id	sid	tid	token	lemma	pos
ap-1213	1	1	ap-3-10.dvi	ap-3-10.dvi	PROPN
ap-1213	1	2	acta	acta	PROPN
ap-1213	1	3	polytechnica	polytechnica	PROPN
ap-1213	1	4	vol	vol	NOUN
ap-1213	1	5	.	.	PROPN
ap-1213	2	1	50	50	NUM
ap-1213	2	2	no	no	NOUN
ap-1213	2	3	.	.	PUNCT
ap-1213	3	1	3/2010	3/2010	NUM
ap-1213	3	2	algebraic	algebraic	ADJ
ap-1213	3	3	solutions	solution	NOUN
ap-1213	3	4	in	in	ADP
ap-1213	3	5	open	open	ADJ
ap-1213	3	6	string	string	NOUN
ap-1213	3	7	field	field	NOUN
ap-1213	3	8	theory	theory	NOUN
ap-1213	3	9	–	–	PUNCT
ap-1213	3	10	a	a	DET
ap-1213	3	11	lightning	lightning	NOUN
ap-1213	3	12	review	review	NOUN
ap-1213	3	13	m.	m.	NOUN
ap-1213	3	14	schnabl	schnabl	PROPN
ap-1213	3	15	abstract	abstract	NOUN
ap-1213	3	16	in	in	ADP
ap-1213	3	17	this	this	DET
ap-1213	3	18	short	short	ADJ
ap-1213	3	19	paper	paper	NOUN
ap-1213	3	20	we	we	PRON
ap-1213	3	21	review	review	VERB
ap-1213	3	22	basic	basic	ADJ
ap-1213	3	23	ideas	idea	NOUN
ap-1213	3	24	of	of	ADP
ap-1213	3	25	string	string	NOUN
ap-1213	3	26	field	field	NOUN
ap-1213	3	27	theory	theory	NOUN
ap-1213	3	28	with	with	ADP
ap-1213	3	29	the	the	DET
ap-1213	3	30	emphasis	emphasis	NOUN
ap-1213	3	31	on	on	ADP
ap-1213	3	32	the	the	DET
ap-1213	3	33	recent	recent	ADJ
ap-1213	3	34	developments	development	NOUN
ap-1213	3	35	.	.	PUNCT
ap-1213	4	1	we	we	PRON
ap-1213	4	2	show	show	VERB
ap-1213	4	3	how	how	SCONJ
ap-1213	4	4	without	without	ADP
ap-1213	4	5	much	much	ADJ
ap-1213	4	6	technicalities	technicality	NOUN
ap-1213	4	7	one	one	PRON
ap-1213	4	8	can	can	AUX
ap-1213	4	9	look	look	VERB
ap-1213	4	10	for	for	SCONJ
ap-1213	4	11	analytic	analytic	ADJ
ap-1213	4	12	solutions	solution	NOUN
ap-1213	4	13	to	to	PART
ap-1213	4	14	witten	witten	VERB
ap-1213	4	15	’s	’s	PART
ap-1213	4	16	open	open	ADJ
ap-1213	4	17	string	string	NOUN
ap-1213	4	18	field	field	NOUN
ap-1213	4	19	theory	theory	NOUN
ap-1213	4	20	.	.	PUNCT
ap-1213	5	1	this	this	PRON
ap-1213	5	2	is	be	AUX
ap-1213	5	3	an	an	DET
ap-1213	5	4	expanded	expand	VERB
ap-1213	5	5	version	version	NOUN
ap-1213	5	6	of	of	ADP
ap-1213	5	7	a	a	DET
ap-1213	5	8	talk	talk	NOUN
ap-1213	5	9	given	give	VERB
ap-1213	5	10	by	by	ADP
ap-1213	5	11	the	the	DET
ap-1213	5	12	author	author	NOUN
ap-1213	5	13	over	over	ADP
ap-1213	5	14	the	the	DET
ap-1213	5	15	last	last	ADJ
ap-1213	5	16	year	year	NOUN
ap-1213	5	17	at	at	ADP
ap-1213	5	18	a	a	DET
ap-1213	5	19	number	number	NOUN
ap-1213	5	20	of	of	ADP
ap-1213	5	21	occasions1	occasions1	NOUN
ap-1213	5	22	and	and	CCONJ
ap-1213	5	23	notably	notably	ADV
ap-1213	5	24	at	at	ADP
ap-1213	5	25	the	the	DET
ap-1213	5	26	conference	conference	NOUN
ap-1213	5	27	selected	select	VERB
ap-1213	5	28	topics	topic	NOUN
ap-1213	5	29	in	in	ADP
ap-1213	5	30	mathematical	mathematical	ADJ
ap-1213	5	31	and	and	CCONJ
ap-1213	5	32	particle	particle	NOUN
ap-1213	5	33	physics	physics	NOUN
ap-1213	5	34	in	in	ADP
ap-1213	5	35	honor	honor	NOUN
ap-1213	5	36	of	of	ADP
ap-1213	5	37	prof	prof	NOUN
ap-1213	5	38	.	.	PUNCT
ap-1213	6	1	jǐŕı	jǐŕı	PROPN
ap-1213	6	2	niederle	niederle	PROPN
ap-1213	6	3	’s	’s	PART
ap-1213	6	4	70th	70th	ADJ
ap-1213	6	5	birthday	birthday	NOUN
ap-1213	6	6	.	.	PUNCT
ap-1213	7	1	1	1	NUM
ap-1213	8	1	what	what	PRON
ap-1213	8	2	is	be	AUX
ap-1213	8	3	string	string	NOUN
ap-1213	8	4	field	field	NOUN
ap-1213	8	5	theory	theory	NOUN
ap-1213	8	6	?	?	PUNCT
ap-1213	9	1	the	the	DET
ap-1213	9	2	traditional	traditional	ADJ
ap-1213	9	3	rules	rule	NOUN
ap-1213	9	4	of	of	ADP
ap-1213	9	5	first	first	ADJ
ap-1213	9	6	quantized	quantize	VERB
ap-1213	9	7	string	string	NOUN
ap-1213	9	8	theory	theory	NOUN
ap-1213	9	9	allow	allow	VERB
ap-1213	9	10	one	one	PRON
ap-1213	9	11	to	to	PART
ap-1213	9	12	compute	compute	VERB
ap-1213	9	13	on	on	ADP
ap-1213	9	14	-	-	PUNCT
ap-1213	9	15	shell	shell	NOUN
ap-1213	9	16	perturbative	perturbative	ADJ
ap-1213	9	17	amplitudes	amplitude	NOUN
ap-1213	9	18	,	,	PUNCT
ap-1213	9	19	but	but	CCONJ
ap-1213	9	20	they	they	PRON
ap-1213	9	21	tell	tell	VERB
ap-1213	9	22	us	we	PRON
ap-1213	9	23	little	little	ADJ
ap-1213	9	24	about	about	ADP
ap-1213	9	25	collective	collective	ADJ
ap-1213	9	26	phenomena	phenomenon	NOUN
ap-1213	9	27	or	or	CCONJ
ap-1213	9	28	non	non	ADJ
ap-1213	9	29	-	-	ADJ
ap-1213	9	30	perturbative	perturbative	ADJ
ap-1213	9	31	effects	effect	NOUN
ap-1213	9	32	.	.	PUNCT
ap-1213	10	1	two	two	NUM
ap-1213	10	2	most	most	ADV
ap-1213	10	3	prominent	prominent	ADJ
ap-1213	10	4	examples	example	NOUN
ap-1213	10	5	of	of	ADP
ap-1213	10	6	such	such	ADJ
ap-1213	10	7	are	be	AUX
ap-1213	10	8	tachyon	tachyon	NOUN
ap-1213	10	9	condensation	condensation	NOUN
ap-1213	10	10	(	(	PUNCT
ap-1213	10	11	a	a	DET
ap-1213	10	12	close	close	ADJ
ap-1213	10	13	relative	relative	NOUN
ap-1213	10	14	of	of	ADP
ap-1213	10	15	the	the	DET
ap-1213	10	16	higgs	higgs	NOUN
ap-1213	10	17	mechanism	mechanism	NOUN
ap-1213	10	18	)	)	PUNCT
ap-1213	10	19	and	and	CCONJ
ap-1213	10	20	instanton	instanton	PROPN
ap-1213	10	21	physics	physics	PROPN
ap-1213	10	22	.	.	PUNCT
ap-1213	11	1	string	string	NOUN
ap-1213	11	2	field	field	NOUN
ap-1213	11	3	theory	theory	NOUN
ap-1213	11	4	is	be	AUX
ap-1213	11	5	an	an	DET
ap-1213	11	6	attempt	attempt	NOUN
ap-1213	11	7	to	to	PART
ap-1213	11	8	turn	turn	VERB
ap-1213	11	9	string	string	NOUN
ap-1213	11	10	theory	theory	NOUN
ap-1213	11	11	into	into	ADP
ap-1213	11	12	some	some	DET
ap-1213	11	13	sort	sort	NOUN
ap-1213	11	14	of	of	ADP
ap-1213	11	15	field	field	NOUN
ap-1213	11	16	theory	theory	NOUN
ap-1213	11	17	by	by	ADP
ap-1213	11	18	writing	write	VERB
ap-1213	11	19	a	a	DET
ap-1213	11	20	field	field	NOUN
ap-1213	11	21	theory	theory	NOUN
ap-1213	11	22	action	action	NOUN
ap-1213	11	23	for	for	ADP
ap-1213	11	24	each	each	PRON
ap-1213	11	25	of	of	ADP
ap-1213	11	26	the	the	DET
ap-1213	11	27	single	single	ADJ
ap-1213	11	28	string	string	NOUN
ap-1213	11	29	modes	mode	NOUN
ap-1213	11	30	and	and	CCONJ
ap-1213	11	31	combining	combine	VERB
ap-1213	11	32	them	they	PRON
ap-1213	11	33	together	together	ADV
ap-1213	11	34	with	with	ADP
ap-1213	11	35	very	very	ADV
ap-1213	11	36	particular	particular	ADJ
ap-1213	11	37	interactions	interaction	NOUN
ap-1213	11	38	.	.	PUNCT
ap-1213	12	1	perturbative	perturbative	ADJ
ap-1213	12	2	quantization	quantization	NOUN
ap-1213	12	3	of	of	ADP
ap-1213	12	4	this	this	DET
ap-1213	12	5	field	field	NOUN
ap-1213	12	6	theory	theory	NOUN
ap-1213	12	7	yields	yield	VERB
ap-1213	12	8	all	all	PRON
ap-1213	12	9	of	of	ADP
ap-1213	12	10	the	the	DET
ap-1213	12	11	perturbative	perturbative	ADJ
ap-1213	12	12	string	string	NOUN
ap-1213	12	13	theory	theory	NOUN
ap-1213	12	14	,	,	PUNCT
ap-1213	12	15	and	and	CCONJ
ap-1213	12	16	one	one	PRON
ap-1213	12	17	might	might	AUX
ap-1213	12	18	hope	hope	VERB
ap-1213	12	19	that	that	SCONJ
ap-1213	12	20	one	one	NUM
ap-1213	12	21	day	day	NOUN
ap-1213	12	22	we	we	PRON
ap-1213	12	23	could	could	AUX
ap-1213	12	24	get	get	VERB
ap-1213	12	25	a	a	DET
ap-1213	12	26	truly	truly	ADV
ap-1213	12	27	nonperturbative	nonperturbative	ADJ
ap-1213	12	28	description	description	NOUN
ap-1213	12	29	of	of	ADP
ap-1213	12	30	the	the	DET
ap-1213	12	31	theory	theory	NOUN
ap-1213	12	32	.	.	PUNCT
ap-1213	13	1	one	one	NUM
ap-1213	13	2	of	of	ADP
ap-1213	13	3	the	the	DET
ap-1213	13	4	most	most	ADV
ap-1213	13	5	interesting	interesting	ADJ
ap-1213	13	6	applications	application	NOUN
ap-1213	13	7	of	of	ADP
ap-1213	13	8	string	string	NOUN
ap-1213	13	9	field	field	NOUN
ap-1213	13	10	theory	theory	NOUN
ap-1213	13	11	to	to	ADP
ap-1213	13	12	date	date	NOUN
ap-1213	13	13	has	have	AUX
ap-1213	13	14	been	be	AUX
ap-1213	13	15	in	in	ADP
ap-1213	13	16	studies	study	NOUN
ap-1213	13	17	of	of	ADP
ap-1213	13	18	the	the	DET
ap-1213	13	19	classical	classical	ADJ
ap-1213	13	20	backgrounds	background	NOUN
ap-1213	13	21	of	of	ADP
ap-1213	13	22	string	string	NOUN
ap-1213	13	23	theory	theory	NOUN
ap-1213	13	24	.	.	PUNCT
ap-1213	14	1	traditionally	traditionally	ADV
ap-1213	14	2	,	,	PUNCT
ap-1213	14	3	string	string	NOUN
ap-1213	14	4	theories	theory	NOUN
ap-1213	14	5	are	be	AUX
ap-1213	14	6	defined	define	VERB
ap-1213	14	7	to	to	PART
ap-1213	14	8	be	be	AUX
ap-1213	14	9	in	in	ADP
ap-1213	14	10	one	one	NUM
ap-1213	14	11	-	-	PUNCT
ap-1213	14	12	to	to	ADP
ap-1213	14	13	-	-	PUNCT
ap-1213	14	14	one	one	NUM
ap-1213	14	15	correspondence	correspondence	NOUN
ap-1213	14	16	with	with	ADP
ap-1213	14	17	worldsheet	worldsheet	ADJ
ap-1213	14	18	conformal	conformal	ADJ
ap-1213	14	19	field	field	NOUN
ap-1213	14	20	theories	theory	NOUN
ap-1213	14	21	(	(	PUNCT
ap-1213	14	22	cft	cft	PROPN
ap-1213	14	23	’s	’s	PART
ap-1213	14	24	)	)	PUNCT
ap-1213	14	25	.	.	PUNCT
ap-1213	15	1	as	as	ADP
ap-1213	15	2	such	such	ADJ
ap-1213	15	3	they	they	PRON
ap-1213	15	4	correspond	correspond	VERB
ap-1213	15	5	to	to	ADP
ap-1213	15	6	the	the	DET
ap-1213	15	7	choice	choice	NOUN
ap-1213	15	8	of	of	ADP
ap-1213	15	9	infinitely	infinitely	ADV
ap-1213	15	10	many	many	ADJ
ap-1213	15	11	couplings	coupling	NOUN
ap-1213	15	12	in	in	ADP
ap-1213	15	13	two	two	NUM
ap-1213	15	14	dimensional	dimensional	ADJ
ap-1213	15	15	worldsheet	worldsheet	NOUN
ap-1213	15	16	theory	theory	NOUN
ap-1213	15	17	.	.	PUNCT
ap-1213	16	1	the	the	DET
ap-1213	16	2	condition	condition	NOUN
ap-1213	16	3	of	of	ADP
ap-1213	16	4	vanishing	vanish	VERB
ap-1213	16	5	beta	beta	NOUN
ap-1213	16	6	functions	function	NOUN
ap-1213	16	7	for	for	ADP
ap-1213	16	8	all	all	PRON
ap-1213	16	9	of	of	ADP
ap-1213	16	10	these	these	DET
ap-1213	16	11	couplings	coupling	NOUN
ap-1213	16	12	is	be	AUX
ap-1213	16	13	equivalent	equivalent	ADJ
ap-1213	16	14	to	to	ADP
ap-1213	16	15	einstein	einstein	NOUN
ap-1213	16	16	or	or	CCONJ
ap-1213	16	17	maxwell	maxwell	PROPN
ap-1213	16	18	like	like	INTJ
ap-1213	16	19	equations	equation	NOUN
ap-1213	16	20	for	for	ADP
ap-1213	16	21	the	the	DET
ap-1213	16	22	classical	classical	ADJ
ap-1213	16	23	backgrounds	background	NOUN
ap-1213	16	24	.	.	PUNCT
ap-1213	17	1	given	give	VERB
ap-1213	17	2	two	two	NUM
ap-1213	17	3	cft	cft	PROPN
ap-1213	17	4	’s	’s	NOUN
ap-1213	17	5	,	,	PUNCT
ap-1213	17	6	the	the	DET
ap-1213	17	7	two	two	NUM
ap-1213	17	8	corresponding	corresponding	ADJ
ap-1213	17	9	string	string	NOUN
ap-1213	17	10	theories	theory	NOUN
ap-1213	17	11	look	look	VERB
ap-1213	17	12	in	in	ADP
ap-1213	17	13	general	general	ADJ
ap-1213	17	14	entirely	entirely	ADV
ap-1213	17	15	different	different	ADJ
ap-1213	17	16	.	.	PUNCT
ap-1213	18	1	for	for	ADP
ap-1213	18	2	cft	cft	PROPN
ap-1213	18	3	’s	’s	PART
ap-1213	18	4	related	relate	VERB
ap-1213	18	5	by	by	ADP
ap-1213	18	6	exactly	exactly	ADV
ap-1213	18	7	marginal	marginal	ADJ
ap-1213	18	8	deformations	deformation	NOUN
ap-1213	18	9	,	,	PUNCT
ap-1213	18	10	the	the	DET
ap-1213	18	11	two	two	NUM
ap-1213	18	12	theories	theory	NOUN
ap-1213	18	13	may	may	AUX
ap-1213	18	14	bear	bear	VERB
ap-1213	18	15	some	some	DET
ap-1213	18	16	resemblance	resemblance	NOUN
ap-1213	18	17	,	,	PUNCT
ap-1213	18	18	but	but	CCONJ
ap-1213	18	19	for	for	ADP
ap-1213	18	20	theories	theory	NOUN
ap-1213	18	21	related	relate	VERB
ap-1213	18	22	by	by	ADP
ap-1213	18	23	relevant	relevant	ADJ
ap-1213	18	24	deformations	deformation	NOUN
ap-1213	18	25	it	it	PRON
ap-1213	18	26	is	be	AUX
ap-1213	18	27	very	very	ADV
ap-1213	18	28	hard	hard	ADJ
ap-1213	18	29	to	to	PART
ap-1213	18	30	see	see	VERB
ap-1213	18	31	how	how	SCONJ
ap-1213	18	32	one	one	NUM
ap-1213	18	33	background	background	NOUN
ap-1213	18	34	can	can	AUX
ap-1213	18	35	be	be	AUX
ap-1213	18	36	a	a	DET
ap-1213	18	37	solution	solution	NOUN
ap-1213	18	38	of	of	ADP
ap-1213	18	39	a	a	DET
ap-1213	18	40	theory	theory	NOUN
ap-1213	18	41	formulated	formulate	VERB
ap-1213	18	42	around	around	ADP
ap-1213	18	43	another	another	DET
ap-1213	18	44	background	background	NOUN
ap-1213	18	45	.	.	PUNCT
ap-1213	19	1	this	this	PRON
ap-1213	19	2	is	be	AUX
ap-1213	19	3	in	in	ADP
ap-1213	19	4	stark	stark	ADJ
ap-1213	19	5	contrast	contrast	NOUN
ap-1213	19	6	to	to	ADP
ap-1213	19	7	general	general	ADJ
ap-1213	19	8	relativity	relativity	NOUN
ap-1213	19	9	,	,	PUNCT
ap-1213	19	10	where	where	SCONJ
ap-1213	19	11	the	the	DET
ap-1213	19	12	einstein	einstein	PROPN
ap-1213	19	13	-	-	PUNCT
ap-1213	19	14	hilbert	hilbert	NOUN
ap-1213	19	15	action	action	NOUN
ap-1213	19	16	does	do	AUX
ap-1213	19	17	not	not	PART
ap-1213	19	18	depend	depend	VERB
ap-1213	19	19	on	on	ADP
ap-1213	19	20	any	any	DET
ap-1213	19	21	particular	particular	ADJ
ap-1213	19	22	background	background	NOUN
ap-1213	19	23	,	,	PUNCT
ap-1213	19	24	but	but	CCONJ
ap-1213	19	25	it	it	PRON
ap-1213	19	26	allows	allow	VERB
ap-1213	19	27	for	for	ADP
ap-1213	19	28	solutions	solution	NOUN
ap-1213	19	29	describing	describe	VERB
ap-1213	19	30	very	very	ADV
ap-1213	19	31	different	different	ADJ
ap-1213	19	32	geometries	geometry	NOUN
ap-1213	19	33	.	.	PUNCT
ap-1213	20	1	one	one	NUM
ap-1213	20	2	of	of	ADP
ap-1213	20	3	the	the	DET
ap-1213	20	4	holy	holy	ADJ
ap-1213	20	5	grails	grail	NOUN
ap-1213	20	6	of	of	ADP
ap-1213	20	7	string	string	NOUN
ap-1213	20	8	theory	theory	NOUN
ap-1213	20	9	research	research	NOUN
ap-1213	20	10	is	be	AUX
ap-1213	20	11	a	a	DET
ap-1213	20	12	manifestly	manifestly	ADV
ap-1213	20	13	background	background	NOUN
ap-1213	20	14	independent	independent	ADJ
ap-1213	20	15	formulation	formulation	NOUN
ap-1213	20	16	of	of	ADP
ap-1213	20	17	string	string	NOUN
ap-1213	20	18	theory	theory	NOUN
ap-1213	20	19	.	.	PUNCT
ap-1213	21	1	string	string	NOUN
ap-1213	21	2	field	field	NOUN
ap-1213	21	3	theory	theory	NOUN
ap-1213	21	4	(	(	PUNCT
ap-1213	21	5	sft	sft	NOUN
ap-1213	21	6	)	)	PUNCT
ap-1213	21	7	goes	go	VERB
ap-1213	21	8	half	half	ADJ
ap-1213	21	9	-	-	PUNCT
ap-1213	21	10	way	way	NOUN
ap-1213	21	11	towards	towards	ADP
ap-1213	21	12	this	this	DET
ap-1213	21	13	goal	goal	NOUN
ap-1213	21	14	.	.	PUNCT
ap-1213	22	1	it	it	PRON
ap-1213	22	2	gives	give	VERB
ap-1213	22	3	us	we	PRON
ap-1213	22	4	a	a	DET
ap-1213	22	5	formulation	formulation	NOUN
ap-1213	22	6	which	which	PRON
ap-1213	22	7	is	be	AUX
ap-1213	22	8	background	background	NOUN
ap-1213	22	9	independent	independent	ADJ
ap-1213	22	10	in	in	ADP
ap-1213	22	11	form	form	NOUN
ap-1213	22	12	(	(	PUNCT
ap-1213	22	13	not	not	PART
ap-1213	22	14	truly	truly	ADV
ap-1213	22	15	in	in	ADP
ap-1213	22	16	essence	essence	NOUN
ap-1213	22	17	)	)	PUNCT
ap-1213	22	18	and	and	CCONJ
ap-1213	22	19	which	which	PRON
ap-1213	22	20	posseses	possese	VERB
ap-1213	22	21	a	a	DET
ap-1213	22	22	multitude	multitude	NOUN
ap-1213	22	23	of	of	ADP
ap-1213	22	24	classical	classical	ADJ
ap-1213	22	25	solutions	solution	NOUN
ap-1213	22	26	representing	represent	VERB
ap-1213	22	27	different	different	ADJ
ap-1213	22	28	backgrounds	background	NOUN
ap-1213	22	29	.	.	PUNCT
ap-1213	23	1	it	it	PRON
ap-1213	23	2	is	be	AUX
ap-1213	23	3	defined	define	VERB
ap-1213	23	4	using	use	VERB
ap-1213	23	5	the	the	DET
ap-1213	23	6	data	datum	NOUN
ap-1213	23	7	of	of	ADP
ap-1213	23	8	a	a	DET
ap-1213	23	9	single	single	ADJ
ap-1213	23	10	reference	reference	NOUN
ap-1213	23	11	cft	cft	NOUN
ap-1213	23	12	.	.	PUNCT
ap-1213	24	1	it	it	PRON
ap-1213	24	2	is	be	AUX
ap-1213	24	3	analogous	analogous	ADJ
ap-1213	24	4	to	to	ADP
ap-1213	24	5	writing	write	VERB
ap-1213	24	6	the	the	DET
ap-1213	24	7	einstein	einstein	ADJ
ap-1213	24	8	-	-	PUNCT
ap-1213	24	9	hilbert	hilbert	NOUN
ap-1213	24	10	action	action	NOUN
ap-1213	24	11	and	and	CCONJ
ap-1213	24	12	substituting	substitute	VERB
ap-1213	24	13	the	the	DET
ap-1213	24	14	metric	metric	ADJ
ap-1213	24	15	gμν(x	gμν(x	NOUN
ap-1213	24	16	)	)	PUNCT
ap-1213	24	17	with	with	ADP
ap-1213	24	18	grefμν	grefμν	NOUN
ap-1213	24	19	(	(	PUNCT
ap-1213	24	20	x	x	NOUN
ap-1213	24	21	)	)	PUNCT
ap-1213	24	22	+	+	X
ap-1213	24	23	hμν(x	hμν(x	NOUN
ap-1213	24	24	)	)	PUNCT
ap-1213	24	25	.	.	PUNCT
ap-1213	25	1	the	the	DET
ap-1213	25	2	fundamental	fundamental	ADJ
ap-1213	25	3	reason	reason	NOUN
ap-1213	25	4	for	for	ADP
ap-1213	25	5	this	this	DET
ap-1213	25	6	difficulty	difficulty	NOUN
ap-1213	25	7	is	be	AUX
ap-1213	25	8	that	that	SCONJ
ap-1213	25	9	what	what	PRON
ap-1213	25	10	are	be	AUX
ap-1213	25	11	the	the	DET
ap-1213	25	12	field	field	NOUN
ap-1213	25	13	theoretic	theoretic	NOUN
ap-1213	25	14	degrees	degree	NOUN
ap-1213	25	15	of	of	ADP
ap-1213	25	16	freedom	freedom	NOUN
ap-1213	25	17	in	in	ADP
ap-1213	25	18	string	string	NOUN
ap-1213	25	19	theory	theory	NOUN
ap-1213	25	20	depends	depend	VERB
ap-1213	25	21	on	on	ADP
ap-1213	25	22	the	the	DET
ap-1213	25	23	background	background	NOUN
ap-1213	25	24	,	,	PUNCT
ap-1213	25	25	unlike	unlike	ADP
ap-1213	25	26	in	in	ADP
ap-1213	25	27	general	general	ADJ
ap-1213	25	28	relativity	relativity	NOUN
ap-1213	25	29	.	.	PUNCT
ap-1213	26	1	following	follow	VERB
ap-1213	26	2	sen	sen	PROPN
ap-1213	26	3	and	and	CCONJ
ap-1213	26	4	zwiebach	zwiebach	PRON
ap-1213	27	1	[	[	X
ap-1213	27	2	1	1	NUM
ap-1213	27	3	,	,	PUNCT
ap-1213	27	4	2	2	NUM
ap-1213	27	5	]	]	PUNCT
ap-1213	27	6	,	,	PUNCT
ap-1213	27	7	it	it	PRON
ap-1213	27	8	is	be	AUX
ap-1213	27	9	believed	believe	VERB
ap-1213	27	10	that	that	SCONJ
ap-1213	27	11	the	the	DET
ap-1213	27	12	space	space	NOUN
ap-1213	27	13	of	of	ADP
ap-1213	27	14	classical	classical	ADJ
ap-1213	27	15	solutions	solution	NOUN
ap-1213	27	16	of	of	ADP
ap-1213	27	17	sft	sft	NOUN
ap-1213	27	18	is	be	AUX
ap-1213	27	19	in	in	ADP
ap-1213	27	20	one	one	NUM
ap-1213	27	21	-	-	PUNCT
ap-1213	27	22	to	to	ADP
ap-1213	27	23	-	-	PUNCT
ap-1213	27	24	one	one	NUM
ap-1213	27	25	correspondence	correspondence	NOUN
ap-1213	27	26	(	(	PUNCT
ap-1213	27	27	modulo	modulo	NOUN
ap-1213	27	28	gauge	gauge	NOUN
ap-1213	27	29	symmetries	symmetry	NOUN
ap-1213	27	30	and	and	CCONJ
ap-1213	27	31	perhaps	perhaps	ADV
ap-1213	27	32	dualities	duality	NOUN
ap-1213	27	33	)	)	PUNCT
ap-1213	27	34	with	with	ADP
ap-1213	27	35	worldsheet	worldsheet	PROPN
ap-1213	27	36	cft	cft	PROPN
ap-1213	27	37	’s	’s	NOUN
ap-1213	27	38	.	.	PUNCT
ap-1213	28	1	in	in	ADP
ap-1213	28	2	this	this	DET
ap-1213	28	3	short	short	ADJ
ap-1213	28	4	paper	paper	NOUN
ap-1213	28	5	we	we	PRON
ap-1213	28	6	review	review	VERB
ap-1213	28	7	the	the	DET
ap-1213	28	8	amazingly	amazingly	ADV
ap-1213	28	9	simple	simple	ADJ
ap-1213	28	10	construction	construction	NOUN
ap-1213	28	11	of	of	ADP
ap-1213	28	12	a	a	DET
ap-1213	28	13	class	class	NOUN
ap-1213	28	14	of	of	ADP
ap-1213	28	15	solutions	solution	NOUN
ap-1213	28	16	that	that	PRON
ap-1213	28	17	can	can	AUX
ap-1213	28	18	be	be	AUX
ap-1213	28	19	determined	determine	VERB
ap-1213	28	20	purely	purely	ADV
ap-1213	28	21	algebraically	algebraically	ADV
ap-1213	28	22	.	.	PUNCT
ap-1213	29	1	these	these	PRON
ap-1213	29	2	are	be	AUX
ap-1213	29	3	just	just	ADV
ap-1213	29	4	the	the	DET
ap-1213	29	5	first	first	ADJ
ap-1213	29	6	steps	step	NOUN
ap-1213	29	7	in	in	ADP
ap-1213	29	8	a	a	DET
ap-1213	29	9	long	long	ADJ
ap-1213	29	10	program	program	NOUN
ap-1213	29	11	of	of	ADP
ap-1213	29	12	constructing	construct	VERB
ap-1213	29	13	and	and	CCONJ
ap-1213	29	14	classifying	classify	VERB
ap-1213	29	15	all	all	DET
ap-1213	29	16	solutions	solution	NOUN
ap-1213	29	17	and	and	CCONJ
ap-1213	29	18	relating	relate	VERB
ap-1213	29	19	them	they	PRON
ap-1213	29	20	to	to	ADP
ap-1213	29	21	some	some	DET
ap-1213	29	22	cft	cft	NOUN
ap-1213	29	23	’s	’s	NOUN
ap-1213	29	24	.	.	PUNCT
ap-1213	30	1	in	in	ADP
ap-1213	30	2	sections	section	NOUN
ap-1213	30	3	5	5	NUM
ap-1213	30	4	and	and	CCONJ
ap-1213	30	5	6	6	NUM
ap-1213	30	6	we	we	PRON
ap-1213	30	7	add	add	VERB
ap-1213	30	8	in	in	ADP
ap-1213	30	9	a	a	DET
ap-1213	30	10	little	little	ADJ
ap-1213	30	11	bit	bit	NOUN
ap-1213	30	12	of	of	ADP
ap-1213	30	13	original	original	ADJ
ap-1213	30	14	material	material	NOUN
ap-1213	30	15	.	.	PUNCT
ap-1213	31	1	borrowing	borrow	VERB
ap-1213	31	2	a	a	DET
ap-1213	31	3	few	few	ADJ
ap-1213	31	4	theorems	theorem	NOUN
ap-1213	31	5	from	from	ADP
ap-1213	31	6	the	the	DET
ap-1213	31	7	theory	theory	NOUN
ap-1213	31	8	of	of	ADP
ap-1213	31	9	distributions	distribution	NOUN
ap-1213	31	10	and	and	CCONJ
ap-1213	31	11	the	the	DET
ap-1213	31	12	laplace	laplace	NOUN
ap-1213	31	13	transform	transform	NOUN
ap-1213	31	14	we	we	PRON
ap-1213	31	15	are	be	AUX
ap-1213	31	16	able	able	ADJ
ap-1213	31	17	to	to	PART
ap-1213	31	18	shed	shed	VERB
ap-1213	31	19	novel	novel	ADJ
ap-1213	31	20	light	light	NOUN
ap-1213	31	21	on	on	ADP
ap-1213	31	22	what	what	PRON
ap-1213	31	23	the	the	DET
ap-1213	31	24	space	space	NOUN
ap-1213	31	25	of	of	ADP
ap-1213	31	26	allowed	allow	VERB
ap-1213	31	27	string	string	NOUN
ap-1213	31	28	fields	field	NOUN
ap-1213	31	29	should	should	AUX
ap-1213	31	30	look	look	VERB
ap-1213	31	31	like	like	ADP
ap-1213	31	32	.	.	PUNCT
ap-1213	32	1	this	this	DET
ap-1213	32	2	seemingly	seemingly	ADV
ap-1213	32	3	academic	academic	ADJ
ap-1213	32	4	question	question	NOUN
ap-1213	32	5	is	be	AUX
ap-1213	32	6	actually	actually	ADV
ap-1213	32	7	important	important	ADJ
ap-1213	32	8	for	for	ADP
ap-1213	32	9	distinguishing	distinguish	VERB
ap-1213	32	10	gauge	gauge	NOUN
ap-1213	32	11	trivial	trivial	ADJ
ap-1213	32	12	and	and	CCONJ
ap-1213	32	13	non	non	ADJ
ap-1213	32	14	-	-	ADJ
ap-1213	32	15	trivial	trivial	ADJ
ap-1213	32	16	solutions	solution	NOUN
ap-1213	32	17	.	.	PUNCT
ap-1213	33	1	2	2	NUM
ap-1213	33	2	précis	précis	NUM
ap-1213	33	3	of	of	ADP
ap-1213	33	4	osft	osft	ADJ
ap-1213	33	5	one	one	NUM
ap-1213	33	6	of	of	ADP
ap-1213	33	7	the	the	DET
ap-1213	33	8	best	well	ADV
ap-1213	33	9	understood	understand	VERB
ap-1213	33	10	string	string	NOUN
ap-1213	33	11	field	field	NOUN
ap-1213	33	12	theories	theory	NOUN
ap-1213	33	13	is	be	AUX
ap-1213	33	14	witten	witten	PROPN
ap-1213	33	15	’s	’s	PART
ap-1213	33	16	covariant	covariant	ADJ
ap-1213	33	17	chern	chern	PROPN
ap-1213	33	18	-	-	PUNCT
ap-1213	33	19	simons	simons	PROPN
ap-1213	33	20	type	type	NOUN
ap-1213	33	21	string	string	NOUN
ap-1213	33	22	field	field	NOUN
ap-1213	33	23	theory	theory	NOUN
ap-1213	33	24	[	[	X
ap-1213	33	25	3	3	X
ap-1213	33	26	]	]	PUNCT
ap-1213	33	27	for	for	ADP
ap-1213	33	28	open	open	ADJ
ap-1213	33	29	bosonic	bosonic	NOUN
ap-1213	33	30	string.2	string.2	NOUN
ap-1213	33	31	as	as	SCONJ
ap-1213	33	32	is	be	AUX
ap-1213	33	33	well	well	ADV
ap-1213	33	34	known	know	VERB
