2101	469	20	,	,	PUNCT
ap-2101	469	21	l′	l′	NUM
ap-2101	469	22	)	)	PUNCT
ap-2101	469	23	]	]	PUNCT
ap-2101	470	1	ϑ(l	ϑ(l	X
ap-2101	470	2	,	,	PUNCT
ap-2101	470	3	l′;m	l′;m	PROPN
ap-2101	470	4	)	)	PUNCT
ap-2101	470	5	,	,	PUNCT
ap-2101	470	6	(	(	PUNCT
ap-2101	470	7	4.16	4.16	NUM
ap-2101	470	8	)	)	PUNCT
ap-2101	470	9	170	170	NUM
ap-2101	470	10	vol	vol	NOUN
ap-2101	470	11	.	.	PUNCT
ap-2101	471	1	54	54	NUM
ap-2101	471	2	no	no	NOUN
ap-2101	471	3	.	.	PUNCT
ap-2101	472	1	2/2014	2/2014	NUM
ap-2101	472	2	exact	exact	ADJ
ap-2101	472	3	renormalization	renormalization	NOUN
ap-2101	472	4	group	group	NOUN
ap-2101	472	5	for	for	ADP
ap-2101	472	6	point	point	NOUN
ap-2101	472	7	interactions	interaction	NOUN
ap-2101	472	8	and	and	CCONJ
ap-2101	472	9	by	by	ADP
ap-2101	472	10	comparing	compare	VERB
ap-2101	472	11	this	this	DET
ap-2101	472	12	result	result	NOUN
ap-2101	472	13	with	with	ADP
ap-2101	472	14	(	(	PUNCT
ap-2101	472	15	4.10	4.10	NUM
ap-2101	472	16	)	)	PUNCT
ap-2101	472	17	we	we	PRON
ap-2101	472	18	obtain	obtain	VERB
ap-2101	472	19	a	a	DET
ap-2101	472	20	recursion	recursion	NOUN
ap-2101	472	21	relation	relation	NOUN
ap-2101	472	22	for	for	ADP
ap-2101	472	23	the	the	DET
ap-2101	472	24	effective	effective	ADJ
ap-2101	472	25	coupling	coupling	NOUN
ap-2101	472	26	constant	constant	ADJ
ap-2101	472	27	.	.	PUNCT
ap-2101	473	1	gλ−1(l	gλ−1(l	NOUN
ap-2101	473	2	,	,	PUNCT
ap-2101	473	3	l′	l′	NUM
ap-2101	473	4	)	)	PUNCT
ap-2101	473	5	=	=	SYM
ap-2101	473	6	gλ(l	gλ(l	NOUN
ap-2101	473	7	,	,	PUNCT
ap-2101	473	8	l′	l′	NUM
ap-2101	473	9	)	)	PUNCT
ap-2101	474	1	+	+	CCONJ
ap-2101	474	2	(	(	PUNCT
ap-2101	474	3	4πλ(λ	4πλ(λ	NUM
ap-2101	474	4	+	+	CCONJ
ap-2101	474	5	1	1	X
ap-2101	474	6	)	)	PUNCT
ap-2101	474	7	+	+	CCONJ
ap-2101	474	8	ν2r2	ν2r2	NOUN
ap-2101	474	9	2λ	2λ	NUM
ap-2101	474	10	+	+	CCONJ
ap-2101	474	11	1	1	NUM
ap-2101	474	12	−	−	NOUN
ap-2101	474	13	gλ(λ	gλ(λ	PUNCT
ap-2101	474	14	,	,	PUNCT
ap-2101	474	15	λ	λ	NOUN
ap-2101	474	16	)	)	PUNCT
ap-2101	474	17	)	)	PUNCT
ap-2101	474	18	−1	−1	NOUN
ap-2101	474	19	gλ(l	gλ(l	NOUN
ap-2101	474	20	,	,	PUNCT
ap-2101	474	21	λ)gλ(λ	λ)gλ(λ	PROPN
ap-2101	474	22	,	,	PUNCT
ap-2101	474	23	l′	l′	NUM
ap-2101	474	24	)	)	PUNCT
ap-2101	474	25	.	.	PUNCT
ap-2101	475	1	(	(	PUNCT
ap-2101	475	2	4.17	4.17	NUM
ap-2101	475	3	)	)	PUNCT
ap-2101	475	4	from	from	ADP
ap-2101	475	5	this	this	DET
ap-2101	475	6	relation	relation	NOUN
ap-2101	475	7	we	we	PRON
ap-2101	475	8	can	can	AUX
ap-2101	475	9	express	express	VERB
ap-2101	475	10	the	the	DET
ap-2101	475	11	effective	effective	ADJ
ap-2101	475	12	coupling	coupling	NOUN
ap-2101	475	13	at	at	ADP
ap-2101	475	14	the	the	DET
ap-2101	475	15	effective	effective	ADJ
ap-2101	475	16	scale	scale	NOUN
ap-2101	475	17	λ	λ	PROPN
ap-2101	475	18	as	as	ADP
ap-2101	475	19	gλ(l	gλ(l	NOUN
ap-2101	475	20	,	,	PUNCT
ap-2101	475	21	l′	l′	NUM
ap-2101	475	22	)	)	PUNCT
ap-2101	476	1	=	=	SYM
ap-2101	476	2	gλ(l	gλ(l	NOUN
ap-2101	476	3	,	,	PUNCT
ap-2101	476	4	l′	l′	NUM
ap-2101	476	5	)	)	PUNCT
ap-2101	477	1	+	+	CCONJ
ap-2101	478	1	λ∑	λ∑	PRON
ap-2101	478	2	s	s	X
ap-2101	478	3	=	=	X
ap-2101	478	4	λ+1	λ+1	X
ap-2101	478	5	(	(	PUNCT
ap-2101	478	6	4π	4π	PRON
ap-2101	478	7	s(s+	s(s+	VERB
ap-2101	478	8	1	1	NUM
ap-2101	478	9	)	)	PUNCT
ap-2101	478	10	+	+	CCONJ
ap-2101	478	11	ν2r2	ν2r2	X
ap-2101	478	12	2s+	2s+	NUM
ap-2101	478	13	1	1	NUM
ap-2101	478	14	−	−	NOUN
ap-2101	478	15	gs(s	gs(s	NOUN
ap-2101	478	16	,	,	PUNCT
ap-2101	478	17	s	s	NOUN
ap-2101	478	18	)	)	PUNCT
ap-2101	478	19	)	)	PUNCT
ap-2101	478	20	−1	−1	NOUN
ap-2101	478	21	gs(l	gs(l	NOUN
ap-2101	478	22	,	,	PUNCT
ap-2101	478	23	s)gs(s	s)gs(s	NOUN
ap-2101	478	24	,	,	PUNCT
ap-2101	478	25	l′	l′	NUM
ap-2101	478	26	)	)	PUNCT
ap-2101	478	27	,	,	PUNCT
ap-2101	478	28	(	(	PUNCT
ap-2101	478	29	4.18	4.18	NUM
ap-2101	478	30	)	)	PUNCT
ap-2101	478	31	or	or	CCONJ
ap-2101	478	32	gλ(l	gλ(l	NOUN
ap-2101	478	33	,	,	PUNCT
ap-2101	478	34	l′	l′	NUM
ap-2101	478	35	)	)	PUNCT
ap-2101	479	1	=	=	SYM
ap-2101	479	2	g	g	ADP
ap-2101	479	3	−	−	PROPN
ap-2101	479	4	xλ(l	xλ(l	NUM
ap-2101	479	5	,	,	PUNCT
ap-2101	479	6	l′	l′	NUM
ap-2101	479	7	)	)	PUNCT
ap-2101	480	1	+	+	CCONJ
ap-2101	481	1	1	1	NUM
ap-2101	481	2	4π	4π	NUM
ap-2101	481	3	λ∑	λ∑	SYM
ap-2101	481	4	s	s	X
ap-2101	481	5	=	=	X
ap-2101	481	6	λ+1	λ+1	X
ap-2101	481	7	(	(	PUNCT
ap-2101	481	8	s(s+	s(s+	NUM
ap-2101	481	9	1	1	NUM
ap-2101	481	10	)	)	PUNCT
ap-2101	481	11	+	+	CCONJ
ap-2101	481	12	ν2r2	ν2r2	X
ap-2101	481	13	2s+	2s+	NUM
ap-2101	481	14	1	1	NUM
ap-2101	481	15	−	−	NOUN
ap-2101	481	16	gs(s	gs(s	NOUN
ap-2101	481	17	,	,	PUNCT
ap-2101	481	18	s	s	X
ap-2101	481	19	)	)	PUNCT
ap-2101	481	20	4π	4π	NUM
ap-2101	481	21	)	)	PUNCT
ap-2101	481	22	−1	−1	NOUN
ap-2101	481	23	gs(l	gs(l	NOUN
ap-2101	481	24	,	,	PUNCT
ap-2101	481	25	s)gs(s	s)gs(s	NOUN
ap-2101	481	26	,	,	PUNCT
ap-2101	481	27	l′	l′	NOUN
ap-2101	481	28	)	)	PUNCT
ap-2101	481	29	.	.	PUNCT
ap-2101	482	1	(	(	PUNCT
ap-2101	482	2	4.19	4.19	NUM
ap-2101	482	3	)	)	PUNCT
ap-2101	482	4	by	by	ADP
ap-2101	482	5	applying	apply	VERB
ap-2101	482	6	the	the	DET
ap-2101	482	7	same	same	ADJ
ap-2101	482	8	iteration	iteration	NOUN
ap-2101	482	9	procedure	procedure	NOUN
ap-2101	482	10	as	as	ADP
ap-2101	482	11	in	in	ADP
ap-2101	482	12	the	the	DET
ap-2101	482	13	previous	previous	ADJ
ap-2101	482	14	cases	case	NOUN
ap-2101	482	15	we	we	PRON
ap-2101	482	16	can	can	AUX
ap-2101	482	17	obtain	obtain	VERB
ap-2101	482	18	g	g	PROPN
ap-2101	482	19	(	(	PUNCT
ap-2101	482	20	n+1	n+1	NOUN
