id	sid	tid	token	lemma	pos
ap-3105	1	1	acta	acta	PROPN
ap-3105	1	2	polytechnica	polytechnica	PROPN
ap-3105	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3105	1	4	/	/	SYM
ap-3105	1	5	ap.2016.56.0224	ap.2016.56.0224	PROPN
ap-3105	1	6	acta	acta	PROPN
ap-3105	1	7	polytechnica	polytechnica	PROPN
ap-3105	1	8	56(3):224–235	56(3):224–235	PROPN
ap-3105	1	9	,	,	PUNCT
ap-3105	1	10	2016	2016	NUM
ap-3105	1	11	©	©	PROPN
ap-3105	1	12	czech	czech	PROPN
ap-3105	1	13	technical	technical	PROPN
ap-3105	1	14	university	university	PROPN
ap-3105	1	15	in	in	ADP
ap-3105	1	16	prague	prague	PROPN
ap-3105	1	17	,	,	PUNCT
ap-3105	1	18	2016	2016	NUM
ap-3105	1	19	available	available	ADJ
ap-3105	1	20	online	online	ADV
ap-3105	1	21	at	at	ADP
ap-3105	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3105	1	23	the	the	DET
ap-3105	1	24	aharonov	aharonov	NOUN
ap-3105	1	25	-	-	PUNCT
ap-3105	1	26	bohm	bohm	PROPN
ap-3105	1	27	hamiltonian	hamiltonian	NOUN
ap-3105	1	28	with	with	ADP
ap-3105	1	29	two	two	NUM
ap-3105	1	30	vortices	vortex	NOUN
ap-3105	1	31	revisited	revisit	VERB
ap-3105	1	32	petra	petra	PROPN
ap-3105	1	33	košťáková	košťáková	PROPN
ap-3105	1	34	,	,	PUNCT
ap-3105	1	35	pavel	pavel	PROPN
ap-3105	1	36	šťovíček∗	šťovíček∗	PROPN
ap-3105	1	37	department	department	PROPN
ap-3105	1	38	of	of	ADP
ap-3105	1	39	mathematics	mathematic	NOUN
ap-3105	1	40	,	,	PUNCT
ap-3105	1	41	faculty	faculty	NOUN
ap-3105	1	42	of	of	ADP
ap-3105	1	43	nuclear	nuclear	ADJ
ap-3105	1	44	sciences	science	NOUN
ap-3105	1	45	and	and	CCONJ
ap-3105	1	46	physical	physical	ADJ
ap-3105	1	47	engineering	engineering	NOUN
ap-3105	1	48	,	,	PUNCT
ap-3105	1	49	czech	czech	PROPN
ap-3105	1	50	technical	technical	PROPN
ap-3105	1	51	university	university	PROPN
ap-3105	1	52	in	in	ADP
ap-3105	1	53	prague	prague	PROPN
ap-3105	1	54	,	,	PUNCT
ap-3105	1	55	trojanova	trojanova	X
ap-3105	1	56	13	13	NUM
ap-3105	1	57	,	,	PUNCT
ap-3105	1	58	120	120	NUM
ap-3105	1	59	00	00	NUM
ap-3105	1	60	praha	praha	PROPN
ap-3105	1	61	,	,	PUNCT
ap-3105	1	62	czech	czech	PROPN
ap-3105	1	63	republic	republic	NOUN
ap-3105	1	64	∗	∗	NOUN
ap-3105	1	65	corresponding	correspond	VERB
ap-3105	1	66	author	author	NOUN
ap-3105	1	67	:	:	PUNCT
ap-3105	1	68	stovipav@kmlinux.fjfi.cvut.cz	stovipav@kmlinux.fjfi.cvut.cz	ADJ
ap-3105	1	69	abstract	abstract	NOUN
ap-3105	1	70	.	.	PUNCT
ap-3105	2	1	we	we	PRON
ap-3105	2	2	consider	consider	VERB
ap-3105	2	3	an	an	DET
ap-3105	2	4	invariant	invariant	ADJ
ap-3105	2	5	quantum	quantum	NOUN
ap-3105	2	6	hamiltonian	hamiltonian	NOUN
ap-3105	2	7	h	h	NOUN
ap-3105	2	8	=	=	PUNCT
ap-3105	2	9	−∆lb	−∆lb	PROPN
ap-3105	2	10	+	+	CCONJ
ap-3105	2	11	v	v	NOUN
ap-3105	2	12	in	in	ADP
ap-3105	2	13	the	the	DET
ap-3105	2	14	l2	l2	NOUN
ap-3105	2	15	space	space	NOUN
ap-3105	2	16	based	base	VERB
ap-3105	2	17	on	on	ADP
ap-3105	2	18	a	a	DET
ap-3105	2	19	riemannian	riemannian	ADJ
ap-3105	2	20	manifold	manifold	ADJ
ap-3105	2	21	m̃	m̃	PROPN
ap-3105	2	22	with	with	ADP
ap-3105	2	23	a	a	DET
ap-3105	2	24	discrete	discrete	ADJ
ap-3105	2	25	symmetry	symmetry	NOUN
ap-3105	2	26	group	group	NOUN
ap-3105	2	27	γ	γ	PROPN
ap-3105	2	28	.	.	PROPN
ap-3105	2	29	to	to	ADP
ap-3105	2	30	any	any	DET
ap-3105	2	31	unitary	unitary	ADJ
ap-3105	2	32	representation	representation	NOUN
ap-3105	2	33	λ	λ	PROPN
ap-3105	2	34	of	of	ADP
ap-3105	2	35	γ	γ	PROPN
ap-3105	2	36	one	one	PRON
ap-3105	2	37	can	can	AUX
ap-3105	2	38	relate	relate	VERB
ap-3105	2	39	another	another	DET
ap-3105	2	40	operator	operator	NOUN
ap-3105	2	41	on	on	ADP
ap-3105	2	42	m	m	PROPN
ap-3105	2	43	=	=	SYM
ap-3105	2	44	m̃/γ	m̃/γ	NOUN
ap-3105	2	45	,	,	PUNCT
ap-3105	2	46	called	call	VERB
ap-3105	2	47	hλ	hλ	ADP
ap-3105	2	48	,	,	PUNCT
ap-3105	2	49	which	which	PRON
ap-3105	2	50	formally	formally	ADV
ap-3105	2	51	corresponds	correspond	VERB
ap-3105	2	52	to	to	ADP
ap-3105	2	53	the	the	DET
ap-3105	2	54	same	same	ADJ
ap-3105	2	55	differential	differential	NOUN
ap-3105	2	56	operator	operator	NOUN
ap-3105	2	57	as	as	ADP
ap-3105	2	58	h	h	NOUN
ap-3105	2	59	but	but	CCONJ
ap-3105	2	60	which	which	PRON
ap-3105	2	61	is	be	AUX
ap-3105	2	62	determined	determine	VERB
ap-3105	2	63	by	by	ADP
ap-3105	2	64	quasi	quasi	ADJ