ap-1213	33	35	,	,	PUNCT
ap-1213	33	36	quantization	quantization	NOUN
ap-1213	33	37	of	of	ADP
ap-1213	33	38	a	a	DET
ap-1213	33	39	single	single	ADJ
ap-1213	33	40	classical	classical	ADJ
ap-1213	33	41	string	string	NOUN
ap-1213	33	42	is	be	AUX
ap-1213	33	43	somewhat	somewhat	ADV
ap-1213	33	44	subtle	subtle	ADJ
ap-1213	33	45	,	,	PUNCT
ap-1213	33	46	due	due	ADP
ap-1213	33	47	to	to	ADP
ap-1213	33	48	the	the	DET
ap-1213	33	49	reparametrization	reparametrization	NOUN
ap-1213	33	50	invariance	invariance	NOUN
ap-1213	33	51	of	of	ADP
ap-1213	33	52	the	the	DET
ap-1213	33	53	worldsheet	worldsheet	ADJ
ap-1213	33	54	action	action	NOUN
ap-1213	33	55	.	.	PUNCT
ap-1213	34	1	this	this	DET
ap-1213	34	2	gauge	gauge	NOUN
ap-1213	34	3	1parts	1part	NOUN
ap-1213	34	4	of	of	ADP
ap-1213	34	5	this	this	DET
ap-1213	34	6	work	work	NOUN
ap-1213	34	7	have	have	AUX
ap-1213	34	8	been	be	AUX
ap-1213	34	9	presented	present	VERB
ap-1213	34	10	at	at	ADP
ap-1213	34	11	the	the	DET
ap-1213	34	12	kavli	kavli	PROPN
ap-1213	34	13	institute	institute	NOUN
ap-1213	34	14	for	for	ADP
ap-1213	34	15	theoretical	theoretical	ADJ
ap-1213	34	16	physics	physics	NOUN
ap-1213	34	17	,	,	PUNCT
ap-1213	34	18	the	the	DET
ap-1213	34	19	aspen	aspen	ADJ
ap-1213	34	20	center	center	NOUN
ap-1213	34	21	for	for	ADP
ap-1213	34	22	physics	physics	NOUN
ap-1213	34	23	,	,	PUNCT
ap-1213	34	24	the	the	DET
ap-1213	34	25	simons	simons	PROPN
ap-1213	34	26	center	center	PROPN
ap-1213	34	27	for	for	ADP
ap-1213	34	28	geometry	geometry	NOUN
ap-1213	34	29	and	and	CCONJ
ap-1213	34	30	physics	physics	NOUN
ap-1213	34	31	and	and	CCONJ
ap-1213	34	32	the	the	DET
ap-1213	34	33	yukawa	yukawa	PROPN
ap-1213	34	34	institute	institute	PROPN
ap-1213	34	35	for	for	ADP
ap-1213	34	36	physics	physics	PROPN
ap-1213	34	37	.	.	PUNCT
ap-1213	35	1	we	we	PRON
ap-1213	35	2	thank	thank	VERB
ap-1213	35	3	these	these	DET
ap-1213	35	4	institutes	institute	NOUN
ap-1213	35	5	for	for	ADP
ap-1213	35	6	their	their	PRON
ap-1213	35	7	warm	warm	ADJ
ap-1213	35	8	hospitality	hospitality	NOUN
ap-1213	35	9	.	.	PUNCT
ap-1213	36	1	2there	2there	NUM
ap-1213	36	2	are	be	AUX
ap-1213	36	3	many	many	ADJ
ap-1213	36	4	other	other	ADJ
ap-1213	36	5	string	string	NOUN
ap-1213	36	6	field	field	NOUN
ap-1213	36	7	theories	theory	NOUN
ap-1213	36	8	,	,	PUNCT
ap-1213	36	9	also	also	ADV
ap-1213	36	10	for	for	ADP
ap-1213	36	11	closed	closed	ADJ
ap-1213	36	12	strings	string	NOUN
ap-1213	36	13	or	or	CCONJ
ap-1213	36	14	superstrings	superstring	NOUN
ap-1213	36	15	,	,	PUNCT
ap-1213	36	16	and	and	CCONJ
ap-1213	36	17	some	some	DET
ap-1213	36	18	theories	theory	NOUN
ap-1213	36	19	have	have	VERB
ap-1213	36	20	more	more	ADJ
ap-1213	36	21	than	than	ADP
ap-1213	36	22	one	one	NUM
ap-1213	36	23	description	description	NOUN
ap-1213	36	24	,	,	PUNCT
ap-1213	36	25	often	often	ADV
ap-1213	36	26	non	non	X
ap-1213	36	27	covariant	covariant	PROPN
ap-1213	36	28	.	.	PUNCT
ap-1213	37	1	some	some	PRON
ap-1213	37	2	are	be	AUX
ap-1213	37	3	also	also	ADV
ap-1213	37	4	non	non	ADJ
ap-1213	37	5	-	-	ADJ
ap-1213	37	6	polynomial	polynomial	ADJ
ap-1213	37	7	.	.	PUNCT
ap-1213	38	1	102	102	NUM
ap-1213	38	2	acta	acta	PROPN
ap-1213	38	3	polytechnica	polytechnica	PROPN
ap-1213	38	4	vol	vol	NOUN
ap-1213	38	5	.	.	PROPN
ap-1213	39	1	50	50	NUM
ap-1213	39	2	no	no	NOUN
ap-1213	39	3	.	.	PUNCT
ap-1213	40	1	3/2010	3/2010	NUM
ap-1213	40	2	symmetry	symmetry	NOUN
ap-1213	40	3	can	can	AUX
ap-1213	40	4	be	be	AUX
ap-1213	40	5	fixed	fix	VERB
ap-1213	40	6	in	in	ADP
ap-1213	40	7	a	a	DET
ap-1213	40	8	number	number	NOUN
ap-1213	40	9	of	of	ADP
ap-1213	40	10	ways	way	NOUN
ap-1213	40	11	.	.	PUNCT
ap-1213	41	1	in	in	ADP
ap-1213	41	2	the	the	DET
ap-1213	41	3	covariant	covariant	ADJ
ap-1213	41	4	quantization	quantization	NOUN
ap-1213	41	5	procedure	procedure	NOUN
ap-1213	41	6	one	one	NUM
ap-1213	41	7	has	have	VERB
ap-1213	41	8	to	to	PART
ap-1213	41	9	gauge	gauge	VERB
ap-1213	41	10	fix	fix	VERB
ap-1213	41	11	the	the	DET
ap-1213	41	12	worldsheet	worldsheet	NOUN
ap-1213	41	13	metric	metric	ADJ
ap-1213	41	14	hαβ	hαβ	NOUN
ap-1213	41	15	and	and	CCONJ
ap-1213	41	16	introduce	introduce	VERB
ap-1213	41	17	the	the	DET
ap-1213	41	18	worldsheet	worldsheet	ADJ
ap-1213	41	19	fadeev	fadeev	NOUN
ap-1213	41	20	-	-	PUNCT
ap-1213	41	21	popov	popov	NOUN
ap-1213	41	22	ghost	ghost	NOUN
ap-1213	41	23	fields	field	NOUN
ap-1213	41	24	b	b	PROPN
ap-1213	41	25	and	and	CCONJ
ap-1213	41	26	c.	c.	PROPN
ap-1213	41	27	the	the	DET
ap-1213	41	28	virasoro	virasoro	NOUN
ap-1213	41	29	constraints	constraint	NOUN
ap-1213	41	30	tαβ	tαβ	PROPN
ap-1213	41	31	=	=	SYM
ap-1213	41	32	0	0	NUM
ap-1213	41	33	resulting	result	VERB
ap-1213	41	34	from	from	ADP
ap-1213	41	35	gauge	gauge	NOUN
ap-1213	41	36	fixing	fixing	NOUN
ap-1213	41	37	can	can	AUX
ap-1213	41	38	then	then	ADV
ap-1213	41	39	be	be	AUX
ap-1213	41	40	conveniently	conveniently	ADV
ap-1213	41	41	imposed	impose	VERB
ap-1213	41	42	using	use	VERB
ap-1213	41	43	the	the	DET
ap-1213	41	44	brst	brst	NOUN
ap-1213	41	45	formalism.3	formalism.3	NOUN
ap-1213	41	46	the	the	DET
ap-1213	41	47	space	space	NOUN
ap-1213	41	48	of	of	ADP
ap-1213	41	49	physical	physical	ADJ
ap-1213	41	50	states	state	NOUN
ap-1213	41	51	of	of	ADP
ap-1213	41	52	the	the	DET
ap-1213	41	53	string	string	NOUN
ap-1213	41	54	is	be	AUX
ap-1213	41	55	then	then	ADV
ap-1213	41	56	identified	identify	VERB
ap-1213	41	57	with	with	ADP
ap-1213	41	58	the	the	DET
ap-1213	41	59	cohomology	cohomology	NOUN
ap-1213	41	60	of	of	ADP
ap-1213	41	61	the	the	DET
ap-1213	41	62	brst	brst	ADJ
ap-1213	41	63	operator	operator	NOUN
ap-1213	42	1	qb	qb	NOUN
ap-1213	42	2	acting	act	VERB
ap-1213	42	3	on	on	ADP
ap-1213	42	4	the	the	DET
ap-1213	42	5	hilbert	hilbert	NOUN
ap-1213	42	6	spacehbcft	spacehbcft	NOUN
ap-1213	42	7	of	of	ADP
ap-1213	42	8	the	the	DET
ap-1213	42	9	matter	matter	NOUN
ap-1213	42	10	-	-	PUNCT
ap-1213	42	11	plusghost	plusghost	NOUN
ap-1213	42	12	boundary	boundary	ADJ
ap-1213	42	13	conformal	conformal	ADJ
ap-1213	42	14	field	field	NOUN
ap-1213	42	15	theory	theory	NOUN
ap-1213	42	16	(	(	PUNCT
ap-1213	42	17	bcft	bcft	NOUN
ap-1213	42	18	)	)	PUNCT
ap-1213	42	19	determined	determine	VERB
ap-1213	42	20	by	by	ADP
ap-1213	42	21	the	the	DET
ap-1213	42	22	string	string	NOUN
ap-1213	42	23	background	background	NOUN
ap-1213	42	24	.	.	PUNCT
ap-1213	43	1	interestingly	interestingly	ADV
ap-1213	43	2	,	,	PUNCT
ap-1213	43	3	and	and	CCONJ
ap-1213	43	4	not	not	PART
ap-1213	43	5	for	for	ADP
ap-1213	43	6	trivial	trivial	ADJ
ap-1213	43	7	reasons	reason	NOUN
ap-1213	43	8	,	,	PUNCT
ap-1213	43	9	this	this	DET
ap-1213	43	10	bcft	bcft	NOUN
ap-1213	43	11	is	be	AUX
ap-1213	43	12	the	the	DET
ap-1213	43	13	most	most	ADV
ap-1213	43	14	convenient	convenient	ADJ
ap-1213	43	15	starting	starting	NOUN
ap-1213	43	16	point	point	NOUN
ap-1213	43	17	for	for	ADP
ap-1213	43	18	string	string	NOUN
ap-1213	43	19	field	field	NOUN
ap-1213	43	20	theory	theory	NOUN
ap-1213	43	21	.	.	PUNCT
ap-1213	44	1	the	the	DET
ap-1213	44	2	classical	classical	ADJ
ap-1213	44	3	degrees	degree	NOUN
ap-1213	44	4	of	of	ADP
ap-1213	44	5	freedom	freedom	NOUN
ap-1213	44	6	of	of	ADP
ap-1213	44	7	open	open	ADJ
ap-1213	44	8	string	string	NOUN
ap-1213	44	9	field	field	NOUN
ap-1213	44	10	theory	theory	NOUN
ap-1213	44	11	are	be	AUX
ap-1213	44	12	fields	field	NOUN
ap-1213	44	13	associated	associate	VERB
ap-1213	44	14	to	to	ADP
ap-1213	44	15	quantum	quantum	ADJ
ap-1213	44	16	states	state	NOUN
ap-1213	44	17	of	of	ADP
ap-1213	44	18	the	the	DET
ap-1213	44	19	first	first	ADJ
ap-1213	44	20	quantized	quantize	VERB
ap-1213	44	21	open	open	ADJ
ap-1213	44	22	string	string	NOUN
ap-1213	44	23	.	.	PUNCT
ap-1213	45	1	it	it	PRON
ap-1213	45	2	is	be	AUX
ap-1213	45	3	very	very	ADV
ap-1213	45	4	convenient	convenient	ADJ
ap-1213	45	5	to	to	PART
ap-1213	45	6	work	work	VERB
ap-1213	45	7	with	with	ADP
ap-1213	45	8	the	the	DET
ap-1213	45	9	extended	extended	ADJ
ap-1213	45	10	space	space	NOUN
ap-1213	45	11	hbcft	hbcft	NOUN
ap-1213	45	12	,	,	PUNCT
ap-1213	45	13	which	which	PRON
ap-1213	45	14	contains	contain	VERB
ap-1213	45	15	not	not	PART
ap-1213	45	16	only	only	ADV
ap-1213	45	17	physical	physical	ADJ
ap-1213	45	18	states	state	NOUN
ap-1213	45	19	of	of	ADP
ap-1213	45	20	the	the	DET
ap-1213	45	21	string	string	NOUN
ap-1213	45	22	but	but	CCONJ
ap-1213	45	23	also	also	ADV
ap-1213	45	24	various	various	ADJ
ap-1213	45	25	other	other	ADJ
ap-1213	45	26	states	state	NOUN
ap-1213	45	27	.	.	PUNCT
ap-1213	46	1	interestingly	interestingly	ADV
ap-1213	46	2	,	,	PUNCT
ap-1213	46	3	these	these	PRON
ap-1213	46	4	turn	turn	NOUN
ap-1213	46	5	into	into	ADP
ap-1213	46	6	auxiliary	auxiliary	ADJ
ap-1213	46	7	and	and	CCONJ
ap-1213	46	8	ghost	ghost	NOUN
ap-1213	46	9	fields	field	NOUN
ap-1213	46	10	of	of	ADP
ap-1213	46	11	string	string	NOUN
ap-1213	46	12	field	field	NOUN
ap-1213	46	13	theory	theory	NOUN
ap-1213	46	14	.	.	PUNCT
ap-1213	47	1	all	all	DET
ap-1213	47	2	the	the	DET
ap-1213	47	3	fields	field	NOUN
ap-1213	47	4	are	be	AUX
ap-1213	47	5	neatly	neatly	ADV
ap-1213	47	6	assembled	assemble	VERB
ap-1213	47	7	into	into	ADP
ap-1213	47	8	a	a	DET
ap-1213	47	9	string	string	NOUN
ap-1213	47	10	field	field	NOUN
ap-1213	47	11	|ψ	|ψ	ADP
ap-1213	47	12	〉	〉	NOUN
ap-1213	47	13	=	=	PUNCT
ap-1213	47	14	∑	∑	PUNCT
ap-1213	48	1	i	i	PRON
ap-1213	48	2	∫	∫	VERB
ap-1213	48	3	dp+1k	dp+1k	PROPN
ap-1213	48	4	φi(k)|i	φi(k)|i	PROPN
ap-1213	48	5	,	,	PUNCT
ap-1213	48	6	k	k	PROPN
ap-1213	48	7	〉	〉	PROPN
ap-1213	48	8	,	,	PUNCT
ap-1213	48	9	(	(	PUNCT
ap-1213	48	10	2.1	2.1	NUM
ap-1213	48	11	)	)	PUNCT
ap-1213	48	12	where	where	SCONJ
ap-1213	48	13	the	the	DET
ap-1213	48	14	index	index	NOUN
ap-1213	48	15	i	i	PRON
ap-1213	48	16	runs	run	VERB
ap-1213	48	17	over	over	ADP
ap-1213	48	18	all	all	DET
ap-1213	48	19	states	state	NOUN
ap-1213	48	20	of	of	ADP
ap-1213	48	21	the	the	DET
ap-1213	48	22	first	first	ADJ
ap-1213	48	23	quantized	quantize	VERB
ap-1213	48	24	string	string	NOUN
ap-1213	48	25	in	in	ADP
ap-1213	48	26	a	a	DET
ap-1213	48	27	sector	sector	NOUN
ap-1213	48	28	of	of	ADP
ap-1213	48	29	momentum	momentum	NOUN
ap-1213	48	30	k.	k.	PROPN
ap-1213	49	1	the	the	DET
ap-1213	49	2	dimensionality	dimensionality	NOUN
ap-1213	49	3	of	of	ADP
ap-1213	49	4	the	the	DET
ap-1213	49	5	momentum	momentum	NOUN
ap-1213	49	6	is	be	AUX
ap-1213	49	7	p+1	p+1	NOUN
ap-1213	49	8	,	,	PUNCT
ap-1213	49	9	as	as	ADP
ap-1213	49	10	appropriate	appropriate	ADJ
ap-1213	49	11	for	for	ADP
ap-1213	49	12	open	open	ADJ
ap-1213	49	13	strings	string	NOUN
ap-1213	49	14	ending	end	VERB
ap-1213	49	15	on	on	ADP
ap-1213	49	16	a	a	DET
ap-1213	49	17	d	d	ADJ
ap-1213	49	18	-	-	PUNCT
ap-1213	49	19	p	p	NOUN
ap-1213	49	20	-	-	PUNCT
ap-1213	49	21	brane	brane	NOUN
ap-1213	49	22	.	.	PUNCT
ap-1213	50	1	the	the	DET
ap-1213	50	2	coefficients	coefficient	NOUN
ap-1213	50	3	φi(k	φi(k	NUM
ap-1213	50	4	)	)	PUNCT
ap-1213	50	5	are	be	AUX
ap-1213	50	6	momentum	momentum	NOUN
ap-1213	50	7	space	space	NOUN
ap-1213	50	8	wave	wave	NOUN
ap-1213	50	9	functions	function	NOUN
ap-1213	50	10	for	for	ADP
ap-1213	50	11	particle	particle	NOUN
ap-1213	50	12	like	like	ADP
ap-1213	50	13	excitations	excitation	NOUN
ap-1213	50	14	of	of	ADP
ap-1213	50	15	the	the	DET
ap-1213	50	16	string	string	NOUN
ap-1213	50	17	,	,	PUNCT
ap-1213	50	18	and	and	CCONJ
ap-1213	50	19	would	would	AUX
ap-1213	50	20	become	become	VERB
ap-1213	50	21	field	field	NOUN
ap-1213	50	22	theory	theory	NOUN
ap-1213	50	23	operators	operator	NOUN
ap-1213	50	24	if	if	SCONJ
ap-1213	50	25	we	we	PRON
ap-1213	50	26	proceeded	proceed	VERB
ap-1213	50	27	to	to	ADP
ap-1213	50	28	second	second	ADJ
ap-1213	50	29	quantization	quantization	NOUN
ap-1213	50	30	.	.	PUNCT
ap-1213	51	1	the	the	DET
ap-1213	51	2	action	action	NOUN
ap-1213	51	3	of	of	ADP
ap-1213	51	4	string	string	NOUN
ap-1213	51	5	field	field	NOUN
ap-1213	51	6	theory	theory	NOUN
ap-1213	51	7	can	can	AUX
ap-1213	51	8	be	be	AUX
ap-1213	51	9	written	write	VERB
ap-1213	51	10	in	in	ADP
ap-1213	51	11	the	the	DET
ap-1213	51	12	form	form	NOUN
ap-1213	51	13	s	s	PART
ap-1213	51	14	=	=	SYM
ap-1213	51	15	−	−	PROPN
ap-1213	51	16	1	1	NUM
ap-1213	51	17	g2o	g2o	PROPN
ap-1213	51	18	[	[	PUNCT
ap-1213	51	19	1	1	NUM
ap-1213	51	20	2	2	NUM
ap-1213	51	21	〈	〈	PROPN
ap-1213	51	22	ψ	ψ	X
ap-1213	51	23	∗qbψ	∗qbψ	X
ap-1213	51	24	〉	〉	NOUN
ap-1213	51	25	+	+	NOUN
ap-1213	51	26	1	1	NUM
ap-1213	51	27	3	3	NUM
ap-1213	51	28	〈	〈	PROPN
ap-1213	51	29	ψ	ψ	X
ap-1213	51	30	∗ψ	∗ψ	PROPN
ap-1213	51	31	∗ψ	∗ψ	PROPN
ap-1213	51	32	〉	〉	PROPN
ap-1213	51	33	]	]	PUNCT
ap-1213	51	34	,	,	PUNCT
ap-1213	51	35	(	(	PUNCT
ap-1213	51	36	2.2	2.2	NUM
ap-1213	51	37	)	)	PUNCT
ap-1213	51	38	where	where	SCONJ
ap-1213	51	39	go	go	VERB
ap-1213	51	40	is	be	AUX
ap-1213	51	41	the	the	DET
ap-1213	51	42	open	open	ADJ
ap-1213	51	43	string	string	NOUN
ap-1213	51	44	coupling	couple	VERB
ap-1213	51	45	constant	constant	ADJ
ap-1213	51	46	and	and	CCONJ
ap-1213	51	47	∗	∗	NOUN
ap-1213	51	48	is	be	AUX
ap-1213	51	49	witten	witten	PROPN
ap-1213	51	50	’s	’s	PART
ap-1213	51	51	star	star	NOUN
ap-1213	51	52	product	product	NOUN
ap-1213	51	53	.	.	PUNCT
ap-1213	52	1	the	the	DET
ap-1213	52	2	action	action	NOUN
ap-1213	52	3	has	have	VERB
ap-1213	52	4	enormous	enormous	ADJ
ap-1213	52	5	gauge	gauge	NOUN
ap-1213	52	6	symmetry	symmetry	NOUN
ap-1213	52	7	given	give	VERB
ap-1213	52	8	by	by	ADP
ap-1213	52	9	δψ	δψ	NOUN
ap-1213	52	10	=	=	PUNCT
ap-1213	52	11	qbλ	qbλ	PROPN
ap-1213	53	1	+	+	NOUN
ap-1213	53	2	ψ	ψ	X
ap-1213	53	3	∗	∗	NOUN
ap-1213	53	4	λ−	λ−	PROPN
ap-1213	53	5	λ	λ	PROPN
ap-1213	53	6	∗ψ	∗ψ	PROPN
ap-1213	53	7	,	,	PUNCT
ap-1213	53	8	(	(	PUNCT
ap-1213	53	9	2.3	2.3	NUM
ap-1213	53	10	)	)	PUNCT
ap-1213	53	11	where	where	SCONJ
ap-1213	53	12	λ	λ	PROPN
ap-1213	53	13	∈	∈	NOUN
ap-1213	53	14	hbcft	hbcft	NOUN
ap-1213	53	15	(	(	PUNCT
ap-1213	53	16	grassman	grassman	NOUN
ap-1213	53	17	even	even	ADV
ap-1213	53	18	)	)	PUNCT
ap-1213	53	19	,	,	PUNCT
ap-1213	53	20	provided	provide	VERB
ap-1213	53	21	the	the	DET
ap-1213	53	22	start	start	NOUN
ap-1213	53	23	product	product	NOUN
ap-1213	53	24	is	be	AUX
ap-1213	53	25	associative	associative	ADJ
ap-1213	53	26	,	,	PUNCT
ap-1213	53	27	qb	qb	PROPN
ap-1213	53	28	acts	act	VERB
ap-1213	53	29	as	as	ADP
ap-1213	53	30	a	a	DET
ap-1213	53	31	graded	grade	VERB
ap-1213	53	32	derivation	derivation	NOUN
ap-1213	53	33	and	and	CCONJ
ap-1213	53	34	〈	〈	PROPN
ap-1213	53	35	.	.	PUNCT
ap-1213	54	1	〉	〉	PROPN
ap-1213	54	2	has	have	VERB
ap-1213	54	3	properties	property	NOUN
ap-1213	54	4	of	of	ADP
ap-1213	54	5	integration	integration	NOUN
ap-1213	54	6	.	.	PUNCT
ap-1213	55	1	to	to	PART
ap-1213	55	2	summarize	summarize	VERB
ap-1213	55	3	,	,	PUNCT
ap-1213	55	4	the	the	DET
ap-1213	55	5	basic	basic	ADJ
ap-1213	55	6	ingredients	ingredient	NOUN
ap-1213	55	7	that	that	PRON
ap-1213	55	8	one	one	NUM
ap-1213	55	9	needs	need	VERB
ap-1213	55	10	in	in	ADP
ap-1213	55	11	order	order	NOUN
ap-1213	55	12	to	to	PART
ap-1213	55	13	write	write	VERB
ap-1213	55	14	down	down	ADP
ap-1213	55	15	witten	witten	PROPN
ap-1213	55	16	’s	’s	PART
ap-1213	55	17	osft	osft	NOUN
ap-1213	55	18	in	in	ADP
ap-1213	55	19	a	a	DET
ap-1213	55	20	particular	particular	ADJ
ap-1213	55	21	background	background	NOUN
ap-1213	55	22	are	be	AUX
ap-1213	55	23	hbcft	hbcft	ADV
ap-1213	55	24	,	,	PUNCT
ap-1213	55	25	∗	∗	NOUN
ap-1213	55	26	,	,	PUNCT
ap-1213	55	27	qb	qb	PROPN
ap-1213	55	28	,	,	PUNCT
ap-1213	55	29	〈	〈	PROPN
ap-1213	55	30	.	.	PROPN
ap-1213	55	31	〉	〉	PROPN
ap-1213	55	32	.	.	PUNCT
ap-1213	56	1	for	for	ADP
ap-1213	56	2	a	a	DET
ap-1213	56	3	more	more	ADV
ap-1213	56	4	comprehensive	comprehensive	ADJ
ap-1213	56	5	review	review	NOUN
ap-1213	56	6	,	,	PUNCT
ap-1213	56	7	the	the	DET
ap-1213	56	8	reader	reader	NOUN
ap-1213	56	9	is	be	AUX
ap-1213	56	10	referred	refer	VERB
ap-1213	56	11	to	to	ADP
ap-1213	56	12	the	the	DET
ap-1213	56	13	excellent	excellent	ADJ
ap-1213	56	14	reviews	review	NOUN
ap-1213	56	15	[	[	X
ap-1213	56	16	4	4	NUM
ap-1213	56	17	,	,	PUNCT
ap-1213	56	18	5].4	5].4	NUM
ap-1213	56	19	3	3	NUM
ap-1213	56	20	demystifying	demystify	VERB
ap-1213	56	21	the	the	DET
ap-1213	56	22	star	star	NOUN
ap-1213	56	23	product	product	NOUN
ap-1213	56	24	the	the	DET
ap-1213	56	25	star	star	NOUN
ap-1213	56	26	product	product	NOUN
ap-1213	56	27	has	have	AUX
ap-1213	56	28	always	always	ADV
ap-1213	56	29	been	be	AUX
ap-1213	56	30	one	one	NUM
ap-1213	56	31	of	of	ADP
ap-1213	56	32	the	the	DET
ap-1213	56	33	most	most	ADV
ap-1213	56	34	difficult	difficult	ADJ
ap-1213	56	35	ingredients	ingredient	NOUN
ap-1213	56	36	of	of	ADP
ap-1213	56	37	the	the	DET
ap-1213	56	38	string	string	NOUN
ap-1213	56	39	field	field	NOUN
ap-1213	56	40	to	to	PART
ap-1213	56	41	understand	understand	VERB
ap-1213	56	42	and	and	CCONJ
ap-1213	56	43	to	to	PART
ap-1213	56	44	work	work	VERB
ap-1213	56	45	with	with	ADP
ap-1213	56	46	.	.	PUNCT
ap-1213	57	1	it	it	PRON
ap-1213	57	2	can	can	AUX
ap-1213	57	3	be	be	AUX
ap-1213	57	4	defined	define	VERB
ap-1213	57	5	very	very	ADV
ap-1213	57	6	intuitively	intuitively	ADV
ap-1213	57	7	using	use	VERB
ap-1213	57	8	the	the	DET
ap-1213	57	9	schrödinger	schrödinger	NOUN
ap-1213	57	10	presentation	presentation	NOUN
ap-1213	57	11	of	of	ADP
ap-1213	57	12	string	string	NOUN
ap-1213	57	13	wave	wave	NOUN
ap-1213	57	14	functionals	functional	NOUN
ap-1213	57	15	(	(	PUNCT
ap-1213	57	16	ψ1	ψ1	ADJ
ap-1213	57	17	�	�	NOUN
ap-1213	57	18	ψ2	ψ2	NOUN
ap-1213	57	19	)	)	PUNCT
ap-1213	58	1	[	[	X
ap-1213	58	2	x(σ	x(σ	NOUN
ap-1213	58	3	)	)	PUNCT
ap-1213	58	4	]	]	PUNCT
ap-1213	59	1	=	=	X
ap-1213	59	2	∫	∫	PROPN
ap-1213	59	3	[	[	X
ap-1213	59	4	dxoverlap	dxoverlap	X
ap-1213	59	5	]	]	PUNCT
ap-1213	59	6	ψ1	ψ1	NOUN
ap-1213	59	7	[	[	PUNCT
ap-1213	59	8	x̂(σ	x̂(σ	NOUN
ap-1213	59	9	)	)	PUNCT
ap-1213	59	10	]	]	PUNCT
ap-1213	59	11	ψ2	ψ2	NOUN
ap-1213	59	12	[	[	PUNCT
ap-1213	59	13	x̌(σ	x̌(σ	PROPN
ap-1213	59	14	)	)	PUNCT
ap-1213	59	15	]	]	PUNCT
ap-1213	59	16	,	,	PUNCT
ap-1213	59	17	(	(	PUNCT
ap-1213	59	18	3.4	3.4	NUM
ap-1213	59	19	)	)	PUNCT
ap-1213	59	20	where	where	SCONJ
ap-1213	59	21	the	the	DET
ap-1213	59	22	hat	hat	NOUN
ap-1213	59	23	and	and	CCONJ
ap-1213	59	24	check	check	NOUN
ap-1213	59	25	means	mean	VERB
ap-1213	59	26	that	that	SCONJ
ap-1213	59	27	the	the	DET
ap-1213	59	28	left	left	ADJ
ap-1213	59	29	and	and	CCONJ
ap-1213	59	30	right	right	ADJ
ap-1213	59	31	halves	half	NOUN
ap-1213	59	32	of	of	ADP
ap-1213	59	33	these	these	DET
ap-1213	59	34	functions	function	NOUN
ap-1213	59	35	respectively	respectively	ADV
ap-1213	59	36	coincide	coincide	VERB
ap-1213	59	37	with	with	ADP
ap-1213	59	38	those	those	PRON
ap-1213	59	39	of	of	ADP
ap-1213	59	40	the	the	DET
ap-1213	59	41	x(σ	x(σ	NOUN
ap-1213	59	42	)	)	PUNCT
ap-1213	59	43	.	.	PUNCT
ap-1213	60	1	it	it	PRON
ap-1213	60	2	took	take	VERB
ap-1213	60	3	some	some	DET
ap-1213	60	4	years	year	NOUN
ap-1213	60	5	and	and	CCONJ
ap-1213	60	6	many	many	ADJ
ap-1213	60	7	research	research	NOUN
ap-1213	60	8	papers	paper	NOUN
ap-1213	60	9	to	to	PART
ap-1213	60	10	understand	understand	VERB
ap-1213	60	11	exactly	exactly	ADV
ap-1213	60	12	whether	whether	SCONJ
ap-1213	60	13	this	this	DET
ap-1213	60	14	path	path	NOUN
ap-1213	60	15	integral	integral	ADJ
ap-1213	60	16	makes	make	VERB
ap-1213	60	17	sense	sense	NOUN
ap-1213	60	18	.	.	PUNCT
ap-1213	61	1	there	there	PRON
ap-1213	61	2	is	be	VERB
ap-1213	61	3	however	however	ADV
ap-1213	61	4	a	a	DET
ap-1213	61	5	modern	modern	ADJ
ap-1213	61	6	definition	definition	NOUN
ap-1213	61	7	which	which	PRON
ap-1213	61	8	makes	make	VERB
ap-1213	61	9	many	many	ADJ
ap-1213	61	10	of	of	ADP
ap-1213	61	11	the	the	DET
ap-1213	61	12	star	star	NOUN
ap-1213	61	13	product	product	NOUN
ap-1213	61	14	properties	property	NOUN
ap-1213	61	15	manifest	manifest	VERB
ap-1213	61	16	.	.	PUNCT
ap-1213	62	1	let	let	VERB
ap-1213	62	2	us	we	PRON
ap-1213	62	3	describe	describe	VERB
ap-1213	62	4	string	string	NOUN
ap-1213	62	5	field	field	NOUN
ap-1213	62	6	theory	theory	NOUN
ap-1213	62	7	states	state	NOUN
ap-1213	62	8	as	as	ADP
ap-1213	62	9	linear	linear	ADJ
ap-1213	62	10	combinations	combination	NOUN
ap-1213	62	11	of	of	ADP
ap-1213	62	12	surfaces	surface	NOUN
ap-1213	62	13	with	with	ADP
ap-1213	62	14	vertex	vertex	NOUN
ap-1213	62	15	operator	operator	NOUN
ap-1213	62	16	insertions	insertion	NOUN
ap-1213	62	17	,	,	PUNCT
ap-1213	62	18	such	such	ADJ
ap-1213	62	19	as	as	ADP
ap-1213	62	20	in	in	ADP
ap-1213	62	21	fig	fig	NOUN
ap-1213	62	22	.	.	PUNCT
ap-1213	63	1	1.5	1.5	NUM
ap-1213	63	2	these	these	PRON
ap-1213	63	3	represent	represent	VERB
ap-1213	63	4	the	the	DET
ap-1213	63	5	worldsheets	worldsheet	NOUN
ap-1213	63	6	of	of	ADP
ap-1213	63	7	a	a	DET
ap-1213	63	8	single	single	ADJ
ap-1213	63	9	string	string	NOUN
ap-1213	63	10	evolving	evolve	VERB
ap-1213	63	11	from	from	ADP
ap-1213	63	12	the	the	DET
ap-1213	63	13	infinite	infinite	ADJ
ap-1213	63	14	past	past	NOUN
ap-1213	63	15	to	to	ADP
ap-1213	63	16	the	the	DET
ap-1213	63	17	infinite	infinite	ADJ
ap-1213	63	18	future	future	NOUN
ap-1213	63	19	.	.	PUNCT
ap-1213	64	1	a	a	DET
ap-1213	64	2	conformal	conformal	ADJ
ap-1213	64	3	transformation	transformation	NOUN
ap-1213	64	4	can	can	AUX
ap-1213	64	5	be	be	AUX
ap-1213	64	6	used	use	VERB
ap-1213	64	7	to	to	PART
ap-1213	64	8	bring	bring	VERB
ap-1213	64	9	the	the	DET
ap-1213	64	10	surface	surface	NOUN
ap-1213	64	11	to	to	ADP
ap-1213	64	12	a	a	DET
ap-1213	64	13	canonical	canonical	ADJ
ap-1213	64	14	form	form	NOUN
ap-1213	64	15	,	,	PUNCT
ap-1213	64	16	but	but	CCONJ
ap-1213	64	17	this	this	PRON
ap-1213	64	18	would	would	AUX
ap-1213	64	19	act	act	VERB
ap-1213	64	20	nontrivially	nontrivially	ADV
ap-1213	64	21	on	on	ADP
ap-1213	64	22	the	the	DET
ap-1213	64	23	in	in	NOUN
ap-1213	64	24	and	and	CCONJ
ap-1213	64	25	out	out	ADP
ap-1213	64	26	states	state	NOUN
ap-1213	64	27	.	.	PUNCT
ap-1213	65	1	we	we	PRON
ap-1213	65	2	will	will	AUX
ap-1213	65	3	consider	consider	VERB
ap-1213	65	4	only	only	ADJ
ap-1213	65	5	shapes	shape	NOUN
ap-1213	65	6	which	which	PRON
ap-1213	65	7	have	have	VERB
ap-1213	65	8	the	the	DET
ap-1213	65	9	future	future	NOUN
ap-1213	65	10	(	(	PUNCT
ap-1213	65	11	upper	upper	ADJ
ap-1213	65	12	)	)	PUNCT