ap-2101	482	21	)	)	PUNCT
ap-2101	482	22	λ	λ	NOUN
ap-2101	482	23	=	=	SYM
ap-2101	483	1	g	g	NOUN
ap-2101	483	2	−	−	PROPN
ap-2101	483	3	1	1	NUM
ap-2101	483	4	4π	4π	NUM
ap-2101	483	5	λ∑	λ∑	SYM
ap-2101	484	1	s	s	NOUN
ap-2101	484	2	=	=	X
ap-2101	484	3	λ0	λ0	NOUN
ap-2101	484	4	(	(	PUNCT
ap-2101	484	5	s(s+	s(s+	NOUN
ap-2101	484	6	1	1	NUM
ap-2101	484	7	)	)	PUNCT
ap-2101	485	1	+	+	CCONJ
ap-2101	485	2	ν2r2	ν2r2	NOUN
ap-2101	485	3	2s+	2s+	NUM
ap-2101	485	4	1	1	NUM
ap-2101	485	5	−	−	PROPN
ap-2101	485	6	g	g	PROPN
ap-2101	485	7	(	(	PUNCT
ap-2101	485	8	n	n	CCONJ
ap-2101	485	9	)	)	PUNCT
ap-2101	485	10	s	s	PART
ap-2101	485	11	4π	4π	NUM
ap-2101	485	12	)	)	PUNCT
ap-2101	485	13	−1	−1	NOUN
ap-2101	485	14	(	(	PUNCT
ap-2101	485	15	g(n	g(n	PROPN
ap-2101	485	16	)	)	PUNCT
ap-2101	485	17	s	s	PART
ap-2101	485	18	)	)	PUNCT
ap-2101	485	19	2	2	NUM
ap-2101	485	20	.	.	PUNCT
ap-2101	486	1	(	(	PUNCT
ap-2101	486	2	4.20	4.20	NUM
ap-2101	486	3	)	)	PUNCT
ap-2101	486	4	this	this	PRON
ap-2101	486	5	is	be	AUX
ap-2101	486	6	a	a	DET
ap-2101	486	7	very	very	ADV
ap-2101	486	8	complicated	complicated	ADJ
ap-2101	486	9	recursive	recursive	ADJ
ap-2101	486	10	relation	relation	NOUN
ap-2101	486	11	,	,	PUNCT
ap-2101	486	12	and	and	CCONJ
ap-2101	486	13	unlike	unlike	ADP
ap-2101	486	14	previous	previous	ADJ
ap-2101	486	15	cases	case	NOUN
ap-2101	486	16	,	,	PUNCT
ap-2101	486	17	we	we	PRON
ap-2101	486	18	could	could	AUX
ap-2101	486	19	not	not	PART
ap-2101	486	20	convert	convert	VERB
ap-2101	486	21	it	it	PRON
ap-2101	486	22	to	to	ADP
ap-2101	486	23	a	a	DET
ap-2101	486	24	differential	differential	ADJ
ap-2101	486	25	equation	equation	NOUN
ap-2101	486	26	from	from	ADP
ap-2101	486	27	which	which	PRON
ap-2101	486	28	we	we	PRON
ap-2101	486	29	can	can	AUX
ap-2101	486	30	solve	solve	VERB
ap-2101	486	31	for	for	ADP
ap-2101	486	32	gλ	gλ	NOUN
ap-2101	486	33	in	in	ADP
ap-2101	486	34	the	the	DET
ap-2101	486	35	n→∞	n→∞	NUM
ap-2101	486	36	limit	limit	NOUN
ap-2101	486	37	.	.	PUNCT
ap-2101	487	1	5	5	X
ap-2101	487	2	.	.	X
ap-2101	487	3	conclusion	conclusion	NOUN
ap-2101	487	4	in	in	ADP
ap-2101	487	5	this	this	DET
ap-2101	487	6	paper	paper	NOUN
ap-2101	487	7	we	we	PRON
ap-2101	487	8	have	have	AUX
ap-2101	487	9	investigated	investigate	VERB
ap-2101	487	10	a	a	DET
ap-2101	487	11	non	non	ADJ
ap-2101	487	12	-	-	ADJ
ap-2101	487	13	perturbative	perturbative	ADJ
ap-2101	487	14	renormalization	renormalization	NOUN
ap-2101	487	15	of	of	ADP
ap-2101	487	16	point	point	NOUN
ap-2101	487	17	interactions	interaction	NOUN
ap-2101	487	18	on	on	ADP
ap-2101	487	19	the	the	DET
ap-2101	487	20	two	two	NUM
ap-2101	487	21	-	-	PUNCT
ap-2101	487	22	dimensional	dimensional	ADJ
ap-2101	487	23	hyperbolic	hyperbolic	ADJ
ap-2101	487	24	space	space	NOUN
ap-2101	487	25	,	,	PUNCT
ap-2101	487	26	using	use	VERB
ap-2101	487	27	the	the	DET
ap-2101	487	28	exact	exact	ADJ
ap-2101	487	29	renormalization	renormalization	NOUN
ap-2101	487	30	group	group	NOUN
ap-2101	487	31	method	method	NOUN
ap-2101	487	32	.	.	PUNCT
ap-2101	488	1	we	we	PRON
ap-2101	488	2	have	have	AUX
ap-2101	488	3	shown	show	VERB
ap-2101	488	4	that	that	SCONJ
ap-2101	488	5	the	the	DET
ap-2101	488	6	theory	theory	NOUN
ap-2101	488	7	is	be	AUX
ap-2101	488	8	asymptotically	asymptotically	ADV
ap-2101	488	9	free	free	ADJ
ap-2101	488	10	and	and	CCONJ
ap-2101	488	11	the	the	DET
ap-2101	488	12	flow	flow	NOUN
ap-2101	488	13	equations	equation	NOUN
ap-2101	488	14	have	have	VERB
ap-2101	488	15	the	the	DET
ap-2101	488	16	same	same	ADJ
ap-2101	488	17	form	form	NOUN
ap-2101	488	18	as	as	ADP
ap-2101	488	19	in	in	ADP
ap-2101	488	20	the	the	DET
ap-2101	488	21	flat	flat	ADJ
ap-2101	488	22	case	case	NOUN
ap-2101	488	23	.	.	PUNCT
ap-2101	489	1	acknowledgements	acknowledgement	NOUN
ap-2101	489	2	o.	o.	PROPN
ap-2101	489	3	t.	t.	PROPN
ap-2101	489	4	turgut	turgut	PROPN
ap-2101	489	5	would	would	AUX
ap-2101	489	6	like	like	VERB
ap-2101	489	7	to	to	PART
ap-2101	489	8	thank	thank	VERB
ap-2101	489	9	prof	prof	NOUN
ap-2101	489	10	.	.	PUNCT
ap-2101	490	1	p.	p.	NOUN
ap-2101	490	2	exner	exner	NOUN
ap-2101	490	3	and	and	CCONJ
ap-2101	490	4	prof	prof	PROPN
ap-2101	490	5	.	.	PUNCT
ap-2101	491	1	m.	m.	NOUN
ap-2101	491	2	znojil	znojil	PROPN
ap-2101	491	3	for	for	ADP
ap-2101	491	4	the	the	DET
ap-2101	491	5	kind	kind	ADJ
ap-2101	491	6	invitation	invitation	NOUN
ap-2101	491	7	to	to	ADP
ap-2101	491	8	the	the	DET
ap-2101	491	9	aamp	aamp	PROPN
ap-2101	491	10	xi	xi	PROPN
ap-2101	491	11	meeting	meeting	NOUN
ap-2101	491	12	which	which	PRON
ap-2101	491	13	was	be	AUX
ap-2101	491	14	held	hold	VERB
ap-2101	491	15	in	in	ADP
ap-2101	491	16	villa	villa	PROPN
ap-2101	491	17	lanna	lanna	PROPN
ap-2101	491	18	,	,	PUNCT
ap-2101	491	19	and	and	CCONJ
ap-2101	491	20	for	for	ADP
ap-2101	491	21	the	the	DET
ap-2101	491	22	kind	kind	ADJ
ap-2101	491	23	support	support	NOUN
ap-2101	491	24	for	for	ADP
ap-2101	491	25	his	his	PRON
ap-2101	491	26	lodging	lodging	NOUN
ap-2101	491	27	there	there	ADV
ap-2101	491	28	.	.	PUNCT
ap-2101	492	1	references	reference	NOUN
ap-2101	492	2	[	[	X
ap-2101	492	3	1	1	NUM
ap-2101	492	4	]	]	PUNCT
ap-2101	492	5	sadhan	sadhan	PROPN
ap-2101	492	6	k.	k.	PROPN
ap-2101	492	7	adhikari	adhikari	PROPN
ap-2101	492	8	and	and	CCONJ
ap-2101	492	9	t.	t.	PROPN
ap-2101	492	10	frederico	frederico	PROPN
ap-2101	492	11	.	.	PUNCT
ap-2101	493	1	renormalization	renormalization	NOUN
ap-2101	493	2	group	group	NOUN
ap-2101	493	3	in	in	ADP