ap-3105	2	65	-	-	ADJ
ap-3105	2	66	periodic	periodic	ADJ
ap-3105	2	67	boundary	boundary	ADJ
ap-3105	2	68	conditions	condition	NOUN
ap-3105	2	69	.	.	PUNCT
ap-3105	3	1	as	as	SCONJ
ap-3105	3	2	originally	originally	ADV
ap-3105	3	3	observed	observe	VERB
ap-3105	3	4	by	by	ADP
ap-3105	3	5	schulman	schulman	NOUN
ap-3105	3	6	in	in	ADP
ap-3105	3	7	theoretical	theoretical	ADJ
ap-3105	3	8	physics	physics	NOUN
ap-3105	3	9	and	and	CCONJ
ap-3105	3	10	sunada	sunada	NOUN
ap-3105	3	11	in	in	ADP
ap-3105	3	12	mathematics	mathematic	NOUN
ap-3105	3	13	,	,	PUNCT
ap-3105	3	14	one	one	PRON
ap-3105	3	15	can	can	AUX
ap-3105	3	16	construct	construct	VERB
ap-3105	3	17	the	the	DET
ap-3105	3	18	propagator	propagator	NOUN
ap-3105	3	19	associated	associate	VERB
ap-3105	3	20	with	with	ADP
ap-3105	3	21	hλ	hλ	NOUN
ap-3105	3	22	provided	provide	VERB
ap-3105	3	23	one	one	NUM
ap-3105	3	24	knows	know	VERB
ap-3105	3	25	the	the	DET
ap-3105	3	26	propagator	propagator	NOUN
ap-3105	3	27	associated	associate	VERB
ap-3105	3	28	with	with	ADP
ap-3105	3	29	h.	h.	PROPN
ap-3105	3	30	this	this	DET
ap-3105	3	31	approach	approach	NOUN
ap-3105	3	32	is	be	AUX
ap-3105	3	33	reviewed	review	VERB
ap-3105	3	34	and	and	CCONJ
ap-3105	3	35	demonstrated	demonstrate	VERB
ap-3105	3	36	on	on	ADP
ap-3105	3	37	a	a	DET
ap-3105	3	38	quantum	quantum	ADJ
ap-3105	3	39	model	model	NOUN
ap-3105	3	40	describing	describe	VERB
ap-3105	3	41	a	a	DET
ap-3105	3	42	charged	charge	VERB
ap-3105	3	43	particle	particle	NOUN
ap-3105	3	44	on	on	ADP
ap-3105	3	45	the	the	DET
ap-3105	3	46	plane	plane	NOUN
ap-3105	3	47	with	with	ADP
ap-3105	3	48	two	two	NUM
ap-3105	3	49	aharonov	aharonov	NOUN
ap-3105	3	50	-	-	PUNCT
ap-3105	3	51	bohm	bohm	PROPN
ap-3105	3	52	vortices	vortex	NOUN
ap-3105	3	53	.	.	PUNCT
ap-3105	4	1	the	the	DET
ap-3105	4	2	construction	construction	NOUN
ap-3105	4	3	of	of	ADP
ap-3105	4	4	the	the	DET
ap-3105	4	5	propagator	propagator	NOUN
ap-3105	4	6	is	be	AUX
ap-3105	4	7	explained	explain	VERB
ap-3105	4	8	in	in	ADP
ap-3105	4	9	full	full	ADJ
ap-3105	4	10	detail	detail	NOUN
ap-3105	4	11	including	include	VERB
ap-3105	4	12	all	all	DET
ap-3105	4	13	substantial	substantial	ADJ
ap-3105	4	14	intermediate	intermediate	ADJ
ap-3105	4	15	steps	step	NOUN
ap-3105	4	16	.	.	PUNCT
ap-3105	5	1	keywords	keyword	NOUN
ap-3105	5	2	:	:	PUNCT
ap-3105	5	3	aharonov	aharonov	NOUN
ap-3105	5	4	-	-	PUNCT
ap-3105	5	5	bohm	bohm	PROPN
ap-3105	5	6	effect	effect	NOUN
ap-3105	5	7	;	;	PUNCT
ap-3105	5	8	propagator	propagator	NOUN
ap-3105	5	9	;	;	PUNCT
ap-3105	5	10	covering	cover	VERB
ap-3105	5	11	space	space	NOUN
ap-3105	5	12	;	;	PUNCT
ap-3105	5	13	bloch	bloch	NOUN
ap-3105	5	14	decomposition	decomposition	NOUN
ap-3105	5	15	.	.	PUNCT
ap-3105	6	1	1	1	X
ap-3105	6	2	.	.	X
ap-3105	6	3	introduction	introduction	NOUN
ap-3105	6	4	suppose	suppose	VERB
ap-3105	6	5	there	there	PRON
ap-3105	6	6	is	be	VERB
ap-3105	6	7	given	give	VERB
ap-3105	6	8	a	a	DET
ap-3105	6	9	riemannian	riemannian	ADJ
ap-3105	6	10	manifold	manifold	ADJ
ap-3105	6	11	m̃	m̃	PROPN
ap-3105	6	12	with	with	ADP
ap-3105	6	13	a	a	DET
ap-3105	6	14	discrete	discrete	ADJ
ap-3105	6	15	symmetry	symmetry	NOUN
ap-3105	6	16	group	group	NOUN
ap-3105	6	17	γ	γ	NOUN
ap-3105	6	18	and	and	CCONJ
ap-3105	6	19	a	a	DET
ap-3105	6	20	γ	γ	ADJ
ap-3105	6	21	-	-	ADJ
ap-3105	6	22	periodic	periodic	ADJ
ap-3105	6	23	hamilton	hamilton	PROPN
ap-3105	6	24	operator	operator	NOUN
ap-3105	6	25	h	h	NOUN
ap-3105	6	26	on	on	ADP
ap-3105	6	27	l2(m̃	l2(m̃	PROPN
ap-3105	6	28	)	)	PUNCT
ap-3105	6	29	.	.	PUNCT
ap-3105	7	1	to	to	ADP
ap-3105	7	2	any	any	DET
ap-3105	7	3	unitary	unitary	ADJ
ap-3105	7	4	representation	representation	NOUN
ap-3105	7	5	λ	λ	PROPN
ap-3105	7	6	of	of	ADP
ap-3105	7	7	γ	γ	PROPN
ap-3105	7	8	one	one	PRON
ap-3105	7	9	can	can	AUX
ap-3105	7	10	relate	relate	VERB
ap-3105	7	11	another	another	DET
ap-3105	7	12	operator	operator	NOUN
ap-3105	7	13	on	on	ADP
ap-3105	7	14	m	m	PROPN
ap-3105	7	15	=	=	SYM
ap-3105	7	16	m̃/γ	m̃/γ	NOUN
ap-3105	7	17	,	,	PUNCT
ap-3105	7	18	called	call	VERB
ap-3105	7	19	hλ	hλ	ADP
ap-3105	7	20	,	,	PUNCT
ap-3105	7	21	which	which	PRON
ap-3105	7	22	is	be	AUX