ap-1213	65	13	part	part	NOUN
ap-1213	65	14	in	in	ADP
ap-1213	65	15	the	the	DET
ap-1213	65	16	canonical	canonical	ADJ
ap-1213	65	17	shape	shape	NOUN
ap-1213	65	18	of	of	ADP
ap-1213	65	19	a	a	DET
ap-1213	65	20	semi	semi	ADJ
ap-1213	65	21	-	-	ADJ
ap-1213	65	22	infinite	infinite	ADJ
ap-1213	65	23	strip	strip	NOUN
ap-1213	65	24	.	.	PUNCT
ap-1213	66	1	by	by	ADP
ap-1213	66	2	putting	put	VERB
ap-1213	66	3	various	various	ADJ
ap-1213	66	4	vertex	vertex	NOUN
ap-1213	66	5	operators	operator	NOUN
ap-1213	66	6	in	in	ADP
ap-1213	66	7	the	the	DET
ap-1213	66	8	far	far	ADJ
ap-1213	66	9	future	future	NOUN
ap-1213	66	10	and	and	CCONJ
ap-1213	66	11	evaluating	evaluate	VERB
ap-1213	66	12	the	the	DET
ap-1213	66	13	path	path	NOUN
ap-1213	66	14	integral	integral	ADJ
ap-1213	66	15	over	over	ADP
ap-1213	66	16	the	the	DET
ap-1213	66	17	surface	surface	NOUN
ap-1213	66	18	,	,	PUNCT
ap-1213	66	19	we	we	PRON
ap-1213	66	20	can	can	AUX
ap-1213	66	21	uniquely	uniquely	ADV
ap-1213	66	22	probe	probe	VERB
ap-1213	66	23	both	both	CCONJ
ap-1213	66	24	the	the	DET
ap-1213	66	25	shape	shape	NOUN
ap-1213	66	26	of	of	ADP
ap-1213	66	27	the	the	DET
ap-1213	66	28	lower	low	ADJ
ap-1213	66	29	part	part	NOUN
ap-1213	66	30	of	of	ADP
ap-1213	66	31	the	the	DET
ap-1213	66	32	surface	surface	NOUN
ap-1213	66	33	and	and	CCONJ
ap-1213	66	34	what	what	DET
ap-1213	66	35	vertex	vertex	NOUN
ap-1213	66	36	operators	operator	NOUN
ap-1213	66	37	are	be	AUX
ap-1213	66	38	inserted	insert	VERB
ap-1213	66	39	there	there	ADV
ap-1213	66	40	.	.	PUNCT
ap-1213	67	1	to	to	PART
ap-1213	67	2	describe	describe	VERB
ap-1213	67	3	the	the	DET
ap-1213	67	4	star	star	NOUN
ap-1213	67	5	product	product	NOUN
ap-1213	67	6	we	we	PRON
ap-1213	67	7	take	take	VERB
ap-1213	67	8	two	two	NUM
ap-1213	67	9	states	state	NOUN
ap-1213	67	10	in	in	ADP
ap-1213	67	11	the	the	DET
ap-1213	67	12	canonical	canonical	ADJ
ap-1213	67	13	form	form	NOUN
ap-1213	67	14	,	,	PUNCT
ap-1213	67	15	cut	cut	VERB
ap-1213	67	16	off	off	ADP
ap-1213	67	17	the	the	DET
ap-1213	67	18	probe	probe	NOUN
ap-1213	67	19	strips	strip	NOUN
ap-1213	67	20	(	(	PUNCT
ap-1213	67	21	in	in	ADP
ap-1213	67	22	light	light	NOUN
ap-1213	67	23	yellow	yellow	ADJ
ap-1213	67	24	)	)	PUNCT
ap-1213	67	25	and	and	CCONJ
ap-1213	67	26	glue	glue	VERB
ap-1213	67	27	the	the	DET
ap-1213	67	28	lower	low	ADJ
ap-1213	67	29	parts	part	NOUN
ap-1213	67	30	of	of	ADP
ap-1213	67	31	the	the	DET
ap-1213	67	32	strips	strip	NOUN
ap-1213	67	33	along	along	ADP
ap-1213	67	34	the	the	DET
ap-1213	67	35	upper	upper	ADJ
ap-1213	67	36	boundaries	boundary	NOUN
ap-1213	67	37	of	of	ADP
ap-1213	67	38	the	the	DET
ap-1213	67	39	hatched	hatched	ADJ
ap-1213	67	40	regions	region	NOUN
ap-1213	67	41	.	.	PUNCT
ap-1213	68	1	one	one	NUM
ap-1213	68	2	gets	get	VERB
ap-1213	68	3	again	again	ADV
ap-1213	68	4	a	a	DET
ap-1213	68	5	state	state	NOUN
ap-1213	68	6	in	in	ADP
ap-1213	68	7	the	the	DET
ap-1213	68	8	form	form	NOUN
ap-1213	68	9	of	of	ADP
ap-1213	68	10	a	a	DET
ap-1213	68	11	surface	surface	NOUN
ap-1213	68	12	with	with	ADP
ap-1213	68	13	insertions	insertion	NOUN
ap-1213	68	14	,	,	PUNCT
ap-1213	68	15	but	but	CCONJ
ap-1213	68	16	the	the	DET
ap-1213	68	17	shape	shape	NOUN
ap-1213	68	18	is	be	AUX
ap-1213	68	19	different	different	ADJ
ap-1213	68	20	from	from	ADP
ap-1213	68	21	those	those	PRON
ap-1213	68	22	we	we	PRON
ap-1213	68	23	started	start	VERB
ap-1213	68	24	with	with	ADP
ap-1213	68	25	.	.	PUNCT
ap-1213	69	1	imagine	imagine	AUX
ap-1213	69	2	now	now	ADV
ap-1213	69	3	factorizing	factorize	VERB
ap-1213	69	4	the	the	DET
ap-1213	69	5	path	path	NOUN
ap-1213	69	6	integral	integral	ADJ
ap-1213	69	7	measure	measure	NOUN
ap-1213	69	8	over	over	ADP
ap-1213	69	9	the	the	DET
ap-1213	69	10	worldsheet	worldsheet	ADJ
ap-1213	69	11	fields	field	NOUN
ap-1213	69	12	in	in	ADP
ap-1213	69	13	the	the	DET
ap-1213	69	14	hatched	hatched	ADJ
ap-1213	69	15	area	area	NOUN
ap-1213	69	16	and	and	CCONJ
ap-1213	69	17	in	in	ADP
ap-1213	69	18	the	the	DET
ap-1213	69	19	rest	rest	NOUN
ap-1213	69	20	of	of	ADP
ap-1213	69	21	the	the	DET
ap-1213	69	22	surface	surface	NOUN
ap-1213	69	23	.	.	PUNCT
ap-1213	70	1	the	the	DET
ap-1213	70	2	path	path	NOUN
ap-1213	70	3	integral	integral	ADJ
ap-1213	70	4	over	over	ADP
ap-1213	70	5	the	the	DET
ap-1213	70	6	hatched	hatched	ADJ
ap-1213	70	7	region	region	NOUN
ap-1213	70	8	is	be	AUX
ap-1213	70	9	performed	perform	VERB
ap-1213	70	10	first	first	ADV
ap-1213	70	11	.	.	PUNCT
ap-1213	71	1	then	then	ADV
ap-1213	71	2	since	since	SCONJ
ap-1213	71	3	there	there	PRON
ap-1213	71	4	are	be	VERB
ap-1213	71	5	no	no	DET
ap-1213	71	6	vertex	vertex	NOUN
ap-1213	71	7	operators	operator	NOUN
ap-1213	71	8	inserted	insert	VERB
ap-1213	71	9	,	,	PUNCT
ap-1213	71	10	one	one	PRON
ap-1213	71	11	can	can	AUX
ap-1213	71	12	replace	replace	VERB
ap-1213	71	13	its	its	PRON
ap-1213	71	14	result	result	NOUN
ap-1213	71	15	by	by	ADP
ap-1213	71	16	an	an	DET
ap-1213	71	17	effective	effective	ADJ
ap-1213	71	18	term	term	NOUN
ap-1213	71	19	in	in	ADP
ap-1213	71	20	the	the	DET
ap-1213	71	21	worldsheet	worldsheet	ADJ
ap-1213	71	22	action	action	NOUN
ap-1213	71	23	,	,	PUNCT
ap-1213	71	24	or	or	CCONJ
ap-1213	71	25	equivalently	equivalently	ADV
ap-1213	71	26	as	as	ADP
ap-1213	71	27	an	an	DET
ap-1213	71	28	insertion	insertion	NOUN
ap-1213	71	29	of	of	ADP
ap-1213	71	30	some	some	DET
ap-1213	71	31	nonlocal	nonlocal	ADJ
ap-1213	71	32	line	line	NOUN
ap-1213	71	33	operator	operator	NOUN
ap-1213	71	34	.	.	PUNCT
ap-1213	72	1	it	it	PRON
ap-1213	72	2	turns	turn	VERB
ap-1213	72	3	out	out	ADP
ap-1213	72	4	that	that	SCONJ
ap-1213	72	5	this	this	DET
ap-1213	72	6	operator	operator	NOUN
ap-1213	72	7	can	can	AUX
ap-1213	72	8	be	be	AUX
ap-1213	72	9	written	write	VERB
ap-1213	72	10	as	as	ADP
ap-1213	72	11	e−k	e−k	PROPN
ap-1213	72	12	,	,	PUNCT
ap-1213	72	13	where	where	SCONJ
ap-1213	72	14	k	k	PROPN
ap-1213	72	15	is	be	AUX
ap-1213	72	16	a	a	DET
ap-1213	72	17	line	line	NOUN
ap-1213	72	18	integral	integral	ADJ
ap-1213	72	19	of	of	ADP
ap-1213	72	20	the	the	DET
ap-1213	72	21	worldsheet	worldsheet	ADJ
ap-1213	72	22	energy	energy	NOUN
ap-1213	72	23	momentum	momentum	NOUN
ap-1213	72	24	tensor	tensor	NOUN
ap-1213	72	25	in	in	ADP
ap-1213	72	26	some	some	DET
ap-1213	72	27	specific	specific	ADJ
ap-1213	72	28	coordinates	coordinate	NOUN
ap-1213	72	29	.	.	PUNCT
ap-1213	73	1	the	the	DET
ap-1213	73	2	integration	integration	NOUN
ap-1213	73	3	extends	extend	VERB
ap-1213	73	4	from	from	ADP
ap-1213	73	5	the	the	DET
ap-1213	73	6	boundary	boundary	NOUN
ap-1213	73	7	to	to	ADP
ap-1213	73	8	the	the	DET
ap-1213	73	9	midpoint	midpoint	NOUN
ap-1213	73	10	of	of	ADP
ap-1213	73	11	the	the	DET
ap-1213	73	12	worldsheet	worldsheet	NOUN
ap-1213	73	13	.	.	PUNCT
ap-1213	74	1	3alternatively	3alternatively	NUM
ap-1213	74	2	,	,	PUNCT
ap-1213	74	3	as	as	ADP
ap-1213	74	4	in	in	ADP
ap-1213	74	5	the	the	DET
ap-1213	74	6	light	light	ADJ
ap-1213	74	7	cone	cone	NOUN
ap-1213	74	8	gauge	gauge	NOUN
ap-1213	74	9	,	,	PUNCT
ap-1213	74	10	one	one	PRON
ap-1213	74	11	could	could	AUX
ap-1213	74	12	use	use	VERB
ap-1213	74	13	the	the	DET
ap-1213	74	14	residual	residual	ADJ
ap-1213	74	15	infinite	infinite	ADJ
ap-1213	74	16	dimensional	dimensional	ADJ
ap-1213	74	17	conformal	conformal	ADJ
ap-1213	74	18	symmetry	symmetry	NOUN
ap-1213	74	19	to	to	PART
ap-1213	74	20	gauge	gauge	VERB
ap-1213	74	21	fix	fix	NOUN
ap-1213	74	22	one	one	NUM
ap-1213	74	23	of	of	ADP
ap-1213	74	24	the	the	DET
ap-1213	74	25	embedding	embed	VERB
ap-1213	74	26	coordinates	coordinate	NOUN
ap-1213	74	27	and	and	CCONJ
ap-1213	74	28	solve	solve	VERB
ap-1213	74	29	the	the	DET
ap-1213	74	30	virasoro	virasoro	NOUN
ap-1213	74	31	constraints	constraint	NOUN
ap-1213	74	32	algebraically	algebraically	ADV
ap-1213	74	33	.	.	PUNCT
ap-1213	75	1	4older	4older	NUM
ap-1213	75	2	reviews	review	NOUN
ap-1213	75	3	are	be	AUX
ap-1213	75	4	[	[	X
ap-1213	75	5	6	6	NUM
ap-1213	75	6	,	,	PUNCT
ap-1213	75	7	7	7	NUM
ap-1213	75	8	]	]	PUNCT
ap-1213	75	9	and	and	CCONJ
ap-1213	75	10	a	a	DET
ap-1213	75	11	more	more	ADV
ap-1213	75	12	recent	recent	ADJ
ap-1213	75	13	development	development	NOUN
ap-1213	75	14	appears	appear	VERB
ap-1213	75	15	in	in	ADP
ap-1213	75	16	[	[	X
ap-1213	75	17	8	8	NUM
ap-1213	75	18	]	]	SYM
ap-1213	75	19	.	.	PUNCT
ap-1213	76	1	5	5	NUM
ap-1213	76	2	in	in	ADP
ap-1213	76	3	order	order	NOUN
ap-1213	76	4	to	to	PART
ap-1213	76	5	match	match	VERB
ap-1213	76	6	with	with	ADP
ap-1213	76	7	witten	witten	PROPN
ap-1213	76	8	’s	’s	PART
ap-1213	76	9	original	original	ADJ
ap-1213	76	10	definition	definition	NOUN
ap-1213	76	11	the	the	DET
ap-1213	76	12	σ	σ	PROPN
ap-1213	76	13	coordinate	coordinate	NOUN
ap-1213	76	14	must	must	AUX
ap-1213	76	15	run	run	VERB
ap-1213	76	16	from	from	ADP
ap-1213	76	17	right	right	ADJ
ap-1213	76	18	to	to	AUX
ap-1213	76	19	left	left	VERB
ap-1213	76	20	.	.	PUNCT
ap-1213	77	1	103	103	NUM
ap-1213	77	2	acta	acta	PROPN
ap-1213	77	3	polytechnica	polytechnica	PROPN
ap-1213	77	4	vol	vol	NOUN
ap-1213	77	5	.	.	PROPN
ap-1213	77	6	50	50	NUM
ap-1213	77	7	no	no	NOUN
ap-1213	77	8	.	.	PUNCT
ap-1213	78	1	3/2010	3/2010	NUM
ap-1213	78	2	fig	fig	NOUN
ap-1213	78	3	.	.	PUNCT
ap-1213	79	1	1	1	NUM
ap-1213	79	2	:	:	PUNCT
ap-1213	79	3	witten	witten	PROPN
ap-1213	79	4	’s	’s	PART
ap-1213	79	5	star	star	NOUN
ap-1213	79	6	product	product	NOUN
ap-1213	79	7	is	be	AUX
ap-1213	79	8	defined	define	VERB
ap-1213	79	9	by	by	ADP
ap-1213	79	10	gluing	glue	VERB
ap-1213	79	11	the	the	DET
ap-1213	79	12	respective	respective	ADJ
ap-1213	79	13	worldsheets	worldsheet	NOUN
ap-1213	79	14	the	the	DET
ap-1213	79	15	upshot	upshot	NOUN
ap-1213	79	16	is	be	AUX
ap-1213	79	17	that	that	SCONJ
ap-1213	79	18	the	the	DET
ap-1213	79	19	star	star	NOUN
ap-1213	79	20	multiplication	multiplication	NOUN
ap-1213	79	21	is	be	AUX
ap-1213	79	22	isomorphic	isomorphic	ADJ
ap-1213	79	23	to	to	PART
ap-1213	79	24	operator	operator	NOUN
ap-1213	79	25	multiplication	multiplication	NOUN
ap-1213	79	26	.	.	PUNCT
ap-1213	80	1	to	to	PART
ap-1213	80	2	see	see	VERB
ap-1213	80	3	this	this	PRON
ap-1213	80	4	more	more	ADV
ap-1213	80	5	explicitly	explicitly	ADV
ap-1213	80	6	,	,	PUNCT
ap-1213	80	7	consider	consider	VERB
ap-1213	80	8	two	two	NUM
ap-1213	80	9	vertex	vertex	NOUN
ap-1213	80	10	operators	operator	NOUN
ap-1213	80	11	φ1,2	φ1,2	NOUN
ap-1213	80	12	.	.	PUNCT
ap-1213	81	1	the	the	DET
ap-1213	81	2	corresponding	correspond	VERB
ap-1213	81	3	states	state	NOUN
ap-1213	81	4	|φ1,2	|φ1,2	VERB
ap-1213	81	5	〉	〉	PROPN
ap-1213	81	6	star	star	NOUN
ap-1213	81	7	multiply	multiply	ADV
ap-1213	81	8	as	as	ADP
ap-1213	81	9	|φ1	|φ1	PROPN
ap-1213	81	10	〉	〉	PROPN
ap-1213	81	11	∗	∗	NOUN
ap-1213	81	12	|φ2	|φ2	NOUN
ap-1213	81	13	〉	〉	PROPN
ap-1213	81	14	=	=	SYM
ap-1213	81	15	|φ1e−kφ2	|φ1e−kφ2	PROPN
ap-1213	81	16	〉	〉	NUM
ap-1213	81	17	.	.	PUNCT
ap-1213	82	1	(	(	PUNCT
ap-1213	82	2	3.5	3.5	NUM
ap-1213	82	3	)	)	PUNCT
ap-1213	82	4	let	let	VERB
ap-1213	82	5	us	we	PRON
ap-1213	82	6	now	now	ADV
ap-1213	82	7	introduce	introduce	VERB
ap-1213	82	8	new	new	ADJ
ap-1213	82	9	(	(	PUNCT
ap-1213	82	10	non	non	ADJ
ap-1213	82	11	-	-	ADJ
ap-1213	82	12	local	local	ADJ
ap-1213	82	13	)	)	PUNCT
ap-1213	82	14	cft	cft	PROPN
ap-1213	82	15	operators	operator	NOUN
ap-1213	82	16	φ̂	φ̂	PUNCT
ap-1213	82	17	=	=	PROPN
ap-1213	82	18	ek/2φek/2	ek/2φek/2	PROPN
ap-1213	82	19	and	and	CCONJ
ap-1213	82	20	associated	associated	ADJ
ap-1213	82	21	states	states	PROPN
ap-1213	82	22	|φ̂	|φ̂	PROPN
ap-1213	82	23	〉	〉	PROPN
ap-1213	82	24	.	.	PUNCT
ap-1213	83	1	then	then	ADV
ap-1213	83	2	clearly	clearly	ADV
ap-1213	83	3	|φ̂1	|φ̂1	VERB
ap-1213	83	4	〉	〉	PROPN
ap-1213	83	5	∗	∗	NOUN
ap-1213	83	6	|φ̂2	|φ̂2	PROPN
ap-1213	83	7	〉	〉	PROPN
ap-1213	83	8	=	=	SYM
ap-1213	83	9	|φ̂1φ2	|φ̂1φ2	PROPN
ap-1213	83	10	〉	〉	PROPN
ap-1213	83	11	.	.	PUNCT
ap-1213	84	1	(	(	PUNCT
ap-1213	84	2	3.6	3.6	NUM
ap-1213	84	3	)	)	PUNCT
ap-1213	84	4	therefore	therefore	ADV
ap-1213	84	5	φ→	φ→	VERB
ap-1213	84	6	|φ̂	|φ̂	PROPN
ap-1213	84	7	〉	〉	PROPN
ap-1213	84	8	is	be	AUX
ap-1213	84	9	the	the	DET
ap-1213	84	10	claimed	claim	VERB
ap-1213	84	11	isomorphism	isomorphism	NOUN
ap-1213	84	12	.	.	PUNCT
ap-1213	85	1	usually	usually	ADV
ap-1213	85	2	one	one	PRON
ap-1213	85	3	does	do	AUX
ap-1213	85	4	not	not	PART
ap-1213	85	5	think	think	VERB
ap-1213	85	6	of	of	ADP
ap-1213	85	7	the	the	DET
ap-1213	85	8	star	star	NOUN
ap-1213	85	9	product	product	NOUN
ap-1213	85	10	and	and	CCONJ
ap-1213	85	11	the	the	DET
ap-1213	85	12	operator	operator	NOUN
ap-1213	85	13	product	product	NOUN
ap-1213	85	14	as	as	ADP
ap-1213	85	15	being	be	AUX
ap-1213	85	16	the	the	DET
ap-1213	85	17	same	same	ADJ
ap-1213	85	18	thing	thing	NOUN
ap-1213	85	19	.	.	PUNCT
ap-1213	86	1	in	in	ADP
ap-1213	86	2	particular	particular	ADJ
ap-1213	86	3	,	,	PUNCT
ap-1213	86	4	there	there	PRON
ap-1213	86	5	are	be	VERB
ap-1213	86	6	well	well	ADV
ap-1213	86	7	known	know	VERB
ap-1213	86	8	short	short	ADJ
ap-1213	86	9	distance	distance	NOUN
ap-1213	86	10	singularities	singularity	NOUN
ap-1213	86	11	for	for	ADP
ap-1213	86	12	local	local	ADJ
ap-1213	86	13	vertex	vertex	NOUN
ap-1213	86	14	operators	operator	NOUN
ap-1213	86	15	in	in	ADP
ap-1213	86	16	nearby	nearby	ADJ
ap-1213	86	17	points	point	NOUN
ap-1213	86	18	,	,	PUNCT
ap-1213	86	19	whereas	whereas	SCONJ
ap-1213	86	20	the	the	DET
ap-1213	86	21	star	star	NOUN
ap-1213	86	22	product	product	NOUN
ap-1213	86	23	is	be	AUX
ap-1213	86	24	usually	usually	ADV
ap-1213	86	25	thought	think	VERB
ap-1213	86	26	to	to	PART
ap-1213	86	27	be	be	AUX
ap-1213	86	28	much	much	ADV
ap-1213	86	29	more	more	ADV
ap-1213	86	30	regular	regular	ADJ
ap-1213	86	31	.	.	PUNCT
ap-1213	87	1	well	well	INTJ
ap-1213	87	2	,	,	PUNCT
ap-1213	87	3	thanks	thank	NOUN
ap-1213	87	4	to	to	ADP
ap-1213	87	5	the	the	DET
ap-1213	87	6	presence	presence	NOUN
ap-1213	87	7	of	of	ADP
ap-1213	87	8	the	the	DET
ap-1213	87	9	ek/2	ek/2	PROPN
ap-1213	87	10	operators	operator	NOUN
ap-1213	87	11	,	,	PUNCT
ap-1213	87	12	we	we	PRON
ap-1213	87	13	do	do	AUX
ap-1213	87	14	indeed	indeed	ADV
ap-1213	87	15	get	get	VERB
ap-1213	87	16	the	the	DET
ap-1213	87	17	same	same	ADJ
ap-1213	87	18	type	type	NOUN
ap-1213	87	19	of	of	ADP
ap-1213	87	20	singularities	singularity	NOUN
ap-1213	87	21	when	when	SCONJ
ap-1213	87	22	we	we	PRON
ap-1213	87	23	try	try	VERB
ap-1213	87	24	to	to	PART
ap-1213	87	25	star	star	VERB
ap-1213	87	26	multiply	multiply	ADP
ap-1213	87	27	two	two	NUM
ap-1213	87	28	φ̂	φ̂	NUM
ap-1213	87	29	states	state	NOUN
ap-1213	87	30	as	as	ADP
ap-1213	87	31	in	in	ADP
ap-1213	87	32	the	the	DET
ap-1213	87	33	vertex	vertex	NOUN
ap-1213	87	34	operator	operator	NOUN
ap-1213	87	35	algebra	algebra	NOUN
ap-1213	87	36	.	.	PUNCT
ap-1213	88	1	the	the	DET
ap-1213	88	2	φ̂	φ̂	NUM
ap-1213	88	3	states	state	NOUN
ap-1213	88	4	can	can	AUX
ap-1213	88	5	be	be	AUX
ap-1213	88	6	represented	represent	VERB
ap-1213	88	7	by	by	ADP
ap-1213	88	8	surfaces	surface	NOUN
ap-1213	88	9	that	that	PRON
ap-1213	88	10	differ	differ	VERB
ap-1213	88	11	from	from	ADP
ap-1213	88	12	those	those	PRON
ap-1213	88	13	in	in	ADP
ap-1213	88	14	fig	fig	NOUN
ap-1213	88	15	.	.	PUNCT
ap-1213	88	16	1	1	NUM
ap-1213	88	17	in	in	ADP
ap-1213	88	18	that	that	SCONJ
ap-1213	88	19	the	the	DET
ap-1213	88	20	lower	low	ADJ
ap-1213	88	21	bluish	bluish	ADJ
ap-1213	88	22	part	part	NOUN
ap-1213	88	23	is	be	AUX
ap-1213	88	24	missing	miss	VERB
ap-1213	88	25	and	and	CCONJ
ap-1213	88	26	is	be	AUX
ap-1213	88	27	replaced	replace	VERB
ap-1213	88	28	by	by	ADP
ap-1213	88	29	the	the	DET
ap-1213	88	30	identification	identification	NOUN
ap-1213	88	31	of	of	ADP
ap-1213	88	32	the	the	DET
ap-1213	88	33	left	left	ADJ
ap-1213	88	34	and	and	CCONJ
ap-1213	88	35	right	right	ADJ
ap-1213	88	36	parts	part	NOUN
ap-1213	88	37	of	of	ADP
ap-1213	88	38	the	the	DET
ap-1213	88	39	base	base	NOUN
ap-1213	88	40	of	of	ADP
ap-1213	88	41	the	the	DET
ap-1213	88	42	upper	upper	ADJ
ap-1213	88	43	semi	semi	ADJ
ap-1213	88	44	-	-	ADJ
ap-1213	88	45	infinite	infinite	ADJ
ap-1213	88	46	strip	strip	NOUN
ap-1213	88	47	with	with	ADP
ap-1213	88	48	a	a	DET
ap-1213	88	49	local	local	ADJ
ap-1213	88	50	operator	operator	NOUN
ap-1213	88	51	inserted	insert	VERB
ap-1213	88	52	at	at	ADP
ap-1213	88	53	the	the	DET
ap-1213	88	54	midpoint	midpoint	NOUN
ap-1213	88	55	.	.	PUNCT
ap-1213	89	1	we	we	PRON
ap-1213	89	2	say	say	VERB
ap-1213	89	3	that	that	SCONJ
ap-1213	89	4	such	such	ADJ
ap-1213	89	5	string	string	NOUN
ap-1213	89	6	states	state	NOUN
ap-1213	89	7	have	have	VERB
ap-1213	89	8	no	no	DET
ap-1213	89	9	security	security	NOUN
ap-1213	89	10	strips	strip	NOUN
ap-1213	89	11	.	.	PUNCT
ap-1213	90	1	4	4	NUM
ap-1213	90	2	algebraic	algebraic	ADJ
ap-1213	90	3	solutions	solution	NOUN
ap-1213	90	4	to	to	PART
ap-1213	90	5	osft	osft	VERB
ap-1213	90	6	to	to	PART
ap-1213	90	7	solve	solve	VERB
ap-1213	90	8	the	the	DET
ap-1213	90	9	classical	classical	ADJ
ap-1213	90	10	equation	equation	NOUN
ap-1213	90	11	of	of	ADP
ap-1213	90	12	motion	motion	NOUN
ap-1213	90	13	qbψ+ψ	qbψ+ψ	PROPN
ap-1213	90	14	∗ψ	∗ψ	PROPN
ap-1213	90	15	=	=	SYM
ap-1213	90	16	0	0	NUM
ap-1213	90	17	(	(	PUNCT
ap-1213	90	18	4.7	4.7	NUM
ap-1213	90	19	)	)	PUNCT
ap-1213	90	20	one	one	PRON
ap-1213	90	21	could	could	AUX
ap-1213	90	22	try	try	VERB
ap-1213	90	23	to	to	PART
ap-1213	90	24	restrict	restrict	VERB
ap-1213	90	25	the	the	DET
ap-1213	90	26	huge	huge	ADJ
ap-1213	90	27	star	star	NOUN
ap-1213	90	28	algebra	algebra	NOUN
ap-1213	90	29	to	to	ADP
ap-1213	90	30	as	as	ADP
ap-1213	90	31	small	small	ADJ
ap-1213	90	32	subsector	subsector	NOUN
ap-1213	90	33	as	as	ADP
ap-1213	90	34	possible	possible	ADJ
ap-1213	90	35	.	.	PUNCT
ap-1213	91	1	as	as	SCONJ
ap-1213	91	2	we	we	PRON
ap-1213	91	3	first	first	ADV
ap-1213	91	4	want	want	VERB
ap-1213	91	5	to	to	PART
ap-1213	91	6	study	study	VERB
ap-1213	91	7	the	the	DET
ap-1213	91	8	tachyon	tachyon	NOUN
ap-1213	91	9	condensation	condensation	NOUN
ap-1213	91	10	,	,	PUNCT
ap-1213	91	11	perhaps	perhaps	ADV
ap-1213	91	12	we	we	PRON
ap-1213	91	13	should	should	AUX
ap-1213	91	14	include	include	VERB
ap-1213	91	15	the	the	DET
ap-1213	91	16	vertex	vertex	NOUN
ap-1213	91	17	operator	operator	NOUN
ap-1213	91	18	of	of	ADP
ap-1213	91	19	the	the	DET
ap-1213	91	20	zero	zero	NUM
ap-1213	91	21	momentum	momentum	NOUN
ap-1213	91	22	tachyon	tachyon	NOUN
ap-1213	91	23	,	,	PUNCT
ap-1213	91	24	which	which	PRON
ap-1213	91	25	is	be	AUX
ap-1213	91	26	just	just	ADV
ap-1213	91	27	the	the	DET
ap-1213	91	28	c	c	NOUN
ap-1213	91	29	-	-	PUNCT
ap-1213	91	30	ghost	ghost	NOUN
ap-1213	91	31	.	.	PUNCT
ap-1213	92	1	for	for	ADP
ap-1213	92	2	the	the	DET
ap-1213	92	3	subalgebra	subalgebra	NOUN
ap-1213	92	4	to	to	PART
ap-1213	92	5	be	be	AUX
ap-1213	92	6	nontrivial	nontrivial	ADJ
ap-1213	92	7	we	we	PRON
ap-1213	92	8	should	should	AUX
ap-1213	92	9	also	also	ADV
ap-1213	92	10	include	include	VERB
ap-1213	92	11	the	the	DET
ap-1213	92	12	non	non	ADJ
ap-1213	92	13	-	-	ADJ
ap-1213	92	14	local	local	ADJ
ap-1213	92	15	operator	operator	NOUN
ap-1213	92	16	k.	k.	PROPN
ap-1213	92	17	one	one	PROPN
ap-1213	92	18	can	can	AUX
ap-1213	92	19	easily	easily	ADV
ap-1213	92	20	(	(	PUNCT
ap-1213	92	21	but	but	CCONJ
ap-1213	92	22	not	not	PART
ap-1213	92	23	necessarily	necessarily	ADV
ap-1213	92	24	)	)	PUNCT
ap-1213	92	25	add	add	VERB
ap-1213	92	26	an	an	DET
ap-1213	92	27	operator	operator	NOUN
ap-1213	92	28	b	b	NOUN
ap-1213	92	29	which	which	PRON
ap-1213	92	30	is	be	AUX
ap-1213	92	31	defined	define	VERB
ap-1213	92	32	by	by	ADP
ap-1213	92	33	the	the	DET
ap-1213	92	34	same	same	ADJ
ap-1213	92	35	type	type	NOUN
ap-1213	92	36	of	of	ADP
ap-1213	92	37	integral	integral	ADJ
ap-1213	92	38	as	as	ADP
ap-1213	92	39	k	k	PROPN
ap-1213	92	40	with	with	ADP
ap-1213	92	41	the	the	DET
ap-1213	92	42	energy	energy	NOUN
ap-1213	92	43	momentum	momentum	NOUN
ap-1213	92	44	tensor	tensor	NOUN
ap-1213	92	45	replaced	replace	VERB
ap-1213	92	46	by	by	ADP
ap-1213	92	47	the	the	DET
ap-1213	92	48	b	b	NOUN
ap-1213	92	49	-	-	PUNCT
ap-1213	92	50	ghost	ghost	NOUN
ap-1213	92	51	.	.	PUNCT
ap-1213	93	1	together	together	ADV
ap-1213	93	2	all	all	DET
ap-1213	93	3	these	these	DET
ap-1213	93	4	elements	element	NOUN
ap-1213	93	5	obey	obey	VERB
ap-1213	93	6	c2	c2	PROPN
ap-1213	93	7	=	=	SYM
ap-1213	93	8	0	0	NUM
ap-1213	93	9	,	,	PUNCT
ap-1213	93	10	b2	b2	NOUN
ap-1213	93	11	=	=	SYM
ap-1213	93	12	0	0	NUM
ap-1213	93	13	,	,	PUNCT
ap-1213	93	14	{	{	PUNCT
ap-1213	93	15	c	c	X
ap-1213	93	16	,	,	PUNCT
ap-1213	93	17	b	b	NOUN
ap-1213	93	18	}	}	PUNCT
ap-1213	93	19	=	=	SYM
ap-1213	93	20	1	1	NUM
ap-1213	93	21	(	(	PUNCT
ap-1213	93	22	4.8	4.8	NUM
ap-1213	93	23	)	)	PUNCT
ap-1213	94	1	[	[	X
ap-1213	94	2	k	k	X
ap-1213	94	3	,	,	PUNCT
ap-1213	94	4	b	b	X
ap-1213	94	5	]	]	X
ap-1213	94	6	=	=	SYM
ap-1213	94	7	0	0	NUM
ap-1213	94	8	,	,	PUNCT
ap-1213	94	9	[	[	X
ap-1213	94	10	k	k	X
ap-1213	94	11	,	,	PUNCT
ap-1213	94	12	c	c	X
ap-1213	94	13	]	]	X
ap-1213	94	14	=	=	PUNCT
ap-1213	94	15	∂c	∂c	PROPN
ap-1213	94	16	.	.	PUNCT
ap-1213	95	1	(	(	PUNCT
ap-1213	95	2	4.9	4.9	NUM
ap-1213	95	3	)	)	PUNCT
ap-1213	95	4	the	the	DET
ap-1213	95	5	action	action	NOUN
ap-1213	95	6	of	of	ADP
ap-1213	95	7	the	the	DET
ap-1213	95	8	exterior	exterior	ADJ
ap-1213	95	9	derivative	derivative	NOUN
ap-1213	95	10	is	be	AUX
ap-1213	95	11	equally	equally	ADV
ap-1213	95	12	simple	simple	ADJ
ap-1213	95	13	qbk	qbk	NOUN
ap-1213	95	14	=	=	SYM
ap-1213	95	15	0	0	NUM
ap-1213	95	16	,	,	PUNCT
ap-1213	95	17	qbb	qbb	ADJ
ap-1213	95	18	=	=	SYM
ap-1213	95	19	k	k	NOUN
ap-1213	95	20	,	,	PUNCT
ap-1213	95	21	qbc	qbc	NOUN
ap-1213	95	22	=	=	SYM
ap-1213	95	23	ckc	ckc	X
ap-1213	95	24	.	.	PUNCT
ap-1213	96	1	(	(	PUNCT
ap-1213	96	2	4.10	4.10	NUM
ap-1213	96	3	)	)	PUNCT
ap-1213	96	4	qb	qb	NOUN
ap-1213	96	5	is	be	AUX
ap-1213	96	6	not	not	PART
ap-1213	96	7	the	the	DET
ap-1213	96	8	only	only	ADJ
ap-1213	96	9	useful	useful	ADJ
ap-1213	96	10	derivation	derivation	NOUN
ap-1213	96	11	.	.	PUNCT
ap-1213	97	1	there	there	PRON
ap-1213	97	2	is	be	VERB
ap-1213	97	3	also	also	ADV
ap-1213	97	4	one	one	NUM
ap-1213	97	5	called	call	VERB
ap-1213	97	6	l−	l−	PROPN
ap-1213	97	7	,	,	PUNCT
ap-1213	97	8	which	which	PRON
ap-1213	97	9	aside	aside	ADV