ap-2101	493	4	potential	potential	ADJ
ap-2101	493	5	scattering	scattering	NOUN
ap-2101	493	6	.	.	PUNCT
ap-2101	494	1	physics	physics	NOUN
ap-2101	494	2	review	review	NOUN
ap-2101	494	3	letters	letter	NOUN
ap-2101	494	4	,	,	PUNCT
ap-2101	494	5	74:4572–4575	74:4572–4575	NUM
ap-2101	494	6	,	,	PUNCT
ap-2101	494	7	1995	1995	NUM
ap-2101	494	8	.	.	PUNCT
ap-2101	495	1	doi	doi	NOUN
ap-2101	495	2	:	:	PUNCT
ap-2101	495	3	10.1103	10.1103	NUM
ap-2101	495	4	/	/	SYM
ap-2101	495	5	physrevlett.74.4572	physrevlett.74.4572	NOUN
ap-2101	496	1	[	[	X
ap-2101	496	2	2	2	NUM
ap-2101	496	3	]	]	PUNCT
ap-2101	496	4	sadhan	sadhan	PROPN
ap-2101	496	5	k	k	PROPN
ap-2101	496	6	adhikari	adhikari	PROPN
ap-2101	496	7	and	and	CCONJ
ap-2101	496	8	angsula	angsula	VERB
ap-2101	496	9	ghosh	ghosh	PROPN
ap-2101	496	10	.	.	PUNCT
ap-2101	497	1	renormalization	renormalization	NOUN
ap-2101	497	2	in	in	ADP
ap-2101	497	3	non	non	ADJ
ap-2101	497	4	-	-	ADJ
ap-2101	497	5	relativistic	relativistic	ADJ
ap-2101	497	6	quantum	quantum	ADJ
ap-2101	497	7	mechanics	mechanic	NOUN
ap-2101	497	8	.	.	PUNCT
ap-2101	498	1	journal	journal	PROPN
ap-2101	498	2	of	of	ADP
ap-2101	498	3	physics	physics	PROPN
ap-2101	498	4	a	a	PRON
ap-2101	498	5	:	:	PUNCT
ap-2101	498	6	mathematical	mathematical	ADJ
ap-2101	498	7	and	and	CCONJ
ap-2101	498	8	general	general	ADJ
ap-2101	498	9	,	,	PUNCT
ap-2101	498	10	30(18):6553	30(18):6553	NUM
ap-2101	498	11	,	,	PUNCT
ap-2101	498	12	1997	1997	NUM
ap-2101	498	13	.	.	PUNCT
ap-2101	499	1	doi	doi	NOUN
ap-2101	499	2	:	:	PUNCT
ap-2101	499	3	10.1088/0305	10.1088/0305	NUM
ap-2101	499	4	-	-	PUNCT
ap-2101	499	5	4470/30/18/029	4470/30/18/029	PROPN
ap-2101	499	6	[	[	X
ap-2101	499	7	3	3	NUM
ap-2101	499	8	]	]	X
ap-2101	499	9	george	george	PROPN
ap-2101	499	10	b.	b.	PROPN
ap-2101	499	11	arfken	arfken	PROPN
ap-2101	499	12	and	and	CCONJ
ap-2101	499	13	hans	hans	PROPN
ap-2101	499	14	j.	j.	PROPN
ap-2101	499	15	weber	weber	PROPN
ap-2101	499	16	.	.	PUNCT
ap-2101	500	1	mathematical	mathematical	ADJ
ap-2101	500	2	methods	method	NOUN
ap-2101	500	3	for	for	ADP
ap-2101	500	4	physicists	physicist	NOUN
ap-2101	500	5	,	,	PUNCT
ap-2101	500	6	6th	6th	ADJ
ap-2101	500	7	edition	edition	NOUN
ap-2101	500	8	.	.	PUNCT
ap-2101	501	1	elsevier	elsevier	PROPN
ap-2101	501	2	academic	academic	PROPN
ap-2101	501	3	press	press	PROPN
ap-2101	501	4	,	,	PUNCT
ap-2101	501	5	burlington	burlington	PROPN
ap-2101	501	6	,	,	PUNCT
ap-2101	501	7	ma	ma	PROPN
ap-2101	501	8	,	,	PUNCT
ap-2101	501	9	usa	usa	PROPN
ap-2101	501	10	,	,	PUNCT
ap-2101	501	11	2005	2005	NUM
ap-2101	501	12	.	.	PUNCT
ap-2101	502	1	[	[	X
ap-2101	502	2	4	4	X
ap-2101	502	3	]	]	X
ap-2101	502	4	david	david	PROPN
ap-2101	502	5	borthwick	borthwick	PROPN
ap-2101	502	6	.	.	PUNCT
ap-2101	502	7	spectral	spectral	ADJ
ap-2101	502	8	theory	theory	NOUN
ap-2101	502	9	of	of	ADP
ap-2101	502	10	infinite	infinite	ADJ
ap-2101	502	11	-	-	PUNCT
ap-2101	502	12	area	area	NOUN
ap-2101	502	13	hyperbolic	hyperbolic	ADJ
ap-2101	502	14	surfaces	surface	NOUN
ap-2101	502	15	.	.	PUNCT
ap-2101	503	1	birkhauser	birkhauser	PROPN
ap-2101	503	2	boston	boston	PROPN
ap-2101	503	3	,	,	PUNCT
ap-2101	503	4	new	new	PROPN
ap-2101	503	5	york	york	PROPN
ap-2101	503	6	,	,	PUNCT
ap-2101	503	7	ny	ny	PROPN
ap-2101	503	8	,	,	PUNCT
ap-2101	503	9	usa	usa	PROPN
ap-2101	503	10	,	,	PUNCT
ap-2101	503	11	2007	2007	NUM
ap-2101	503	12	.	.	PUNCT
ap-2101	504	1	[	[	X
ap-2101	504	2	5	5	NUM
ap-2101	504	3	]	]	X
ap-2101	504	4	r.	r.	PROPN
ap-2101	504	5	m.	m.	PROPN
ap-2101	504	6	cavalcanti	cavalcanti	PROPN
ap-2101	504	7	.	.	PROPN
ap-2101	505	1	exact	exact	PROPN
ap-2101	505	2	green	green	PROPN
ap-2101	505	3	’s	’s	PART
ap-2101	505	4	functions	function	NOUN
ap-2101	505	5	for	for	ADP
ap-2101	505	6	delta	delta	NOUN
ap-2101	505	7	-	-	PUNCT
ap-2101	505	8	function	function	NOUN
ap-2101	505	9	potentials	potential	NOUN
ap-2101	505	10	and	and	CCONJ
ap-2101	505	11	renormalization	renormalization	NOUN
ap-2101	505	12	in	in	ADP
ap-2101	505	13	quantum	quantum	ADJ
ap-2101	505	14	mechanics	mechanic	NOUN
ap-2101	505	15	.	.	PUNCT
ap-2101	506	1	e	e	X
ap-2101	506	2	-	-	NOUN
ap-2101	506	3	print	print	NOUN
ap-2101	506	4	:	:	PUNCT
ap-2101	506	5	arxiv	arxiv	NOUN
ap-2101	506	6	:	:	PUNCT
ap-2101	506	7	quant	quant	NOUN
ap-2101	506	8	-	-	PUNCT
ap-2101	506	9	ph/9801033v2	ph/9801033v2	NOUN
ap-2101	506	10	,	,	PUNCT
ap-2101	506	11	2000	2000	NUM
ap-2101	506	12	.	.	PUNCT
ap-2101	507	1	[	[	X
ap-2101	507	2	6	6	NUM
ap-2101	507	3	]	]	PUNCT
ap-2101	507	4	carlos	carlos	PROPN
ap-2101	507	5	f	f	PROPN
ap-2101	507	6	de	de	PROPN
ap-2101	507	7	araujo	araujo	PROPN
ap-2101	507	8	,	,	PUNCT
ap-2101	507	9	lauro	lauro	PROPN
ap-2101	507	10	tomio	tomio	PROPN
ap-2101	507	11	,	,	PUNCT
ap-2101	507	12	sadhan	sadhan	PROPN
ap-2101	507	13	k	k	PROPN
ap-2101	507	14	adhikari	adhikari	PROPN
ap-2101	507	15	,	,	PUNCT
ap-2101	507	16	and	and	CCONJ
ap-2101	507	17	t	t	PROPN
ap-2101	507	18	frederico	frederico	PROPN
ap-2101	507	19	.	.	PUNCT
ap-2101	508	1	application	application	NOUN
ap-2101	508	2	of	of	ADP
ap-2101	508	3	renormalization	renormalization	NOUN
ap-2101	508	4	to	to	ADP
ap-2101	508	5	potential	potential	ADJ
ap-2101	508	6	scattering	scattering	NOUN
ap-2101	508	7	.	.	PUNCT
ap-2101	509	1	journal	journal	PROPN
ap-2101	509	2	of	of	ADP
ap-2101	509	3	physics	physics	PROPN
ap-2101	509	4	a	a	PRON
ap-2101	509	5	:	:	PUNCT
ap-2101	509	6	mathematical	mathematical	ADJ
ap-2101	509	7	and	and	CCONJ
ap-2101	509	8	general	general	ADJ