ap-3105	7	23	determined	determine	VERB
ap-3105	7	24	by	by	ADP
ap-3105	7	25	quasi	quasi	ADJ
ap-3105	7	26	-	-	ADJ
ap-3105	7	27	periodic	periodic	ADJ
ap-3105	7	28	boundary	boundary	ADJ
ap-3105	7	29	conditions	condition	NOUN
ap-3105	7	30	.	.	PUNCT
ap-3105	8	1	a	a	DET
ap-3105	8	2	formula	formula	NOUN
ap-3105	8	3	relating	relate	VERB
ap-3105	8	4	the	the	DET
ap-3105	8	5	propagators	propagator	NOUN
ap-3105	8	6	kλ	kλ	X
ap-3105	8	7	t	t	PROPN
ap-3105	8	8	(	(	PUNCT
ap-3105	8	9	x	x	X
ap-3105	8	10	,	,	PUNCT
ap-3105	8	11	x0	x0	PROPN
ap-3105	8	12	)	)	PUNCT
ap-3105	8	13	and	and	CCONJ
ap-3105	8	14	kt(x	kt(x	PROPN
ap-3105	8	15	,	,	PUNCT
ap-3105	8	16	x0	x0	PROPN
ap-3105	8	17	)	)	PUNCT
ap-3105	8	18	associated	associate	VERB
ap-3105	8	19	with	with	ADP
ap-3105	8	20	hλ	hλ	NOUN
ap-3105	8	21	and	and	CCONJ
ap-3105	8	22	h	h	NOUN
ap-3105	8	23	,	,	PUNCT
ap-3105	8	24	respectively	respectively	ADV
ap-3105	8	25	,	,	PUNCT
ap-3105	8	26	has	have	AUX
ap-3105	8	27	been	be	AUX
ap-3105	8	28	derived	derive	VERB
ap-3105	8	29	in	in	ADP
ap-3105	8	30	the	the	DET
ap-3105	8	31	framework	framework	NOUN
ap-3105	8	32	of	of	ADP
ap-3105	8	33	the	the	DET
ap-3105	8	34	feynman	feynman	PROPN
ap-3105	8	35	path	path	PROPN
ap-3105	8	36	integral	integral	ADJ
ap-3105	8	37	[	[	X
ap-3105	8	38	18	18	NUM
ap-3105	8	39	,	,	PUNCT
ap-3105	8	40	19	19	NUM
ap-3105	8	41	]	]	PUNCT
ap-3105	8	42	.	.	PUNCT
ap-3105	9	1	an	an	DET
ap-3105	9	2	analogous	analogous	ADJ
ap-3105	9	3	formula	formula	NOUN
ap-3105	9	4	is	be	AUX
ap-3105	9	5	also	also	ADV
ap-3105	9	6	known	know	VERB
ap-3105	9	7	for	for	ADP
ap-3105	9	8	heat	heat	NOUN
ap-3105	9	9	kernels	kernel	NOUN
ap-3105	9	10	[	[	X
ap-3105	9	11	4	4	NUM
ap-3105	9	12	]	]	PUNCT
ap-3105	9	13	.	.	PUNCT
ap-3105	10	1	an	an	DET
ap-3105	10	2	opposite	opposite	ADJ
ap-3105	10	3	point	point	NOUN
ap-3105	10	4	of	of	ADP
ap-3105	10	5	view	view	NOUN
ap-3105	10	6	is	be	AUX
ap-3105	10	7	taken	take	VERB
ap-3105	10	8	when	when	SCONJ
ap-3105	10	9	one	one	NUM
ap-3105	10	10	decomposes	decompose	VERB
ap-3105	10	11	the	the	DET
ap-3105	10	12	operator	operator	NOUN
ap-3105	10	13	h	h	NOUN
ap-3105	10	14	into	into	ADP
ap-3105	10	15	a	a	DET
ap-3105	10	16	direct	direct	ADJ
ap-3105	10	17	integral	integral	NOUN
ap-3105	10	18	with	with	ADP
ap-3105	10	19	components	component	NOUN
ap-3105	10	20	hλ	hλ	ADP
ap-3105	10	21	where	where	SCONJ
ap-3105	10	22	λ	λ	PROPN
ap-3105	10	23	runs	run	VERB
ap-3105	10	24	over	over	ADP
ap-3105	10	25	all	all	DET
ap-3105	10	26	irreducible	irreducible	ADJ
ap-3105	10	27	unitary	unitary	ADJ
ap-3105	10	28	representations	representation	NOUN
ap-3105	10	29	of	of	ADP
ap-3105	10	30	γ	γ	NOUN
ap-3105	10	31	[	[	X
ap-3105	10	32	3	3	NUM
ap-3105	10	33	,	,	PUNCT
ap-3105	10	34	6	6	NUM
ap-3105	10	35	,	,	PUNCT
ap-3105	10	36	23	23	NUM
ap-3105	10	37	]	]	PUNCT
ap-3105	10	38	.	.	PUNCT
ap-3105	11	1	the	the	DET
ap-3105	11	2	evolution	evolution	NOUN
ap-3105	11	3	operator	operator	NOUN
ap-3105	11	4	then	then	ADV
ap-3105	11	5	decomposes	decompose	VERB
ap-3105	11	6	correspondingly	correspondingly	ADV
ap-3105	11	7	.	.	PUNCT
ap-3105	12	1	this	this	DET
ap-3105	12	2	type	type	NOUN
ap-3105	12	3	of	of	ADP
ap-3105	12	4	decomposition	decomposition	NOUN
ap-3105	12	5	is	be	AUX
ap-3105	12	6	a	a	DET
ap-3105	12	7	substantial	substantial	ADJ
ap-3105	12	8	step	step	NOUN
ap-3105	12	9	in	in	ADP
ap-3105	12	10	the	the	DET
ap-3105	12	11	bloch	bloch	PROPN
ap-3105	12	12	analysis	analysis	NOUN
ap-3105	12	13	.	.	PUNCT
ap-3105	13	1	the	the	DET
ap-3105	13	2	both	both	DET
ap-3105	13	3	relations	relation	NOUN
ap-3105	13	4	,	,	PUNCT
ap-3105	13	5	the	the	DET
ap-3105	13	6	propagator	propagator	NOUN
ap-3105	13	7	formula	formula	NOUN
ap-3105	13	8	on	on	ADP
ap-3105	13	9	one	one	NUM
ap-3105	13	10	hand	hand	NOUN
ap-3105	13	11	and	and	CCONJ
ap-3105	13	12	the	the	DET
ap-3105	13	13	generalized	generalized	ADJ
ap-3105	13	14	bloch	bloch	NOUN
ap-3105	13	15	decomposition	decomposition	NOUN
ap-3105	13	16	on	on	ADP
ap-3105	13	17	the	the	DET
ap-3105	13	18	other	other	ADJ
ap-3105	13	19	hand	hand	NOUN
ap-3105	13	20	,	,	PUNCT
ap-3105	13	21	are	be	AUX
ap-3105	13	22	in	in	ADP
ap-3105	13	23	a	a	DET
ap-3105	13	24	sense	sense	NOUN
ap-3105	13	25	mutually	mutually	ADV