ap-1213	97	10	of	of	ADP
ap-1213	97	11	the	the	DET
ap-1213	97	12	usual	usual	ADJ
ap-1213	97	13	leibnitz	leibnitz	NOUN
ap-1213	97	14	rule	rule	NOUN
ap-1213	97	15	also	also	ADV
ap-1213	97	16	obeys	obey	VERB
ap-1213	97	17	l−c	l−c	PROPN
ap-1213	97	18	=	=	SYM
ap-1213	97	19	−c	−c	NOUN
ap-1213	97	20	,	,	PUNCT
ap-1213	97	21	l−b	l−b	VERB
ap-1213	97	22	=	=	SYM
ap-1213	97	23	b	b	NOUN
ap-1213	97	24	,	,	PUNCT
ap-1213	97	25	l−k	l−k	NOUN
ap-1213	97	26	=	=	SYM
ap-1213	97	27	k.	k.	PROPN
ap-1213	97	28	(	(	PUNCT
ap-1213	97	29	4.11	4.11	NUM
ap-1213	97	30	)	)	PUNCT
ap-1213	97	31	at	at	ADP
ap-1213	97	32	a	a	DET
ap-1213	97	33	given	give	VERB
ap-1213	97	34	ghost	ghost	NOUN
ap-1213	97	35	number	number	NOUN
ap-1213	97	36	,	,	PUNCT
ap-1213	97	37	the	the	DET
ap-1213	97	38	derivative	derivative	ADJ
ap-1213	97	39	l−	l−	NOUN
ap-1213	97	40	counts	count	VERB
ap-1213	97	41	the	the	DET
ap-1213	97	42	number	number	NOUN
ap-1213	97	43	of	of	ADP
ap-1213	97	44	k	k	PROPN
ap-1213	97	45	’s	’s	X
ap-1213	97	46	and	and	CCONJ
ap-1213	97	47	is	be	AUX
ap-1213	97	48	bounded	bound	VERB
ap-1213	97	49	from	from	ADP
ap-1213	97	50	below	below	ADV
ap-1213	97	51	.	.	PUNCT
ap-1213	98	1	one	one	PRON
ap-1213	98	2	could	could	AUX
ap-1213	98	3	therefore	therefore	ADV
ap-1213	98	4	use	use	VERB
ap-1213	98	5	it	it	PRON
ap-1213	98	6	to	to	PART
ap-1213	98	7	solve	solve	VERB
ap-1213	98	8	the	the	DET
ap-1213	98	9	equation	equation	NOUN
ap-1213	98	10	of	of	ADP
ap-1213	98	11	motion	motion	NOUN
ap-1213	98	12	order	order	NOUN
ap-1213	98	13	by	by	ADP
ap-1213	98	14	order	order	NOUN
ap-1213	98	15	in	in	ADP
ap-1213	98	16	l−	l−	NOUN
ap-1213	98	17	within	within	ADP
ap-1213	98	18	the	the	DET
ap-1213	98	19	subalgebra	subalgebra	NOUN
ap-1213	98	20	generated	generate	VERB
ap-1213	98	21	by	by	ADP
ap-1213	98	22	k	k	PROPN
ap-1213	98	23	,	,	PUNCT
ap-1213	98	24	b	b	PROPN
ap-1213	98	25	,	,	PUNCT
ap-1213	98	26	c.	c.	NOUN
ap-1213	98	27	the	the	DET
ap-1213	98	28	simplest	simple	ADJ
ap-1213	98	29	possible	possible	ADJ
ap-1213	98	30	solution	solution	NOUN
ap-1213	98	31	is	be	AUX
ap-1213	98	32	ψ	ψ	NOUN
ap-1213	98	33	=	=	SYM
ap-1213	98	34	αc−	αc−	NOUN
ap-1213	98	35	ck	ck	NOUN
ap-1213	98	36	.	.	PUNCT
ap-1213	99	1	(	(	PUNCT
ap-1213	99	2	4.12	4.12	NUM
ap-1213	99	3	)	)	PUNCT
ap-1213	99	4	clearly	clearly	ADV
ap-1213	99	5	qbψ	qbψ	VERB
ap-1213	99	6	=	=	SYM
ap-1213	99	7	αckc	αckc	NOUN
ap-1213	99	8	−	−	PROPN
ap-1213	99	9	ckck	ckck	PROPN
ap-1213	99	10	=	=	SYM
ap-1213	99	11	−ψ2	−ψ2	ADJ
ap-1213	99	12	.	.	PUNCT
ap-1213	100	1	a	a	DET
ap-1213	100	2	more	more	ADV
ap-1213	100	3	general	general	ADJ
ap-1213	100	4	solution	solution	NOUN
ap-1213	100	5	has	have	AUX
ap-1213	100	6	been	be	AUX
ap-1213	100	7	found	find	VERB
ap-1213	100	8	by	by	ADP
ap-1213	100	9	okawa	okawa	NOUN
ap-1213	101	1	[	[	X
ap-1213	101	2	9	9	NUM
ap-1213	101	3	]	]	PUNCT
ap-1213	101	4	,	,	PUNCT
ap-1213	101	5	following	follow	VERB
ap-1213	101	6	[	[	X
ap-1213	101	7	10	10	NUM
ap-1213	101	8	]	]	PUNCT
ap-1213	101	9	(	(	PUNCT
ap-1213	101	10	see	see	VERB
ap-1213	101	11	also	also	ADV
ap-1213	101	12	the	the	DET
ap-1213	101	13	works	work	NOUN
ap-1213	101	14	by	by	ADP
ap-1213	101	15	erler	erler	NOUN
ap-1213	101	16	[	[	X
ap-1213	101	17	11	11	NUM
ap-1213	101	18	,	,	PUNCT
ap-1213	101	19	12	12	NUM
ap-1213	101	20	]	]	PUNCT
ap-1213	101	21	)	)	PUNCT
ap-1213	102	1	ψ	ψ	X
ap-1213	102	2	=	=	X
ap-1213	102	3	fc	fc	PROPN
ap-1213	102	4	kb	kb	PROPN
ap-1213	102	5	1−	1−	NUM
ap-1213	102	6	f	f	PROPN
ap-1213	102	7	2	2	NUM
ap-1213	102	8	cf	cf	NOUN
ap-1213	102	9	,	,	PUNCT
ap-1213	102	10	(	(	PUNCT
ap-1213	102	11	4.13	4.13	NUM
ap-1213	102	12	)	)	PUNCT
ap-1213	102	13	where	where	SCONJ
ap-1213	102	14	f	f	PROPN
ap-1213	102	15	=	=	SYM
ap-1213	102	16	f	f	PROPN
ap-1213	102	17	(	(	PUNCT
ap-1213	102	18	k	k	NOUN
ap-1213	102	19	)	)	PUNCT
ap-1213	102	20	is	be	AUX
ap-1213	102	21	an	an	DET
ap-1213	102	22	arbitrary	arbitrary	ADJ
ap-1213	102	23	function	function	NOUN
ap-1213	102	24	of	of	ADP
ap-1213	102	25	k.	k.	PROPN
ap-1213	102	26	to	to	PART
ap-1213	102	27	prove	prove	VERB
ap-1213	102	28	that	that	SCONJ
ap-1213	102	29	it	it	PRON
ap-1213	102	30	obeys	obey	VERB
ap-1213	102	31	the	the	DET
ap-1213	102	32	equation	equation	NOUN
ap-1213	102	33	of	of	ADP
ap-1213	102	34	motion	motion	NOUN
ap-1213	102	35	requires	require	VERB
ap-1213	102	36	some	some	DET
ap-1213	102	37	straightforward	straightforward	ADJ
ap-1213	102	38	if	if	SCONJ
ap-1213	102	39	a	a	DET
ap-1213	102	40	bit	bit	NOUN
ap-1213	102	41	tedious	tedious	ADJ
ap-1213	102	42	algebra	algebra	NOUN
ap-1213	102	43	.	.	PUNCT
ap-1213	103	1	the	the	DET
ap-1213	103	2	solution	solution	NOUN
ap-1213	103	3	can	can	AUX
ap-1213	103	4	be	be	AUX
ap-1213	103	5	formally	formally	ADV
ap-1213	103	6	written	write	VERB
ap-1213	103	7	in	in	ADP
ap-1213	103	8	the	the	DET
ap-1213	103	9	form	form	NOUN
ap-1213	103	10	ψ	ψ	X
ap-1213	103	11	=	=	PUNCT
ap-1213	103	12	(	(	PUNCT
ap-1213	103	13	1	1	NUM
ap-1213	103	14	−	−	PROPN
ap-1213	103	15	fbcf	fbcf	PROPN
ap-1213	103	16	)	)	PUNCT
ap-1213	104	1	qb	qb	PROPN
ap-1213	104	2	(	(	PUNCT
ap-1213	104	3	1	1	NUM
ap-1213	104	4	1−	1−	NUM
ap-1213	104	5	fbcf	fbcf	PROPN
ap-1213	104	6	)	)	PUNCT
ap-1213	104	7	,	,	PUNCT
ap-1213	104	8	(	(	PUNCT
ap-1213	104	9	4.14	4.14	NUM
ap-1213	104	10	)	)	PUNCT
ap-1213	104	11	which	which	PRON
ap-1213	104	12	makes	make	VERB
ap-1213	104	13	the	the	DET
ap-1213	104	14	proof	proof	NOUN
ap-1213	104	15	of	of	ADP
ap-1213	104	16	the	the	DET
ap-1213	104	17	equations	equation	NOUN
ap-1213	104	18	of	of	ADP
ap-1213	104	19	motion	motion	NOUN
ap-1213	104	20	trivial	trivial	ADJ
ap-1213	104	21	.	.	PUNCT
ap-1213	105	1	what	what	PRON
ap-1213	105	2	is	be	AUX
ap-1213	105	3	not	not	PART
ap-1213	105	4	so	so	ADV
ap-1213	105	5	trivial	trivial	ADJ
ap-1213	105	6	is	be	AUX
ap-1213	105	7	to	to	PART
ap-1213	105	8	distinguish	distinguish	VERB
ap-1213	105	9	a	a	DET
ap-1213	105	10	trivial	trivial	ADJ
ap-1213	105	11	pure	pure	ADJ
ap-1213	105	12	gauge	gauge	NOUN
ap-1213	105	13	solution	solution	NOUN
ap-1213	105	14	from	from	ADP
ap-1213	105	15	the	the	DET
ap-1213	105	16	nontrivial	nontrivial	ADJ
ap-1213	105	17	solutions	solution	NOUN
ap-1213	105	18	.	.	PUNCT
ap-1213	106	1	note	note	VERB
ap-1213	106	2	that	that	SCONJ
ap-1213	106	3	104	104	NUM
ap-1213	106	4	acta	acta	PROPN
ap-1213	106	5	polytechnica	polytechnica	PROPN
ap-1213	106	6	vol	vol	NOUN
ap-1213	106	7	.	.	PROPN
ap-1213	107	1	50	50	NUM
ap-1213	107	2	no	no	NOUN
ap-1213	107	3	.	.	PUNCT
ap-1213	108	1	3/2010	3/2010	NUM
ap-1213	108	2	bc	bc	PROPN
ap-1213	108	3	is	be	AUX
ap-1213	108	4	a	a	DET
ap-1213	108	5	projector	projector	NOUN
ap-1213	108	6	,	,	PUNCT
ap-1213	108	7	in	in	ADP
ap-1213	108	8	the	the	DET
ap-1213	108	9	sense	sense	NOUN
ap-1213	108	10	that	that	SCONJ
ap-1213	108	11	it	it	PRON
ap-1213	108	12	squares	square	VERB
ap-1213	108	13	to	to	ADP
ap-1213	108	14	itself	itself	PRON
ap-1213	108	15	,	,	PUNCT
ap-1213	108	16	and	and	CCONJ
ap-1213	108	17	therefore	therefore	ADV
ap-1213	108	18	(	(	PUNCT
ap-1213	108	19	1−	1−	NUM
ap-1213	108	20	fbcf	fbcf	NOUN
ap-1213	108	21	)	)	PUNCT
ap-1213	108	22	−1	−1	NOUN
ap-1213	108	23	=	=	SYM
ap-1213	108	24	1	1	NUM
ap-1213	109	1	+	+	NUM
ap-1213	109	2	f	f	PROPN
ap-1213	109	3	1−	1−	NUM
ap-1213	109	4	f	f	PROPN
ap-1213	109	5	2	2	NUM
ap-1213	109	6	bcf	bcf	NOUN
ap-1213	109	7	.	.	PUNCT
ap-1213	110	1	(	(	PUNCT
ap-1213	110	2	4.15	4.15	NUM
ap-1213	110	3	)	)	PUNCT
ap-1213	110	4	for	for	ADP
ap-1213	110	5	a	a	DET
ap-1213	110	6	solution	solution	NOUN
ap-1213	110	7	to	to	PART
ap-1213	110	8	be	be	AUX
ap-1213	110	9	nontrivial	nontrivial	ADJ
ap-1213	110	10	,	,	PUNCT
ap-1213	110	11	the	the	DET
ap-1213	110	12	factor	factor	NOUN
ap-1213	110	13	f/(1−	f/(1−	PROPN
ap-1213	110	14	f	f	PROPN
ap-1213	110	15	2	2	X
ap-1213	110	16	)	)	PUNCT
ap-1213	110	17	must	must	AUX
ap-1213	110	18	be	be	AUX
ap-1213	110	19	ill	ill	ADV
ap-1213	110	20	defined	define	VERB
ap-1213	110	21	,	,	PUNCT
ap-1213	110	22	whereas	whereas	SCONJ
ap-1213	110	23	the	the	DET
ap-1213	110	24	similar	similar	ADJ
ap-1213	110	25	looking	look	VERB
ap-1213	110	26	factor	factor	NOUN
ap-1213	110	27	appearing	appear	VERB
ap-1213	110	28	in	in	ADP
ap-1213	110	29	the	the	DET
ap-1213	110	30	string	string	NOUN
ap-1213	110	31	field	field	NOUN
ap-1213	110	32	itself	itself	PRON
ap-1213	110	33	f̃	f̃	PROPN
ap-1213	110	34	≡	≡	PROPN
ap-1213	111	1	k/(1	k/(1	PUNCT
ap-1213	112	1	−	−	NOUN
ap-1213	112	2	f	f	NOUN
ap-1213	112	3	2	2	X
ap-1213	112	4	)	)	PUNCT
ap-1213	112	5	must	must	AUX
ap-1213	112	6	be	be	AUX
ap-1213	112	7	well	well	ADV
ap-1213	112	8	defined	define	VERB
ap-1213	112	9	.	.	PUNCT
ap-1213	113	1	before	before	SCONJ
ap-1213	113	2	we	we	PRON
ap-1213	113	3	go	go	VERB
ap-1213	113	4	in	in	ADP
ap-1213	113	5	depth	depth	NOUN
ap-1213	113	6	into	into	ADP
ap-1213	113	7	what	what	PRON
ap-1213	113	8	ill	ill	ADV
ap-1213	113	9	/	/	SYM
ap-1213	113	10	well	well	ADV
ap-1213	113	11	defined	define	VERB
ap-1213	113	12	means	mean	NOUN
ap-1213	113	13	,	,	PUNCT
ap-1213	113	14	let	let	VERB
ap-1213	113	15	us	we	PRON
ap-1213	113	16	discuss	discuss	VERB
ap-1213	113	17	another	another	DET
ap-1213	113	18	interesting	interesting	ADJ
ap-1213	113	19	property	property	NOUN
ap-1213	113	20	of	of	ADP
ap-1213	113	21	these	these	DET
ap-1213	113	22	solutions	solution	NOUN
ap-1213	113	23	.	.	PUNCT
ap-1213	114	1	expanding	expand	VERB
ap-1213	114	2	string	string	NOUN
ap-1213	114	3	field	field	NOUN
ap-1213	114	4	theory	theory	NOUN
ap-1213	114	5	around	around	ADP
ap-1213	114	6	these	these	DET
ap-1213	114	7	solutions	solution	NOUN
ap-1213	114	8	one	one	NOUN
ap-1213	114	9	obtains	obtain	VERB
ap-1213	114	10	a	a	DET
ap-1213	114	11	similar	similar	ADJ
ap-1213	114	12	looking	look	VERB
ap-1213	114	13	theory	theory	NOUN
ap-1213	114	14	with	with	ADP
ap-1213	114	15	qb	qb	PROPN
ap-1213	114	16	replaced	replace	VERB
ap-1213	114	17	by	by	ADP
ap-1213	114	18	qψ	qψ	PROPN
ap-1213	114	19	=	=	SYM
ap-1213	114	20	qb	qb	PROPN
ap-1213	114	21	+	+	CCONJ
ap-1213	114	22	{	{	PUNCT
ap-1213	114	23	ψ	ψ	NOUN
ap-1213	114	24	,	,	PUNCT
ap-1213	114	25	·	·	PUNCT
ap-1213	114	26	}	}	PUNCT
ap-1213	114	27	∗.	∗.	PROPN
ap-1213	114	28	(	(	PUNCT
ap-1213	114	29	4.16	4.16	NUM
ap-1213	114	30	)	)	PUNCT
ap-1213	114	31	the	the	DET
ap-1213	114	32	second	second	ADJ
ap-1213	114	33	term	term	NOUN
ap-1213	114	34	acts	act	VERB
ap-1213	114	35	as	as	ADP
ap-1213	114	36	a	a	DET
ap-1213	114	37	graded	grade	VERB
ap-1213	114	38	star	star	NOUN
ap-1213	114	39	-	-	PUNCT
ap-1213	114	40	commutator	commutator	NOUN
ap-1213	114	41	with	with	ADP
ap-1213	114	42	ψ	ψ	PROPN
ap-1213	114	43	.	.	PUNCT
ap-1213	115	1	the	the	DET
ap-1213	115	2	fluctuations	fluctuation	NOUN
ap-1213	115	3	around	around	ADP
ap-1213	115	4	the	the	DET
ap-1213	115	5	vacuum	vacuum	NOUN
ap-1213	115	6	are	be	AUX
ap-1213	115	7	described	describe	VERB
ap-1213	115	8	by	by	ADP
ap-1213	115	9	the	the	DET
ap-1213	115	10	cohomology	cohomology	NOUN
ap-1213	115	11	of	of	ADP
ap-1213	115	12	this	this	DET
ap-1213	115	13	operator	operator	NOUN
ap-1213	115	14	.	.	PUNCT
ap-1213	116	1	interestingly	interestingly	ADV
ap-1213	116	2	,	,	PUNCT
ap-1213	116	3	one	one	PRON
ap-1213	116	4	could	could	AUX
ap-1213	116	5	find	find	VERB
ap-1213	116	6	a	a	DET
ap-1213	116	7	homotopy	homotopy	NOUN
ap-1213	116	8	operator	operator	NOUN
ap-1213	116	9	a	a	PRON
ap-1213	116	10	which	which	PRON
ap-1213	116	11	formally	formally	ADV
ap-1213	116	12	trivializes	trivialize	VERB
ap-1213	116	13	the	the	DET
ap-1213	116	14	cohomology	cohomology	NOUN
ap-1213	116	15	[	[	X
ap-1213	116	16	13	13	NUM
ap-1213	116	17	]	]	PUNCT
ap-1213	116	18	a	a	DET
ap-1213	116	19	=	=	SYM
ap-1213	116	20	1−	1−	NUM
ap-1213	116	21	f	f	NOUN
ap-1213	116	22	2	2	NUM
ap-1213	116	23	k	k	PROPN
ap-1213	116	24	b	b	PROPN
ap-1213	116	25	,	,	PUNCT
ap-1213	116	26	(	(	PUNCT
ap-1213	116	27	4.17	4.17	NUM
ap-1213	116	28	)	)	PUNCT
ap-1213	116	29	i.e.	i.e.	X
ap-1213	116	30	it	it	PRON
ap-1213	116	31	obeys	obey	VERB
ap-1213	116	32	{	{	PUNCT
ap-1213	116	33	qψ	qψ	PROPN
ap-1213	116	34	,	,	PUNCT
ap-1213	116	35	a	a	PRON
ap-1213	116	36	}	}	PUNCT
ap-1213	116	37	=	=	SYM
ap-1213	116	38	1	1	X
ap-1213	116	39	.	.	PUNCT
ap-1213	117	1	therefore	therefore	ADV
ap-1213	117	2	,	,	PUNCT
ap-1213	117	3	formally	formally	ADV
ap-1213	117	4	,	,	PUNCT
ap-1213	117	5	any	any	DET
ap-1213	117	6	qψ	qψ	PROPN
ap-1213	117	7	closed	close	VERB
ap-1213	117	8	state	state	NOUN
ap-1213	117	9	χ	χ	X
ap-1213	117	10	can	can	AUX
ap-1213	117	11	be	be	AUX
ap-1213	117	12	written	write	VERB
ap-1213	117	13	as	as	ADP
ap-1213	117	14	qψ	qψ	PRON
ap-1213	117	15	exact	exact	NOUN
ap-1213	117	16	:	:	PUNCT
ap-1213	117	17	χ	χ	X
ap-1213	117	18	=	=	SYM
ap-1213	117	19	qψ(aχ	qψ(aχ	NOUN
ap-1213	117	20	)	)	PUNCT
ap-1213	117	21	.	.	PUNCT
ap-1213	118	1	absence	absence	NOUN
ap-1213	118	2	of	of	ADP
ap-1213	118	3	nontrivial	nontrivial	ADJ
ap-1213	118	4	excitations	excitation	NOUN
ap-1213	118	5	around	around	ADP
ap-1213	118	6	a	a	DET
ap-1213	118	7	given	give	VERB
ap-1213	118	8	state	state	NOUN
ap-1213	118	9	ψ	ψ	NOUN
ap-1213	118	10	is	be	AUX
ap-1213	118	11	a	a	DET
ap-1213	118	12	property	property	NOUN
ap-1213	118	13	expected	expect	VERB
ap-1213	118	14	by	by	ADP
ap-1213	118	15	sen	sen	PROPN
ap-1213	118	16	’s	’s	PART
ap-1213	118	17	conjectures	conjecture	VERB
ap-1213	118	18	[	[	X
ap-1213	118	19	14	14	NUM
ap-1213	118	20	]	]	PUNCT
ap-1213	118	21	around	around	ADP
ap-1213	118	22	the	the	DET
ap-1213	118	23	tachyon	tachyon	NOUN
ap-1213	118	24	vacuum	vacuum	NOUN
ap-1213	118	25	,	,	PUNCT
ap-1213	118	26	but	but	CCONJ
ap-1213	118	27	definitely	definitely	ADV
ap-1213	118	28	not	not	PART
ap-1213	118	29	around	around	ADP
ap-1213	118	30	a	a	DET
ap-1213	118	31	generic	generic	ADJ
ap-1213	118	32	state	state	NOUN
ap-1213	118	33	.	.	PUNCT
ap-1213	119	1	we	we	PRON
ap-1213	119	2	thus	thus	ADV
ap-1213	119	3	find	find	VERB
ap-1213	119	4	an	an	DET
ap-1213	119	5	analogous	analogous	ADJ
ap-1213	119	6	condition	condition	NOUN
ap-1213	119	7	to	to	ADP
ap-1213	119	8	the	the	DET
ap-1213	119	9	one	one	NUM
ap-1213	119	10	above	above	ADP
ap-1213	119	11	:	:	PUNCT
ap-1213	119	12	(	(	PUNCT
ap-1213	119	13	1−f	1−f	NUM
ap-1213	119	14	2)/k	2)/k	NUM
ap-1213	119	15	should	should	AUX
ap-1213	119	16	be	be	AUX
ap-1213	119	17	well	well	ADV
ap-1213	119	18	defined	define	VERB
ap-1213	119	19	for	for	ADP
ap-1213	119	20	the	the	DET
ap-1213	119	21	tachyon	tachyon	NOUN
ap-1213	119	22	vacuum	vacuum	NOUN
ap-1213	119	23	,	,	PUNCT
ap-1213	119	24	but	but	CCONJ
ap-1213	119	25	ill	ill	ADV
ap-1213	119	26	defined	define	VERB
ap-1213	119	27	for	for	ADP
ap-1213	119	28	the	the	DET
ap-1213	119	29	perturbative	perturbative	ADJ
ap-1213	119	30	vacuum	vacuum	NOUN
ap-1213	119	31	(	(	PUNCT
ap-1213	119	32	f	f	NOUN
ap-1213	119	33	=	=	NOUN
ap-1213	119	34	0	0	NUM
ap-1213	119	35	)	)	PUNCT
ap-1213	119	36	.	.	PUNCT
ap-1213	120	1	assuming	assume	VERB
ap-1213	120	2	that	that	SCONJ
ap-1213	120	3	f	f	PROPN
ap-1213	120	4	(	(	PUNCT
ap-1213	120	5	k	k	NOUN
ap-1213	120	6	)	)	PUNCT
ap-1213	120	7	is	be	AUX
ap-1213	120	8	a	a	DET
ap-1213	120	9	well	well	ADV
ap-1213	120	10	defined	define	VERB
ap-1213	120	11	string	string	NOUN
ap-1213	120	12	field	field	NOUN
ap-1213	120	13	,	,	PUNCT
ap-1213	120	14	and	and	CCONJ
ap-1213	120	15	adopting	adopt	VERB
ap-1213	120	16	a	a	DET
ap-1213	120	17	simplifying	simplifying	NOUN
ap-1213	120	18	assumption	assumption	NOUN
ap-1213	120	19	that	that	SCONJ
ap-1213	120	20	f	f	PROPN
ap-1213	120	21	is	be	AUX
ap-1213	120	22	analytic	analytic	ADJ
ap-1213	120	23	around	around	ADP
ap-1213	120	24	the	the	DET
ap-1213	120	25	origin	origin	NOUN
ap-1213	120	26	,	,	PUNCT
ap-1213	120	27	we	we	PRON
ap-1213	120	28	find	find	VERB
ap-1213	120	29	that	that	SCONJ
ap-1213	120	30	f	f	PROPN
ap-1213	120	31	(	(	PUNCT
ap-1213	120	32	k	k	NOUN
ap-1213	120	33	)	)	PUNCT
ap-1213	120	34	=	=	PRON
ap-1213	120	35	a+	a+	PUNCT
ap-1213	120	36	bk	bk	NOUN
ap-1213	120	37	+	+	PROPN
ap-1213	120	38	.	.	PUNCT
ap-1213	120	39	.	.	PUNCT
ap-1213	120	40	.	.	PUNCT
ap-1213	121	1	(	(	PUNCT
ap-1213	121	2	4.18	4.18	NUM
ap-1213	121	3	)	)	PUNCT
ap-1213	121	4	gives	give	VERB
ap-1213	121	5	the	the	DET
ap-1213	121	6	tachyon	tachyon	NOUN
ap-1213	121	7	vacuum	vacuum	NOUN
ap-1213	121	8	if	if	SCONJ
ap-1213	121	9	a	a	DET
ap-1213	121	10	=	=	SYM
ap-1213	121	11	1	1	NUM
ap-1213	121	12	and	and	CCONJ
ap-1213	121	13	b	b	PROPN
ap-1213	121	14	�	�	PROPN
ap-1213	121	15	=	=	SYM
ap-1213	121	16	0	0	NUM
ap-1213	121	17	,	,	PUNCT
ap-1213	121	18	and	and	CCONJ
ap-1213	121	19	gives	give	VERB
ap-1213	121	20	the	the	DET
ap-1213	121	21	trivial	trivial	ADJ
ap-1213	121	22	vacuum	vacuum	NOUN
ap-1213	121	23	for	for	ADP
ap-1213	121	24	a	a	DET
ap-1213	121	25	�	�	NOUN
ap-1213	121	26	=	=	SYM
ap-1213	121	27	1	1	NUM
ap-1213	121	28	.	.	PUNCT
ap-1213	121	29	solutions	solution	NOUN
ap-1213	121	30	with	with	ADP
ap-1213	121	31	a	a	PRON
ap-1213	121	32	=	=	SYM
ap-1213	121	33	1	1	NUM
ap-1213	121	34	and	and	CCONJ
ap-1213	121	35	b	b	X
ap-1213	121	36	=	=	SYM
ap-1213	121	37	0	0	PROPN
ap-1213	121	38	might	might	AUX
ap-1213	121	39	correspond	correspond	VERB
ap-1213	121	40	to	to	ADP
ap-1213	121	41	something	something	PRON
ap-1213	121	42	more	more	ADV
ap-1213	121	43	exotic	exotic	ADJ
ap-1213	121	44	such	such	ADJ
ap-1213	121	45	as	as	ADP
ap-1213	121	46	multiple	multiple	ADJ
ap-1213	121	47	brane	brane	NOUN
ap-1213	121	48	solutions	solution	NOUN
ap-1213	121	49	,	,	PUNCT
ap-1213	121	50	but	but	CCONJ
ap-1213	121	51	this	this	PRON
ap-1213	121	52	has	have	AUX
ap-1213	121	53	not	not	PART
ap-1213	121	54	yet	yet	ADV
ap-1213	121	55	been	be	AUX
ap-1213	121	56	shown	show	VERB
ap-1213	121	57	convincingly	convincingly	ADV
ap-1213	121	58	.	.	PUNCT
ap-1213	122	1	5	5	NUM
ap-1213	123	1	what	what	PRON
ap-1213	123	2	constitutes	constitute	VERB
ap-1213	123	3	a	a	DET
ap-1213	123	4	well	well	ADV
ap-1213	123	5	defined	define	VERB
ap-1213	123	6	string	string	NOUN
ap-1213	123	7	field	field	NOUN
ap-1213	123	8	?	?	PUNCT
ap-1213	124	1	this	this	PRON
ap-1213	124	2	is	be	AUX
ap-1213	124	3	still	still	ADV
ap-1213	124	4	an	an	DET
ap-1213	124	5	open	open	ADJ
ap-1213	124	6	question	question	NOUN
ap-1213	124	7	,	,	PUNCT
ap-1213	124	8	so	so	SCONJ
ap-1213	124	9	we	we	PRON
ap-1213	124	10	will	will	AUX
ap-1213	124	11	rather	rather	ADV
ap-1213	124	12	ask	ask	VERB
ap-1213	124	13	a	a	DET
ap-1213	124	14	more	more	ADV
ap-1213	124	15	specific	specific	ADJ
ap-1213	124	16	question	question	NOUN
ap-1213	124	17	of	of	ADP
ap-1213	124	18	when	when	SCONJ
ap-1213	124	19	a	a	DET
ap-1213	124	20	function	function	NOUN
ap-1213	124	21	f	f	X
ap-1213	124	22	(	(	PUNCT
ap-1213	124	23	k	k	NOUN
ap-1213	124	24	)	)	PUNCT
ap-1213	124	25	constitutes	constitute	VERB
ap-1213	124	26	a	a	DET
ap-1213	124	27	well	well	ADV
ap-1213	124	28	defined	define	VERB
ap-1213	124	29	string	string	NOUN
ap-1213	124	30	field	field	NOUN
ap-1213	124	31	.	.	PUNCT
ap-1213	125	1	even	even	ADV
ap-1213	125	2	this	this	DET
ap-1213	125	3	question	question	NOUN
ap-1213	125	4	might	might	AUX
ap-1213	125	5	not	not	PART
ap-1213	125	6	have	have	VERB
ap-1213	125	7	a	a	DET
ap-1213	125	8	unique	unique	ADJ
ap-1213	125	9	answer	answer	NOUN
ap-1213	125	10	,	,	PUNCT
ap-1213	125	11	as	as	SCONJ
ap-1213	125	12	there	there	PRON
ap-1213	125	13	are	be	VERB
ap-1213	125	14	several	several	ADJ
ap-1213	125	15	possible	possible	ADJ
ap-1213	125	16	definitions	definition	NOUN
ap-1213	125	17	of	of	ADP
ap-1213	125	18	what	what	PRON
ap-1213	125	19	might	might	AUX
ap-1213	125	20	constitute	constitute	VERB
ap-1213	125	21	‘	'	PUNCT
ap-1213	125	22	good	good	ADJ
ap-1213	125	23	’	'	PUNCT
ap-1213	125	24	or	or	CCONJ
ap-1213	125	25	‘	'	PUNCT
ap-1213	125	26	bad	bad	ADJ
ap-1213	125	27	’	'	PUNCT
ap-1213	125	28	,	,	PUNCT
ap-1213	125	29	depending	depend	VERB
ap-1213	125	30	on	on	ADP
ap-1213	125	31	the	the	DET
ap-1213	125	32	context	context	NOUN
ap-1213	125	33	.	.	PUNCT
ap-1213	126	1	we	we	PRON
ap-1213	126	2	define	define	VERB
ap-1213	126	3	a	a	DET
ap-1213	126	4	set	set	NOUN
ap-1213	126	5	of	of	ADP
ap-1213	126	6	geometric	geometric	ADJ
ap-1213	126	7	string	string	NOUN
ap-1213	126	8	field	field	NOUN
ap-1213	126	9	functions	function	NOUN
ap-1213	126	10	f	f	X
ap-1213	126	11	(	(	PUNCT
ap-1213	126	12	k	k	NOUN
ap-1213	126	13	)	)	PUNCT
ap-1213	126	14	to	to	PART
ap-1213	126	15	be	be	AUX
ap-1213	126	16	those	those	PRON
ap-1213	126	17	expressible	expressible	ADJ
ap-1213	126	18	as6	as6	ADP
ap-1213	126	19	f	f	PROPN
ap-1213	126	20	(	(	PUNCT
ap-1213	126	21	k	k	NOUN
ap-1213	126	22	)	)	PUNCT
ap-1213	126	23	=	=	SYM
ap-1213	127	1	∫	∫	PROPN
ap-1213	128	1	∞	∞	NUM
ap-1213	128	2	0	0	PROPN
ap-1213	128	3	dαf(α)e−αk	dαf(α)e−αk	NOUN
ap-1213	128	4	.	.	PUNCT
ap-1213	129	1	(	(	PUNCT
ap-1213	129	2	5.19	5.19	NUM
ap-1213	129	3	)	)	PUNCT
ap-1213	129	4	the	the	DET
ap-1213	129	5	name	name	NOUN
ap-1213	129	6	geometric	geometric	ADJ
ap-1213	129	7	means	mean	VERB
ap-1213	129	8	that	that	SCONJ
ap-1213	129	9	we	we	PRON
ap-1213	129	10	consider	consider	VERB
ap-1213	129	11	superpositions	superposition	NOUN
ap-1213	129	12	of	of	ADP
ap-1213	129	13	surfaces	surface	NOUN
ap-1213	129	14	,	,	PUNCT
ap-1213	129	15	recall	recall	VERB
ap-1213	129	16	that	that	SCONJ
ap-1213	129	17	e−αk	e−αk	NOUN
ap-1213	129	18	represents	represent	VERB
ap-1213	129	19	a	a	DET
ap-1213	129	20	surface	surface	NOUN
ap-1213	129	21	.	.	PUNCT
ap-1213	130	1	for	for	ADP
ap-1213	130	2	α	α	PROPN
ap-1213	130	3	∈	∈	PROPN
ap-1213	130	4	n0	n0	NOUN
ap-1213	130	5	it	it	PRON
ap-1213	130	6	is	be	AUX
ap-1213	130	7	the	the	DET
ap-1213	130	8	α	α	NOUN
ap-1213	130	9	-	-	PUNCT
ap-1213	130	10	th	th	VERB
ap-1213	130	11	power	power	NOUN
ap-1213	130	12	of	of	ADP
ap-1213	130	13	the	the	DET
ap-1213	130	14	sl(2	sl(2	PROPN
ap-1213	130	15	,	,	PUNCT
ap-1213	130	16	r	r	NOUN
ap-1213	130	17	)	)	PUNCT
ap-1213	130	18	vacuum	vacuum	NOUN
ap-1213	130	19	|0	|0	NUM
ap-1213	130	20	〉	〉	PROPN
ap-1213	130	21	,	,	PUNCT
ap-1213	130	22	and	and	CCONJ
ap-1213	130	23	for	for	ADP
ap-1213	130	24	generic	generic	ADJ
ap-1213	130	25	α	α	PROPN
ap-1213	130	26	≥	≥	NOUN
ap-1213	130	27	0	0	NUM
ap-1213	130	28	one	one	PRON
ap-1213	130	29	can	can	AUX
ap-1213	130	30	find	find	VERB
ap-1213	130	31	a	a	DET
ap-1213	130	32	frame	frame	NOUN
ap-1213	130	33	(	(	PUNCT