ap-2101	509	9	,	,	PUNCT
ap-2101	509	10	30(13):4687	30(13):4687	NUM
ap-2101	509	11	,	,	PUNCT
ap-2101	509	12	1997	1997	NUM
ap-2101	509	13	.	.	PUNCT
ap-2101	510	1	doi	doi	NOUN
ap-2101	510	2	:	:	PUNCT
ap-2101	510	3	10.1088/0305	10.1088/0305	NUM
ap-2101	510	4	-	-	SYM
ap-2101	510	5	4470/30/13/020	4470/30/13/020	NOUN
ap-2101	510	6	[	[	X
ap-2101	510	7	7	7	NUM
ap-2101	510	8	]	]	X
ap-2101	510	9	stanislaw	stanislaw	PROPN
ap-2101	510	10	d.	d.	PROPN
ap-2101	510	11	glazek	glazek	PROPN
ap-2101	510	12	.	.	PUNCT
ap-2101	511	1	renormalization	renormalization	NOUN
ap-2101	511	2	group	group	NOUN
ap-2101	511	3	and	and	CCONJ
ap-2101	511	4	bound	bound	ADJ
ap-2101	511	5	states	state	NOUN
ap-2101	511	6	.	.	PUNCT
ap-2101	512	1	arxiv:0810.5258	arxiv:0810.5258	PRON
ap-2101	513	1	[	[	PUNCT
ap-2101	513	2	hep	hep	NOUN
ap-2101	513	3	-	-	PUNCT
ap-2101	513	4	th	th	X
ap-2101	513	5	]	]	PUNCT
ap-2101	513	6	,	,	PUNCT
ap-2101	513	7	october	october	PROPN
ap-2101	513	8	2008	2008	NUM
ap-2101	513	9	.	.	PUNCT
ap-2101	514	1	acta	acta	PROPN
ap-2101	514	2	phys.polon.b39:3395	phys.polon.b39:3395	PROPN
ap-2101	514	3	-	-	PUNCT
ap-2101	514	4	3421,2008	3421,2008	NOUN
ap-2101	514	5	.	.	PUNCT
ap-2101	515	1	[	[	X
ap-2101	515	2	8	8	NUM
ap-2101	515	3	]	]	X
ap-2101	515	4	stanislaw	stanislaw	PROPN
ap-2101	515	5	d.	d.	PROPN
ap-2101	515	6	głazek	głazek	PROPN
ap-2101	515	7	and	and	CCONJ
ap-2101	515	8	tomasz	tomasz	PROPN
ap-2101	515	9	maslowski	maslowski	NOUN
ap-2101	515	10	.	.	PUNCT
ap-2101	516	1	renormalization	renormalization	NOUN
ap-2101	516	2	of	of	ADP
ap-2101	516	3	hamiltonians	hamiltonian	NOUN
ap-2101	516	4	.	.	PUNCT
ap-2101	517	1	lecture	lecture	NOUN
ap-2101	517	2	notes	note	NOUN
ap-2101	517	3	distributed	distribute	VERB
ap-2101	517	4	in	in	ADP
ap-2101	517	5	the	the	DET
ap-2101	517	6	sixth	sixth	ADJ
ap-2101	517	7	international	international	ADJ
ap-2101	517	8	school	school	NOUN
ap-2101	517	9	and	and	CCONJ
ap-2101	517	10	workshop	workshop	NOUN
ap-2101	517	11	on	on	ADP
ap-2101	517	12	light	light	ADJ
ap-2101	517	13	-	-	PUNCT
ap-2101	517	14	front	front	NOUN
ap-2101	517	15	quantization	quantization	NOUN
ap-2101	517	16	and	and	CCONJ
ap-2101	517	17	non	non	ADJ
ap-2101	517	18	-	-	ADJ
ap-2101	517	19	perturbative	perturbative	ADJ
ap-2101	517	20	qcd	qcd	NOUN
ap-2101	517	21	at	at	ADP
ap-2101	517	22	iowa	iowa	PROPN
ap-2101	517	23	state	state	PROPN
ap-2101	517	24	university	university	PROPN
ap-2101	517	25	,	,	PUNCT
ap-2101	517	26	ames	ame	NOUN
ap-2101	517	27	on	on	ADP
ap-2101	517	28	may	may	PROPN
ap-2101	517	29	6	6	NUM
ap-2101	517	30	june	june	PROPN
ap-2101	517	31	14	14	NUM
ap-2101	517	32	,	,	PUNCT
ap-2101	517	33	1996	1996	NUM
ap-2101	517	34	.	.	PUNCT
ap-2101	518	1	[	[	X
ap-2101	518	2	9	9	NUM
ap-2101	518	3	]	]	PUNCT
ap-2101	518	4	stanisław	stanisław	VERB
ap-2101	518	5	d.	d.	PROPN
ap-2101	518	6	głazek	głazek	PROPN
ap-2101	518	7	and	and	CCONJ
ap-2101	518	8	kenneth	kenneth	PROPN
ap-2101	518	9	g.	g.	PROPN
ap-2101	518	10	wilson	wilson	PROPN
ap-2101	518	11	.	.	PUNCT
ap-2101	519	1	renormalization	renormalization	NOUN
ap-2101	519	2	of	of	ADP
ap-2101	519	3	hamiltonians	hamiltonian	NOUN
ap-2101	519	4	.	.	PUNCT
ap-2101	520	1	phys	phy	NOUN
ap-2101	520	2	.	.	PUNCT
ap-2101	521	1	rev	rev	PROPN
ap-2101	521	2	.	.	PROPN
ap-2101	522	1	d	d	X
ap-2101	522	2	,	,	PUNCT
ap-2101	522	3	48:5863–5872	48:5863–5872	NUM
ap-2101	522	4	,	,	PUNCT
ap-2101	522	5	dec	dec	PROPN
ap-2101	522	6	1993	1993	NUM
ap-2101	522	7	.	.	PUNCT
ap-2101	523	1	doi	doi	NOUN
ap-2101	523	2	:	:	PUNCT
ap-2101	523	3	10.1103	10.1103	NUM
ap-2101	523	4	/	/	SYM
ap-2101	523	5	physrevd.48.5863	physrevd.48.5863	NOUN
ap-2101	523	6	[	[	X
ap-2101	523	7	10	10	NUM
ap-2101	523	8	]	]	X
ap-2101	523	9	stanislaw	stanislaw	PROPN
ap-2101	523	10	d.	d.	PROPN
ap-2101	523	11	glazek	glazek	PROPN
ap-2101	523	12	and	and	CCONJ
ap-2101	523	13	kenneth	kenneth	PROPN
ap-2101	523	14	g.	g.	PROPN
ap-2101	523	15	wilson	wilson	PROPN
ap-2101	523	16	.	.	PUNCT
ap-2101	524	1	perturbative	perturbative	ADJ
ap-2101	524	2	renormalization	renormalization	NOUN
ap-2101	524	3	group	group	NOUN
ap-2101	524	4	for	for	ADP
ap-2101	524	5	hamiltonians	hamiltonian	NOUN
ap-2101	524	6	.	.	PUNCT
ap-2101	525	1	phys	phy	NOUN
ap-2101	525	2	.	.	PUNCT
ap-2101	526	1	rev	rev	PROPN
ap-2101	526	2	.	.	PROPN
ap-2101	527	1	d	d	X
ap-2101	527	2	,	,	PUNCT
ap-2101	527	3	49:4214–4218	49:4214–4218	NOUN
ap-2101	527	4	,	,	PUNCT
ap-2101	527	5	apr	apr	PROPN
ap-2101	527	6	1994	1994	NUM
ap-2101	527	7	.	.	PUNCT
ap-2101	528	1	doi	doi	NOUN
ap-2101	528	2	:	:	PUNCT
ap-2101	528	3	10.1103	10.1103	NUM
ap-2101	528	4	/	/	SYM
ap-2101	528	5	physrevd.49.4214	physrevd.49.4214	NOUN
ap-2101	529	1	[	[	X
ap-2101	529	2	11	11	NUM
ap-2101	529	3	]	]	PUNCT
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ap-2101	529	5	d.	d.	PROPN
ap-2101	529	6	głazek	głazek	PROPN
ap-2101	529	7	and	and	CCONJ
ap-2101	529	8	kenneth	kenneth	PROPN
ap-2101	529	9	g.	g.	PROPN
ap-2101	529	10	wilson	wilson	PROPN
ap-2101	529	11	.	.	PUNCT
ap-2101	530	1	asymptotic	asymptotic	ADJ
ap-2101	530	2	freedom	freedom	NOUN
ap-2101	530	3	and	and	CCONJ
ap-2101	530	4	bound	bind	VERB
ap-2101	530	5	states	state	NOUN
ap-2101	530	6	in	in	ADP
ap-2101	530	7	hamiltonian	hamiltonian	ADJ
ap-2101	530	8	dynamics	dynamic	NOUN
ap-2101	530	9	.	.	PUNCT
ap-2101	531	1	phys	phy	NOUN
ap-2101	531	2	.	.	PUNCT
ap-2101	532	1	rev	rev	PROPN
ap-2101	532	2	.	.	PROPN
ap-2101	533	1	d	d	X
ap-2101	533	2	,	,	PUNCT