ap-3105	13	26	inverse	inverse	ADJ
ap-3105	13	27	[	[	X
ap-3105	13	28	11	11	NUM
ap-3105	13	29	,	,	PUNCT
ap-3105	13	30	12	12	NUM
ap-3105	13	31	]	]	PUNCT
ap-3105	13	32	.	.	PUNCT
ap-3105	14	1	in	in	ADP
ap-3105	14	2	the	the	DET
ap-3105	14	3	current	current	ADJ
ap-3105	14	4	paper	paper	NOUN
ap-3105	14	5	we	we	PRON
ap-3105	14	6	wish	wish	VERB
ap-3105	14	7	to	to	PART
ap-3105	14	8	demonstrate	demonstrate	VERB
ap-3105	14	9	how	how	SCONJ
ap-3105	14	10	this	this	DET
ap-3105	14	11	relationship	relationship	NOUN
ap-3105	14	12	can	can	AUX
ap-3105	14	13	be	be	AUX
ap-3105	14	14	effectively	effectively	ADV
ap-3105	14	15	used	use	VERB
ap-3105	14	16	on	on	ADP
ap-3105	14	17	a	a	DET
ap-3105	14	18	concrete	concrete	ADJ
ap-3105	14	19	example	example	NOUN
ap-3105	14	20	of	of	ADP
ap-3105	14	21	interest	interest	NOUN
ap-3105	14	22	.	.	PUNCT
ap-3105	15	1	we	we	PRON
ap-3105	15	2	consider	consider	VERB
ap-3105	15	3	the	the	DET
ap-3105	15	4	formula	formula	NOUN
ap-3105	15	5	for	for	ADP
ap-3105	15	6	propagators	propagator	NOUN
ap-3105	15	7	in	in	ADP
ap-3105	15	8	the	the	DET
ap-3105	15	9	case	case	NOUN
ap-3105	15	10	of	of	ADP
ap-3105	15	11	the	the	DET
ap-3105	15	12	aharonov	aharonov	PROPN
ap-3105	15	13	-	-	PUNCT
ap-3105	15	14	bohm	bohm	PROPN
ap-3105	15	15	effect	effect	NOUN
ap-3105	15	16	with	with	ADP
ap-3105	15	17	two	two	NUM
ap-3105	15	18	vortices	vortex	NOUN
ap-3105	15	19	.	.	PUNCT
ap-3105	16	1	in	in	ADP
ap-3105	16	2	this	this	DET
ap-3105	16	3	quantum	quantum	NOUN
ap-3105	16	4	model	model	NOUN
ap-3105	16	5	,	,	PUNCT
ap-3105	16	6	m̃	m̃	PROPN
ap-3105	16	7	is	be	AUX
ap-3105	16	8	identified	identify	VERB
ap-3105	16	9	with	with	ADP
ap-3105	16	10	the	the	DET
ap-3105	16	11	universal	universal	ADJ
ap-3105	16	12	covering	covering	NOUN
ap-3105	16	13	space	space	NOUN
ap-3105	16	14	of	of	ADP
ap-3105	16	15	the	the	DET
ap-3105	16	16	plane	plane	NOUN
ap-3105	16	17	with	with	ADP
ap-3105	16	18	two	two	NUM
ap-3105	16	19	excluded	exclude	VERB
ap-3105	16	20	points	point	NOUN
ap-3105	16	21	and	and	CCONJ
ap-3105	16	22	γ	γ	NOUN
ap-3105	16	23	is	be	AUX
ap-3105	16	24	the	the	DET
ap-3105	16	25	fundamental	fundamental	ADJ
ap-3105	16	26	group	group	NOUN
ap-3105	16	27	of	of	ADP
ap-3105	16	28	the	the	DET
ap-3105	16	29	same	same	ADJ
ap-3105	16	30	manifold	manifold	NOUN
ap-3105	16	31	.	.	PUNCT
ap-3105	17	1	this	this	DET
ap-3105	17	2	problem	problem	NOUN
ap-3105	17	3	has	have	AUX
ap-3105	17	4	already	already	ADV
ap-3105	17	5	been	be	AUX
ap-3105	17	6	treated	treat	VERB
ap-3105	17	7	by	by	ADP
ap-3105	17	8	one	one	NUM
ap-3105	17	9	of	of	ADP
ap-3105	17	10	the	the	DET
ap-3105	17	11	authors	author	NOUN
ap-3105	17	12	quite	quite	DET
ap-3105	17	13	a	a	DET
ap-3105	17	14	long	long	ADJ
ap-3105	17	15	time	time	NOUN
ap-3105	17	16	ago	ago	ADV
ap-3105	17	17	in	in	ADP
ap-3105	17	18	[	[	X
ap-3105	17	19	21	21	NUM
ap-3105	17	20	]	]	PUNCT
ap-3105	17	21	.	.	PUNCT
ap-3105	18	1	but	but	CCONJ
ap-3105	18	2	the	the	DET
ap-3105	18	3	topic	topic	NOUN
ap-3105	18	4	is	be	AUX
ap-3105	18	5	in	in	ADP
ap-3105	18	6	no	no	DET
ap-3105	18	7	way	way	NOUN
ap-3105	18	8	exhausted	exhaust	VERB
ap-3105	18	9	completely	completely	ADV
ap-3105	18	10	,	,	PUNCT
ap-3105	18	11	and	and	CCONJ
ap-3105	18	12	this	this	DET
ap-3105	18	13	quantum	quantum	NOUN
ap-3105	18	14	model	model	NOUN
ap-3105	18	15	was	be	AUX
ap-3105	18	16	intensively	intensively	ADV
ap-3105	18	17	discussed	discuss	VERB
ap-3105	18	18	in	in	ADP
ap-3105	18	19	a	a	DET
ap-3105	18	20	number	number	NOUN
ap-3105	18	21	of	of	ADP
ap-3105	18	22	papers	paper	NOUN
ap-3105	18	23	,	,	PUNCT
ap-3105	18	24	in	in	ADP
ap-3105	18	25	some	some	DET
ap-3105	18	26	cases	case	NOUN
ap-3105	18	27	even	even	ADV
ap-3105	18	28	very	very	ADV
ap-3105	18	29	recently	recently	ADV
ap-3105	18	30	.	.	PUNCT
ap-3105	19	1	these	these	DET
ap-3105	19	2	discussions	discussion	NOUN
ap-3105	19	3	rely	rely	VERB
ap-3105	19	4	on	on	ADP
ap-3105	19	5	completely	completely	ADV
ap-3105	19	6	different	different	ADJ
ap-3105	19	7	approaches	approach	NOUN
ap-3105	19	8	,	,	PUNCT
ap-3105	19	9	however	however	ADV
ap-3105	19	10	,	,	PUNCT
ap-3105	19	11	like	like	ADP
ap-3105	19	12	asymptotic	asymptotic	ADJ