ap-1213	130	34	a	a	DET
ap-1213	130	35	so	so	ADV
ap-1213	130	36	called	call	VERB
ap-1213	130	37	cylinder	cylinder	NOUN
ap-1213	130	38	frame	frame	NOUN
ap-1213	130	39	)	)	PUNCT
ap-1213	130	40	,	,	PUNCT
ap-1213	130	41	in	in	ADP
ap-1213	130	42	which	which	PRON
ap-1213	130	43	the	the	DET
ap-1213	130	44	surface	surface	NOUN
ap-1213	130	45	is	be	AUX
ap-1213	130	46	a	a	DET
ap-1213	130	47	strip	strip	NOUN
ap-1213	130	48	of	of	ADP
ap-1213	130	49	size	size	NOUN
ap-1213	130	50	α	α	NOUN
ap-1213	130	51	.	.	PUNCT
ap-1213	131	1	what	what	PRON
ap-1213	131	2	space	space	NOUN
ap-1213	131	3	do	do	AUX
ap-1213	131	4	we	we	PRON
ap-1213	131	5	want	want	VERB
ap-1213	131	6	f(α	f(α	NOUN
ap-1213	131	7	)	)	PUNCT
ap-1213	131	8	to	to	PART
ap-1213	131	9	belong	belong	VERB
ap-1213	131	10	to	to	ADP
ap-1213	131	11	?	?	PUNCT
ap-1213	132	1	obviously	obviously	ADV
ap-1213	132	2	a	a	DET
ap-1213	132	3	space	space	NOUN
ap-1213	132	4	of	of	ADP
ap-1213	132	5	functions	function	NOUN
ap-1213	132	6	would	would	AUX
ap-1213	132	7	be	be	AUX
ap-1213	132	8	too	too	ADV
ap-1213	132	9	restrictive	restrictive	ADJ
ap-1213	132	10	,	,	PUNCT
ap-1213	132	11	as	as	SCONJ
ap-1213	132	12	one	one	PRON
ap-1213	132	13	would	would	AUX
ap-1213	132	14	have	have	VERB
ap-1213	132	15	no	no	DET
ap-1213	132	16	hope	hope	NOUN
ap-1213	132	17	of	of	ADP
ap-1213	132	18	representing	represent	VERB
ap-1213	132	19	even	even	ADV
ap-1213	132	20	the	the	DET
ap-1213	132	21	vacuum	vacuum	NOUN
ap-1213	132	22	corresponding	correspond	VERB
ap-1213	132	23	to	to	ADP
ap-1213	132	24	f	f	PROPN
ap-1213	132	25	(	(	PUNCT
ap-1213	132	26	k	k	NOUN
ap-1213	132	27	)	)	PUNCT
ap-1213	132	28	=	=	PUNCT
ap-1213	132	29	e−k	e−k	PROPN
ap-1213	132	30	.	.	PUNCT
ap-1213	133	1	the	the	DET
ap-1213	133	2	theory	theory	NOUN
ap-1213	133	3	of	of	ADP
ap-1213	133	4	distributions	distribution	NOUN
ap-1213	133	5	,	,	PUNCT
ap-1213	133	6	developed	develop	VERB
ap-1213	133	7	to	to	ADP
ap-1213	133	8	a	a	DET
ap-1213	133	9	large	large	ADJ
ap-1213	133	10	extent	extent	NOUN
ap-1213	133	11	by	by	ADP
ap-1213	133	12	laurent	laurent	PROPN
ap-1213	133	13	schwartz	schwartz	PROPN
ap-1213	133	14	more	more	ADJ
ap-1213	133	15	than	than	ADP
ap-1213	133	16	sixty	sixty	NUM
ap-1213	133	17	years	year	NOUN
ap-1213	133	18	ago	ago	ADV
ap-1213	133	19	,	,	PUNCT
ap-1213	133	20	is	be	AUX
ap-1213	133	21	exactly	exactly	ADV
ap-1213	133	22	what	what	PRON
ap-1213	133	23	we	we	PRON
ap-1213	133	24	need	need	VERB
ap-1213	133	25	.	.	PUNCT
ap-1213	134	1	let	let	VERB
ap-1213	134	2	us	we	PRON
ap-1213	134	3	now	now	ADV
ap-1213	134	4	remind	remind	VERB
ap-1213	134	5	the	the	DET
ap-1213	134	6	reader	reader	NOUN
ap-1213	134	7	of	of	ADP
ap-1213	134	8	some	some	PRON
ap-1213	134	9	of	of	ADP
ap-1213	134	10	the	the	DET
ap-1213	134	11	useful	useful	ADJ
ap-1213	134	12	spaces	space	NOUN
ap-1213	134	13	that	that	PRON
ap-1213	134	14	are	be	AUX
ap-1213	134	15	introduced	introduce	VERB
ap-1213	134	16	in	in	ADP
ap-1213	134	17	a	a	DET
ap-1213	134	18	beautiful	beautiful	ADJ
ap-1213	134	19	treatise	treatise	NOUN
ap-1213	134	20	[	[	X
ap-1213	134	21	15	15	NUM
ap-1213	134	22	]	]	PUNCT
ap-1213	134	23	.	.	PUNCT
ap-1213	135	1	schwartz	schwartz	PROPN
ap-1213	135	2	introduces	introduce	VERB
ap-1213	135	3	the	the	DET
ap-1213	135	4	following	follow	VERB
ap-1213	135	5	spaces	space	NOUN
ap-1213	135	6	d	d	X
ap-1213	135	7	⊂	⊂	PROPN
ap-1213	135	8	s	s	PART
ap-1213	135	9	⊂	⊂	PROPN
ap-1213	135	10	dlp	dlp	PROPN
ap-1213	135	11	⊂	⊂	PROPN
ap-1213	135	12	dlq	dlq	PROPN
ap-1213	136	1	⊂	⊂	PROPN
ap-1213	136	2	ḃ	ḃ	PROPN
ap-1213	137	1	⊂	⊂	PROPN
ap-1213	137	2	b	b	X
ap-1213	137	3	⊂	⊂	PROPN
ap-1213	137	4	om	om	PROPN
ap-1213	137	5	⊂	⊂	PROPN
ap-1213	137	6	e	e	PROPN
ap-1213	137	7	∩	∩	NOUN
ap-1213	137	8	∩	∩	NOUN
ap-1213	137	9	∩	∩	NOUN
ap-1213	137	10	∩	∩	NOUN
ap-1213	137	11	∩	∩	NOUN
ap-1213	137	12	∩	∩	NOUN
ap-1213	137	13	∩	∩	NOUN
ap-1213	137	14	∩	∩	NOUN
ap-1213	137	15	e	e	NOUN
ap-1213	137	16	′	′	NOUN
ap-1213	137	17	⊂	⊂	X
ap-1213	137	18	o′	o′	X
ap-1213	138	1	c	c	X
ap-1213	138	2	⊂	⊂	PRON
ap-1213	138	3	d′	d′	X
ap-1213	138	4	lp	lp	ADP
ap-1213	138	5	⊂	⊂	PRON
ap-1213	138	6	d′	d′	NUM
ap-1213	138	7	lq	lq	ADP
ap-1213	138	8	⊂	⊂	PROPN
ap-1213	138	9	ḃ′	ḃ′	PROPN
ap-1213	138	10	⊂	⊂	PROPN
ap-1213	138	11	b′	b′	PROPN
ap-1213	138	12	⊂	⊂	X
ap-1213	138	13	s′	s′	VERB
ap-1213	138	14	⊂	⊂	X
ap-1213	138	15	d′	d′	NUM
ap-1213	138	16	where	where	SCONJ
ap-1213	138	17	in	in	ADP
ap-1213	138	18	both	both	DET
ap-1213	138	19	lines	line	NOUN
ap-1213	138	20	1	1	NUM
ap-1213	138	21	≤	≤	NOUN
ap-1213	138	22	p	p	X
ap-1213	138	23	<	<	X
ap-1213	138	24	q	q	X
ap-1213	138	25	<	<	X
ap-1213	138	26	∞.	∞.	PROPN
ap-1213	138	27	the	the	DET
ap-1213	138	28	first	first	ADJ
ap-1213	138	29	line	line	NOUN
ap-1213	138	30	denotes	denote	NOUN
ap-1213	138	31	spaces	space	NOUN
ap-1213	138	32	of	of	ADP
ap-1213	138	33	infinitely	infinitely	ADV
ap-1213	138	34	differentiable	differentiable	ADJ
ap-1213	138	35	functions	function	NOUN
ap-1213	138	36	(	(	PUNCT
ap-1213	138	37	in	in	ADP
ap-1213	138	38	general	general	ADJ
ap-1213	138	39	on	on	ADP
ap-1213	138	40	r	r	NOUN
ap-1213	138	41	n	n	CCONJ
ap-1213	138	42	,	,	PUNCT
ap-1213	138	43	but	but	CCONJ
ap-1213	138	44	here	here	ADV
ap-1213	138	45	we	we	PRON
ap-1213	138	46	restrict	restrict	VERB
ap-1213	138	47	to	to	ADP
ap-1213	138	48	r	r	NOUN
ap-1213	138	49	)	)	PUNCT
ap-1213	138	50	which	which	PRON
ap-1213	138	51	in	in	ADP
ap-1213	138	52	addition	addition	NOUN
ap-1213	138	53	satisfy	satisfy	NOUN
ap-1213	138	54	(	(	PUNCT
ap-1213	138	55	together	together	ADV
ap-1213	138	56	with	with	ADP
ap-1213	138	57	their	their	PRON
ap-1213	138	58	derivatives	derivative	NOUN
ap-1213	138	59	):	):	PUNCT
ap-1213	138	60	d	d	NOUN
ap-1213	138	61	are	be	AUX
ap-1213	138	62	of	of	ADP
ap-1213	138	63	compact	compact	ADJ
ap-1213	138	64	support	support	NOUN
ap-1213	138	65	,	,	PUNCT
ap-1213	138	66	s	s	VERB
ap-1213	138	67	is	be	AUX
ap-1213	138	68	the	the	DET
ap-1213	138	69	space	space	NOUN
ap-1213	138	70	of	of	ADP
ap-1213	138	71	fast	fast	ADJ
ap-1213	138	72	decaying	decay	VERB
ap-1213	138	73	schwartz	schwartz	NOUN
ap-1213	138	74	functions	function	NOUN
ap-1213	138	75	,	,	PUNCT
ap-1213	138	76	dlp	dlp	PROPN
ap-1213	138	77	must	must	AUX
ap-1213	138	78	also	also	ADV
ap-1213	138	79	belong	belong	VERB
ap-1213	138	80	to	to	ADP
ap-1213	138	81	lp	lp	NOUN
ap-1213	138	82	,	,	PUNCT
ap-1213	138	83	b	b	PROPN
ap-1213	138	84	≡	≡	PROPN
ap-1213	138	85	dl∞	dl∞	PROPN
ap-1213	138	86	are	be	AUX
ap-1213	138	87	bounded	bound	VERB
ap-1213	138	88	,	,	PUNCT
ap-1213	138	89	ḃ	ḃ	PROPN
ap-1213	138	90	are	be	AUX
ap-1213	138	91	both	both	PRON
ap-1213	138	92	bounded	bound	VERB
ap-1213	138	93	and	and	CCONJ
ap-1213	138	94	possess	possess	VERB
ap-1213	138	95	a	a	DET
ap-1213	138	96	finite	finite	ADJ
ap-1213	138	97	limit	limit	NOUN
ap-1213	138	98	at	at	ADP
ap-1213	138	99	infinity	infinity	NOUN
ap-1213	138	100	,	,	PUNCT
ap-1213	138	101	om	om	PROPN
ap-1213	138	102	can	can	AUX
ap-1213	138	103	not	not	PART
ap-1213	138	104	grow	grow	VERB
ap-1213	138	105	too	too	ADV
ap-1213	138	106	fast	fast	ADV
ap-1213	138	107	,	,	PUNCT
ap-1213	138	108	but	but	CCONJ
ap-1213	138	109	finally	finally	ADV
ap-1213	138	110	e	e	AUX
ap-1213	138	111	have	have	VERB
ap-1213	138	112	no	no	DET
ap-1213	138	113	restrictions	restriction	NOUN
ap-1213	138	114	on	on	ADP
ap-1213	138	115	their	their	PRON
ap-1213	138	116	growth	growth	NOUN
ap-1213	138	117	.	.	PUNCT
ap-1213	139	1	on	on	ADP
ap-1213	139	2	the	the	DET
ap-1213	139	3	second	second	ADJ
ap-1213	139	4	line	line	NOUN
ap-1213	139	5	we	we	PRON
ap-1213	139	6	have	have	VERB
ap-1213	139	7	spaces	space	NOUN
ap-1213	139	8	of	of	ADP
ap-1213	139	9	distributions	distribution	NOUN
ap-1213	139	10	that	that	PRON
ap-1213	139	11	are	be	AUX
ap-1213	139	12	defined	define	VERB
ap-1213	139	13	as	as	ADP
ap-1213	139	14	continuous	continuous	ADJ
ap-1213	139	15	linear	linear	ADJ
ap-1213	139	16	functionals	functional	NOUN
ap-1213	139	17	on	on	ADP
ap-1213	139	18	some	some	DET
ap-1213	139	19	function	function	NOUN
ap-1213	139	20	space	space	NOUN
ap-1213	139	21	from	from	ADP
ap-1213	139	22	the	the	DET
ap-1213	139	23	first	first	ADJ
ap-1213	139	24	line	line	NOUN
ap-1213	139	25	(	(	PUNCT
ap-1213	139	26	in	in	ADP
ap-1213	139	27	the	the	DET
ap-1213	139	28	case	case	NOUN
ap-1213	139	29	of	of	ADP
ap-1213	139	30	o′	o′	PROPN
ap-1213	139	31	c	c	NOUN
ap-1213	139	32	and	and	CCONJ
ap-1213	139	33	b′	b′	NUM
ap-1213	139	34	with	with	ADP
ap-1213	139	35	an	an	DET
ap-1213	139	36	additional	additional	ADJ
ap-1213	139	37	restriction	restriction	NOUN
ap-1213	139	38	)	)	PUNCT
ap-1213	139	39	.	.	PUNCT
ap-1213	140	1	for	for	ADP
ap-1213	140	2	example	example	NOUN
ap-1213	140	3	,	,	PUNCT
ap-1213	140	4	e	e	NOUN
ap-1213	140	5	′	′	NOUN
ap-1213	140	6	is	be	AUX
ap-1213	140	7	dual	dual	ADJ
ap-1213	140	8	to	to	ADP
ap-1213	140	9	e	e	NOUN
ap-1213	140	10	and	and	CCONJ
ap-1213	140	11	represents	represent	VERB
ap-1213	140	12	the	the	DET
ap-1213	140	13	space	space	NOUN
ap-1213	140	14	of	of	ADP
ap-1213	140	15	distributions	distribution	NOUN
ap-1213	140	16	with	with	ADP
ap-1213	140	17	compact	compact	ADJ
ap-1213	140	18	support	support	NOUN
ap-1213	140	19	.	.	PUNCT
ap-1213	141	1	o′	o′	X
ap-1213	142	1	c	c	NOUN
ap-1213	142	2	are	be	AUX
ap-1213	142	3	rapidly	rapidly	ADV
ap-1213	142	4	decaying	decay	VERB
ap-1213	142	5	distributions	distribution	NOUN
ap-1213	142	6	,	,	PUNCT
ap-1213	142	7	i.e.	i.e.	X
ap-1213	142	8	those	those	PRON
ap-1213	142	9	which	which	PRON
ap-1213	142	10	together	together	ADV
ap-1213	142	11	with	with	ADP
ap-1213	142	12	all	all	DET
ap-1213	142	13	their	their	PRON
ap-1213	142	14	derivatives	derivative	NOUN
ap-1213	142	15	are	be	AUX
ap-1213	142	16	bounded	bound	VERB
ap-1213	142	17	even	even	ADV
ap-1213	142	18	after	after	ADP
ap-1213	142	19	multiplication	multiplication	NOUN
ap-1213	142	20	with	with	ADP
ap-1213	142	21	(	(	PUNCT
ap-1213	142	22	1	1	NUM
ap-1213	142	23	+	+	CCONJ
ap-1213	142	24	x2)k/2	x2)k/2	VERB
ap-1213	142	25	for	for	ADP
ap-1213	142	26	all	all	DET
ap-1213	142	27	k	k	PROPN
ap-1213	142	28	∈	∈	PROPN
ap-1213	142	29	r.	r.	NOUN
ap-1213	142	30	the	the	DET
ap-1213	142	31	space	space	NOUN
ap-1213	142	32	d′	d′	NUM
ap-1213	142	33	l1	l1	PROPN
ap-1213	142	34	is	be	AUX
ap-1213	142	35	dual	dual	ADJ
ap-1213	142	36	to	to	ADP
ap-1213	142	37	ḃ.	ḃ.	NUM
ap-1213	142	38	d′	d′	X
ap-1213	142	39	lp	lp	NOUN
ap-1213	142	40	for	for	ADP
ap-1213	142	41	p	p	PROPN
ap-1213	142	42	∈	∈	PROPN
ap-1213	142	43	(	(	PUNCT
ap-1213	142	44	1,∞	1,∞	NUM
ap-1213	142	45	)	)	PUNCT
ap-1213	142	46	are	be	AUX
ap-1213	142	47	dual	dual	ADJ
ap-1213	142	48	to	to	PART
ap-1213	142	49	dlp′	dlp′	VERB
ap-1213	142	50	for	for	ADP
ap-1213	142	51	p′	p′	NOUN
ap-1213	142	52	=	=	SYM
ap-1213	142	53	p/(p	p/(p	PROPN
ap-1213	142	54	−	−	NOUN
ap-1213	142	55	1	1	NUM
ap-1213	142	56	)	)	PUNCT
ap-1213	142	57	.	.	PUNCT
ap-1213	143	1	a	a	DET
ap-1213	143	2	useful	useful	ADJ
ap-1213	143	3	characterization	characterization	NOUN
ap-1213	143	4	of	of	ADP
ap-1213	143	5	the	the	DET
ap-1213	143	6	d′	d′	NUM
ap-1213	143	7	lp	lp	NOUN
ap-1213	143	8	spaces	space	VERB
ap-1213	143	9	for	for	ADP
ap-1213	143	10	all	all	DET
ap-1213	143	11	1	1	NUM
ap-1213	143	12	≤	≤	NOUN
ap-1213	143	13	p	p	NOUN
ap-1213	143	14	≤	≤	NUM
ap-1213	143	15	∞	∞	NUM
ap-1213	143	16	is	be	AUX
ap-1213	143	17	that	that	SCONJ
ap-1213	143	18	they	they	PRON
ap-1213	143	19	are	be	AUX
ap-1213	143	20	finite	finite	ADJ
ap-1213	143	21	sums	sum	NOUN
ap-1213	143	22	of	of	ADP
ap-1213	143	23	derivatives	derivative	NOUN
ap-1213	143	24	of	of	ADP
ap-1213	143	25	functions	function	NOUN
ap-1213	143	26	from	from	ADP
ap-1213	143	27	lp	lp	PROPN
ap-1213	143	28	(	(	PUNCT
ap-1213	143	29	hence	hence	ADV
ap-1213	143	30	dlp	dlp	PROPN
ap-1213	143	31	⊂	⊂	PROPN
ap-1213	143	32	lp	lp	PROPN
ap-1213	143	33	⊂	⊂	X
ap-1213	143	34	d′	d′	X
ap-1213	143	35	lp	lp	ADJ
ap-1213	143	36	)	)	PUNCT
ap-1213	143	37	,	,	PUNCT
ap-1213	143	38	or	or	CCONJ
ap-1213	143	39	,	,	PUNCT
ap-1213	143	40	equivalently	equivalently	ADV
ap-1213	143	41	,	,	PUNCT
ap-1213	143	42	that	that	SCONJ
ap-1213	143	43	their	their	PRON
ap-1213	143	44	convolution	convolution	NOUN
ap-1213	143	45	with	with	ADP
ap-1213	143	46	any	any	DET
ap-1213	143	47	a	a	DET
ap-1213	143	48	∈	∈	NOUN
ap-1213	143	49	d	d	AUX
ap-1213	143	50	belongs	belong	VERB
ap-1213	143	51	to	to	ADP
ap-1213	143	52	lp	lp	PROPN
ap-1213	143	53	.	.	PUNCT
ap-1213	144	1	the	the	DET
ap-1213	144	2	space	space	NOUN
ap-1213	144	3	ḃ′	ḃ′	VERB
ap-1213	144	4	is	be	AUX
ap-1213	144	5	dual	dual	ADJ
ap-1213	144	6	to	to	PART
ap-1213	144	7	dl1	dl1	VERB
ap-1213	144	8	and	and	CCONJ
ap-1213	144	9	the	the	DET
ap-1213	144	10	distributions	distribution	NOUN
ap-1213	144	11	are	be	AUX
ap-1213	144	12	characterized	characterize	VERB
ap-1213	144	13	by	by	ADP
ap-1213	144	14	convergence	convergence	NOUN
ap-1213	144	15	towards	towards	ADP
ap-1213	144	16	infinity	infinity	NOUN
ap-1213	144	17	.	.	PUNCT
ap-1213	145	1	whereas	whereas	SCONJ
ap-1213	145	2	d	d	NOUN
ap-1213	145	3	is	be	AUX
ap-1213	145	4	dense	dense	ADJ
ap-1213	145	5	in	in	ADP
ap-1213	145	6	ḃ′	ḃ′	VERB
ap-1213	145	7	,	,	PUNCT
ap-1213	145	8	it	it	PRON
ap-1213	145	9	is	be	AUX
ap-1213	145	10	not	not	PART
ap-1213	145	11	dense	dense	ADJ
ap-1213	145	12	in	in	ADP
ap-1213	145	13	b′	b′	ADJ
ap-1213	145	14	≡	≡	PROPN
ap-1213	145	15	d′	d′	X
ap-1213	145	16	l∞	l∞	NOUN
ap-1213	145	17	,	,	PUNCT
ap-1213	145	18	the	the	DET
ap-1213	145	19	space	space	NOUN
ap-1213	145	20	of	of	ADP
ap-1213	145	21	bounded	bounded	ADJ
ap-1213	145	22	distributions	distribution	NOUN
ap-1213	145	23	.	.	PUNCT
ap-1213	146	1	s′	s′	PROPN
ap-1213	146	2	is	be	AUX
ap-1213	146	3	the	the	DET
ap-1213	146	4	well	well	ADV
ap-1213	146	5	known	know	VERB
ap-1213	146	6	schwartz	schwartz	NOUN
ap-1213	146	7	space	space	NOUN
ap-1213	146	8	of	of	ADP
ap-1213	146	9	tempered	temper	VERB
ap-1213	146	10	distributions	distribution	NOUN
ap-1213	146	11	(	(	PUNCT
ap-1213	146	12	those	those	PRON
ap-1213	146	13	with	with	ADP
ap-1213	146	14	at	at	ADP
ap-1213	146	15	most	most	ADJ
ap-1213	146	16	polynomial	polynomial	ADJ
ap-1213	146	17	growth	growth	NOUN
ap-1213	146	18	)	)	PUNCT
ap-1213	146	19	dual	dual	ADV
ap-1213	146	20	to	to	ADP
ap-1213	146	21	s	s	NUM
ap-1213	146	22	,	,	PUNCT
ap-1213	146	23	and	and	CCONJ
ap-1213	146	24	finally	finally	ADV
ap-1213	146	25	d′	d′	PRON
ap-1213	146	26	is	be	AUX
ap-1213	146	27	the	the	DET
ap-1213	146	28	biggest	big	ADJ
ap-1213	146	29	space	space	NOUN
ap-1213	146	30	of	of	ADP
ap-1213	146	31	all	all	DET
ap-1213	146	32	distributions	distribution	NOUN
ap-1213	146	33	dual	dual	ADJ
ap-1213	146	34	to	to	AUX
ap-1213	146	35	d.	d.	VERB
ap-1213	146	36	6a	6a	NOUN
ap-1213	146	37	much	much	ADV
ap-1213	146	38	broader	broad	ADJ
ap-1213	146	39	class	class	NOUN
ap-1213	146	40	of	of	ADP
ap-1213	146	41	interesting	interesting	ADJ
ap-1213	146	42	non	non	ADJ
ap-1213	146	43	-	-	ADJ
ap-1213	146	44	geometric	geometric	ADJ
ap-1213	146	45	states	state	NOUN
ap-1213	146	46	has	have	AUX
ap-1213	146	47	been	be	AUX
ap-1213	146	48	considered	consider	VERB
ap-1213	146	49	recently	recently	ADV
ap-1213	146	50	by	by	ADP
ap-1213	146	51	erler	erler	NOUN
ap-1213	146	52	[	[	X
ap-1213	146	53	16	16	NUM
ap-1213	146	54	]	]	PUNCT
ap-1213	146	55	,	,	PUNCT
ap-1213	146	56	inspired	inspire	VERB
ap-1213	146	57	by	by	ADP
ap-1213	146	58	rastelli	rastelli	PROPN
ap-1213	146	59	[	[	X
ap-1213	146	60	17	17	NUM
ap-1213	146	61	]	]	PUNCT
ap-1213	146	62	.	.	PUNCT
ap-1213	147	1	105	105	NUM
ap-1213	147	2	acta	acta	PROPN
ap-1213	147	3	polytechnica	polytechnica	PROPN
ap-1213	147	4	vol	vol	NOUN
ap-1213	147	5	.	.	PROPN
ap-1213	148	1	50	50	NUM
ap-1213	148	2	no	no	NOUN
ap-1213	148	3	.	.	PUNCT
ap-1213	149	1	3/2010	3/2010	NUM
ap-1213	149	2	after	after	ADP
ap-1213	149	3	this	this	DET
ap-1213	149	4	little	little	ADJ
ap-1213	149	5	exposé	exposé	ADJ
ap-1213	149	6	,	,	PUNCT
ap-1213	149	7	we	we	PRON
ap-1213	149	8	are	be	AUX
ap-1213	149	9	ready	ready	ADJ
ap-1213	149	10	to	to	PART
ap-1213	149	11	answer	answer	VERB
ap-1213	149	12	the	the	DET
ap-1213	149	13	question	question	NOUN
ap-1213	149	14	which	which	DET
ap-1213	149	15	space	space	NOUN
ap-1213	149	16	should	should	AUX
ap-1213	149	17	f(α	f(α	VERB
ap-1213	149	18	)	)	PUNCT
ap-1213	149	19	in	in	ADP
ap-1213	149	20	(	(	PUNCT
ap-1213	149	21	5.19	5.19	NUM
ap-1213	149	22	)	)	PUNCT
ap-1213	149	23	belong	belong	VERB
ap-1213	149	24	to	to	ADP
ap-1213	149	25	.	.	PUNCT
ap-1213	150	1	let	let	VERB
ap-1213	150	2	us	we	PRON
ap-1213	150	3	define	define	VERB
ap-1213	150	4	geometric	geometric	ADJ
ap-1213	150	5	states	state	NOUN
ap-1213	150	6	as	as	ADP
ap-1213	150	7	those	those	PRON
ap-1213	150	8	for	for	ADP
ap-1213	150	9	which	which	PRON
ap-1213	150	10	f	f	PROPN
ap-1213	150	11	is	be	AUX
ap-1213	150	12	a	a	DET
ap-1213	150	13	laplace	laplace	NOUN
ap-1213	150	14	transformable	transformable	ADJ
ap-1213	150	15	distribution	distribution	NOUN
ap-1213	150	16	,	,	PUNCT
ap-1213	150	17	i.e.	i.e.	X
ap-1213	150	18	f	f	PROPN
ap-1213	150	19	∈	∈	PROPN
ap-1213	150	20	d′	d′	PROPN
ap-1213	150	21	,	,	PUNCT
ap-1213	150	22	but	but	CCONJ
ap-1213	150	23	such	such	ADJ
ap-1213	150	24	that	that	SCONJ
ap-1213	150	25	there	there	PRON
ap-1213	150	26	exists	exist	VERB
ap-1213	150	27	ξ	ξ	PROPN
ap-1213	150	28	,	,	PUNCT
ap-1213	150	29	for	for	ADP
ap-1213	150	30	which	which	PRON
ap-1213	150	31	e−ξαf	e−ξαf	NOUN
ap-1213	150	32	∈	∈	PROPN
ap-1213	151	1	s′.	s′.	X
ap-1213	152	1	we	we	PRON
ap-1213	152	2	could	could	AUX
ap-1213	152	3	perhaps	perhaps	ADV
ap-1213	152	4	have	have	AUX
ap-1213	152	5	been	be	AUX
ap-1213	152	6	more	more	ADV
ap-1213	152	7	generous	generous	ADJ
ap-1213	152	8	and	and	CCONJ
ap-1213	152	9	have	have	AUX
ap-1213	152	10	kept	keep	VERB
ap-1213	152	11	only	only	ADV
ap-1213	152	12	the	the	DET
ap-1213	152	13	f	f	PROPN
ap-1213	152	14	∈	∈	PROPN
ap-1213	152	15	d′	d′	NUM
ap-1213	152	16	condition	condition	NOUN
ap-1213	152	17	,	,	PUNCT
ap-1213	152	18	but	but	CCONJ
ap-1213	152	19	such	such	ADJ
ap-1213	152	20	states	state	NOUN
ap-1213	152	21	would	would	AUX
ap-1213	152	22	be	be	AUX
ap-1213	152	23	even	even	ADV
ap-1213	152	24	more	more	ADV
ap-1213	152	25	meaningless	meaningless	ADJ
ap-1213	152	26	from	from	ADP
ap-1213	152	27	the	the	DET
ap-1213	152	28	string	string	NOUN
ap-1213	152	29	field	field	NOUN
ap-1213	152	30	perspective	perspective	NOUN
ap-1213	152	31	.	.	PUNCT
ap-1213	153	1	what	what	PRON
ap-1213	153	2	we	we	PRON
ap-1213	153	3	need	need	VERB
ap-1213	153	4	are	be	AUX
ap-1213	153	5	not	not	PART
ap-1213	153	6	the	the	DET
ap-1213	153	7	most	most	ADV
ap-1213	153	8	general	general	ADJ
ap-1213	153	9	geometric	geometric	ADJ
ap-1213	153	10	states	state	NOUN
ap-1213	153	11	,	,	PUNCT
ap-1213	153	12	but	but	CCONJ
ap-1213	153	13	more	more	ADV
ap-1213	153	14	restricted	restricted	ADJ
ap-1213	153	15	ones	one	NOUN
ap-1213	153	16	.	.	PUNCT
ap-1213	154	1	let	let	VERB
ap-1213	154	2	us	we	PRON
ap-1213	154	3	define	define	VERB
ap-1213	154	4	a	a	DET
ap-1213	154	5	space	space	NOUN
ap-1213	154	6	of	of	ADP
ap-1213	154	7	l0	l0	NOUN
ap-1213	154	8	-	-	PUNCT
ap-1213	154	9	safe	safe	ADJ
ap-1213	154	10	geometric	geometric	ADJ
ap-1213	154	11	string	string	NOUN
ap-1213	154	12	field	field	NOUN
ap-1213	154	13	functions	function	NOUN
ap-1213	154	14	f	f	X
ap-1213	154	15	(	(	PUNCT
ap-1213	154	16	k	k	NOUN
ap-1213	154	17	)	)	PUNCT
ap-1213	154	18	to	to	PART
ap-1213	154	19	be	be	AUX
ap-1213	154	20	those	those	PRON
ap-1213	154	21	for	for	ADP
ap-1213	154	22	which	which	PRON
ap-1213	154	23	f	f	PROPN
ap-1213	154	24	∈	∈	PROPN
ap-1213	154	25	d′	d′	NUM
ap-1213	154	26	l1	l1	PROPN
ap-1213	154	27	.	.	PUNCT
ap-1213	155	1	this	this	DET
ap-1213	155	2	conditions	condition	NOUN
ap-1213	155	3	comes	come	VERB
ap-1213	155	4	from	from	ADP
ap-1213	155	5	considering	consider	VERB
ap-1213	155	6	states	state	NOUN
ap-1213	155	7	f	f	PROPN
ap-1213	156	1	(	(	PUNCT
ap-1213	156	2	k)|i	k)|i	PROPN
ap-1213	156	3	〉	〉	PROPN
ap-1213	156	4	expanded	expand	VERB
ap-1213	156	5	in	in	ADP
ap-1213	156	6	the	the	DET
ap-1213	156	7	virasoro	virasoro	NOUN
ap-1213	156	8	basis	basis	NOUN
ap-1213	156	9	.	.	PUNCT
ap-1213	157	1	the	the	DET
ap-1213	157	2	coefficients	coefficient	NOUN
ap-1213	157	3	are	be	AUX
ap-1213	157	4	given	give	VERB
ap-1213	157	5	by	by	ADP
ap-1213	157	6	sums	sum	NOUN
ap-1213	157	7	of	of	ADP
ap-1213	157	8	integrals	integral	NOUN
ap-1213	157	9	of	of	ADP
ap-1213	157	10	the	the	DET
ap-1213	157	11	form∫	form∫	ADJ
ap-1213	157	12	∞	∞	PROPN
ap-1213	157	13	0	0	PUNCT
ap-1213	158	1	dα	dα	ADJ
ap-1213	158	2	f(α)(α	f(α)(α	NOUN
ap-1213	158	3	+	+	CCONJ
ap-1213	158	4	1)−n	1)−n	NUM
ap-1213	158	5	for	for	ADP
ap-1213	158	6	n	n	NOUN
ap-1213	158	7	=	=	SYM
ap-1213	158	8	0	0	NUM
ap-1213	158	9	,	,	PUNCT
ap-1213	158	10	2	2	NUM
ap-1213	158	11	,	,	PUNCT
ap-1213	158	12	4	4	NUM
ap-1213	158	13	,	,	PUNCT
ap-1213	158	14	.	.	PUNCT
ap-1213	158	15	.	.	PUNCT
ap-1213	158	16	.	.	PUNCT
ap-1213	159	1	for	for	SCONJ
ap-1213	159	2	these	these	DET
ap-1213	159	3	integrals	integral	NOUN
ap-1213	159	4	to	to	PART
ap-1213	159	5	be	be	AUX
ap-1213	159	6	absolutely	absolutely	ADV
ap-1213	159	7	convergent	convergent	ADJ
ap-1213	159	8	,	,	PUNCT
ap-1213	159	9	we	we	PRON
ap-1213	159	10	must	must	AUX
ap-1213	159	11	have	have	VERB
ap-1213	159	12	f	f	PROPN
ap-1213	159	13	∈	∈	PROPN
ap-1213	159	14	d′	d′	NUM
ap-1213	159	15	l1	l1	PROPN
ap-1213	159	16	.	.	PUNCT
ap-1213	160	1	this	this	DET
ap-1213	160	2	definition	definition	NOUN
ap-1213	160	3	gives	give	VERB
ap-1213	160	4	us	we	PRON
ap-1213	160	5	a	a	DET
ap-1213	160	6	very	very	ADV
ap-1213	160	7	nice	nice	ADJ
ap-1213	160	8	surprise	surprise	NOUN
ap-1213	160	9	.	.	PUNCT
ap-1213	161	1	since	since	SCONJ
ap-1213	161	2	the	the	DET
ap-1213	161	3	star	star	NOUN
ap-1213	161	4	product	product	NOUN
ap-1213	161	5	of	of	ADP
ap-1213	161	6	string	string	NOUN
ap-1213	161	7	fields	field	NOUN
ap-1213	161	8	f1(k	f1(k	NOUN
ap-1213	161	9	)	)	PUNCT
ap-1213	161	10	and	and	CCONJ
ap-1213	161	11	f2(k	f2(k	NOUN
ap-1213	161	12	)	)	PUNCT
ap-1213	161	13	is	be	AUX
ap-1213	161	14	just	just	ADV
ap-1213	161	15	a	a	DET
ap-1213	161	16	multiplication	multiplication	NOUN
ap-1213	161	17	,	,	PUNCT
ap-1213	161	18	in	in	ADP
ap-1213	161	19	terms	term	NOUN