ap-2101	533	3	57:3558–3566	57:3558–3566	PROPN
ap-2101	533	4	,	,	PUNCT
ap-2101	533	5	mar	mar	PROPN
ap-2101	533	6	1998	1998	NUM
ap-2101	533	7	.	.	PUNCT
ap-2101	534	1	doi	doi	NOUN
ap-2101	534	2	:	:	PUNCT
ap-2101	534	3	10.1103	10.1103	NUM
ap-2101	534	4	/	/	SYM
ap-2101	534	5	physrevd.57.3558	physrevd.57.3558	NOUN
ap-2101	535	1	[	[	X
ap-2101	535	2	12	12	NUM
ap-2101	535	3	]	]	PUNCT
ap-2101	535	4	p.	p.	NOUN
ap-2101	535	5	gosdzinsky	gosdzinsky	NOUN
ap-2101	535	6	and	and	CCONJ
ap-2101	535	7	r.	r.	PROPN
ap-2101	535	8	tarrach	tarrach	PROPN
ap-2101	535	9	.	.	PUNCT
ap-2101	536	1	learning	learn	VERB
ap-2101	536	2	quantum	quantum	ADJ
ap-2101	536	3	field	field	NOUN
ap-2101	536	4	theory	theory	NOUN
ap-2101	536	5	from	from	ADP
ap-2101	536	6	elementary	elementary	ADJ
ap-2101	536	7	quantum	quantum	ADJ
ap-2101	536	8	mechanics	mechanic	NOUN
ap-2101	536	9	.	.	PUNCT
ap-2101	537	1	american	american	PROPN
ap-2101	537	2	journal	journal	PROPN
ap-2101	537	3	of	of	ADP
ap-2101	537	4	physics	physics	PROPN
ap-2101	537	5	,	,	PUNCT
ap-2101	537	6	59(1):70–74	59(1):70–74	NUM
ap-2101	537	7	,	,	PUNCT
ap-2101	537	8	1991	1991	NUM
ap-2101	537	9	.	.	PUNCT
ap-2101	538	1	doi	doi	NOUN
ap-2101	538	2	:	:	PUNCT
ap-2101	538	3	10.1119/1.16691	10.1119/1.16691	NUM
ap-2101	538	4	171	171	NUM
ap-2101	538	5	http://dx.doi.org/10.1103/physrevlett.74.4572	http://dx.doi.org/10.1103/physrevlett.74.4572	NOUN
ap-2101	538	6	http://dx.doi.org/10.1088/0305-4470/30/18/029	http://dx.doi.org/10.1088/0305-4470/30/18/029	NOUN
ap-2101	538	7	http://dx.doi.org/10.1088/0305-4470/30/13/020	http://dx.doi.org/10.1088/0305-4470/30/13/020	VERB
ap-2101	538	8	http://dx.doi.org/10.1103/physrevd.48.5863	http://dx.doi.org/10.1103/physrevd.48.5863	PROPN
ap-2101	538	9	http://dx.doi.org/10.1103/physrevd.49.4214	http://dx.doi.org/10.1103/physrevd.49.4214	PROPN
ap-2101	538	10	http://dx.doi.org/10.1103/physrevd.57.3558	http://dx.doi.org/10.1103/physrevd.57.3558	PROPN
ap-2101	538	11	http://dx.doi.org/10.1119/1.16691	http://dx.doi.org/10.1119/1.16691	PROPN
ap-2101	538	12	osman	osman	PROPN
ap-2101	538	13	teoman	teoman	PROPN
ap-2101	538	14	turgut	turgut	PROPN
ap-2101	538	15	,	,	PUNCT
ap-2101	538	16	cem	cem	NOUN
ap-2101	538	17	eröncel	eröncel	VERB
ap-2101	538	18	acta	acta	PROPN
ap-2101	538	19	polytechnica	polytechnica	PROPN
ap-2101	539	1	[	[	X
ap-2101	539	2	13	13	NUM
ap-2101	539	3	]	]	X
ap-2101	539	4	i.	i.	PROPN
ap-2101	539	5	s.	s.	PROPN
ap-2101	539	6	gradshteyn	gradshteyn	PROPN
ap-2101	539	7	and	and	CCONJ
ap-2101	539	8	i.m	i.m	PROPN
ap-2101	539	9	.	.	PROPN
ap-2101	539	10	ryzhik	ryzhik	ADJ
ap-2101	539	11	.	.	PUNCT
ap-2101	540	1	table	table	NOUN
ap-2101	540	2	of	of	ADP
ap-2101	540	3	integrals	integral	NOUN
ap-2101	540	4	,	,	PUNCT
ap-2101	540	5	series	series	NOUN
ap-2101	540	6	and	and	CCONJ
ap-2101	540	7	products	product	NOUN
ap-2101	540	8	,	,	PUNCT
ap-2101	540	9	7th	7th	ADJ
ap-2101	540	10	edition	edition	NOUN
ap-2101	540	11	.	.	PUNCT
ap-2101	541	1	elsevier	elsevier	PROPN
ap-2101	541	2	academic	academic	PROPN
ap-2101	541	3	press	press	PROPN
ap-2101	541	4	,	,	PUNCT
ap-2101	541	5	burlington	burlington	PROPN
ap-2101	541	6	,	,	PUNCT
ap-2101	541	7	ma	ma	PROPN
ap-2101	541	8	,	,	PUNCT
ap-2101	541	9	usa	usa	PROPN
ap-2101	541	10	,	,	PUNCT
ap-2101	541	11	2007	2007	NUM
ap-2101	541	12	.	.	PUNCT
ap-2101	542	1	[	[	X
ap-2101	542	2	14	14	NUM
ap-2101	542	3	]	]	X
ap-2101	542	4	michel	michel	PROPN
ap-2101	542	5	hans	hans	PROPN
ap-2101	542	6	.	.	PUNCT
ap-2101	543	1	an	an	DET
ap-2101	543	2	electrostatic	electrostatic	ADJ
ap-2101	543	3	example	example	NOUN
ap-2101	543	4	to	to	PART
ap-2101	543	5	illustrate	illustrate	VERB
ap-2101	543	6	dimensional	dimensional	ADJ
ap-2101	543	7	regularization	regularization	NOUN
ap-2101	543	8	and	and	CCONJ
ap-2101	543	9	renormalization	renormalization	NOUN
ap-2101	543	10	group	group	NOUN
ap-2101	543	11	technique	technique	NOUN
ap-2101	543	12	.	.	PUNCT
ap-2101	544	1	american	american	ADJ
ap-2101	544	2	journal	journal	PROPN
ap-2101	544	3	of	of	ADP
ap-2101	544	4	physics	physics	PROPN
ap-2101	544	5	,	,	PUNCT
ap-2101	544	6	51(8):694–698	51(8):694–698	PROPN
ap-2101	544	7	,	,	PUNCT
ap-2101	544	8	1983	1983	NUM
ap-2101	544	9	.	.	PUNCT
ap-2101	545	1	doi	doi	NOUN
ap-2101	545	2	:	:	PUNCT
ap-2101	545	3	10.1119/1.13148	10.1119/1.13148	NUM
ap-2101	546	1	[	[	X
ap-2101	546	2	15	15	NUM
ap-2101	546	3	]	]	X
ap-2101	546	4	peter	peter	PROPN
ap-2101	546	5	d.	d.	PROPN
ap-2101	546	6	hislop	hislop	PROPN
ap-2101	546	7	.	.	PUNCT
ap-2101	547	1	the	the	DET
ap-2101	547	2	geometry	geometry	NOUN
ap-2101	547	3	and	and	CCONJ
ap-2101	547	4	spectra	spectra	NOUN
ap-2101	547	5	of	of	ADP
ap-2101	547	6	hyperbolic	hyperbolic	ADJ
ap-2101	547	7	manifolds	manifold	NOUN
ap-2101	547	8	.	.	PUNCT
ap-2101	548	1	proceedings	proceeding	NOUN
ap-2101	548	2	of	of	ADP
ap-2101	548	3	the	the	DET
ap-2101	548	4	indian	indian	PROPN
ap-2101	548	5	academy	academy	PROPN
ap-2101	548	6	of	of	ADP
ap-2101	548	7	sciences	sciences	PROPN
ap-2101	548	8	mathematical	mathematical	PROPN
ap-2101	548	9	sciences	sciences	PROPN
ap-2101	548	10	,	,	PUNCT
ap-2101	548	11	104:715–776	104:715–776	NUM
ap-2101	548	12	,	,	PUNCT
ap-2101	548	13	1994	1994	NUM
ap-2101	548	14	.	.	PUNCT
ap-2101	549	1	[	[	X
ap-2101	549	2	16	16	NUM
ap-2101	549	3	]	]	X
ap-2101	549	4	n.	n.	PROPN
ap-2101	549	5	n.	n.	PROPN
ap-2101	549	6	lebedev	lebedev	PROPN
ap-2101	549	7	.	.	PUNCT
ap-2101	550	1	special	special	ADJ
ap-2101	550	2	functions	function	NOUN