ap-3105	19	13	methods	method	NOUN
ap-3105	19	14	for	for	ADP
ap-3105	19	15	largely	largely	ADV
ap-3105	19	16	separated	separate	VERB
ap-3105	19	17	vortices	vortex	NOUN
ap-3105	19	18	,	,	PUNCT
ap-3105	19	19	semiclassical	semiclassical	ADJ
ap-3105	19	20	analysis	analysis	NOUN
ap-3105	19	21	and	and	CCONJ
ap-3105	19	22	a	a	DET
ap-3105	19	23	complex	complex	ADJ
ap-3105	19	24	scaling	scaling	NOUN
ap-3105	19	25	method	method	NOUN
ap-3105	19	26	[	[	X
ap-3105	19	27	1	1	NUM
ap-3105	19	28	,	,	PUNCT
ap-3105	19	29	2	2	NUM
ap-3105	19	30	,	,	PUNCT
ap-3105	19	31	9	9	NUM
ap-3105	19	32	,	,	PUNCT
ap-3105	19	33	25	25	NUM
ap-3105	19	34	]	]	PUNCT
ap-3105	19	35	.	.	PUNCT
ap-3105	20	1	one	one	PRON
ap-3105	20	2	may	may	AUX
ap-3105	20	3	also	also	ADV
ap-3105	20	4	mention	mention	VERB
ap-3105	20	5	more	more	ADJ
ap-3105	20	6	complex	complex	ADJ
ap-3105	20	7	models	model	NOUN
ap-3105	20	8	comprising	comprise	VERB
ap-3105	20	9	,	,	PUNCT
ap-3105	20	10	apart	apart	ADV
ap-3105	20	11	of	of	ADP
ap-3105	20	12	magnetic	magnetic	ADJ
ap-3105	20	13	vortices	vortex	NOUN
ap-3105	20	14	,	,	PUNCT
ap-3105	20	15	also	also	ADV
ap-3105	20	16	additional	additional	ADJ
ap-3105	20	17	potentials	potential	NOUN
ap-3105	20	18	or	or	CCONJ
ap-3105	20	19	magnetic	magnetic	ADJ
ap-3105	20	20	fields	field	NOUN
ap-3105	20	21	[	[	X
ap-3105	20	22	14	14	NUM
ap-3105	20	23	,	,	PUNCT
ap-3105	20	24	16	16	NUM
ap-3105	20	25	]	]	PUNCT
ap-3105	20	26	,	,	PUNCT
ap-3105	20	27	or	or	CCONJ
ap-3105	20	28	models	model	NOUN
ap-3105	20	29	with	with	ADP
ap-3105	20	30	an	an	DET
ap-3105	20	31	arbitrary	arbitrary	ADJ
ap-3105	20	32	finite	finite	ADJ
ap-3105	20	33	number	number	NOUN
ap-3105	20	34	of	of	ADP
ap-3105	20	35	magnetic	magnetic	ADJ
ap-3105	20	36	vortices	vortex	NOUN
ap-3105	20	37	or	or	CCONJ
ap-3105	20	38	even	even	ADV
ap-3105	20	39	with	with	ADP
ap-3105	20	40	countably	countably	ADV
ap-3105	20	41	many	many	ADJ
ap-3105	20	42	vortices	vortex	NOUN
ap-3105	20	43	arranged	arrange	VERB
ap-3105	20	44	in	in	ADP
ap-3105	20	45	a	a	DET
ap-3105	20	46	lattice	lattice	NOUN
ap-3105	21	1	[	[	X
ap-3105	21	2	15	15	NUM
ap-3105	21	3	,	,	PUNCT
ap-3105	21	4	17	17	NUM
ap-3105	21	5	,	,	PUNCT
ap-3105	21	6	22	22	NUM
ap-3105	21	7	]	]	PUNCT
ap-3105	21	8	.	.	PUNCT
ap-3105	22	1	on	on	ADP
ap-3105	22	2	the	the	DET
ap-3105	22	3	other	other	ADJ
ap-3105	22	4	hand	hand	NOUN
ap-3105	22	5	,	,	PUNCT
ap-3105	22	6	the	the	DET
ap-3105	22	7	method	method	NOUN
ap-3105	22	8	stemming	stem	VERB
ap-3105	22	9	from	from	ADP
ap-3105	22	10	the	the	DET
ap-3105	22	11	original	original	ADJ
ap-3105	22	12	ideas	idea	NOUN
ap-3105	22	13	of	of	ADP
ap-3105	22	14	schulman	schulman	NOUN
ap-3105	22	15	and	and	CCONJ
ap-3105	22	16	sunada	sunada	NOUN
ap-3105	22	17	turned	turn	VERB
ap-3105	22	18	out	out	ADP
ap-3105	22	19	to	to	PART
ap-3105	22	20	be	be	AUX
ap-3105	22	21	fruitful	fruitful	ADJ
ap-3105	22	22	also	also	ADV
ap-3105	22	23	in	in	ADP
ap-3105	22	24	analysis	analysis	NOUN
ap-3105	22	25	of	of	ADP
ap-3105	22	26	other	other	ADJ
ap-3105	22	27	interesting	interesting	ADJ
ap-3105	22	28	models	model	NOUN
ap-3105	22	29	like	like	ADP
ap-3105	22	30	brownian	brownian	ADJ
ap-3105	22	31	random	random	ADJ
ap-3105	22	32	walk	walk	NOUN
ap-3105	22	33	on	on	ADP
ap-3105	22	34	the	the	DET
ap-3105	22	35	twice	twice	ADV
ap-3105	22	36	punctured	punctured	ADJ
ap-3105	22	37	plane	plane	NOUN
ap-3105	22	38	[	[	X
ap-3105	22	39	5	5	NUM
ap-3105	22	40	,	,	PUNCT
ap-3105	22	41	7	7	NUM
ap-3105	22	42	]	]	PUNCT
ap-3105	22	43	.	.	PUNCT
ap-3105	23	1	here	here	ADV
ap-3105	23	2	we	we	PRON
ap-3105	23	3	return	return	VERB
ap-3105	23	4	to	to	ADP
ap-3105	23	5	the	the	DET
ap-3105	23	6	article	article	NOUN
ap-3105	23	7	[	[	X
ap-3105	23	8	21	21	NUM
ap-3105	23	9	]	]	PUNCT
ap-3105	23	10	which	which	PRON
ap-3105	23	11	is	be	AUX
ap-3105	23	12	in	in	ADP
ap-3105	23	13	its	its	PRON
ap-3105	23	14	character	character	NOUN
ap-3105	23	15	a	a	DET
ap-3105	23	16	brief	brief	ADJ
ap-3105	23	17	letter	letter	NOUN
ap-3105	23	18	presenting	present	VERB
ap-3105	23	19	the	the	DET
ap-3105	23	20	final	final	ADJ
ap-3105	23	21	formulas	formula	NOUN
ap-3105	23	22	without	without	ADP
ap-3105	23	23	a	a	DET