ap-1213	161	20	of	of	ADP
ap-1213	161	21	its	its	PRON
ap-1213	161	22	inverse	inverse	NOUN
ap-1213	161	23	laplace	laplace	NOUN
ap-1213	161	24	transforms	transform	VERB
ap-1213	161	25	f1	f1	NOUN
ap-1213	161	26	and	and	CCONJ
ap-1213	161	27	f2	f2	PROPN
ap-1213	161	28	it	it	PRON
ap-1213	161	29	is	be	AUX
ap-1213	161	30	a	a	DET
ap-1213	161	31	convolution	convolution	NOUN
ap-1213	161	32	f1	f1	NOUN
ap-1213	161	33	∗	∗	NOUN
ap-1213	161	34	f2(x	f2(x	NOUN
ap-1213	161	35	)	)	PUNCT
ap-1213	161	36	=	=	SYM
ap-1213	162	1	∫	∫	PROPN
ap-1213	162	2	x	x	SYM
ap-1213	162	3	0	0	NUM
ap-1213	162	4	dyf1(y)f2(x	dyf1(y)f2(x	NOUN
ap-1213	162	5	−	−	PROPN
ap-1213	162	6	y	y	PROPN
ap-1213	162	7	)	)	PUNCT
ap-1213	162	8	(	(	PUNCT
ap-1213	162	9	defined	define	VERB
ap-1213	162	10	in	in	ADP
ap-1213	162	11	a	a	DET
ap-1213	162	12	more	more	ADV
ap-1213	162	13	sophisticated	sophisticated	ADJ
ap-1213	162	14	way	way	NOUN
ap-1213	162	15	when	when	SCONJ
ap-1213	162	16	fi	fi	NOUN
ap-1213	162	17	are	be	AUX
ap-1213	162	18	both	both	PRON
ap-1213	162	19	actual	actual	ADJ
ap-1213	162	20	distributions	distribution	NOUN
ap-1213	162	21	)	)	PUNCT
ap-1213	162	22	.	.	PUNCT
ap-1213	163	1	now	now	ADV
ap-1213	163	2	it	it	PRON
ap-1213	163	3	is	be	AUX
ap-1213	163	4	known	know	VERB
ap-1213	163	5	that	that	SCONJ
ap-1213	163	6	the	the	DET
ap-1213	163	7	space	space	NOUN
ap-1213	163	8	d′	d′	NUM
ap-1213	163	9	l1	l1	PROPN
ap-1213	163	10	is	be	AUX
ap-1213	163	11	closed	close	VERB
ap-1213	163	12	under	under	ADP
ap-1213	163	13	convolution	convolution	NOUN
ap-1213	163	14	.	.	PUNCT
ap-1213	164	1	therefore	therefore	ADV
ap-1213	164	2	the	the	DET
ap-1213	164	3	space	space	NOUN
ap-1213	164	4	of	of	ADP
ap-1213	164	5	l0	l0	NOUN
ap-1213	164	6	-	-	PUNCT
ap-1213	164	7	safe	safe	ADJ
ap-1213	164	8	geometric	geometric	ADJ
ap-1213	164	9	string	string	NOUN
ap-1213	164	10	fields	field	NOUN
ap-1213	164	11	is	be	AUX
ap-1213	164	12	closed	close	VERB
ap-1213	164	13	under	under	ADP
ap-1213	164	14	star	star	NOUN
ap-1213	164	15	multiplication	multiplication	NOUN
ap-1213	164	16	!	!	PUNCT
ap-1213	165	1	we	we	PRON
ap-1213	165	2	now	now	ADV
ap-1213	165	3	proceed	proceed	VERB
ap-1213	165	4	to	to	PART
ap-1213	165	5	define	define	VERB
ap-1213	165	6	a	a	DET
ap-1213	165	7	space	space	NOUN
ap-1213	165	8	of	of	ADP
ap-1213	165	9	l0	l0	NOUN
ap-1213	165	10	-	-	PUNCT
ap-1213	165	11	safe	safe	ADJ
ap-1213	165	12	geometric	geometric	ADJ
ap-1213	165	13	string	string	NOUN
ap-1213	165	14	field	field	NOUN
ap-1213	165	15	functions	function	NOUN
ap-1213	165	16	f	f	X
ap-1213	165	17	(	(	PUNCT
ap-1213	165	18	k	k	NOUN
ap-1213	165	19	)	)	PUNCT
ap-1213	165	20	by	by	ADP
ap-1213	165	21	the	the	DET
ap-1213	165	22	condition	condition	NOUN
ap-1213	165	23	f	f	PROPN
ap-1213	165	24	∈	∈	PROPN
ap-1213	165	25	o′	o′	PROPN
ap-1213	166	1	c.	c.	NOUN
ap-1213	167	1	this	this	DET
ap-1213	167	2	condition	condition	NOUN
ap-1213	167	3	comes	come	VERB
ap-1213	167	4	from	from	ADP
ap-1213	167	5	considering	consider	VERB
ap-1213	167	6	states	state	NOUN
ap-1213	167	7	f	f	PROPN
ap-1213	168	1	(	(	PUNCT
ap-1213	168	2	k)|i	k)|i	PROPN
ap-1213	168	3	〉	〉	PROPN
ap-1213	168	4	expanded	expand	VERB
ap-1213	168	5	in	in	ADP
ap-1213	168	6	the	the	DET
ap-1213	168	7	basis	basis	NOUN
ap-1213	168	8	of	of	ADP
ap-1213	168	9	l0	l0	NOUN
ap-1213	168	10	eigenstates	eigenstate	NOUN
ap-1213	168	11	(	(	PUNCT
ap-1213	168	12	see	see	VERB
ap-1213	168	13	[	[	X
ap-1213	168	14	10	10	NUM
ap-1213	168	15	]	]	PUNCT
ap-1213	168	16	for	for	ADP
ap-1213	168	17	definition	definition	NOUN
ap-1213	168	18	)	)	PUNCT
ap-1213	168	19	,	,	PUNCT
ap-1213	168	20	or	or	CCONJ
ap-1213	168	21	equivalently	equivalently	ADV
ap-1213	168	22	from	from	ADP
ap-1213	168	23	expanding	expand	VERB
ap-1213	168	24	f	f	PROPN
ap-1213	168	25	(	(	PUNCT
ap-1213	168	26	k	k	NOUN
ap-1213	168	27	)	)	PUNCT
ap-1213	168	28	in	in	ADP
ap-1213	168	29	the	the	DET
ap-1213	168	30	l−	l−	NOUN
ap-1213	168	31	eigenstates	eigenstate	NOUN
ap-1213	168	32	(	(	PUNCT
ap-1213	168	33	see	see	VERB
ap-1213	168	34	[	[	X
ap-1213	168	35	18	18	NUM
ap-1213	168	36	]	]	NUM
ap-1213	168	37	)	)	PUNCT
ap-1213	168	38	.	.	PUNCT
ap-1213	169	1	we	we	PRON
ap-1213	169	2	demand	demand	VERB
ap-1213	169	3	that	that	SCONJ
ap-1213	169	4	∫	∫	PROPN
ap-1213	169	5	∞	∞	PROPN
ap-1213	169	6	0	0	NUM
ap-1213	170	1	dα	dα	ADP
ap-1213	170	2	f(α)αn	f(α)αn	ADV
ap-1213	170	3	for	for	ADP
ap-1213	170	4	n	n	DET
ap-1213	170	5	∈	∈	PROPN
ap-1213	170	6	n0	n0	X
ap-1213	170	7	be	be	AUX
ap-1213	170	8	absolutely	absolutely	ADV
ap-1213	170	9	convergent	convergent	ADJ
ap-1213	170	10	.	.	PUNCT
ap-1213	171	1	this	this	DET
ap-1213	171	2	forces	force	NOUN
ap-1213	171	3	f	f	PROPN
ap-1213	171	4	∈	∈	PROPN
ap-1213	171	5	o′	o′	X
ap-1213	172	1	c.	c.	PROPN
ap-1213	172	2	again	again	ADV
ap-1213	172	3	this	this	DET
ap-1213	172	4	space	space	NOUN
ap-1213	172	5	is	be	AUX
ap-1213	172	6	closed	close	VERB
ap-1213	172	7	under	under	ADP
ap-1213	172	8	convolution	convolution	NOUN
ap-1213	172	9	and	and	CCONJ
ap-1213	172	10	hence	hence	ADV
ap-1213	172	11	the	the	DET
ap-1213	172	12	space	space	NOUN
ap-1213	172	13	of	of	ADP
ap-1213	172	14	l0	l0	NOUN
ap-1213	172	15	-	-	PUNCT
ap-1213	172	16	safe	safe	ADJ
ap-1213	172	17	geometric	geometric	ADJ
ap-1213	172	18	string	string	NOUN
ap-1213	172	19	fields	field	NOUN
ap-1213	172	20	is	be	AUX
ap-1213	172	21	also	also	ADV
ap-1213	172	22	closed	close	VERB
ap-1213	172	23	under	under	ADP
ap-1213	172	24	star	star	NOUN
ap-1213	172	25	multiplication	multiplication	NOUN
ap-1213	172	26	!	!	PUNCT
ap-1213	173	1	both	both	DET
ap-1213	173	2	definitions	definition	NOUN
ap-1213	173	3	of	of	ADP
ap-1213	173	4	safe	safe	ADJ
ap-1213	173	5	string	string	NOUN
ap-1213	173	6	fields	field	NOUN
ap-1213	173	7	can	can	AUX
ap-1213	173	8	be	be	AUX
ap-1213	173	9	recast	recast	VERB
ap-1213	173	10	in	in	ADP
ap-1213	173	11	terms	term	NOUN
ap-1213	173	12	of	of	ADP
ap-1213	173	13	the	the	DET
ap-1213	173	14	properties	property	NOUN
ap-1213	173	15	of	of	ADP
ap-1213	173	16	the	the	DET
ap-1213	173	17	function	function	NOUN
ap-1213	173	18	f	f	PROPN
ap-1213	173	19	(	(	PUNCT
ap-1213	173	20	z	z	NOUN
ap-1213	173	21	)	)	PUNCT
ap-1213	174	1	=	=	NOUN
ap-1213	174	2	∫	∫	PROPN
ap-1213	174	3	∞	∞	NUM
ap-1213	174	4	0	0	NUM
ap-1213	174	5	f(α)e−αz	f(α)e−αz	PROPN
ap-1213	174	6	.	.	PROPN
ap-1213	174	7	string	string	NOUN
ap-1213	174	8	field	field	PROPN
ap-1213	174	9	function	function	NOUN
ap-1213	174	10	f	f	PROPN
ap-1213	174	11	(	(	PUNCT
ap-1213	174	12	k	k	NOUN
ap-1213	174	13	)	)	PUNCT
ap-1213	174	14	is	be	AUX
ap-1213	174	15	1	1	NUM
ap-1213	174	16	.	.	PUNCT
ap-1213	174	17	geometric	geometric	ADJ
ap-1213	174	18	if	if	SCONJ
ap-1213	175	1	and	and	CCONJ
ap-1213	175	2	only	only	ADV
ap-1213	175	3	if	if	SCONJ
ap-1213	175	4	there	there	PRON
ap-1213	175	5	exists	exist	VERB
ap-1213	175	6	ξ	ξ	PRON
ap-1213	175	7	such	such	ADJ
ap-1213	175	8	that	that	PRON
ap-1213	175	9	for	for	ADP
ap-1213	175	10	all	all	DET
ap-1213	175	11	z	z	NOUN
ap-1213	175	12	with	with	ADP
ap-1213	175	13	re	re	PROPN
ap-1213	175	14	z	z	X
ap-1213	175	15	>	>	X
ap-1213	175	16	ξ	ξ	PROPN
ap-1213	175	17	,	,	PUNCT
ap-1213	175	18	f	f	PROPN
ap-1213	175	19	(	(	PUNCT
ap-1213	175	20	z	z	NOUN
ap-1213	175	21	)	)	PUNCT
ap-1213	175	22	is	be	AUX
ap-1213	175	23	holomorphic	holomorphic	ADJ
ap-1213	175	24	and	and	CCONJ
ap-1213	175	25	|f	|f	PROPN
ap-1213	176	1	(	(	PUNCT
ap-1213	176	2	z)|	z)|	PROPN
ap-1213	176	3	is	be	AUX
ap-1213	176	4	majorized	majorize	VERB
ap-1213	176	5	(	(	PUNCT
ap-1213	176	6	i.e.	i.e.	X
ap-1213	176	7	bounded	bound	VERB
ap-1213	176	8	)	)	PUNCT
ap-1213	176	9	by	by	ADP
ap-1213	176	10	a	a	DET
ap-1213	176	11	polynomial	polynomial	NOUN
ap-1213	176	12	in	in	ADP
ap-1213	176	13	|z|	|z|	NOUN
ap-1213	176	14	.	.	PUNCT
ap-1213	177	1	2	2	NUM
ap-1213	177	2	.	.	X
ap-1213	177	3	l0	l0	NOUN
ap-1213	177	4	-	-	PUNCT
ap-1213	177	5	safe	safe	ADJ
ap-1213	177	6	geometric	geometric	ADJ
ap-1213	177	7	if	if	SCONJ
ap-1213	177	8	and	and	CCONJ
ap-1213	177	9	only	only	ADV
ap-1213	177	10	if	if	SCONJ
ap-1213	177	11	f	f	PROPN
ap-1213	177	12	(	(	PUNCT
ap-1213	177	13	z	z	NOUN
ap-1213	177	14	)	)	PUNCT
ap-1213	177	15	is	be	AUX
ap-1213	177	16	holomorphic	holomorphic	ADJ
ap-1213	177	17	for	for	ADP
ap-1213	177	18	all	all	DET
ap-1213	177	19	z	z	NOUN
ap-1213	177	20	with	with	ADP
ap-1213	177	21	re	re	NOUN
ap-1213	177	22	z	z	X
ap-1213	177	23	>	>	X
ap-1213	177	24	0	0	PUNCT
ap-1213	178	1	and	and	CCONJ
ap-1213	178	2	|f	|f	PROPN
ap-1213	178	3	(	(	PUNCT
ap-1213	178	4	z)|	z)|	PROPN
ap-1213	178	5	is	be	AUX
ap-1213	178	6	majorized	majorize	VERB
ap-1213	178	7	by	by	ADP
ap-1213	178	8	a	a	DET
ap-1213	178	9	polynomial	polynomial	NOUN
ap-1213	178	10	in	in	ADP
ap-1213	178	11	|z|	|z|	NOUN
ap-1213	178	12	for	for	ADP
ap-1213	178	13	all	all	DET
ap-1213	178	14	re	re	ADP
ap-1213	178	15	z	z	PROPN
ap-1213	178	16	≥	≥	NUM
ap-1213	178	17	0	0	NUM
ap-1213	178	18	.	.	NOUN
ap-1213	179	1	3	3	X
ap-1213	179	2	.	.	X
ap-1213	179	3	l0	l0	NOUN
ap-1213	179	4	-	-	PUNCT
ap-1213	179	5	safe	safe	ADJ
ap-1213	179	6	geometric	geometric	ADJ
ap-1213	179	7	if	if	SCONJ
ap-1213	179	8	and	and	CCONJ
ap-1213	179	9	only	only	ADV
ap-1213	179	10	if	if	SCONJ
ap-1213	179	11	f	f	PROPN
ap-1213	179	12	(	(	PUNCT
ap-1213	179	13	z	z	NOUN
ap-1213	179	14	)	)	PUNCT
ap-1213	179	15	is	be	AUX
ap-1213	179	16	holomorphic	holomorphic	ADJ
ap-1213	179	17	for	for	ADP
ap-1213	179	18	all	all	DET
ap-1213	179	19	z	z	NOUN
ap-1213	179	20	with	with	ADP
ap-1213	179	21	re	re	NOUN
ap-1213	179	22	z	z	X
ap-1213	179	23	>	>	X
ap-1213	179	24	0	0	PROPN
ap-1213	179	25	,	,	PUNCT
ap-1213	179	26	|f	|f	PROPN
ap-1213	180	1	(	(	PUNCT
ap-1213	180	2	z)|	z)|	PROPN
ap-1213	180	3	is	be	AUX
ap-1213	180	4	majorized	majorize	VERB
ap-1213	180	5	by	by	ADP
ap-1213	180	6	a	a	DET
ap-1213	180	7	polynomial	polynomial	NOUN
ap-1213	180	8	in	in	ADP
ap-1213	180	9	|z|	|z|	NOUN
ap-1213	180	10	for	for	ADP
ap-1213	180	11	all	all	DET
ap-1213	180	12	re	re	ADP
ap-1213	180	13	z	z	PROPN
ap-1213	180	14	≥	≥	NUM
ap-1213	180	15	0	0	NUM
ap-1213	180	16	,	,	PUNCT
ap-1213	180	17	and	and	CCONJ
ap-1213	180	18	f	f	PROPN
ap-1213	180	19	(	(	PUNCT
ap-1213	180	20	z	z	NOUN
ap-1213	180	21	)	)	PUNCT
ap-1213	180	22	can	can	AUX
ap-1213	180	23	be	be	AUX
ap-1213	180	24	extended	extend	VERB
ap-1213	180	25	to	to	ADP
ap-1213	180	26	a	a	DET
ap-1213	180	27	c∞	c∞	ADJ
ap-1213	180	28	function	function	NOUN
ap-1213	180	29	on	on	ADP
ap-1213	180	30	the	the	DET
ap-1213	180	31	complex	complex	ADJ
ap-1213	180	32	half	half	ADJ
ap-1213	180	33	-	-	PUNCT
ap-1213	180	34	plane	plane	NOUN
ap-1213	180	35	re	re	NOUN
ap-1213	180	36	z	z	PROPN
ap-1213	180	37	≥	≥	PROPN
ap-1213	180	38	0	0	NUM
ap-1213	180	39	.	.	PUNCT
ap-1213	181	1	the	the	DET
ap-1213	181	2	proof	proof	NOUN
ap-1213	181	3	of	of	ADP
ap-1213	181	4	the	the	DET
ap-1213	181	5	first	first	ADJ
ap-1213	181	6	statement	statement	NOUN
ap-1213	181	7	can	can	AUX
ap-1213	181	8	be	be	AUX
ap-1213	181	9	found	find	VERB
ap-1213	181	10	in	in	ADP
ap-1213	181	11	textbooks	textbook	NOUN
ap-1213	181	12	,	,	PUNCT
ap-1213	181	13	and	and	CCONJ
ap-1213	181	14	the	the	DET
ap-1213	181	15	latter	latter	ADJ
ap-1213	181	16	two	two	NUM
ap-1213	181	17	can	can	AUX
ap-1213	181	18	be	be	AUX
ap-1213	181	19	established	establish	VERB
ap-1213	181	20	by	by	ADP
ap-1213	181	21	a	a	DET
ap-1213	181	22	slight	slight	ADJ
ap-1213	181	23	modification	modification	NOUN
ap-1213	181	24	.	.	PUNCT
ap-1213	182	1	to	to	PART
ap-1213	182	2	end	end	VERB
ap-1213	182	3	this	this	DET
ap-1213	182	4	mathematical	mathematical	ADJ
ap-1213	182	5	discussion	discussion	NOUN
ap-1213	182	6	,	,	PUNCT
ap-1213	182	7	let	let	VERB
ap-1213	182	8	us	we	PRON
ap-1213	182	9	now	now	ADV
ap-1213	182	10	give	give	VERB
ap-1213	182	11	a	a	DET
ap-1213	182	12	few	few	ADJ
ap-1213	182	13	examples	example	NOUN
ap-1213	182	14	.	.	PUNCT
ap-1213	183	1	the	the	DET
ap-1213	183	2	string	string	NOUN
ap-1213	183	3	fields	field	NOUN
ap-1213	183	4	(	(	PUNCT
ap-1213	183	5	1+k)p	1+k)p	NUM
ap-1213	183	6	are	be	AUX
ap-1213	183	7	both	both	PRON
ap-1213	183	8	l0	l0	PROPN
ap-1213	183	9	and	and	CCONJ
ap-1213	183	10	l0	l0	NOUN
ap-1213	183	11	-	-	PUNCT
ap-1213	183	12	safe	safe	ADJ
ap-1213	183	13	geometric	geometric	NOUN
ap-1213	183	14	since	since	SCONJ
ap-1213	183	15	the	the	DET
ap-1213	183	16	function	function	NOUN
ap-1213	183	17	(	(	PUNCT
ap-1213	183	18	1	1	NUM
ap-1213	183	19	+	+	CCONJ
ap-1213	183	20	z)p	z)p	X
ap-1213	183	21	is	be	AUX
ap-1213	183	22	holomorphic	holomorphic	ADJ
ap-1213	183	23	for	for	ADP
ap-1213	183	24	re	re	X
ap-1213	183	25	z	z	NOUN
ap-1213	183	26	>	>	X
ap-1213	183	27	−1	−1	NOUN
ap-1213	183	28	and	and	CCONJ
ap-1213	183	29	obeys	obey	VERB
ap-1213	183	30	all	all	DET
ap-1213	183	31	the	the	DET
ap-1213	183	32	above	above	ADJ
ap-1213	183	33	conditions	condition	NOUN
ap-1213	183	34	.	.	PUNCT
ap-1213	184	1	the	the	DET
ap-1213	184	2	inverse	inverse	ADJ
ap-1213	184	3	laplace	laplace	NOUN
ap-1213	184	4	transform	transform	VERB
ap-1213	184	5	f	f	PROPN
ap-1213	184	6	∈	∈	PROPN
ap-1213	184	7	o′	o′	PUNCT
ap-1213	184	8	c	c	NOUN
ap-1213	184	9	can	can	AUX
ap-1213	184	10	be	be	AUX
ap-1213	184	11	easily	easily	ADV
ap-1213	184	12	computed	compute	VERB
ap-1213	184	13	:	:	PUNCT
ap-1213	184	14	1	1	NUM
ap-1213	184	15	γ(−p	γ(−p	NOUN
ap-1213	184	16	)	)	PUNCT
ap-1213	184	17	α−p−1e−α	α−p−1e−α	NUM
ap-1213	184	18	,	,	PUNCT
ap-1213	184	19	p	p	X
ap-1213	184	20	<	<	X
ap-1213	184	21	0	0	NUM
ap-1213	184	22	(	(	PUNCT
ap-1213	184	23	1	1	NUM
ap-1213	184	24	+	+	CCONJ
ap-1213	184	25	d	d	NOUN
ap-1213	184	26	dα	dα	ADJ
ap-1213	184	27	)	)	PUNCT
ap-1213	185	1	[	[	X
ap-1213	185	2	p]+1	p]+1	NOUN
ap-1213	185	3	·	·	PUNCT
ap-1213	185	4	[	[	PUNCT
ap-1213	185	5	1	1	NUM
ap-1213	185	6	γ([p	γ([p	PROPN
ap-1213	185	7	]	]	PUNCT
ap-1213	185	8	+	+	CCONJ
ap-1213	185	9	1−	1−	NUM
ap-1213	185	10	p	p	NOUN
ap-1213	185	11	)	)	PUNCT
ap-1213	185	12	α[p]−pe−α	α[p]−pe−α	NUM
ap-1213	185	13	]	]	PUNCT
ap-1213	185	14	,	,	PUNCT
ap-1213	185	15	p	p	X
ap-1213	185	16	>	>	X
ap-1213	185	17	0	0	NUM
ap-1213	185	18	,	,	PUNCT
ap-1213	185	19	p	p	NOUN
ap-1213	185	20	/∈	/∈	PUNCT
ap-1213	185	21	n	n	CCONJ
ap-1213	185	22	(	(	PUNCT
ap-1213	185	23	5.20	5.20	NUM
ap-1213	185	24	)	)	PUNCT
ap-1213	185	25	(	(	PUNCT
ap-1213	185	26	1	1	NUM
ap-1213	185	27	+	+	CCONJ
ap-1213	185	28	d	d	NOUN
ap-1213	185	29	dα	dα	ADJ
ap-1213	185	30	)	)	PUNCT
ap-1213	185	31	p	p	NOUN
ap-1213	185	32	δ(α	δ(α	PROPN
ap-1213	185	33	)	)	PUNCT
ap-1213	185	34	,	,	PUNCT
ap-1213	185	35	p	p	PROPN
ap-1213	185	36	∈	∈	PROPN
ap-1213	185	37	n0	n0	PROPN
ap-1213	185	38	.	.	PUNCT
ap-1213	186	1	here	here	ADV
ap-1213	186	2	[	[	X
ap-1213	186	3	p	p	X
ap-1213	186	4	]	]	X
ap-1213	186	5	denotes	denote	VERB
ap-1213	186	6	the	the	DET
ap-1213	186	7	integer	integer	NOUN
ap-1213	186	8	part	part	NOUN
ap-1213	186	9	of	of	ADP
ap-1213	186	10	p	p	NOUN
ap-1213	186	11	,	,	PUNCT
ap-1213	186	12	but	but	CCONJ
ap-1213	186	13	in	in	ADP
ap-1213	186	14	fact	fact	NOUN
ap-1213	186	15	any	any	DET
ap-1213	186	16	integer	integer	NOUN
ap-1213	186	17	greater	great	ADJ
ap-1213	186	18	than	than	SCONJ
ap-1213	186	19	that	that	PRON
ap-1213	186	20	can	can	AUX
ap-1213	186	21	be	be	AUX
ap-1213	186	22	taken	take	VERB
ap-1213	186	23	.	.	PUNCT
ap-1213	187	1	for	for	ADP
ap-1213	187	2	p	p	PROPN
ap-1213	187	3	∈	∈	PROPN
ap-1213	187	4	n0	n0	NOUN
ap-1213	187	5	the	the	DET
ap-1213	187	6	inverse	inverse	NOUN
ap-1213	187	7	laplace	laplace	NOUN
ap-1213	187	8	transform	transform	NOUN
ap-1213	187	9	actually	actually	ADV
ap-1213	187	10	belongs	belong	VERB
ap-1213	187	11	to	to	ADP
ap-1213	187	12	the	the	DET
ap-1213	187	13	smaller	small	ADJ
ap-1213	187	14	space	space	NOUN
ap-1213	187	15	e	e	NOUN
ap-1213	187	16	′	′	NOUN
ap-1213	187	17	of	of	ADP
ap-1213	187	18	distributions	distribution	NOUN
ap-1213	187	19	with	with	ADP
ap-1213	187	20	compact	compact	ADJ
ap-1213	187	21	support	support	NOUN
ap-1213	187	22	.	.	PUNCT
ap-1213	188	1	note	note	VERB
ap-1213	188	2	that	that	SCONJ
ap-1213	188	3	for	for	ADP
ap-1213	188	4	p	p	PROPN
ap-1213	188	5	>	>	X
ap-1213	188	6	0	0	PROPN
ap-1213	188	7	,	,	PUNCT
ap-1213	188	8	p	p	NOUN
ap-1213	188	9	/∈	/∈	NOUN
ap-1213	188	10	n	n	CCONJ
ap-1213	188	11	distribution	distribution	NOUN
ap-1213	188	12	theory	theory	NOUN
ap-1213	188	13	takes	take	VERB
ap-1213	188	14	care	care	NOUN
ap-1213	188	15	beautifully	beautifully	ADV
ap-1213	188	16	of	of	ADP
ap-1213	188	17	the	the	DET
ap-1213	188	18	singularities	singularity	NOUN
ap-1213	188	19	that	that	PRON
ap-1213	188	20	would	would	AUX
ap-1213	188	21	be	be	AUX
ap-1213	188	22	present	present	ADJ
ap-1213	188	23	if	if	SCONJ
ap-1213	188	24	one	one	NUM
ap-1213	188	25	thought	thought	NOUN
ap-1213	188	26	of	of	ADP
ap-1213	188	27	the	the	DET
ap-1213	188	28	inverse	inverse	NOUN
ap-1213	188	29	laplace	laplace	NOUN
ap-1213	188	30	transform	transform	NOUN
ap-1213	188	31	as	as	ADP
ap-1213	188	32	a	a	DET
ap-1213	188	33	function	function	NOUN
ap-1213	188	34	.	.	PUNCT
ap-1213	189	1	had	have	AUX
ap-1213	189	2	we	we	PRON
ap-1213	189	3	considered	consider	VERB
ap-1213	189	4	functions	function	NOUN
ap-1213	189	5	(	(	PUNCT
ap-1213	189	6	1	1	NUM
ap-1213	189	7	+	+	CCONJ
ap-1213	189	8	γ−1k)p	γ−1k)p	PROPN
ap-1213	189	9	,	,	PUNCT
ap-1213	189	10	with	with	SCONJ
ap-1213	189	11	γ	γ	PROPN
ap-1213	189	12	∈	∈	PROPN
ap-1213	189	13	r+	r+	PUNCT
ap-1213	189	14	the	the	DET
ap-1213	189	15	domain	domain	NOUN
ap-1213	189	16	of	of	ADP
ap-1213	189	17	holomorphicity	holomorphicity	NOUN
ap-1213	189	18	would	would	AUX
ap-1213	189	19	change	change	VERB
ap-1213	189	20	,	,	PUNCT
ap-1213	189	21	the	the	DET
ap-1213	189	22	maximal	maximal	ADJ
ap-1213	189	23	half	half	ADJ
ap-1213	189	24	-	-	PUNCT
ap-1213	189	25	plane	plane	NOUN
ap-1213	189	26	being	being	NOUN
ap-1213	189	27	re	re	ADP
ap-1213	189	28	z	z	NOUN
ap-1213	189	29	>	>	X
ap-1213	189	30	−γ	−γ	NOUN
ap-1213	189	31	.	.	PUNCT
ap-1213	190	1	the	the	DET
ap-1213	190	2	inverse	inverse	ADJ
ap-1213	190	3	laplace	laplace	NOUN
ap-1213	190	4	transform	transform	NOUN
ap-1213	190	5	for	for	ADP
ap-1213	190	6	these	these	DET
ap-1213	190	7	functions	function	NOUN
ap-1213	190	8	is	be	AUX
ap-1213	190	9	γf(γα	γf(γα	NOUN
ap-1213	190	10	)	)	PUNCT
ap-1213	190	11	.	.	PUNCT
ap-1213	191	1	the	the	DET
ap-1213	191	2	closer	close	ADJ
ap-1213	191	3	γ	γ	NOUN
ap-1213	191	4	is	be	AUX
ap-1213	191	5	to	to	ADP
ap-1213	191	6	zero	zero	NUM
ap-1213	191	7	,	,	PUNCT
ap-1213	191	8	the	the	DET
ap-1213	191	9	slower	slow	ADJ
ap-1213	191	10	falloff	falloff	NOUN
ap-1213	191	11	of	of	ADP
ap-1213	191	12	f	f	PRON
ap-1213	191	13	we	we	PRON
ap-1213	191	14	get	get	VERB
ap-1213	191	15	.	.	PUNCT
ap-1213	192	1	if	if	SCONJ
ap-1213	192	2	γ	γ	NOUN
ap-1213	192	3	were	be	AUX
ap-1213	192	4	taken	take	VERB
ap-1213	192	5	negative	negative	ADJ
ap-1213	192	6	,	,	PUNCT
ap-1213	192	7	the	the	DET
ap-1213	192	8	inverse	inverse	ADJ
ap-1213	192	9	laplace	laplace	NOUN
ap-1213	192	10	transform	transform	NOUN
ap-1213	192	11	would	would	AUX
ap-1213	192	12	grow	grow	VERB
ap-1213	192	13	exponentially	exponentially	ADV
ap-1213	192	14	(	(	PUNCT
ap-1213	192	15	definitely	definitely	ADV
ap-1213	192	16	not	not	PART
ap-1213	192	17	what	what	PRON
ap-1213	192	18	we	we	PRON
ap-1213	192	19	want	want	VERB
ap-1213	192	20	in	in	ADP
ap-1213	192	21	osft	osft	NOUN
ap-1213	192	22	)	)	PUNCT
ap-1213	192	23	which	which	PRON
ap-1213	192	24	would	would	AUX
ap-1213	192	25	manifest	manifest	VERB
ap-1213	192	26	itself	itself	PRON
ap-1213	192	27	as	as	ADP
ap-1213	192	28	singularities	singularity	NOUN
ap-1213	192	29	of	of	ADP
ap-1213	192	30	f	f	PROPN
ap-1213	192	31	(	(	PUNCT
ap-1213	192	32	z	z	NOUN
ap-1213	192	33	)	)	PUNCT
ap-1213	192	34	for	for	ADP
ap-1213	192	35	re	re	X
ap-1213	192	36	z	z	NOUN
ap-1213	192	37	>	>	X
ap-1213	192	38	0	0	X
ap-1213	192	39	.	.	PUNCT
ap-1213	193	1	another	another	DET
ap-1213	193	2	example	example	NOUN
ap-1213	193	3	is	be	AUX
ap-1213	193	4	the	the	DET
ap-1213	193	5	string	string	NOUN
ap-1213	193	6	field	field	NOUN
ap-1213	193	7	1/	1/	NUM
ap-1213	193	8	√	√	PROPN
ap-1213	193	9	1	1	NUM
ap-1213	194	1	+	+	SYM
ap-1213	194	2	k2	k2	ADJ
ap-1213	194	3	.	.	PUNCT
ap-1213	195	1	it	it	PRON
ap-1213	195	2	is	be	AUX
ap-1213	195	3	geometric	geometric	ADJ
ap-1213	195	4	and	and	CCONJ
ap-1213	195	5	l0	l0	NOUN
ap-1213	195	6	-	-	PUNCT
ap-1213	195	7	finite	finite	NOUN
ap-1213	195	8	but	but	CCONJ
ap-1213	195	9	neither	neither	CCONJ
ap-1213	195	10	l0	l0	PROPN
ap-1213	195	11	nor	nor	CCONJ
ap-1213	195	12	l0	l0	NOUN
ap-1213	195	13	-	-	PUNCT
ap-1213	195	14	safe	safe	ADJ
ap-1213	195	15	.	.	PUNCT
ap-1213	196	1	the	the	DET
ap-1213	196	2	inverse	inverse	ADJ
ap-1213	196	3	laplace	laplace	NOUN
ap-1213	196	4	transform	transform	NOUN
ap-1213	196	5	is	be	AUX
ap-1213	196	6	the	the	DET
ap-1213	196	7	bessel	bessel	NOUN
ap-1213	196	8	function	function	NOUN
ap-1213	196	9	j0(α	j0(α	PROPN
ap-1213	196	10	)	)	PUNCT
ap-1213	196	11	.	.	PUNCT
ap-1213	197	1	it	it	PRON
ap-1213	197	2	belongs	belong	VERB
ap-1213	197	3	to	to	ADP
ap-1213	197	4	the	the	DET
ap-1213	197	5	space	space	NOUN
ap-1213	197	6	d′	d′	X
ap-1213	197	7	lp	lp	NOUN
ap-1213	197	8	for	for	ADP
ap-1213	197	9	p	p	PROPN
ap-1213	197	10	>	>	X
ap-1213	197	11	2	2	NUM
ap-1213	197	12	.	.	PUNCT
ap-1213	198	1	the	the	DET
ap-1213	198	2	reason	reason	NOUN
ap-1213	198	3	for	for	ADP
ap-1213	198	4	l0	l0	PROPN
ap-1213	198	5	finiteness	finiteness	NOUN
ap-1213	198	6	is	be	AUX
ap-1213	198	7	the	the	DET
ap-1213	198	8	cancelations	cancelation	NOUN
ap-1213	198	9	due	due	ADP
ap-1213	198	10	to	to	ADP
ap-1213	198	11	the	the	DET
ap-1213	198	12	oscillatory	oscillatory	ADJ
ap-1213	198	13	behavior	behavior	NOUN
ap-1213	198	14	of	of	ADP
ap-1213	198	15	the	the	DET
ap-1213	198	16	bessel	bessel	ADJ
ap-1213	198	17	function	function	NOUN
ap-1213	198	18	.	.	PUNCT
ap-1213	199	1	finally	finally	ADV
ap-1213	199	2	,	,	PUNCT
ap-1213	199	3	let	let	VERB
ap-1213	199	4	us	we	PRON
ap-1213	199	5	consider	consider	VERB
ap-1213	199	6	string	string	NOUN
ap-1213	199	7	field	field	NOUN
ap-1213	200	1	√	√	ADV
ap-1213	200	2	1	1	NUM
ap-1213	200	3	+	+	SYM
ap-1213	200	4	k2	k2	ADJ
ap-1213	200	5	.	.	PUNCT
ap-1213	201	1	the	the	DET
ap-1213	201	2	inverse	inverse	ADJ
ap-1213	201	3	laplace	laplace	NOUN
ap-1213	201	4	transform	transform	NOUN