ap-2101	550	3	and	and	CCONJ
ap-2101	550	4	their	their	PRON
ap-2101	550	5	applications	application	NOUN
ap-2101	550	6	.	.	PUNCT
ap-2101	551	1	prentice	prentice	NOUN
ap-2101	551	2	-	-	PUNCT
ap-2101	551	3	hall	hall	PROPN
ap-2101	551	4	inc	inc	PROPN
ap-2101	551	5	.	.	PROPN
ap-2101	551	6	,	,	PUNCT
ap-2101	551	7	englewood	englewood	PROPN
ap-2101	551	8	cliffs	cliffs	PROPN
ap-2101	551	9	,	,	PUNCT
ap-2101	551	10	nj	nj	PROPN
ap-2101	551	11	,	,	PUNCT
ap-2101	551	12	usa	usa	PROPN
ap-2101	551	13	,	,	PUNCT
ap-2101	551	14	1965	1965	NUM
ap-2101	551	15	.	.	PUNCT
ap-2101	552	1	[	[	X
ap-2101	552	2	17	17	NUM
ap-2101	552	3	]	]	X
ap-2101	552	4	lawrence	lawrence	PROPN
ap-2101	552	5	r.	r.	PROPN
ap-2101	552	6	mead	mead	PROPN
ap-2101	552	7	and	and	CCONJ
ap-2101	552	8	john	john	PROPN
ap-2101	552	9	godines	godine	NOUN
ap-2101	552	10	.	.	PUNCT
ap-2101	553	1	an	an	DET
ap-2101	553	2	analytical	analytical	ADJ
ap-2101	553	3	example	example	NOUN
ap-2101	553	4	of	of	ADP
ap-2101	553	5	renormalization	renormalization	NOUN
ap-2101	553	6	in	in	ADP
ap-2101	553	7	two	two	NUM
ap-2101	553	8	-	-	PUNCT
ap-2101	553	9	dimensional	dimensional	ADJ
ap-2101	553	10	quantum	quantum	ADJ
ap-2101	553	11	mechanics	mechanic	NOUN
ap-2101	553	12	.	.	PUNCT
ap-2101	554	1	american	american	PROPN
ap-2101	554	2	journal	journal	PROPN
ap-2101	554	3	of	of	ADP
ap-2101	554	4	physics	physics	PROPN
ap-2101	554	5	,	,	PUNCT
ap-2101	554	6	59(10):935–937	59(10):935–937	NUM
ap-2101	554	7	,	,	PUNCT
ap-2101	554	8	1991	1991	NUM
ap-2101	554	9	.	.	PUNCT
ap-2101	555	1	doi	doi	NOUN
ap-2101	555	2	:	:	PUNCT
ap-2101	555	3	10.1119/1.16675	10.1119/1.16675	NUM
ap-2101	555	4	[	[	X
ap-2101	555	5	18	18	NUM
ap-2101	555	6	]	]	PUNCT
ap-2101	555	7	indrajit	indrajit	NOUN
ap-2101	555	8	mitra	mitra	PROPN
ap-2101	555	9	,	,	PUNCT
ap-2101	555	10	ananda	ananda	PROPN
ap-2101	555	11	dasgupta	dasgupta	PROPN
ap-2101	555	12	,	,	PUNCT
ap-2101	555	13	and	and	CCONJ
ap-2101	555	14	binayak	binayak	NOUN
ap-2101	555	15	dutta	dutta	PROPN
ap-2101	555	16	-	-	PUNCT
ap-2101	555	17	roy	roy	PROPN
ap-2101	555	18	.	.	PROPN
ap-2101	555	19	regularization	regularization	NOUN
ap-2101	555	20	and	and	CCONJ
ap-2101	555	21	renormalization	renormalization	NOUN
ap-2101	555	22	in	in	ADP
ap-2101	555	23	scattering	scatter	VERB
ap-2101	555	24	from	from	ADP
ap-2101	555	25	dirac	dirac	NOUN
ap-2101	555	26	delta	delta	PROPN
ap-2101	555	27	potentials	potential	NOUN
ap-2101	555	28	.	.	PUNCT
ap-2101	556	1	american	american	PROPN
ap-2101	556	2	journal	journal	PROPN
ap-2101	556	3	of	of	ADP
ap-2101	556	4	physics	physics	PROPN
ap-2101	556	5	,	,	PUNCT
ap-2101	556	6	66(12):1101–1109	66(12):1101–1109	NUM
ap-2101	556	7	,	,	PUNCT
ap-2101	556	8	1998	1998	NUM
ap-2101	556	9	.	.	PUNCT
ap-2101	557	1	doi	doi	NOUN
ap-2101	557	2	:	:	PUNCT
ap-2101	557	3	10.1119/1.19051	10.1119/1.19051	NUM
ap-2101	557	4	[	[	X
ap-2101	557	5	19	19	NUM
ap-2101	557	6	]	]	PUNCT
ap-2101	557	7	p.	p.	NOUN
ap-2101	557	8	k.	k.	PROPN
ap-2101	557	9	mitter	mitter	PROPN
ap-2101	557	10	and	and	CCONJ
ap-2101	557	11	c.-m	c.-m	NOUN
ap-2101	557	12	.	.	PUNCT
ap-2101	558	1	viallet	viallet	NOUN
ap-2101	558	2	.	.	PUNCT
ap-2101	559	1	on	on	ADP
ap-2101	559	2	the	the	DET
ap-2101	559	3	bundle	bundle	NOUN
ap-2101	559	4	of	of	ADP
ap-2101	559	5	connections	connection	NOUN
ap-2101	559	6	and	and	CCONJ
ap-2101	559	7	the	the	DET
ap-2101	559	8	gauge	gauge	NOUN
ap-2101	559	9	orbit	orbit	NOUN
ap-2101	559	10	manifold	manifold	ADJ
ap-2101	559	11	in	in	ADP
ap-2101	559	12	yang	yang	PROPN
ap-2101	559	13	-	-	PUNCT
ap-2101	559	14	mills	mill	NOUN
ap-2101	559	15	theory	theory	NOUN
ap-2101	559	16	.	.	PUNCT
ap-2101	560	1	communications	communication	NOUN
ap-2101	560	2	in	in	ADP
ap-2101	560	3	mathematical	mathematical	ADJ
ap-2101	560	4	physics	physic	NOUN
ap-2101	560	5	,	,	PUNCT
ap-2101	560	6	79(4):457–472	79(4):457–472	PROPN
ap-2101	560	7	,	,	PUNCT
ap-2101	560	8	1981	1981	NUM
ap-2101	560	9	.	.	PUNCT
ap-2101	561	1	doi	doi	NOUN
ap-2101	561	2	:	:	PUNCT
ap-2101	561	3	10.1007	10.1007	NUM
ap-2101	561	4	/	/	SYM
ap-2101	561	5	bf01209307	bf01209307	PROPN
ap-2101	562	1	[	[	X
ap-2101	562	2	20	20	NUM
ap-2101	562	3	]	]	SYM
ap-2101	562	4	su	su	NOUN
ap-2101	562	5	long	long	ADJ
ap-2101	562	6	nyeo	nyeo	PROPN
ap-2101	562	7	.	.	PUNCT
ap-2101	563	1	regularization	regularization	NOUN
ap-2101	563	2	methods	method	NOUN
ap-2101	563	3	for	for	ADP
ap-2101	563	4	delta	delta	NOUN
ap-2101	563	5	-	-	PUNCT
ap-2101	563	6	function	function	NOUN
ap-2101	563	7	potential	potential	NOUN
ap-2101	563	8	in	in	ADP
ap-2101	563	9	two	two	NUM
ap-2101	563	10	-	-	PUNCT
ap-2101	563	11	dimensional	dimensional	ADJ
ap-2101	563	12	quantum	quantum	ADJ
ap-2101	563	13	mechanics	mechanic	NOUN
ap-2101	563	14	.	.	PUNCT
ap-2101	564	1	american	american	PROPN
ap-2101	564	2	journal	journal	PROPN
ap-2101	564	3	of	of	ADP
ap-2101	564	4	physics	physics	PROPN
ap-2101	564	5	,	,	PUNCT
ap-2101	564	6	68(6):571–575	68(6):571–575	PROPN
ap-2101	564	7	,	,	PUNCT
ap-2101	564	8	2000	2000	NUM
ap-2101	564	9	.	.	PUNCT
ap-2101	565	1	doi	doi	NOUN
ap-2101	565	2	:	:	PUNCT
ap-2101	565	3	10.1119/1.19485	10.1119/1.19485	NUM
ap-2101	565	4	[	[	SYM
ap-2101	565	5	21	21	NUM
ap-2101	565	6	]	]	PUNCT
ap-2101	565	7	audrey	audrey	PROPN
ap-2101	565	8	terras	terra	NOUN
ap-2101	565	9	.	.	PUNCT
ap-2101	566	1	harmonic	harmonic	ADJ
ap-2101	566	2	analysis	analysis	NOUN
ap-2101	566	3	on	on	ADP
ap-2101	566	4	symmetric	symmetric	ADJ
ap-2101	566	5	spaces	space	NOUN