ap-3105	23	24	detailed	detailed	ADJ
ap-3105	23	25	derivation	derivation	NOUN
ap-3105	23	26	.	.	PUNCT
ap-3105	24	1	but	but	CCONJ
ap-3105	24	2	the	the	DET
ap-3105	24	3	technique	technique	NOUN
ap-3105	24	4	applied	apply	VERB
ap-3105	24	5	therein	therein	ADV
ap-3105	24	6	is	be	AUX
ap-3105	24	7	of	of	ADP
ap-3105	24	8	independent	independent	ADJ
ap-3105	24	9	interest	interest	NOUN
ap-3105	24	10	and	and	CCONJ
ap-3105	24	11	can	can	AUX
ap-3105	24	12	prove	prove	VERB
ap-3105	24	13	useful	useful	ADJ
ap-3105	24	14	in	in	ADP
ap-3105	24	15	other	other	ADJ
ap-3105	24	16	situations	situation	NOUN
ap-3105	24	17	as	as	ADV
ap-3105	24	18	well	well	ADV
ap-3105	24	19	,	,	PUNCT
ap-3105	24	20	as	as	SCONJ
ap-3105	24	21	already	already	ADV
ap-3105	24	22	mentioned	mention	VERB
ap-3105	24	23	above	above	ADV
ap-3105	24	24	.	.	PUNCT
ap-3105	25	1	this	this	PRON
ap-3105	25	2	is	be	AUX
ap-3105	25	3	why	why	SCONJ
ap-3105	25	4	we	we	PRON
ap-3105	25	5	focus	focus	VERB
ap-3105	25	6	,	,	PUNCT
ap-3105	25	7	in	in	ADP
ap-3105	25	8	the	the	DET
ap-3105	25	9	present	present	ADJ
ap-3105	25	10	paper	paper	NOUN
ap-3105	25	11	,	,	PUNCT
ap-3105	25	12	primarily	primarily	ADV
ap-3105	25	13	on	on	ADP
ap-3105	25	14	the	the	DET
ap-3105	25	15	method	method	NOUN
ap-3105	25	16	itself	itself	PRON
ap-3105	25	17	and	and	CCONJ
ap-3105	25	18	aim	aim	VERB
ap-3105	25	19	to	to	PART
ap-3105	25	20	explain	explain	VERB
ap-3105	25	21	the	the	DET
ap-3105	25	22	approach	approach	NOUN
ap-3105	25	23	on	on	ADP
ap-3105	25	24	a	a	DET
ap-3105	25	25	concrete	concrete	ADJ
ap-3105	25	26	example	example	NOUN
ap-3105	25	27	while	while	SCONJ
ap-3105	25	28	indicating	indicate	VERB
ap-3105	25	29	all	all	DET
ap-3105	25	30	necessary	necessary	ADJ
ap-3105	25	31	intermediate	intermediate	ADJ
ap-3105	25	32	steps	step	NOUN
ap-3105	25	33	in	in	ADP
ap-3105	25	34	full	full	ADJ
ap-3105	25	35	detail	detail	NOUN
ap-3105	25	36	.	.	PUNCT
ap-3105	26	1	hopefully	hopefully	ADV
ap-3105	26	2	,	,	PUNCT
ap-3105	26	3	the	the	DET
ap-3105	26	4	provided	provide	VERB
ap-3105	26	5	analysis	analysis	NOUN
ap-3105	26	6	may	may	AUX
ap-3105	26	7	open	open	VERB
ap-3105	26	8	the	the	DET
ap-3105	26	9	way	way	NOUN
ap-3105	26	10	to	to	ADP
ap-3105	26	11	new	new	ADJ
ap-3105	26	12	applications	application	NOUN
ap-3105	26	13	of	of	ADP
ap-3105	26	14	the	the	DET
ap-3105	26	15	method	method	NOUN
ap-3105	26	16	.	.	PUNCT
ap-3105	27	1	the	the	DET
ap-3105	27	2	paper	paper	NOUN
ap-3105	27	3	is	be	AUX
ap-3105	27	4	organized	organize	VERB
ap-3105	27	5	as	as	SCONJ
ap-3105	27	6	follows	follow	VERB
ap-3105	27	7	.	.	PUNCT
ap-3105	28	1	the	the	DET
ap-3105	28	2	main	main	ADJ
ap-3105	28	3	ideas	idea	NOUN
ap-3105	28	4	and	and	CCONJ
ap-3105	28	5	results	result	NOUN
ap-3105	28	6	of	of	ADP
ap-3105	28	7	the	the	DET
ap-3105	28	8	general	general	ADJ
ap-3105	28	9	approach	approach	NOUN
ap-3105	28	10	are	be	AUX
ap-3105	28	11	outlined	outline	VERB
ap-3105	28	12	in	in	ADP
ap-3105	28	13	section	section	NOUN
ap-3105	28	14	2	2	NUM
ap-3105	28	15	following	follow	VERB
ap-3105	28	16	papers	paper	NOUN
ap-3105	28	17	[	[	X
ap-3105	28	18	11	11	NUM
ap-3105	28	19	,	,	PUNCT
ap-3105	28	20	12	12	NUM
ap-3105	28	21	]	]	PUNCT
ap-3105	28	22	.	.	PUNCT
ap-3105	29	1	section	section	NOUN
ap-3105	29	2	3	3	NUM
ap-3105	29	3	is	be	AUX
ap-3105	29	4	the	the	DET
ap-3105	29	5	key	key	ADJ
ap-3105	29	6	section	section	NOUN
ap-3105	29	7	of	of	ADP
ap-3105	29	8	the	the	DET
ap-3105	29	9	present	present	ADJ
ap-3105	29	10	paper	paper	NOUN
ap-3105	29	11	.	.	PUNCT
ap-3105	30	1	in	in	ADP
ap-3105	30	2	subsection	subsection	NOUN
ap-3105	30	3	3.1	3.1	NUM
ap-3105	30	4	,	,	PUNCT
ap-3105	30	5	a	a	DET
ap-3105	30	6	formula	formula	NOUN
ap-3105	30	7	for	for	ADP
ap-3105	30	8	the	the	DET
ap-3105	30	9	propagator	propagator	NOUN
ap-3105	30	10	on	on	ADP
ap-3105	30	11	the	the	DET
ap-3105	30	12	universal	universal	ADJ
ap-3105	30	13	covering	covering	NOUN
ap-3105	30	14	space	space	NOUN
ap-3105	30	15	of	of	ADP
ap-3105	30	16	the	the	DET
ap-3105	30	17	twice	twice	ADV
ap-3105	30	18	punctured	punctured	ADJ
ap-3105	30	19	plane	plane	NOUN
ap-3105	30	20	,	,	PUNCT
ap-3105	30	21	as	as	SCONJ
ap-3105	30	22	originally	originally	ADV