ap-1213	201	5	is	be	AUX
ap-1213	201	6	δ′(α	δ′(α	PROPN
ap-1213	201	7	)	)	PUNCT
ap-1213	202	1	+	+	CCONJ
ap-1213	202	2	1	1	NUM
ap-1213	202	3	2	2	NUM
ap-1213	202	4	(	(	PUNCT
ap-1213	202	5	j0(α	j0(α	X
ap-1213	202	6	)	)	PUNCT
ap-1213	202	7	+	+	NUM
ap-1213	202	8	j2(α	j2(α	NOUN
ap-1213	202	9	)	)	PUNCT
ap-1213	202	10	)	)	PUNCT
ap-1213	203	1	and	and	CCONJ
ap-1213	203	2	belongs	belong	VERB
ap-1213	203	3	to	to	ADP
ap-1213	203	4	d′	d′	PROPN
ap-1213	203	5	l1	l1	PROPN
ap-1213	203	6	but	but	CCONJ
ap-1213	203	7	not	not	PART
ap-1213	203	8	to	to	ADP
ap-1213	203	9	o′	o′	PROPN
ap-1213	203	10	c.	c.	PROPN
ap-1213	203	11	correspondingly	correspondingly	ADV
ap-1213	203	12	it	it	PRON
ap-1213	203	13	is	be	AUX
ap-1213	203	14	l0	l0	NOUN
ap-1213	203	15	-	-	PUNCT
ap-1213	203	16	safe	safe	ADJ
ap-1213	203	17	,	,	PUNCT
ap-1213	203	18	but	but	CCONJ
ap-1213	203	19	not	not	PART
ap-1213	203	20	l0	l0	NOUN
ap-1213	203	21	-	-	PUNCT
ap-1213	203	22	safe	safe	ADJ
ap-1213	203	23	.	.	PUNCT
ap-1213	204	1	6	6	NUM
ap-1213	204	2	examples	example	NOUN
ap-1213	204	3	let	let	VERB
ap-1213	204	4	us	we	PRON
ap-1213	204	5	go	go	VERB
ap-1213	204	6	through	through	ADP
ap-1213	204	7	some	some	PRON
ap-1213	204	8	of	of	ADP
ap-1213	204	9	the	the	DET
ap-1213	204	10	simplest	simple	ADJ
ap-1213	204	11	examples	example	NOUN
ap-1213	204	12	of	of	ADP
ap-1213	204	13	osft	osft	ADJ
ap-1213	204	14	algebraic	algebraic	ADJ
ap-1213	204	15	solutions	solution	NOUN
ap-1213	204	16	of	of	ADP
ap-1213	204	17	the	the	DET
ap-1213	204	18	form	form	NOUN
ap-1213	204	19	ψ	ψ	X
ap-1213	204	20	=	=	X
ap-1213	204	21	fc	fc	PROPN
ap-1213	204	22	kb	kb	PROPN
ap-1213	204	23	1−	1−	NUM
ap-1213	204	24	f	f	PROPN
ap-1213	204	25	2	2	NUM
ap-1213	204	26	cf	cf	NOUN
ap-1213	204	27	in	in	ADP
ap-1213	204	28	more	more	ADJ
ap-1213	204	29	detail	detail	NOUN
ap-1213	204	30	,	,	PUNCT
ap-1213	204	31	and	and	CCONJ
ap-1213	204	32	let	let	VERB
ap-1213	204	33	us	we	PRON
ap-1213	204	34	try	try	VERB
ap-1213	204	35	to	to	PART
ap-1213	204	36	see	see	VERB
ap-1213	204	37	what	what	PRON
ap-1213	204	38	the	the	DET
ap-1213	204	39	generalities	generality	NOUN
ap-1213	204	40	of	of	ADP
ap-1213	204	41	the	the	DET
ap-1213	204	42	previous	previous	ADJ
ap-1213	204	43	section	section	NOUN
ap-1213	204	44	tell	tell	VERB
ap-1213	204	45	us	we	PRON
ap-1213	204	46	.	.	PUNCT
ap-1213	205	1	let	let	VERB
ap-1213	205	2	us	we	PRON
ap-1213	205	3	remind	remind	VERB
ap-1213	205	4	106	106	NUM
ap-1213	205	5	acta	acta	PROPN
ap-1213	205	6	polytechnica	polytechnica	PROPN
ap-1213	205	7	vol	vol	NOUN
ap-1213	205	8	.	.	PROPN
ap-1213	206	1	50	50	NUM
ap-1213	206	2	no	no	NOUN
ap-1213	206	3	.	.	PUNCT
ap-1213	207	1	3/2010	3/2010	NUM
ap-1213	207	2	the	the	DET
ap-1213	207	3	reader	reader	NOUN
ap-1213	207	4	of	of	ADP
ap-1213	207	5	the	the	DET
ap-1213	207	6	definition	definition	NOUN
ap-1213	207	7	f̃	f̃	PROPN
ap-1213	207	8	≡	≡	PROPN
ap-1213	207	9	k/(1−	k/(1−	PROPN
ap-1213	207	10	f	f	PROPN
ap-1213	207	11	2	2	NUM
ap-1213	207	12	)	)	PUNCT
ap-1213	207	13	in	in	ADP
ap-1213	207	14	terms	term	NOUN
ap-1213	207	15	of	of	ADP
ap-1213	207	16	which	which	PRON
ap-1213	207	17	ψ	ψ	X
ap-1213	207	18	=	=	SYM
ap-1213	207	19	fcbf̃	fcbf̃	PROPN
ap-1213	207	20	cf	cf	NOUN
ap-1213	207	21	and	and	CCONJ
ap-1213	207	22	the	the	DET
ap-1213	207	23	homotopy	homotopy	NOUN
ap-1213	207	24	operator	operator	NOUN
ap-1213	207	25	is	be	AUX
ap-1213	207	26	a	a	DET
ap-1213	207	27	=	=	NOUN
ap-1213	207	28	f̃−1b	f̃−1b	PROPN
ap-1213	207	29	.	.	PUNCT
ap-1213	208	1	•	•	NUM
ap-1213	208	2	f	f	PROPN
ap-1213	208	3	(	(	PUNCT
ap-1213	208	4	k	k	NOUN
ap-1213	208	5	)	)	PUNCT
ap-1213	208	6	=	=	SYM
ap-1213	208	7	a	a	PRON
ap-1213	208	8	,	,	PUNCT
ap-1213	208	9	a	a	DET
ap-1213	208	10	�	�	NOUN
ap-1213	208	11	=	=	SYM
ap-1213	208	12	1	1	NUM
ap-1213	208	13	the	the	DET
ap-1213	208	14	solution	solution	NOUN
ap-1213	208	15	can	can	AUX
ap-1213	208	16	be	be	AUX
ap-1213	208	17	simplified	simplify	VERB
ap-1213	208	18	as	as	ADP
ap-1213	208	19	ψ	ψ	NOUN
ap-1213	208	20	=	=	PROPN
ap-1213	208	21	a2	a2	PROPN
ap-1213	208	22	1−	1−	NUM
ap-1213	208	23	a2	a2	PROPN
ap-1213	208	24	·	·	PUNCT
ap-1213	208	25	q(bc	q(bc	NUM
ap-1213	208	26	)	)	PUNCT
ap-1213	208	27	.	.	PUNCT
ap-1213	209	1	for	for	ADP
ap-1213	209	2	this	this	DET
ap-1213	209	3	object	object	NOUN
ap-1213	209	4	both	both	PRON
ap-1213	209	5	f/(1	f/(1	NOUN
ap-1213	209	6	−	−	PROPN
ap-1213	209	7	f	f	NOUN
ap-1213	209	8	2	2	NUM
ap-1213	209	9	)	)	PUNCT
ap-1213	209	10	=	=	PUNCT
ap-1213	209	11	a/(1−	a/(1−	PROPN
ap-1213	209	12	a2	a2	PROPN
ap-1213	209	13	)	)	PUNCT
ap-1213	209	14	and	and	CCONJ
ap-1213	209	15	f̃	f̃	PROPN
ap-1213	209	16	=	=	SYM
ap-1213	209	17	k	k	PROPN
ap-1213	209	18	1−	1−	NUM
ap-1213	209	19	a2	a2	PROPN
ap-1213	209	20	are	be	AUX
ap-1213	209	21	regular	regular	ADJ
ap-1213	209	22	,	,	PUNCT
ap-1213	209	23	the	the	DET
ap-1213	209	24	solution	solution	NOUN
ap-1213	209	25	is	be	AUX
ap-1213	209	26	therefore	therefore	ADV
ap-1213	209	27	a	a	DET
ap-1213	209	28	pure	pure	ADJ
ap-1213	209	29	gauge	gauge	NOUN
ap-1213	209	30	and	and	CCONJ
ap-1213	209	31	is	be	AUX
ap-1213	209	32	thus	thus	ADV
ap-1213	209	33	the	the	DET
ap-1213	209	34	perturbative	perturbative	ADJ
ap-1213	209	35	vacuum	vacuum	NOUN
ap-1213	209	36	.	.	PUNCT
ap-1213	210	1	the	the	PRON
ap-1213	210	2	would	would	AUX
ap-1213	210	3	be	be	AUX
ap-1213	210	4	homotopy	homotopy	NOUN
ap-1213	210	5	operator	operator	NOUN
ap-1213	210	6	a	a	DET
ap-1213	210	7	=	=	X
ap-1213	210	8	(	(	PUNCT
ap-1213	210	9	1	1	NUM
ap-1213	210	10	−	−	NOUN
ap-1213	210	11	a2)b	a2)b	NOUN
ap-1213	210	12	/	/	SYM
ap-1213	210	13	k	k	PROPN
ap-1213	210	14	is	be	AUX
ap-1213	210	15	singular	singular	ADJ
ap-1213	210	16	.	.	PUNCT
ap-1213	211	1	this	this	PRON
ap-1213	211	2	is	be	AUX
ap-1213	211	3	so	so	ADV
ap-1213	211	4	,	,	PUNCT
ap-1213	211	5	because	because	SCONJ
ap-1213	211	6	the	the	DET
ap-1213	211	7	inverse	inverse	NOUN
ap-1213	211	8	laplace	laplace	NOUN
ap-1213	211	9	transform	transform	NOUN
ap-1213	211	10	of	of	ADP
ap-1213	211	11	1	1	NUM
ap-1213	211	12	/	/	SYM
ap-1213	211	13	z	z	NOUN
ap-1213	211	14	is	be	AUX
ap-1213	211	15	1	1	NUM
ap-1213	211	16	(	(	PUNCT
ap-1213	211	17	when	when	SCONJ
ap-1213	211	18	restricted	restrict	VERB
ap-1213	211	19	to	to	ADP
ap-1213	211	20	r+	r+	NOUN
ap-1213	211	21	)	)	PUNCT
ap-1213	211	22	which	which	PRON
ap-1213	211	23	does	do	AUX
ap-1213	211	24	not	not	PART
ap-1213	211	25	belong	belong	VERB
ap-1213	211	26	to	to	ADP
ap-1213	211	27	neither	neither	CCONJ
ap-1213	211	28	o′	o′	NOUN
ap-1213	211	29	c	c	NOUN
ap-1213	211	30	,	,	PUNCT
ap-1213	211	31	nor	nor	CCONJ
ap-1213	211	32	d′	d′	NUM
ap-1213	211	33	l1	l1	PROPN
ap-1213	211	34	.	.	PUNCT
ap-1213	212	1	•	•	NUM
ap-1213	212	2	f	f	PROPN
ap-1213	212	3	(	(	PUNCT
ap-1213	212	4	k	k	NOUN
ap-1213	212	5	)	)	PUNCT
ap-1213	212	6	=	=	SYM
ap-1213	213	1	√	√	PROPN
ap-1213	213	2	1−	1−	NUM
ap-1213	213	3	βk	βk	NOUN
ap-1213	213	4	,	,	PUNCT
ap-1213	213	5	β	β	X
ap-1213	213	6	�	�	PROPN
ap-1213	213	7	=	=	SYM
ap-1213	213	8	0	0	PUNCT
ap-1213	213	9	the	the	DET
ap-1213	213	10	solution	solution	NOUN
ap-1213	213	11	is	be	AUX
ap-1213	213	12	geometric	geometric	ADJ
ap-1213	213	13	only	only	ADV
ap-1213	213	14	for	for	ADP
ap-1213	213	15	β	β	X
ap-1213	213	16	<	<	X
ap-1213	213	17	0	0	NUM
ap-1213	213	18	,	,	PUNCT
ap-1213	213	19	but	but	CCONJ
ap-1213	213	20	formally	formally	ADV
ap-1213	213	21	for	for	ADP
ap-1213	213	22	all	all	DET
ap-1213	213	23	values	value	NOUN
ap-1213	213	24	one	one	NUM
ap-1213	213	25	obtains	obtain	VERB
ap-1213	213	26	ψ	ψ	NOUN
ap-1213	213	27	=	=	NOUN
ap-1213	213	28	√	√	ADJ
ap-1213	213	29	1−	1−	NUM
ap-1213	213	30	βkβ−1c	βkβ−1c	NOUN
ap-1213	213	31	√	√	PROPN
ap-1213	213	32	1−	1−	NUM
ap-1213	213	33	βk	βk	NOUN
ap-1213	213	34	.	.	PUNCT
ap-1213	214	1	this	this	PRON
ap-1213	214	2	is	be	AUX
ap-1213	214	3	nothing	nothing	PRON
ap-1213	214	4	but	but	SCONJ
ap-1213	214	5	a	a	DET
ap-1213	214	6	real	real	ADJ
ap-1213	214	7	form	form	NOUN
ap-1213	214	8	of	of	ADP
ap-1213	214	9	the	the	DET
ap-1213	214	10	solution	solution	NOUN
ap-1213	214	11	(	(	PUNCT
ap-1213	214	12	4.12	4.12	NUM
ap-1213	214	13	)	)	PUNCT
ap-1213	214	14	with	with	ADP
ap-1213	214	15	the	the	DET
ap-1213	214	16	identification	identification	NOUN
ap-1213	214	17	β	β	NOUN
ap-1213	214	18	=	=	SYM
ap-1213	214	19	α−1	α−1	PROPN
ap-1213	214	20	.	.	PUNCT
ap-1213	215	1	for	for	ADP
ap-1213	215	2	this	this	DET
ap-1213	215	3	solution	solution	NOUN
ap-1213	215	4	both	both	CCONJ
ap-1213	215	5	f̃	f̃	PROPN
ap-1213	215	6	=	=	SYM
ap-1213	215	7	β−1	β−1	PUNCT
ap-1213	215	8	and	and	CCONJ
ap-1213	215	9	the	the	DET
ap-1213	215	10	homotopy	homotopy	NOUN
ap-1213	215	11	operator	operator	NOUN
ap-1213	215	12	a	a	PRON
ap-1213	215	13	=	=	X
ap-1213	215	14	βb	βb	ADJ
ap-1213	215	15	are	be	AUX
ap-1213	215	16	very	very	ADV
ap-1213	215	17	simple	simple	ADJ
ap-1213	215	18	and	and	CCONJ
ap-1213	215	19	belong	belong	VERB
ap-1213	215	20	to	to	ADP
ap-1213	215	21	our	our	PRON
ap-1213	215	22	l0	l0	NOUN
ap-1213	215	23	and	and	CCONJ
ap-1213	215	24	l0	l0	NOUN
ap-1213	215	25	-	-	PUNCT
ap-1213	215	26	safe	safe	ADJ
ap-1213	215	27	spaces	space	NOUN
ap-1213	215	28	.	.	PUNCT
ap-1213	216	1	thanks	thank	NOUN
ap-1213	216	2	to	to	ADP
ap-1213	216	3	the	the	DET
ap-1213	216	4	vanishing	vanish	VERB
ap-1213	216	5	cohomology	cohomology	NOUN
ap-1213	216	6	around	around	ADP
ap-1213	216	7	the	the	DET
ap-1213	216	8	vacuum	vacuum	NOUN
ap-1213	216	9	,	,	PUNCT
ap-1213	216	10	it	it	PRON
ap-1213	216	11	is	be	AUX
ap-1213	216	12	believed	believe	VERB
ap-1213	216	13	to	to	PART
ap-1213	216	14	represent	represent	VERB
ap-1213	216	15	the	the	DET
ap-1213	216	16	tachyon	tachyon	NOUN
ap-1213	216	17	vacuum	vacuum	NOUN
ap-1213	216	18	(	(	PUNCT
ap-1213	216	19	it	it	PRON
ap-1213	216	20	can	can	AUX
ap-1213	216	21	also	also	ADV
ap-1213	216	22	be	be	AUX
ap-1213	216	23	shown	show	VERB
ap-1213	216	24	to	to	PART
ap-1213	216	25	be	be	AUX
ap-1213	216	26	formally	formally	ADV
ap-1213	216	27	gauge	gauge	VERB
ap-1213	216	28	equivalent	equivalent	ADJ
ap-1213	216	29	to	to	ADP
ap-1213	216	30	it	it	PRON
ap-1213	216	31	)	)	PUNCT
ap-1213	217	1	but	but	CCONJ
ap-1213	217	2	we	we	PRON
ap-1213	217	3	have	have	AUX
ap-1213	217	4	not	not	PART
ap-1213	217	5	yet	yet	ADV
ap-1213	217	6	succeeded	succeed	VERB
ap-1213	217	7	in	in	ADP
ap-1213	217	8	computing	compute	VERB
ap-1213	217	9	its	its	PRON
ap-1213	217	10	energy	energy	NOUN
ap-1213	217	11	.	.	PUNCT
ap-1213	218	1	the	the	DET
ap-1213	218	2	reason	reason	NOUN
ap-1213	218	3	for	for	ADP
ap-1213	218	4	the	the	DET
ap-1213	218	5	difficulty	difficulty	NOUN
ap-1213	218	6	is	be	AUX
ap-1213	218	7	that	that	SCONJ
ap-1213	218	8	the	the	DET
ap-1213	218	9	string	string	NOUN
ap-1213	218	10	field	field	NOUN
ap-1213	218	11	is	be	AUX
ap-1213	218	12	too	too	ADV
ap-1213	218	13	identity	identity	NOUN
ap-1213	218	14	like	like	ADP
ap-1213	218	15	and	and	CCONJ
ap-1213	218	16	gives	give	VERB
ap-1213	218	17	rise	rise	NOUN
ap-1213	218	18	to	to	ADP
ap-1213	218	19	divergences	divergence	NOUN
ap-1213	218	20	in	in	ADP
ap-1213	218	21	the	the	DET
ap-1213	218	22	energy	energy	NOUN
ap-1213	218	23	correlator	correlator	NOUN
ap-1213	218	24	.	.	PUNCT
ap-1213	219	1	perhaps	perhaps	ADV
ap-1213	219	2	rephrasing	rephrase	VERB
ap-1213	219	3	the	the	DET
ap-1213	219	4	problem	problem	NOUN
ap-1213	219	5	in	in	ADP
ap-1213	219	6	terms	term	NOUN
ap-1213	219	7	of	of	ADP
ap-1213	219	8	distribution	distribution	NOUN
ap-1213	219	9	theory	theory	NOUN
ap-1213	219	10	could	could	AUX
ap-1213	219	11	solve	solve	VERB
ap-1213	219	12	this	this	DET
ap-1213	219	13	issue	issue	NOUN
ap-1213	219	14	.	.	PUNCT
ap-1213	220	1	•	•	NUM
ap-1213	220	2	f	f	PROPN
ap-1213	220	3	(	(	PUNCT
ap-1213	220	4	k	k	NOUN
ap-1213	220	5	)	)	PUNCT
ap-1213	220	6	=	=	PUNCT
ap-1213	220	7	e−k/2	e−k/2	VERB
ap-1213	220	8	the	the	DET
ap-1213	220	9	solution	solution	NOUN
ap-1213	220	10	in	in	ADP
ap-1213	220	11	this	this	DET
ap-1213	220	12	case	case	NOUN
ap-1213	220	13	is	be	AUX
ap-1213	220	14	the	the	DET
ap-1213	220	15	first	first	ADJ
ap-1213	220	16	discovered	discover	VERB
ap-1213	220	17	analytic	analytic	ADJ
ap-1213	220	18	solution	solution	NOUN
ap-1213	220	19	for	for	ADP
ap-1213	220	20	the	the	DET
ap-1213	220	21	tachyon	tachyon	NOUN
ap-1213	220	22	vacuum	vacuum	NOUN
ap-1213	221	1	[	[	X
ap-1213	221	2	10	10	NUM
ap-1213	221	3	]	]	PUNCT
ap-1213	221	4	.	.	PUNCT
ap-1213	222	1	there	there	PRON
ap-1213	222	2	is	be	VERB
ap-1213	222	3	however	however	ADV
ap-1213	222	4	one	one	NUM
ap-1213	222	5	subtlety	subtlety	NOUN
ap-1213	222	6	with	with	ADP
ap-1213	222	7	this	this	DET
ap-1213	222	8	solution	solution	NOUN
ap-1213	222	9	.	.	PUNCT
ap-1213	223	1	since	since	SCONJ
ap-1213	223	2	f̃	f̃	PROPN
ap-1213	223	3	=	=	SYM
ap-1213	223	4	k	k	PROPN
ap-1213	223	5	1−	1−	NUM
ap-1213	223	6	e−k	e−k	NOUN
ap-1213	223	7	=	=	SYM
ap-1213	223	8	(	(	PUNCT
ap-1213	223	9	6.21)∫	6.21)∫	NUM
ap-1213	223	10	∞	∞	PROPN
ap-1213	223	11	0	0	PUNCT
ap-1213	224	1	dα	dα	NOUN
ap-1213	224	2	(	(	PUNCT
ap-1213	224	3	∞∑	∞∑	NUM
ap-1213	224	4	n=0	n=0	PROPN
ap-1213	224	5	δ′(α−	δ′(α−	NOUN
ap-1213	224	6	n	n	CCONJ
ap-1213	224	7	)	)	PUNCT
ap-1213	224	8	)	)	PUNCT
ap-1213	225	1	e−αk	e−αk	PROPN
ap-1213	225	2	,	,	PUNCT
ap-1213	225	3	the	the	DET
ap-1213	225	4	inverse	inverse	ADJ
ap-1213	225	5	laplace	laplace	NOUN
ap-1213	225	6	transform	transform	NOUN
ap-1213	225	7	of	of	ADP
ap-1213	225	8	f̃	f̃	PROPN
ap-1213	225	9	does	do	AUX
ap-1213	225	10	not	not	PART
ap-1213	225	11	vanish	vanish	VERB
ap-1213	225	12	for	for	ADP
ap-1213	225	13	large	large	ADJ
ap-1213	225	14	α	α	NOUN
ap-1213	225	15	.	.	PUNCT
ap-1213	226	1	consequently	consequently	ADV
ap-1213	226	2	f̃	f̃	PROPN
ap-1213	226	3	∈	∈	PROPN
ap-1213	226	4	b′	b′	NOUN
ap-1213	226	5	and	and	CCONJ
ap-1213	226	6	does	do	AUX
ap-1213	226	7	not	not	PART
ap-1213	226	8	belong	belong	VERB
ap-1213	226	9	to	to	ADP
ap-1213	226	10	either	either	DET
ap-1213	226	11	d′	d′	NUM
ap-1213	226	12	l1	l1	PROPN
ap-1213	226	13	or	or	CCONJ
ap-1213	226	14	o′	o′	PROPN
ap-1213	226	15	c.	c.	NOUN
ap-1213	226	16	it	it	PRON
ap-1213	226	17	is	be	AUX
ap-1213	226	18	therefore	therefore	ADV
ap-1213	226	19	an	an	DET
ap-1213	226	20	example	example	NOUN
ap-1213	226	21	of	of	ADP
ap-1213	226	22	a	a	DET
ap-1213	226	23	geometric	geometric	ADJ
ap-1213	226	24	string	string	NOUN
ap-1213	226	25	field	field	NOUN
ap-1213	226	26	that	that	PRON
ap-1213	226	27	is	be	AUX
ap-1213	226	28	neither	neither	CCONJ
ap-1213	226	29	l0	l0	PROPN
ap-1213	226	30	nor	nor	CCONJ
ap-1213	226	31	l0	l0	NOUN
ap-1213	226	32	-	-	PUNCT
ap-1213	226	33	safe	safe	ADJ
ap-1213	226	34	,	,	PUNCT
ap-1213	226	35	but	but	CCONJ
ap-1213	226	36	is	be	AUX
ap-1213	226	37	nevertheless	nevertheless	ADV
ap-1213	226	38	l0	l0	NOUN
ap-1213	226	39	-	-	PUNCT
ap-1213	226	40	finite	finite	NOUN
ap-1213	226	41	.	.	PUNCT
ap-1213	227	1	this	this	PRON
ap-1213	227	2	is	be	AUX
ap-1213	227	3	also	also	ADV
ap-1213	227	4	manifested	manifest	VERB
ap-1213	227	5	by	by	ADP
ap-1213	227	6	the	the	DET
ap-1213	227	7	fact	fact	NOUN
ap-1213	227	8	that	that	SCONJ
ap-1213	227	9	f	f	PROPN
ap-1213	227	10	(	(	PUNCT
ap-1213	227	11	z	z	NOUN
ap-1213	227	12	)	)	PUNCT
ap-1213	227	13	has	have	AUX
ap-1213	227	14	poles	pole	NOUN
ap-1213	227	15	on	on	ADP
ap-1213	227	16	the	the	DET
ap-1213	227	17	imaginary	imaginary	ADJ
ap-1213	227	18	axes	axis	NOUN
ap-1213	227	19	.	.	PUNCT
ap-1213	228	1	there	there	PRON
ap-1213	228	2	are	be	VERB
ap-1213	228	3	interesting	interesting	ADJ
ap-1213	228	4	consequences	consequence	NOUN
ap-1213	228	5	to	to	ADP
ap-1213	228	6	this	this	PRON
ap-1213	228	7	.	.	PUNCT
ap-1213	229	1	truncating	truncate	VERB
ap-1213	229	2	the	the	DET
ap-1213	229	3	sum	sum	NOUN
ap-1213	229	4	∑	∑	VERB
ap-1213	229	5	ke−nk	ke−nk	NOUN
ap-1213	229	6	at	at	ADP
ap-1213	229	7	some	some	DET
ap-1213	229	8	finite	finite	ADJ
ap-1213	229	9	value	value	NOUN
ap-1213	229	10	of	of	ADP
ap-1213	229	11	n	n	NOUN
ap-1213	229	12	=	=	SYM
ap-1213	229	13	n	n	PRON
ap-1213	229	14	one	one	NOUN
ap-1213	229	15	gets	get	VERB
ap-1213	229	16	a	a	DET
ap-1213	229	17	remnant	remnant	NOUN
ap-1213	229	18	ke−(n+1)k	ke−(n+1)k	PROPN
ap-1213	229	19	1−	1−	NUM
ap-1213	229	20	e−k	e−k	NOUN
ap-1213	229	21	which	which	PRON
ap-1213	229	22	still	still	ADV
ap-1213	229	23	contributes	contribute	VERB
ap-1213	229	24	significantly	significantly	ADV
ap-1213	229	25	to	to	ADP
ap-1213	229	26	certain	certain	ADJ
ap-1213	229	27	observables	observable	NOUN
ap-1213	229	28	,	,	PUNCT
ap-1213	229	29	in	in	ADP
ap-1213	229	30	particular	particular	ADJ
ap-1213	229	31	to	to	ADP
ap-1213	229	32	the	the	DET
ap-1213	229	33	energy	energy	NOUN
ap-1213	229	34	.	.	PUNCT
ap-1213	230	1	this	this	PRON
ap-1213	230	2	is	be	AUX
ap-1213	230	3	the	the	DET
ap-1213	230	4	origin	origin	NOUN
ap-1213	230	5	of	of	ADP
ap-1213	230	6	the	the	DET
ap-1213	230	7	so	so	ADV
ap-1213	230	8	called	call	VERB
ap-1213	230	9	phantom	phantom	ADJ
ap-1213	230	10	term	term	NOUN
ap-1213	230	11	in	in	ADP
ap-1213	230	12	the	the	DET
ap-1213	230	13	tachyon	tachyon	NOUN
ap-1213	230	14	vacuum	vacuum	NOUN
ap-1213	230	15	solution	solution	NOUN
ap-1213	230	16	.	.	PUNCT
ap-1213	231	1	the	the	DET
ap-1213	231	2	homotopy	homotopy	NOUN
ap-1213	231	3	operator	operator	NOUN
ap-1213	231	4	,	,	PUNCT
ap-1213	231	5	on	on	ADP
ap-1213	231	6	the	the	DET
ap-1213	231	7	other	other	ADJ
ap-1213	231	8	hand	hand	NOUN
ap-1213	231	9	,	,	PUNCT
ap-1213	231	10	is	be	AUX
ap-1213	231	11	very	very	ADV
ap-1213	231	12	well	well	ADV
ap-1213	231	13	defined	define	VERB
ap-1213	231	14	,	,	PUNCT
ap-1213	231	15	and	and	CCONJ
ap-1213	231	16	is	be	AUX
ap-1213	231	17	both	both	PRON
ap-1213	231	18	l0	l0	PROPN
ap-1213	231	19	and	and	CCONJ
ap-1213	231	20	l0	l0	NOUN
ap-1213	231	21	-	-	PUNCT
ap-1213	231	22	safe	safe	ADJ
ap-1213	231	23	.	.	PUNCT
ap-1213	232	1	•	•	NUM
ap-1213	232	2	f	f	PROPN
ap-1213	232	3	(	(	PUNCT
ap-1213	232	4	k	k	NOUN
ap-1213	232	5	)	)	PUNCT
ap-1213	232	6	=	=	SYM
ap-1213	233	1	1√	1√	NUM
ap-1213	233	2	1	1	NUM
ap-1213	234	1	+	+	NOUN
ap-1213	234	2	k	k	NOUN
ap-1213	234	3	this	this	PRON
ap-1213	234	4	is	be	AUX
ap-1213	234	5	the	the	DET
ap-1213	234	6	tachyon	tachyon	NOUN
ap-1213	234	7	vacuum	vacuum	NOUN
ap-1213	234	8	solution	solution	NOUN
ap-1213	234	9	found	find	VERB
ap-1213	234	10	by	by	ADP
ap-1213	234	11	ted	ted	PROPN
ap-1213	234	12	erler	erler	PROPN
ap-1213	234	13	and	and	CCONJ
ap-1213	234	14	the	the	DET
ap-1213	234	15	author	author	NOUN
ap-1213	234	16	[	[	X
ap-1213	234	17	19	19	NUM
ap-1213	234	18	]	]	SYM
ap-1213	234	19	ψ	ψ	NOUN
ap-1213	234	20	=	=	SYM
ap-1213	234	21	1√	1√	PROPN
ap-1213	234	22	1	1	NUM
ap-1213	234	23	+	+	PROPN
ap-1213	234	24	k	k	PROPN
ap-1213	234	25	cb(1	cb(1	PROPN
ap-1213	234	26	+	+	PROPN
ap-1213	234	27	k)c	k)c	NOUN
ap-1213	234	28	1√	1√	ADJ
ap-1213	234	29	1	1	NUM
ap-1213	234	30	+	+	NOUN
ap-1213	234	31	k	k	PROPN
ap-1213	234	32	.	.	PUNCT
ap-1213	235	1	(	(	PUNCT
ap-1213	235	2	6.22	6.22	NUM
ap-1213	235	3	)	)	PUNCT
ap-1213	235	4	the	the	DET
ap-1213	235	5	homotopy	homotopy	NOUN
ap-1213	235	6	operator	operator	NOUN
ap-1213	235	7	is	be	AUX
ap-1213	235	8	simply	simply	ADV
ap-1213	235	9	a	a	DET
ap-1213	235	10	=	=	SYM
ap-1213	235	11	b/(1+k	b/(1+k	PROPN
ap-1213	235	12	)	)	PUNCT
ap-1213	235	13	,	,	PUNCT
ap-1213	235	14	which	which	PRON
ap-1213	235	15	is	be	AUX
ap-1213	235	16	perfectly	perfectly	ADV
ap-1213	235	17	regular	regular	ADJ
ap-1213	235	18	.	.	PUNCT
ap-1213	236	1	the	the	DET
ap-1213	236	2	inverse	inverse	ADJ
ap-1213	236	3	laplace	laplace	NOUN
ap-1213	236	4	transform	transform	NOUN
ap-1213	236	5	of	of	ADP
ap-1213	236	6	f̃	f̃	PROPN
ap-1213	236	7	=	=	SYM
ap-1213	236	8	1	1	NUM
ap-1213	236	9	+	+	CCONJ
ap-1213	236	10	k	k	PROPN
ap-1213	236	11	is	be	AUX
ap-1213	236	12	f̃	f̃	PROPN
ap-1213	236	13	=	=	SYM
ap-1213	236	14	δ(α	δ(α	PROPN
ap-1213	236	15	)	)	PUNCT
ap-1213	236	16	+	+	NUM
ap-1213	236	17	δ′(α	δ′(α	PROPN
ap-1213	236	18	)	)	PUNCT
ap-1213	236	19	,	,	PUNCT
ap-1213	236	20	which	which	PRON
ap-1213	236	21	actually	actually	ADV
ap-1213	236	22	belongs	belong	VERB
ap-1213	236	23	to	to	ADP
ap-1213	236	24	e	e	PROPN
ap-1213	236	25	′	′	NOUN
ap-1213	237	1	and	and	CCONJ
ap-1213	237	2	we	we	PRON
ap-1213	237	3	thus	thus	ADV
ap-1213	237	4	see	see	VERB
ap-1213	237	5	no	no	DET
ap-1213	237	6	need	need	NOUN
ap-1213	237	7	for	for	ADP
ap-1213	237	8	the	the	DET
ap-1213	237	9	phantom	phantom	ADJ
ap-1213	237	10	term	term	NOUN
ap-1213	237	11	.	.	PUNCT
ap-1213	238	1	in	in	ADP
ap-1213	238	2	fact	fact	NOUN
ap-1213	238	3	the	the	DET
ap-1213	238	4	energy	energy	NOUN
ap-1213	238	5	for	for	ADP
ap-1213	238	6	this	this	DET
ap-1213	238	7	solution	solution	NOUN
ap-1213	238	8	can	can	AUX
ap-1213	238	9	be	be	AUX
ap-1213	238	10	computed	compute	VERB
ap-1213	238	11	very	very	ADV
ap-1213	238	12	easily	easily	ADV
ap-1213	238	13	e	e	NOUN
ap-1213	238	14	=	=	NOUN
ap-1213	238	15	−s	−s	NOUN
ap-1213	238	16	=	=	NOUN
ap-1213	238	17	1	1	NUM
ap-1213	238	18	6	6	NUM
ap-1213	238	19	〈	〈	PROPN
ap-1213	238	20	ψ	ψ	NOUN
ap-1213	238	21	,	,	PUNCT
ap-1213	238	22	qψ	qψ	PROPN
ap-1213	238	23	〉	〉	NUM
ap-1213	238	24	=	=	SYM
ap-1213	238	25	(	(	PUNCT
ap-1213	238	26	6.23	6.23	NUM
ap-1213	238	27	)	)	PUNCT
ap-1213	238	28	1	1	NUM
ap-1213	238	29	6	6	NUM
ap-1213	238	30	〈	〈	PROPN
ap-1213	238	31	(	(	PUNCT
ap-1213	238	32	c+q(bc	c+q(bc	NOUN
ap-1213	238	33	)	)	PUNCT
ap-1213	238	34	)	)	PUNCT
ap-1213	238	35	1	1	NUM
ap-1213	238	36	1	1	NUM
ap-1213	238	37	+	+	NOUN
ap-1213	238	38	k	k	NOUN
ap-1213	238	39	c∂c	c∂c	ADJ
ap-1213	238	40	1	1	NUM
ap-1213	238	41	1	1	NUM
ap-1213	238	42	+	+	NOUN
ap-1213	238	43	k	k	X
ap-1213	238	44	〉	〉	NOUN
ap-1213	238	45	=	=	SYM
ap-1213	238	46	1	1	NUM
ap-1213	238	47	6	6	NUM
ap-1213	238	48	∫	∫	NOUN
ap-1213	238	49	∞	∞	NOUN
ap-1213	238	50	0	0	NUM
ap-1213	239	1	dt1	dt1	PROPN
ap-1213	239	2	∫	∫	PROPN
ap-1213	239	3	∞	∞	PROPN
ap-1213	239	4	0	0	NUM
ap-1213	239	5	dt2e−t1−t2	dt2e−t1−t2	PUNCT
ap-1213	239	6	〈	〈	PROPN
ap-1213	239	7	c	c	NOUN
ap-1213	239	8	e−t1k	e−t1k	PROPN
ap-1213	239	9	c∂c	c∂c	PROPN
ap-1213	239	10	e−t2k	e−t2k	X
ap-1213	239	11	〉	〉	NOUN
ap-1213	239	12	=	=	SYM
ap-1213	239	13	−	−	PROPN
ap-1213	239	14	1	1	NUM
ap-1213	239	15	6π2	6π2	NUM
ap-1213	239	16	∫	∫	NUM
ap-1213	239	17	∞	∞	NOUN
ap-1213	239	18	0	0	NUM
ap-1213	240	1	duu3e−u	duu3e−u	NOUN