ap-2101	566	6	and	and	CCONJ
ap-2101	566	7	applications	application	NOUN
ap-2101	566	8	,	,	PUNCT
ap-2101	566	9	volume	volume	NOUN
ap-2101	566	10	i.	i.	PROPN
ap-2101	566	11	springer	springer	PROPN
ap-2101	566	12	-	-	PUNCT
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ap-2101	566	14	,	,	PUNCT
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ap-2101	566	17	,	,	PUNCT
ap-2101	566	18	ny	ny	PROPN
ap-2101	566	19	,	,	PUNCT
ap-2101	566	20	usa	usa	PROPN
ap-2101	566	21	,	,	PUNCT
ap-2101	566	22	1985	1985	NUM
ap-2101	566	23	.	.	PUNCT
ap-2101	567	1	[	[	X
ap-2101	567	2	22	22	NUM
ap-2101	567	3	]	]	X
ap-2101	567	4	wolfgang	wolfgang	PROPN
ap-2101	567	5	walter	walter	PROPN
ap-2101	567	6	.	.	PUNCT
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ap-2101	568	2	differential	differential	ADJ
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ap-2101	568	4	.	.	PUNCT
ap-2101	569	1	springer	springer	NOUN
ap-2101	569	2	-	-	PUNCT
ap-2101	569	3	verlag	verlag	PROPN
ap-2101	569	4	,	,	PUNCT
ap-2101	569	5	new	new	PROPN
ap-2101	569	6	york	york	PROPN
ap-2101	569	7	,	,	PUNCT
ap-2101	569	8	ny	ny	PROPN
ap-2101	569	9	,	,	PUNCT
ap-2101	569	10	usa	usa	PROPN
ap-2101	569	11	,	,	PUNCT
ap-2101	569	12	1998	1998	NUM
ap-2101	569	13	.	.	PUNCT
ap-2101	570	1	[	[	X
ap-2101	570	2	23	23	NUM
ap-2101	570	3	]	]	X
ap-2101	570	4	kenneth	kenneth	PROPN
ap-2101	570	5	g.	g.	PROPN
ap-2101	570	6	wilson	wilson	PROPN
ap-2101	570	7	.	.	PUNCT
ap-2101	571	1	model	model	PROPN
ap-2101	571	2	of	of	ADP
ap-2101	571	3	coupling	couple	VERB
ap-2101	571	4	-	-	PUNCT
ap-2101	571	5	constant	constant	ADJ
ap-2101	571	6	renormalization	renormalization	NOUN
ap-2101	571	7	.	.	PUNCT
ap-2101	572	1	phys	phy	NOUN
ap-2101	572	2	.	.	PUNCT
ap-2101	573	1	rev	rev	PROPN
ap-2101	573	2	.	.	PROPN
ap-2101	574	1	d	d	X
ap-2101	574	2	,	,	PUNCT
ap-2101	574	3	2:1438–1472	2:1438–1472	NUM
ap-2101	574	4	,	,	PUNCT
ap-2101	574	5	oct	oct	PROPN
ap-2101	574	6	1970	1970	NUM
ap-2101	574	7	.	.	PUNCT
ap-2101	575	1	doi	doi	NOUN
ap-2101	575	2	:	:	PUNCT
ap-2101	575	3	10.1103	10.1103	NUM
ap-2101	575	4	/	/	SYM
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ap-2101	577	1	[	[	X
ap-2101	577	2	24	24	NUM
ap-2101	577	3	]	]	PUNCT
ap-2101	577	4	kenneth	kenneth	PROPN
ap-2101	577	5	g.	g.	PROPN
ap-2101	577	6	wilson	wilson	PROPN
ap-2101	577	7	.	.	PUNCT
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ap-2101	577	9	group	group	NOUN
ap-2101	577	10	and	and	CCONJ
ap-2101	577	11	critical	critical	ADJ
ap-2101	577	12	phenomena	phenomenon	NOUN
ap-2101	577	13	.	.	PUNCT
ap-2101	578	1	i.	i.	PROPN
ap-2101	578	2	renormalization	renormalization	PROPN
ap-2101	578	3	group	group	NOUN
ap-2101	578	4	and	and	CCONJ
ap-2101	578	5	the	the	DET
ap-2101	578	6	kadanoff	kadanoff	NOUN
ap-2101	578	7	scaling	scale	VERB
ap-2101	578	8	picture	picture	NOUN
ap-2101	578	9	.	.	PUNCT
ap-2101	579	1	physical	physical	ADJ
ap-2101	579	2	review	review	PROPN
ap-2101	579	3	b	b	PROPN
ap-2101	579	4	,	,	PUNCT
ap-2101	579	5	4:3174–3183	4:3174–3183	NUM
ap-2101	579	6	,	,	PUNCT
ap-2101	579	7	1971	1971	NUM
ap-2101	579	8	.	.	PUNCT
ap-2101	580	1	doi	doi	NOUN
ap-2101	580	2	:	:	PUNCT
ap-2101	580	3	10.1103	10.1103	NUM
ap-2101	580	4	/	/	SYM
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ap-2101	580	6	[	[	X
ap-2101	580	7	25	25	NUM
ap-2101	580	8	]	]	PUNCT
ap-2101	580	9	kenneth	kenneth	PROPN
ap-2101	580	10	g.	g.	PROPN
ap-2101	580	11	wilson	wilson	PROPN
ap-2101	580	12	.	.	PUNCT
ap-2101	581	1	renormalization	renormalization	NOUN
ap-2101	581	2	group	group	NOUN
ap-2101	581	3	and	and	CCONJ
ap-2101	581	4	critical	critical	ADJ
ap-2101	581	5	phenomena	phenomenon	NOUN
ap-2101	581	6	.	.	PUNCT
ap-2101	582	1	ii	ii	PROPN
ap-2101	582	2	.	.	PUNCT
ap-2101	582	3	phase	phase	NOUN
ap-2101	582	4	-	-	PUNCT
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ap-2101	582	8	of	of	ADP
ap-2101	582	9	critical	critical	ADJ
ap-2101	582	10	behavior	behavior	NOUN
ap-2101	582	11	.	.	PUNCT
ap-2101	583	1	physical	physical	PROPN
ap-2101	583	2	review	review	PROPN
ap-2101	583	3	b	b	PROPN
ap-2101	583	4	,	,	PUNCT
ap-2101	583	5	4:3184–3205	4:3184–3205	NUM
ap-2101	583	6	,	,	PUNCT
ap-2101	583	7	1971	1971	NUM
ap-2101	583	8	.	.	PUNCT
ap-2101	584	1	doi	doi	NOUN
ap-2101	584	2	:	:	PUNCT
ap-2101	584	3	10.1103	10.1103	NUM
ap-2101	584	4	/	/	SYM
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ap-2101	584	6	[	[	X
ap-2101	584	7	26	26	NUM
ap-2101	584	8	]	]	X
ap-2101	584	9	kenneth	kenneth	PROPN
ap-2101	584	10	g.	g.	PROPN
ap-2101	584	11	wilson	wilson	PROPN
ap-2101	584	12	.	.	PUNCT
ap-2101	585	1	the	the	DET
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ap-2101	585	3	group	group	NOUN
ap-2101	585	4	:	:	PUNCT
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ap-2101	585	6	phenomena	phenomenon	NOUN
ap-2101	585	7	and	and	CCONJ
ap-2101	585	8	the	the	DET
ap-2101	585	9	kondo	kondo	PROPN
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ap-2101	585	11	.	.	PUNCT
ap-2101	586	1	reviews	review	NOUN
ap-2101	586	2	of	of	ADP
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ap-2101	586	5	,	,	PUNCT
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ap-2101	586	7	,	,	PUNCT
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ap-2101	586	9	.	.	PUNCT
ap-2101	587	1	doi	doi	NOUN
ap-2101	587	2	:	:	PUNCT
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ap-2101	587	4	/	/	SYM
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ap-2101	588	3	]	]	X