ap-3105	30	23	presented	present	VERB
ap-3105	30	24	in	in	ADP
ap-3105	30	25	[	[	X
ap-3105	30	26	21	21	NUM
ap-3105	30	27	]	]	PUNCT
ap-3105	30	28	,	,	PUNCT
ap-3105	30	29	is	be	AUX
ap-3105	30	30	briefly	briefly	ADV
ap-3105	30	31	recalled	recall	VERB
ap-3105	30	32	.	.	PUNCT
ap-3105	31	1	subsection	subsection	NOUN
ap-3105	31	2	3.2	3.2	NUM
ap-3105	31	3	has	have	VERB
ap-3105	31	4	a	a	DET
ap-3105	31	5	preliminary	preliminary	ADJ
ap-3105	31	6	character	character	NOUN
ap-3105	31	7	and	and	CCONJ
ap-3105	31	8	provides	provide	VERB
ap-3105	31	9	a	a	DET
ap-3105	31	10	summary	summary	NOUN
ap-3105	31	11	of	of	ADP
ap-3105	31	12	some	some	DET
ap-3105	31	13	auxiliary	auxiliary	ADJ
ap-3105	31	14	useful	useful	ADJ
ap-3105	31	15	identities	identity	NOUN
ap-3105	31	16	.	.	PUNCT
ap-3105	32	1	subsection	subsection	NOUN
ap-3105	32	2	3.3	3.3	NUM
ap-3105	32	3	is	be	AUX
ap-3105	32	4	fully	fully	ADV
ap-3105	32	5	dedicated	dedicated	ADJ
ap-3105	32	6	to	to	ADP
ap-3105	32	7	the	the	DET
ap-3105	32	8	proof	proof	NOUN
ap-3105	32	9	of	of	ADP
ap-3105	32	10	the	the	DET
ap-3105	32	11	propagator	propagator	NOUN
ap-3105	32	12	formula	formula	NOUN
ap-3105	32	13	,	,	PUNCT
ap-3105	32	14	as	as	SCONJ
ap-3105	32	15	given	give	VERB
ap-3105	32	16	in	in	ADP
ap-3105	32	17	(	(	PUNCT
ap-3105	32	18	9	9	NUM
ap-3105	32	19	)	)	PUNCT
ap-3105	32	20	,	,	PUNCT
ap-3105	32	21	(	(	PUNCT
ap-3105	32	22	10	10	NUM
ap-3105	32	23	)	)	PUNCT
ap-3105	32	24	.	.	PUNCT
ap-3105	33	1	more	more	ADV
ap-3105	33	2	precisely	precisely	ADV
ap-3105	33	3	,	,	PUNCT
ap-3105	33	4	the	the	DET
ap-3105	33	5	goal	goal	NOUN
ap-3105	33	6	of	of	ADP
ap-3105	33	7	this	this	DET
ap-3105	33	8	subsection	subsection	NOUN
ap-3105	33	9	is	be	AUX
ap-3105	33	10	a	a	DET
ap-3105	33	11	verification	verification	NOUN
ap-3105	33	12	of	of	ADP
ap-3105	33	13	equation	equation	NOUN
ap-3105	33	14	(	(	PUNCT
ap-3105	33	15	17	17	NUM
ap-3105	33	16	)	)	PUNCT
ap-3105	33	17	.	.	PUNCT
ap-3105	34	1	as	as	ADP
ap-3105	34	2	a	a	DET
ap-3105	34	3	corollary	corollary	NOUN
ap-3105	34	4	,	,	PUNCT
ap-3105	34	5	in	in	ADP
ap-3105	34	6	section	section	NOUN
ap-3105	34	7	4	4	NUM
ap-3105	34	8	,	,	PUNCT
ap-3105	34	9	more	more	ADJ
ap-3105	34	10	details	detail	NOUN
ap-3105	34	11	224	224	NUM
ap-3105	34	12	http://dx.doi.org/10.14311/ap.2016.56.0224	http://dx.doi.org/10.14311/ap.2016.56.0224	NOUN
ap-3105	34	13	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3105	34	14	vol	vol	NOUN
ap-3105	34	15	.	.	PUNCT
ap-3105	35	1	56	56	NUM
ap-3105	35	2	no	no	NOUN
ap-3105	35	3	.	.	PUNCT
ap-3105	36	1	3/2016	3/2016	NUM
ap-3105	36	2	the	the	DET
ap-3105	36	3	aharonov	aharonov	PROPN
ap-3105	36	4	-	-	PUNCT
ap-3105	36	5	bohm	bohm	PROPN
ap-3105	36	6	hamiltonian	hamiltonian	NOUN
ap-3105	36	7	with	with	ADP
ap-3105	36	8	two	two	NUM
ap-3105	36	9	vortices	vortex	NOUN
ap-3105	36	10	revisited	revisit	VERB
ap-3105	36	11	are	be	AUX
ap-3105	36	12	provided	provide	VERB
ap-3105	36	13	,	,	PUNCT
ap-3105	36	14	if	if	SCONJ
ap-3105	36	15	compared	compare	VERB
ap-3105	36	16	to	to	ADP
ap-3105	36	17	[	[	X
ap-3105	36	18	21	21	NUM
ap-3105	36	19	]	]	X
ap-3105	36	20	,	,	PUNCT
ap-3105	36	21	about	about	ADP
ap-3105	36	22	a	a	DET
ap-3105	36	23	formal	formal	ADJ
ap-3105	36	24	application	application	NOUN
ap-3105	36	25	of	of	ADP
ap-3105	36	26	the	the	DET
ap-3105	36	27	schulman	schulman	NOUN
ap-3105	36	28	-	-	PUNCT
ap-3105	36	29	sunada	sunada	NOUN
ap-3105	36	30	formula	formula	NOUN
ap-3105	36	31	,	,	PUNCT
ap-3105	36	32	as	as	SCONJ
ap-3105	36	33	recalled	recall	VERB
ap-3105	36	34	in	in	ADP
ap-3105	36	35	(	(	PUNCT
ap-3105	36	36	5	5	NUM
ap-3105	36	37	)	)	PUNCT
ap-3105	36	38	,	,	PUNCT
ap-3105	36	39	to	to	ADP
ap-3105	36	40	the	the	DET
ap-3105	36	41	studied	studied	ADJ
ap-3105	36	42	example	example	NOUN
ap-3105	36	43	while	while	SCONJ
ap-3105	36	44	making	make	VERB
ap-3105	36	45	use	use	NOUN
ap-3105	36	46	of	of	ADP
ap-3105	36	47	the	the	DET
ap-3105	36	48	knowledge	knowledge	NOUN
ap-3105	36	49	of	of	ADP
ap-3105	36	50	the	the	DET
ap-3105	36	51	propagator	propagator	NOUN
ap-3105	36	52	on	on	ADP
ap-3105	36	53	the	the	DET
ap-3105	36	54	covering	covering	NOUN
ap-3105	36	55	space	space	NOUN
ap-3105	36	56	.	.	PUNCT