ap-1213	240	2	∫	∫	PROPN
ap-1213	240	3	1	1	NUM
ap-1213	240	4	0	0	NUM
ap-1213	240	5	dv	dv	PROPN
ap-1213	240	6	sin2	sin2	PROPN
ap-1213	240	7	πv	πv	PROPN
ap-1213	241	1	=	=	SYM
ap-1213	241	2	−	−	PROPN
ap-1213	241	3	1	1	NUM
ap-1213	241	4	2π2	2π2	NUM
ap-1213	241	5	,	,	PUNCT
ap-1213	241	6	(	(	PUNCT
ap-1213	241	7	6.24	6.24	NUM
ap-1213	241	8	)	)	PUNCT
ap-1213	241	9	which	which	PRON
ap-1213	241	10	is	be	AUX
ap-1213	241	11	the	the	DET
ap-1213	241	12	correct	correct	ADJ
ap-1213	241	13	value	value	NOUN
ap-1213	241	14	,	,	PUNCT
ap-1213	241	15	minus	minus	CCONJ
ap-1213	241	16	the	the	DET
ap-1213	241	17	tension	tension	NOUN
ap-1213	241	18	of	of	ADP
ap-1213	241	19	the	the	DET
ap-1213	241	20	d	d	NOUN
ap-1213	241	21	-	-	NOUN
ap-1213	241	22	brane	brane	ADJ
ap-1213	241	23	,	,	PUNCT
ap-1213	241	24	according	accord	VERB
ap-1213	241	25	to	to	ADP
ap-1213	241	26	sen	sen	PROPN
ap-1213	241	27	’s	’s	PART
ap-1213	241	28	conjecture	conjecture	NOUN
ap-1213	241	29	[	[	X
ap-1213	241	30	14	14	NUM
ap-1213	241	31	]	]	PUNCT
ap-1213	241	32	.	.	PUNCT
ap-1213	242	1	the	the	DET
ap-1213	242	2	last	last	ADJ
ap-1213	242	3	correlator	correlator	NOUN
ap-1213	242	4	that	that	PRON
ap-1213	242	5	we	we	PRON
ap-1213	242	6	had	have	VERB
ap-1213	242	7	to	to	PART
ap-1213	242	8	evaluate	evaluate	VERB
ap-1213	242	9	is	be	AUX
ap-1213	242	10	indeed	indeed	ADV
ap-1213	242	11	very	very	ADV
ap-1213	242	12	simple	simple	ADJ
ap-1213	242	13	:	:	PUNCT
ap-1213	242	14	two	two	NUM
ap-1213	242	15	ghost	ghost	NOUN
ap-1213	242	16	insertions	insertion	NOUN
ap-1213	242	17	of	of	ADP
ap-1213	242	18	c	c	NOUN
ap-1213	242	19	and	and	CCONJ
ap-1213	242	20	c∂c	c∂c	NOUN
ap-1213	242	21	on	on	ADP
ap-1213	242	22	a	a	DET
ap-1213	242	23	boundary	boundary	NOUN
ap-1213	242	24	of	of	ADP
ap-1213	242	25	a	a	DET
ap-1213	242	26	semi	semi	ADJ
ap-1213	242	27	-	-	ADJ
ap-1213	242	28	infinite	infinite	ADJ
ap-1213	242	29	cylinder	cylinder	NOUN
ap-1213	242	30	of	of	ADP
ap-1213	242	31	circumference	circumference	NOUN
ap-1213	242	32	t1	t1	NOUN
ap-1213	242	33	+	+	CCONJ
ap-1213	243	1	t2	t2	NOUN
ap-1213	243	2	separated	separate	VERB
ap-1213	243	3	by	by	ADP
ap-1213	243	4	the	the	DET
ap-1213	243	5	distance	distance	NOUN
ap-1213	243	6	of	of	ADP
ap-1213	243	7	t1	t1	PROPN
ap-1213	243	8	.	.	PUNCT
ap-1213	244	1	acknowledgement	acknowledgement	NOUN
ap-1213	244	2	i	i	PRON
ap-1213	244	3	would	would	AUX
ap-1213	244	4	like	like	VERB
ap-1213	244	5	to	to	PART
ap-1213	244	6	thank	thank	VERB
ap-1213	244	7	ted	ted	PROPN
ap-1213	244	8	erler	erler	NOUN
ap-1213	244	9	for	for	ADP
ap-1213	244	10	collaborating	collaborate	VERB
ap-1213	244	11	on	on	ADP
ap-1213	244	12	many	many	ADJ
ap-1213	244	13	of	of	ADP
ap-1213	244	14	the	the	DET
ap-1213	244	15	topics	topic	NOUN
ap-1213	244	16	discussed	discuss	VERB
ap-1213	244	17	in	in	ADP
ap-1213	244	18	this	this	DET
ap-1213	244	19	review	review	NOUN
ap-1213	244	20	,	,	PUNCT
ap-1213	244	21	and	and	CCONJ
ap-1213	244	22	for	for	ADP
ap-1213	244	23	his	his	PRON
ap-1213	244	24	insightful	insightful	ADJ
ap-1213	244	25	comments	comment	NOUN
ap-1213	244	26	.	.	PUNCT
ap-1213	245	1	i	i	PRON
ap-1213	245	2	would	would	AUX
ap-1213	245	3	also	also	ADV
ap-1213	245	4	like	like	VERB
ap-1213	245	5	to	to	PART
ap-1213	245	6	thank	thank	VERB
ap-1213	245	7	the	the	DET
ap-1213	245	8	kavli	kavli	PROPN
ap-1213	245	9	institute	institute	NOUN
ap-1213	245	10	for	for	ADP
ap-1213	245	11	theoretical	theoretical	ADJ
ap-1213	245	12	physics	physics	NOUN
ap-1213	245	13	,	,	PUNCT
ap-1213	245	14	the	the	DET
ap-1213	245	15	aspen	aspen	ADJ
ap-1213	245	16	center	center	NOUN
ap-1213	245	17	for	for	ADP
ap-1213	245	18	physics	physics	NOUN
ap-1213	245	19	,	,	PUNCT
ap-1213	245	20	the	the	DET
ap-1213	245	21	simons	simons	PROPN
ap-1213	245	22	center	center	PROPN
ap-1213	245	23	for	for	ADP
ap-1213	245	24	geometry	geometry	NOUN
ap-1213	245	25	and	and	CCONJ
ap-1213	245	26	physics	physics	NOUN
ap-1213	245	27	,	,	PUNCT
ap-1213	245	28	the	the	DET
ap-1213	245	29	yukawa	yukawa	PROPN
ap-1213	245	30	institute	institute	PROPN
ap-1213	245	31	for	for	ADP
ap-1213	245	32	physics	physics	PROPN
ap-1213	245	33	and	and	CCONJ
ap-1213	245	34	apctp	apctp	PROPN
ap-1213	245	35	in	in	ADP
ap-1213	245	36	pohang	pohang	PROPN
ap-1213	245	37	,	,	PUNCT
ap-1213	245	38	korea	korea	PROPN
ap-1213	245	39	,	,	PUNCT
ap-1213	245	40	for	for	ADP
ap-1213	245	41	their	their	PRON
ap-1213	245	42	hospitality	hospitality	NOUN
ap-1213	245	43	while	while	SCONJ
ap-1213	245	44	i	i	PRON
ap-1213	245	45	was	be	AUX
ap-1213	245	46	working	work	VERB
ap-1213	245	47	on	on	ADP
ap-1213	245	48	parts	part	NOUN
ap-1213	245	49	of	of	ADP
ap-1213	245	50	the	the	DET
ap-1213	245	51	present	present	ADJ
ap-1213	245	52	work	work	NOUN
ap-1213	245	53	.	.	PUNCT
ap-1213	246	1	this	this	DET
ap-1213	246	2	research	research	NOUN
ap-1213	246	3	was	be	AUX
ap-1213	246	4	supported	support	VERB
ap-1213	246	5	by	by	ADP
ap-1213	246	6	the	the	DET
ap-1213	246	7	euryi	euryi	PROPN
ap-1213	246	8	grant	grant	PROPN
ap-1213	246	9	gacr	gacr	PROPN
ap-1213	246	10	eyi/07	eyi/07	PROPN
ap-1213	246	11	/	/	SYM
ap-1213	246	12	e010	e010	PROPN
ap-1213	246	13	from	from	ADP
ap-1213	246	14	eurohorc	eurohorc	ADV
ap-1213	246	15	and	and	CCONJ
ap-1213	246	16	esf	esf	PROPN
ap-1213	246	17	.	.	PROPN
ap-1213	247	1	references	reference	NOUN
ap-1213	247	2	[	[	X
ap-1213	247	3	1	1	NUM
ap-1213	247	4	]	]	X
ap-1213	247	5	sen	sen	PROPN
ap-1213	247	6	,	,	PUNCT
ap-1213	247	7	a.	a.	NOUN
ap-1213	247	8	:	:	PUNCT
ap-1213	247	9	on	on	ADP
ap-1213	247	10	the	the	DET
ap-1213	247	11	background	background	NOUN
ap-1213	247	12	independence	independence	NOUN
ap-1213	247	13	of	of	ADP
ap-1213	247	14	string	string	NOUN
ap-1213	247	15	field	field	NOUN
ap-1213	247	16	theory	theory	NOUN
ap-1213	247	17	,	,	PUNCT
ap-1213	247	18	’	'	PUNCT
ap-1213	247	19	nucl	nucl	NOUN
ap-1213	247	20	.	.	PUNCT
ap-1213	248	1	phys	phy	NOUN
ap-1213	248	2	.	.	PUNCT
ap-1213	249	1	b	b	ADP
ap-1213	249	2	345	345	NUM
ap-1213	249	3	(	(	PUNCT
ap-1213	249	4	1990	1990	NUM
ap-1213	249	5	)	)	PUNCT
ap-1213	249	6	551	551	NUM
ap-1213	249	7	.	.	PUNCT
ap-1213	250	1	[	[	X
ap-1213	250	2	2	2	NUM
ap-1213	250	3	]	]	X
ap-1213	250	4	sen	sen	PROPN
ap-1213	250	5	,	,	PUNCT
ap-1213	250	6	a.	a.	PROPN
ap-1213	250	7	,	,	PUNCT
ap-1213	250	8	zwiebach	zwiebach	PROPN
ap-1213	250	9	,	,	PUNCT
ap-1213	250	10	b.	b.	PROPN
ap-1213	250	11	:	:	PUNCT
ap-1213	250	12	a	a	DET
ap-1213	250	13	proof	proof	NOUN
ap-1213	250	14	of	of	ADP
ap-1213	250	15	local	local	ADJ
ap-1213	250	16	background	background	NOUN
ap-1213	250	17	independence	independence	NOUN
ap-1213	250	18	of	of	ADP
ap-1213	250	19	classical	classical	ADJ
ap-1213	250	20	closed	closed	ADJ
ap-1213	250	21	string	string	NOUN
ap-1213	250	22	field	field	NOUN
ap-1213	250	23	theory	theory	NOUN
ap-1213	250	24	,	,	PUNCT
ap-1213	250	25	nucl	nucl	PROPN
ap-1213	250	26	.	.	PUNCT
ap-1213	251	1	phys	phy	NOUN
ap-1213	251	2	.	.	PUNCT
ap-1213	252	1	b	b	X
ap-1213	252	2	414	414	NUM
ap-1213	252	3	(	(	PUNCT
ap-1213	252	4	1994	1994	NUM
ap-1213	252	5	)	)	PUNCT
ap-1213	252	6	649	649	NUM
ap-1213	253	1	[	[	X
ap-1213	253	2	arxiv	arxiv	NOUN
ap-1213	253	3	:	:	PUNCT
ap-1213	253	4	hep	hep	NOUN
ap-1213	253	5	-	-	PUNCT
ap-1213	253	6	th/9307088	th/9307088	PROPN
ap-1213	253	7	]	]	PUNCT
ap-1213	253	8	.	.	PUNCT
ap-1213	254	1	[	[	X
ap-1213	254	2	3	3	NUM
ap-1213	254	3	]	]	PUNCT
ap-1213	254	4	witten	witten	PROPN
ap-1213	254	5	,	,	PUNCT
ap-1213	254	6	e.	e.	PROPN
ap-1213	254	7	:	:	PUNCT
ap-1213	254	8	noncommutative	noncommutative	ADJ
ap-1213	254	9	geometry	geometry	NOUN
ap-1213	254	10	and	and	CCONJ
ap-1213	254	11	string	string	NOUN
ap-1213	254	12	field	field	NOUN
ap-1213	254	13	theory	theory	NOUN
ap-1213	254	14	,	,	PUNCT
ap-1213	254	15	nucl	nucl	PROPN
ap-1213	254	16	.	.	PUNCT
ap-1213	255	1	phys	phy	NOUN
ap-1213	255	2	.	.	PUNCT
ap-1213	256	1	b	b	X
ap-1213	256	2	268	268	NUM
ap-1213	256	3	,	,	PUNCT
ap-1213	256	4	253	253	NUM
ap-1213	256	5	(	(	PUNCT
ap-1213	256	6	1986	1986	NUM
ap-1213	256	7	)	)	PUNCT
ap-1213	256	8	.	.	PUNCT
ap-1213	257	1	107	107	NUM
ap-1213	257	2	acta	acta	PROPN
ap-1213	257	3	polytechnica	polytechnica	PROPN
ap-1213	257	4	vol	vol	NOUN
ap-1213	257	5	.	.	PROPN
ap-1213	258	1	50	50	NUM
ap-1213	258	2	no	no	NOUN
ap-1213	258	3	.	.	PUNCT
ap-1213	259	1	3/2010	3/2010	NUM
ap-1213	259	2	[	[	X
ap-1213	259	3	4	4	NUM
ap-1213	259	4	]	]	X
ap-1213	259	5	taylor	taylor	PROPN
ap-1213	259	6	,	,	PUNCT
ap-1213	259	7	w.	w.	PROPN
ap-1213	259	8	,	,	PUNCT
ap-1213	259	9	zwiebach	zwiebach	PROPN
ap-1213	259	10	,	,	PUNCT
ap-1213	259	11	b.	b.	PROPN
ap-1213	259	12	:	:	PUNCT
ap-1213	260	1	d	d	X
ap-1213	260	2	-	-	PUNCT
ap-1213	260	3	branes	brane	NOUN
ap-1213	260	4	,	,	PUNCT
ap-1213	260	5	tachyons	tachyon	NOUN
ap-1213	260	6	,	,	PUNCT
ap-1213	260	7	and	and	CCONJ
ap-1213	260	8	string	string	NOUN
ap-1213	260	9	field	field	NOUN
ap-1213	260	10	theory	theory	NOUN
ap-1213	260	11	,	,	PUNCT
ap-1213	260	12	arxiv	arxiv	PROPN
ap-1213	260	13	:	:	PUNCT
ap-1213	260	14	hep	hep	NOUN
ap-1213	260	15	-	-	PUNCT
ap-1213	260	16	th/0311017	th/0311017	NOUN
ap-1213	260	17	.	.	PUNCT
ap-1213	261	1	[	[	X
ap-1213	261	2	5	5	NUM
ap-1213	261	3	]	]	X
ap-1213	261	4	sen	sen	PROPN
ap-1213	261	5	,	,	PUNCT
ap-1213	261	6	a.	a.	NOUN
ap-1213	261	7	:	:	PUNCT
ap-1213	261	8	tachyon	tachyon	NOUN
ap-1213	261	9	dynamics	dynamic	NOUN
ap-1213	261	10	in	in	ADP
ap-1213	261	11	open	open	ADJ
ap-1213	261	12	string	string	NOUN
ap-1213	261	13	theory	theory	NOUN
ap-1213	261	14	,	,	PUNCT
ap-1213	261	15	arxiv	arxiv	PROPN
ap-1213	261	16	:	:	PUNCT
ap-1213	261	17	hep	hep	NOUN
ap-1213	261	18	-	-	PUNCT
ap-1213	261	19	th/0410103	th/0410103	NOUN
ap-1213	261	20	.	.	PUNCT
ap-1213	262	1	[	[	X
ap-1213	262	2	6	6	NUM
ap-1213	262	3	]	]	X
ap-1213	262	4	thorn	thorn	PROPN
ap-1213	262	5	,	,	PUNCT
ap-1213	262	6	c.	c.	PROPN
ap-1213	262	7	b.	b.	PROPN
ap-1213	262	8	:	:	PUNCT
ap-1213	262	9	string	string	NOUN
ap-1213	262	10	field	field	NOUN
ap-1213	262	11	theory	theory	NOUN
ap-1213	262	12	,	,	PUNCT
ap-1213	262	13	phys	phy	NOUN
ap-1213	262	14	.	.	PUNCT
ap-1213	263	1	rept	rept	NOUN
ap-1213	263	2	.	.	PUNCT
ap-1213	264	1	175	175	NUM
ap-1213	264	2	,	,	PUNCT
ap-1213	264	3	1	1	NUM
ap-1213	264	4	(	(	PUNCT
ap-1213	264	5	1989	1989	NUM
ap-1213	264	6	)	)	PUNCT
ap-1213	264	7	.	.	PUNCT
ap-1213	265	1	[	[	X
ap-1213	265	2	7	7	NUM
ap-1213	265	3	]	]	X
ap-1213	265	4	bonora	bonora	NOUN
ap-1213	265	5	,	,	PUNCT
ap-1213	265	6	l.	l.	PROPN
ap-1213	265	7	,	,	PUNCT
ap-1213	265	8	maccaferri	maccaferri	PROPN
ap-1213	265	9	,	,	PUNCT
ap-1213	265	10	c.	c.	PROPN
ap-1213	265	11	,	,	PUNCT
ap-1213	265	12	mamone	mamone	NOUN
ap-1213	265	13	,	,	PUNCT
ap-1213	265	14	d.	d.	PROPN
ap-1213	265	15	,	,	PUNCT
ap-1213	265	16	salizzoni	salizzoni	PROPN
ap-1213	265	17	,	,	PUNCT
ap-1213	265	18	m.	m.	NOUN
ap-1213	265	19	:	:	PUNCT
ap-1213	265	20	topics	topic	NOUN
ap-1213	265	21	in	in	ADP
ap-1213	265	22	string	string	NOUN
ap-1213	265	23	field	field	NOUN
ap-1213	265	24	theory	theory	NOUN
ap-1213	265	25	,	,	PUNCT
ap-1213	265	26	arxiv	arxiv	PROPN
ap-1213	265	27	:	:	PUNCT
ap-1213	265	28	hepth/0304270	hepth/0304270	PROPN
ap-1213	265	29	.	.	PUNCT
ap-1213	266	1	[	[	X
ap-1213	266	2	8	8	NUM
ap-1213	266	3	]	]	X
ap-1213	266	4	fuchs	fuch	NOUN
ap-1213	266	5	,	,	PUNCT
ap-1213	266	6	e.	e.	PROPN
ap-1213	266	7	,	,	PUNCT
ap-1213	266	8	kroyter	kroyter	PROPN
ap-1213	266	9	,	,	PUNCT
ap-1213	266	10	m.	m.	NOUN
ap-1213	266	11	:	:	PUNCT
ap-1213	266	12	analytical	analytical	ADJ
ap-1213	266	13	solutions	solution	NOUN
ap-1213	266	14	of	of	ADP
ap-1213	266	15	open	open	ADJ
ap-1213	266	16	string	string	NOUN
ap-1213	266	17	field	field	NOUN
ap-1213	266	18	theory	theory	NOUN
ap-1213	266	19	,	,	PUNCT
ap-1213	266	20	arxiv:0807.4722	arxiv:0807.4722	NOUN
ap-1213	266	21	[	[	X
ap-1213	266	22	hepth	hepth	X
ap-1213	266	23	]	]	PUNCT
ap-1213	266	24	.	.	PUNCT
ap-1213	267	1	[	[	X
ap-1213	267	2	9	9	NUM
ap-1213	267	3	]	]	PUNCT
ap-1213	267	4	okawa	okawa	PROPN
ap-1213	267	5	,	,	PUNCT
ap-1213	267	6	y.	y.	PROPN
ap-1213	267	7	:	:	PUNCT
ap-1213	267	8	comments	comment	NOUN
ap-1213	267	9	on	on	ADP
ap-1213	267	10	schnabl	schnabl	NOUN
ap-1213	267	11	’s	’s	PART
ap-1213	267	12	analytic	analytic	ADJ
ap-1213	267	13	solution	solution	NOUN
ap-1213	267	14	for	for	ADP
ap-1213	267	15	tachyon	tachyon	NOUN
ap-1213	267	16	condensation	condensation	NOUN
ap-1213	267	17	in	in	ADP
ap-1213	267	18	witten	witten	PROPN
ap-1213	267	19	’s	’s	PART
ap-1213	267	20	open	open	ADJ
ap-1213	267	21	string	string	NOUN
ap-1213	267	22	field	field	NOUN
ap-1213	267	23	theory	theory	NOUN
ap-1213	267	24	,	,	PUNCT
ap-1213	267	25	jhep	jhep	ADJ
ap-1213	267	26	0604	0604	NUM
ap-1213	267	27	(	(	PUNCT
ap-1213	267	28	2006	2006	NUM
ap-1213	267	29	)	)	PUNCT
ap-1213	267	30	055	055	NUM
ap-1213	268	1	[	[	X
ap-1213	268	2	arxiv	arxiv	NOUN
ap-1213	268	3	:	:	PUNCT
ap-1213	268	4	hep	hep	NOUN
ap-1213	268	5	-	-	PUNCT
ap-1213	268	6	th/0603159	th/0603159	NOUN
ap-1213	268	7	]	]	PUNCT
ap-1213	268	8	.	.	PUNCT
ap-1213	269	1	[	[	X
ap-1213	269	2	10	10	NUM
ap-1213	269	3	]	]	X
ap-1213	269	4	schnabl	schnabl	NOUN
ap-1213	269	5	,	,	PUNCT
ap-1213	269	6	m.	m.	NOUN
ap-1213	269	7	:	:	PUNCT
ap-1213	269	8	analytic	analytic	ADJ
ap-1213	269	9	solution	solution	NOUN
ap-1213	269	10	for	for	ADP
ap-1213	269	11	tachyon	tachyon	NOUN
ap-1213	269	12	condensation	condensation	NOUN
ap-1213	269	13	in	in	ADP
ap-1213	269	14	open	open	ADJ
ap-1213	269	15	string	string	NOUN
ap-1213	269	16	field	field	NOUN
ap-1213	269	17	theory	theory	NOUN
ap-1213	269	18	,	,	PUNCT
ap-1213	269	19	adv	adv	PROPN
ap-1213	269	20	.	.	PUNCT
ap-1213	270	1	theor	theor	PROPN
ap-1213	270	2	.	.	PUNCT
ap-1213	270	3	math	math	NOUN
ap-1213	270	4	.	.	PUNCT
ap-1213	271	1	phys	phy	NOUN
ap-1213	271	2	.	.	PUNCT
ap-1213	272	1	10	10	NUM
ap-1213	272	2	(	(	PUNCT
ap-1213	272	3	2006	2006	NUM
ap-1213	272	4	)	)	PUNCT
ap-1213	272	5	433	433	NUM
ap-1213	273	1	[	[	X
ap-1213	273	2	arxiv	arxiv	NOUN
ap-1213	273	3	:	:	PUNCT
ap-1213	273	4	hepth/0511286	hepth/0511286	ADJ
ap-1213	273	5	]	]	PUNCT
ap-1213	273	6	.	.	PUNCT
ap-1213	274	1	[	[	X
ap-1213	274	2	11	11	NUM
ap-1213	274	3	]	]	SYM
ap-1213	274	4	erler	erler	NOUN
ap-1213	274	5	,	,	PUNCT
ap-1213	274	6	t.	t.	PROPN
ap-1213	274	7	:	:	PUNCT
ap-1213	274	8	split	split	ADJ
ap-1213	274	9	string	string	NOUN
ap-1213	274	10	formalism	formalism	NOUN
ap-1213	274	11	and	and	CCONJ
ap-1213	274	12	the	the	DET
ap-1213	274	13	closed	closed	ADJ
ap-1213	274	14	string	string	NOUN
ap-1213	274	15	vacuum	vacuum	NOUN
ap-1213	274	16	,	,	PUNCT
ap-1213	274	17	jhep	jhep	ADJ
ap-1213	274	18	0705	0705	NUM
ap-1213	274	19	(	(	PUNCT
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ap-1213	274	21	)	)	PUNCT
ap-1213	274	22	083	083	NUM
ap-1213	275	1	[	[	X
ap-1213	275	2	arxiv	arxiv	NOUN
ap-1213	275	3	:	:	PUNCT
ap-1213	275	4	hep	hep	NOUN
ap-1213	275	5	-	-	PUNCT
ap-1213	275	6	th/0611200	th/0611200	X
ap-1213	275	7	]	]	PUNCT
ap-1213	275	8	.	.	PUNCT
ap-1213	276	1	[	[	X
ap-1213	276	2	12	12	NUM
ap-1213	276	3	]	]	SYM
ap-1213	276	4	erler	erler	NOUN
ap-1213	276	5	,	,	PUNCT
ap-1213	276	6	t.	t.	PROPN
ap-1213	276	7	:	:	PUNCT
ap-1213	276	8	split	split	ADJ
ap-1213	276	9	string	string	NOUN
ap-1213	276	10	formalism	formalism	NOUN
ap-1213	276	11	and	and	CCONJ
ap-1213	276	12	the	the	DET
ap-1213	276	13	closed	closed	ADJ
ap-1213	276	14	string	string	NOUN
ap-1213	276	15	vacuum	vacuum	PROPN
ap-1213	276	16	.	.	PUNCT
ap-1213	277	1	ii	ii	PROPN
ap-1213	277	2	,	,	PUNCT
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ap-1213	277	4	0705	0705	NUM
ap-1213	277	5	(	(	PUNCT
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ap-1213	277	7	)	)	PUNCT
ap-1213	277	8	084	084	NUM
ap-1213	278	1	[	[	X
ap-1213	278	2	arxiv	arxiv	NOUN
ap-1213	278	3	:	:	PUNCT
ap-1213	278	4	hep	hep	PROPN
ap-1213	278	5	-	-	PROPN
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ap-1213	278	7	]	]	PUNCT
ap-1213	278	8	.	.	PUNCT
ap-1213	279	1	[	[	X
ap-1213	279	2	13	13	NUM
ap-1213	279	3	]	]	SYM
ap-1213	279	4	ellwood	ellwood	PROPN
ap-1213	279	5	,	,	PUNCT
ap-1213	279	6	i.	i.	PROPN
ap-1213	279	7	,	,	PUNCT
ap-1213	279	8	schnabl	schnabl	NOUN
ap-1213	279	9	,	,	PUNCT
ap-1213	279	10	m.	m.	NOUN
ap-1213	279	11	:	:	PUNCT
ap-1213	279	12	proof	proof	NOUN
ap-1213	279	13	of	of	ADP
ap-1213	279	14	vanishing	vanish	VERB
ap-1213	279	15	cohomology	cohomology	NOUN
ap-1213	279	16	at	at	ADP
ap-1213	279	17	the	the	DET
ap-1213	279	18	tachyon	tachyon	NOUN
ap-1213	279	19	vacuum	vacuum	NOUN
ap-1213	279	20	,	,	PUNCT
ap-1213	279	21	jhep	jhep	ADJ
ap-1213	279	22	0702	0702	NUM
ap-1213	279	23	(	(	PUNCT
ap-1213	279	24	2007	2007	NUM
ap-1213	279	25	)	)	PUNCT
ap-1213	279	26	096	096	NUM
ap-1213	280	1	[	[	X
ap-1213	280	2	arxiv	arxiv	NOUN
ap-1213	280	3	:	:	PUNCT
ap-1213	280	4	hep	hep	NOUN
ap-1213	280	5	-	-	PUNCT
ap-1213	280	6	th/0606142	th/0606142	PROPN
ap-1213	280	7	]	]	X
ap-1213	280	8	.	.	PUNCT
ap-1213	281	1	[	[	X
ap-1213	281	2	14	14	NUM
ap-1213	281	3	]	]	X
ap-1213	281	4	sen	sen	PROPN
ap-1213	281	5	,	,	PUNCT
ap-1213	281	6	a.	a.	NOUN
ap-1213	281	7	:	:	PUNCT
ap-1213	281	8	universality	universality	NOUN
ap-1213	281	9	of	of	ADP
ap-1213	281	10	the	the	DET
ap-1213	281	11	tachyon	tachyon	NOUN
ap-1213	281	12	potential	potential	NOUN
ap-1213	281	13	,	,	PUNCT
ap-1213	281	14	jhep	jhep	ADJ
ap-1213	281	15	9912	9912	NUM
ap-1213	281	16	(	(	PUNCT
ap-1213	281	17	1999	1999	NUM
ap-1213	281	18	)	)	PUNCT
ap-1213	281	19	027	027	NUM
ap-1213	282	1	[	[	X
ap-1213	282	2	arxiv	arxiv	NOUN
ap-1213	282	3	:	:	PUNCT
ap-1213	282	4	hep	hep	NOUN
ap-1213	282	5	-	-	PUNCT
ap-1213	282	6	th/9911116	th/9911116	NOUN
ap-1213	282	7	]	]	X
ap-1213	282	8	.	.	PUNCT
ap-1213	283	1	[	[	X
ap-1213	283	2	15	15	NUM
ap-1213	283	3	]	]	X
ap-1213	283	4	schwartz	schwartz	PROPN
ap-1213	283	5	,	,	PUNCT
ap-1213	283	6	l.	l.	PROPN
ap-1213	283	7	:	:	PUNCT
ap-1213	283	8	théorie	théorie	PROPN
ap-1213	283	9	des	des	PROPN
ap-1213	283	10	distributions	distribution	NOUN
ap-1213	283	11	,	,	PUNCT
ap-1213	283	12	hermann	hermann	PROPN
ap-1213	283	13	,	,	PUNCT
ap-1213	283	14	paris	paris	PROPN
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ap-1213	283	16	.	.	PUNCT
ap-1213	284	1	[	[	X
ap-1213	284	2	16	16	NUM
ap-1213	284	3	]	]	SYM
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ap-1213	284	5	,	,	PUNCT
ap-1213	284	6	t.	t.	PROPN
ap-1213	284	7	:	:	PUNCT
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ap-1213	284	9	appear	appear	VERB
ap-1213	284	10	[	[	X
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ap-1213	284	12	]	]	PUNCT
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ap-1213	284	14	,	,	PUNCT
ap-1213	284	15	l.	l.	PROPN
ap-1213	284	16	:	:	PUNCT
ap-1213	284	17	comments	comment	NOUN
ap-1213	284	18	on	on	ADP
ap-1213	284	19	the	the	DET
ap-1213	284	20	open	open	ADJ
ap-1213	284	21	string	string	NOUN
ap-1213	284	22	c	c	NOUN
ap-1213	284	23	*	*	PUNCT
ap-1213	284	24	algebra	algebra	NOUN
ap-1213	284	25	,	,	PUNCT
ap-1213	284	26	talk	talk	NOUN
ap-1213	284	27	at	at	ADP
ap-1213	284	28	simons	simon	NOUN
ap-1213	284	29	center	center	PROPN
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ap-1213	284	31	geometry	geometry	NOUN
ap-1213	284	32	and	and	CCONJ
ap-1213	284	33	physics	physics	NOUN
ap-1213	284	34	workshop	workshop	NOUN
ap-1213	284	35	on	on	ADP
ap-1213	284	36	string	string	NOUN
ap-1213	284	37	field	field	NOUN
ap-1213	284	38	theory	theory	NOUN
ap-1213	284	39	,	,	PUNCT
ap-1213	284	40	stony	stony	PROPN
ap-1213	284	41	brook	brook	PROPN
ap-1213	284	42	,	,	PUNCT
ap-1213	284	43	march	march	PROPN
ap-1213	284	44	23–27	23–27	NUM
ap-1213	284	45	,	,	PUNCT
ap-1213	284	46	2009	2009	NUM
ap-1213	284	47	.	.	PUNCT
ap-1213	285	1	[	[	X
ap-1213	285	2	18	18	NUM
ap-1213	285	3	]	]	PUNCT
ap-1213	285	4	okawa	okawa	PROPN
ap-1213	285	5	,	,	PUNCT
ap-1213	285	6	y.	y.	PROPN
ap-1213	285	7	,	,	PUNCT
ap-1213	285	8	rastelli	rastelli	PROPN
ap-1213	285	9	,	,	PUNCT
ap-1213	285	10	l.	l.	PROPN
ap-1213	285	11	,	,	PUNCT
ap-1213	285	12	zwiebach	zwiebach	PROPN
ap-1213	285	13	,	,	PUNCT
ap-1213	285	14	b.	b.	PROPN
ap-1213	285	15	:	:	PUNCT
ap-1213	285	16	analytic	analytic	ADJ
ap-1213	285	17	solutions	solution	NOUN
ap-1213	285	18	for	for	ADP
ap-1213	285	19	tachyon	tachyon	NOUN
ap-1213	285	20	condensation	condensation	NOUN
ap-1213	285	21	with	with	ADP
ap-1213	285	22	general	general	ADJ
ap-1213	285	23	projectors	projector	NOUN
ap-1213	285	24	,	,	PUNCT
ap-1213	285	25	arxiv	arxiv	NOUN
ap-1213	285	26	:	:	PUNCT
ap-1213	285	27	hep	hep	NOUN
ap-1213	285	28	-	-	PROPN
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ap-1213	285	30	.	.	PUNCT
ap-1213	286	1	[	[	X
ap-1213	286	2	19	19	NUM
ap-1213	286	3	]	]	SYM
ap-1213	286	4	erler	erler	NOUN
ap-1213	286	5	,	,	PUNCT
ap-1213	286	6	t.	t.	PROPN
ap-1213	286	7	,	,	PUNCT
ap-1213	286	8	schnabl	schnabl	NOUN
ap-1213	286	9	,	,	PUNCT
ap-1213	286	10	m.	m.	NOUN
ap-1213	286	11	:	:	PUNCT
ap-1213	286	12	a	a	DET
ap-1213	286	13	simple	simple	ADJ
ap-1213	286	14	analytic	analytic	ADJ
ap-1213	286	15	solution	solution	NOUN
ap-1213	286	16	for	for	ADP
ap-1213	286	17	tachyon	tachyon	NOUN
ap-1213	286	18	condensation	condensation	NOUN
ap-1213	286	19	,	,	PUNCT
ap-1213	286	20	jhep	jhep	ADJ
ap-1213	286	21	0910	0910	NUM
ap-1213	286	22	(	(	PUNCT
ap-1213	286	23	2009	2009	NUM
ap-1213	286	24	)	)	PUNCT
ap-1213	286	25	066	066	NUM
ap-1213	287	1	[	[	X
ap-1213	287	2	arxiv:0906.0979	arxiv:0906.0979	X
ap-1213	287	3	[	[	PUNCT
ap-1213	287	4	hep	hep	NOUN
ap-1213	287	5	-	-	PUNCT
ap-1213	287	6	th	th	X
ap-1213	287	7	]	]	X
ap-1213	287	8	]	]	PUNCT
ap-1213	287	9	.	.	PUNCT
ap-1213	288	1	martin	martin	PROPN
ap-1213	288	2	schnabl	schnabl	PROPN
ap-1213	288	3	e	e	NOUN
ap-1213	288	4	-	-	NOUN
ap-1213	288	5	mail	mail	NOUN
ap-1213	288	6	:	:	PUNCT
ap-1213	288	7	schnabl.martin@gmail.com	schnabl.martin@gmail.com	PROPN
ap-1213	288	8	institute	institute	PROPN
ap-1213	288	9	of	of	ADP
ap-1213	288	10	physics	physics	PROPN
ap-1213	288	11	as	as	ADP
ap-1213	288	12	cr	cr	PROPN
ap-1213	288	13	na	na	PART
ap-1213	288	14	slovance	slovance	PROPN
ap-1213	288	15	2	2	NUM
ap-1213	288	16	,	,	PUNCT
ap-1213	288	17	prague	prague	NOUN
ap-1213	288	18	8	8	NUM
ap-1213	288	19	,	,	PUNCT
ap-1213	288	20	czech	czech	PROPN
ap-1213	288	21	republic	republic	NOUN
ap-1213	288	22	108	108	NUM