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ap-2101	588	5	g.	g.	PROPN
ap-2101	588	6	wilson	wilson	PROPN
ap-2101	588	7	.	.	PUNCT
ap-2101	589	1	the	the	DET
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ap-2101	589	3	group	group	NOUN
ap-2101	589	4	and	and	CCONJ
ap-2101	589	5	critical	critical	ADJ
ap-2101	589	6	phenomena	phenomenon	NOUN
ap-2101	589	7	.	.	PUNCT
ap-2101	590	1	reviews	review	NOUN
ap-2101	590	2	of	of	ADP
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ap-2101	590	7	,	,	PUNCT
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ap-2101	590	9	.	.	PUNCT
ap-2101	591	1	doi	doi	NOUN
ap-2101	591	2	:	:	PUNCT
ap-2101	591	3	10.1103	10.1103	NUM
ap-2101	591	4	/	/	SYM
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ap-2101	592	3	]	]	X
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ap-2101	593	1	the	the	DET
ap-2101	593	2	renormalization	renormalization	NOUN
ap-2101	593	3	group	group	NOUN
ap-2101	593	4	and	and	CCONJ
ap-2101	593	5	the	the	DET
ap-2101	593	6	ε	ε	PROPN
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ap-2101	593	8	.	.	PUNCT
ap-2101	594	1	physics	physics	NOUN
ap-2101	594	2	reports	report	NOUN
ap-2101	594	3	,	,	PUNCT
ap-2101	594	4	12(2):75	12(2):75	NUM
ap-2101	594	5	–	–	PUNCT
ap-2101	594	6	199	199	NUM
ap-2101	594	7	,	,	PUNCT
ap-2101	594	8	1974	1974	NUM
ap-2101	594	9	.	.	PUNCT
ap-2101	595	1	doi	doi	NOUN
ap-2101	595	2	:	:	PUNCT
ap-2101	595	3	10.1016/0370	10.1016/0370	NUM
ap-2101	595	4	-	-	SYM
ap-2101	595	5	1573(74)90023	1573(74)90023	NUM
ap-2101	595	6	-	-	SYM
ap-2101	595	7	4	4	NUM
ap-2101	595	8	172	172	NUM
ap-2101	595	9	http://dx.doi.org/10.1119/1.13148	http://dx.doi.org/10.1119/1.13148	NOUN
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ap-2101	595	12	http://dx.doi.org/10.1007/bf01209307	http://dx.doi.org/10.1007/bf01209307	NOUN
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ap-2101	595	17	http://dx.doi.org/10.1103/revmodphys.47.773	http://dx.doi.org/10.1103/revmodphys.47.773	PROPN
ap-2101	595	18	http://dx.doi.org/10.1103/revmodphys.55.583	http://dx.doi.org/10.1103/revmodphys.55.583	PROPN
ap-2101	595	19	http://dx.doi.org/10.1016/0370-1573(74)90023-4	http://dx.doi.org/10.1016/0370-1573(74)90023-4	PROPN
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ap-2101	595	23	,	,	PUNCT
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ap-2101	595	25	1	1	NUM
ap-2101	595	26	introduction	introduction	NOUN
ap-2101	595	27	2	2	NUM
ap-2101	595	28	exact	exact	ADJ
ap-2101	595	29	renormalization	renormalization	NOUN
ap-2101	595	30	group	group	NOUN
ap-2101	595	31	on	on	ADP
ap-2101	595	32	the	the	DET
ap-2101	595	33	euclidean	euclidean	ADJ
ap-2101	595	34	plane	plane	NOUN
ap-2101	595	35	2.1	2.1	NUM
ap-2101	595	36	formulation	formulation	NOUN
ap-2101	595	37	of	of	ADP
ap-2101	595	38	the	the	DET
ap-2101	595	39	problem	problem	NOUN
ap-2101	595	40	2.2	2.2	NUM
ap-2101	595	41	renormalization	renormalization	NOUN
ap-2101	595	42	of	of	ADP
ap-2101	595	43	hamiltonians	hamiltonian	NOUN
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ap-2101	595	46	the	the	DET
ap-2101	595	47	erg	erg	PROPN
ap-2101	595	48	procedure	procedure	NOUN
ap-2101	595	49	2.4	2.4	NUM
ap-2101	595	50	estimating	estimate	VERB
ap-2101	595	51	the	the	DET
ap-2101	595	52	range	range	NOUN
ap-2101	595	53	of	of	ADP
ap-2101	595	54	renormalizability	renormalizability	NOUN
ap-2101	595	55	2.5	2.5	NUM
ap-2101	595	56	bound	bind	VERB
ap-2101	595	57	state	state	NOUN
ap-2101	595	58	solution	solution	NOUN
ap-2101	595	59	3	3	NUM
ap-2101	595	60	exact	exact	ADJ
ap-2101	595	61	renormalization	renormalization	NOUN
ap-2101	595	62	group	group	NOUN
ap-2101	595	63	on	on	ADP
ap-2101	595	64	the	the	DET
ap-2101	595	65	hyperbolic	hyperbolic	ADJ
ap-2101	595	66	plane	plane	NOUN
ap-2101	595	67	3.1	3.1	NUM
ap-2101	595	68	the	the	DET
ap-2101	595	69	geometry	geometry	NOUN
ap-2101	595	70	and	and	CCONJ
ap-2101	595	71	spectra	spectra	NOUN
ap-2101	595	72	of	of	ADP
ap-2101	595	73	the	the	DET
ap-2101	595	74	hyperbolic	hyperbolic	ADJ
ap-2101	595	75	plane	plane	NOUN
ap-2101	595	76	3.2	3.2	NUM
ap-2101	595	77	formulation	formulation	NOUN
ap-2101	595	78	of	of	ADP
ap-2101	595	79	the	the	DET
ap-2101	595	80	problem	problem	NOUN
ap-2101	595	81	3.3	3.3	NUM
ap-2101	595	82	applying	apply	VERB
ap-2101	595	83	the	the	DET
ap-2101	595	84	erg	erg	PROPN
ap-2101	595	85	procedure	procedure	NOUN
ap-2101	595	86	3.4	3.4	NUM
ap-2101	595	87	estimating	estimate	VERB
ap-2101	595	88	the	the	DET
ap-2101	595	89	range	range	NOUN
ap-2101	595	90	of	of	ADP
ap-2101	595	91	renormalizability	renormalizability	NOUN
ap-2101	595	92	3.5	3.5	NUM
ap-2101	595	93	bound	bind	VERB
ap-2101	595	94	state	state	NOUN
ap-2101	595	95	solution	solution	NOUN
ap-2101	595	96	4	4	NUM
ap-2101	595	97	exact	exact	ADJ
ap-2101	595	98	renormalization	renormalization	NOUN
ap-2101	595	99	group	group	NOUN
ap-2101	595	100	on	on	ADP
ap-2101	595	101	the	the	DET
ap-2101	595	102	sphere	sphere	NOUN
ap-2101	595	103	4.1	4.1	NUM
ap-2101	595	104	formulation	formulation	NOUN
ap-2101	595	105	of	of	ADP
ap-2101	595	106	the	the	DET
ap-2101	595	107	problem	problem	NOUN
ap-2101	595	108	4.2	4.2	NUM
ap-2101	595	109	applying	apply	VERB
ap-2101	595	110	the	the	DET
ap-2101	595	111	erg	erg	NOUN
ap-2101	595	112	procedure	procedure	NOUN
ap-2101	595	113	5	5	NUM
ap-2101	595	114	conclusion	conclusion	NOUN
ap-2101	595	115	acknowledgements	acknowledgement	NOUN
ap-2101	595	116	references	reference	NOUN