ap-3105	37	1	2	2	X
ap-3105	37	2	.	.	X
ap-3105	37	3	a	a	DET
ap-3105	37	4	summary	summary	NOUN
ap-3105	37	5	of	of	ADP
ap-3105	37	6	the	the	DET
ap-3105	37	7	general	general	ADJ
ap-3105	37	8	approach	approach	NOUN
ap-3105	37	9	2.1	2.1	NUM
ap-3105	37	10	.	.	PUNCT
ap-3105	38	1	periodic	periodic	ADJ
ap-3105	38	2	hamiltonians	hamiltonian	NOUN
ap-3105	38	3	let	let	VERB
ap-3105	38	4	m̃	m̃	PROPN
ap-3105	38	5	be	be	AUX
ap-3105	38	6	a	a	DET
ap-3105	38	7	connected	connect	VERB
ap-3105	38	8	riemannian	riemannian	NOUN
ap-3105	38	9	manifold	manifold	ADJ
ap-3105	38	10	with	with	ADP
ap-3105	38	11	a	a	DET
ap-3105	38	12	discrete	discrete	ADJ
ap-3105	38	13	and	and	CCONJ
ap-3105	38	14	at	at	ADP
ap-3105	38	15	most	most	ADJ
ap-3105	38	16	countable	countable	ADJ
ap-3105	38	17	symmetry	symmetry	NOUN
ap-3105	38	18	group	group	NOUN
ap-3105	38	19	γ	γ	PROPN
ap-3105	38	20	.	.	PUNCT
ap-3105	39	1	the	the	DET
ap-3105	39	2	action	action	NOUN
ap-3105	39	3	of	of	ADP
ap-3105	39	4	γ	γ	NOUN
ap-3105	39	5	on	on	ADP
ap-3105	39	6	m̃	m̃	PROPN
ap-3105	39	7	is	be	AUX
ap-3105	39	8	assumed	assume	VERB
ap-3105	39	9	to	to	PART
ap-3105	39	10	be	be	AUX
ap-3105	39	11	smooth	smooth	ADJ
ap-3105	39	12	,	,	PUNCT
ap-3105	39	13	free	free	ADJ
ap-3105	39	14	and	and	CCONJ
ap-3105	39	15	proper	proper	ADJ
ap-3105	39	16	.	.	PUNCT
ap-3105	40	1	let	let	VERB
ap-3105	40	2	us	we	PRON
ap-3105	40	3	recall	recall	VERB
ap-3105	40	4	that	that	SCONJ
ap-3105	40	5	under	under	ADP
ap-3105	40	6	these	these	DET
ap-3105	40	7	assumptions	assumption	NOUN
ap-3105	40	8	any	any	DET
ap-3105	40	9	element	element	NOUN
ap-3105	40	10	s	s	PART
ap-3105	40	11	∈	∈	NOUN
ap-3105	40	12	γ	γ	NOUN
ap-3105	40	13	different	different	ADJ
ap-3105	40	14	from	from	ADP
ap-3105	40	15	the	the	DET
ap-3105	40	16	unity	unity	NOUN
ap-3105	40	17	has	have	VERB
ap-3105	40	18	no	no	DET
ap-3105	40	19	fixed	fix	VERB
ap-3105	40	20	points	point	NOUN
ap-3105	40	21	on	on	ADP
ap-3105	40	22	m̃	m̃	PROPN
ap-3105	40	23	,	,	PUNCT
ap-3105	40	24	and	and	CCONJ
ap-3105	40	25	for	for	ADP
ap-3105	40	26	any	any	DET
ap-3105	40	27	compact	compact	ADJ
ap-3105	40	28	set	set	NOUN
ap-3105	40	29	k	k	PROPN
ap-3105	40	30	⊂	⊂	PROPN
ap-3105	40	31	m̃	m̃	PROPN
ap-3105	40	32	,	,	PUNCT
ap-3105	41	1	the	the	DET
ap-3105	41	2	intersection	intersection	NOUN
ap-3105	41	3	k	k	PROPN
ap-3105	41	4	∩	∩	PROPN
ap-3105	41	5	s	s	PART
ap-3105	41	6	·	·	PUNCT
ap-3105	41	7	k	k	X
ap-3105	41	8	is	be	AUX
ap-3105	41	9	nonempty	nonempty	ADJ
ap-3105	41	10	for	for	ADP
ap-3105	41	11	at	at	ADV
ap-3105	41	12	most	most	ADV
ap-3105	41	13	finitely	finitely	ADV
ap-3105	41	14	many	many	ADJ
ap-3105	41	15	elements	element	NOUN
ap-3105	41	16	s	s	PART
ap-3105	41	17	∈	∈	PROPN
ap-3105	41	18	γ	γ	X
ap-3105	41	19	.	.	PUNCT
ap-3105	42	1	this	this	PRON
ap-3105	42	2	also	also	ADV
ap-3105	42	3	implies	imply	VERB
ap-3105	42	4	that	that	SCONJ
ap-3105	42	5	any	any	DET
ap-3105	42	6	point	point	NOUN
ap-3105	42	7	y	y	PROPN
ap-3105	42	8	∈	∈	PROPN
ap-3105	42	9	m̃	m̃	PROPN
ap-3105	42	10	has	have	VERB
ap-3105	42	11	a	a	DET
ap-3105	42	12	neighborhood	neighborhood	NOUN
ap-3105	42	13	u	u	NOUN
ap-3105	42	14	such	such	ADJ
ap-3105	42	15	that	that	SCONJ
ap-3105	42	16	the	the	DET
ap-3105	42	17	sets	set	NOUN
ap-3105	42	18	s	s	PART
ap-3105	42	19	·	·	PUNCT
ap-3105	42	20	u	u	NOUN
ap-3105	42	21	,	,	PUNCT
ap-3105	42	22	s	s	PROPN
ap-3105	42	23	∈	∈	PROPN
ap-3105	42	24	γ	γ	NOUN
ap-3105	42	25	,	,	PUNCT
ap-3105	42	26	are	be	AUX
ap-3105	42	27	mutually	mutually	ADV
ap-3105	42	28	disjoint	disjoint	ADJ
ap-3105	43	1	[	[	X
ap-3105	43	2	13	13	NUM
ap-3105	43	3	,	,	PUNCT
ap-3105	43	4	corollary	corollary	ADJ
ap-3105	43	5	12.10	12.10	NUM
ap-3105	43	6	]	]	PUNCT
ap-3105	43	7	.	.	PUNCT
ap-3105	44	1	denote	denote	VERB
ap-3105	44	2	by	by	ADP
ap-3105	44	3	µ̃	µ̃	PROPN
ap-3105	44	4	the	the	DET
ap-3105	44	5	measure	measure	NOUN
ap-3105	44	6	on	on	ADP
ap-3105	44	7	m̃	m̃	PROPN
ap-3105	44	8	induced	induce	VERB
ap-3105	44	9	by	by	ADP
ap-3105	44	10	the	the	DET
ap-3105	44	11	riemannian	riemannian	ADJ
ap-3105	44	12	metric	metric	NOUN
ap-3105	44	13	.	.	PUNCT
ap-3105	45	1	the	the	DET
ap-3105	45	2	quotient	quotient	NOUN
ap-3105	45	3	m	m	NOUN
ap-3105	45	4	=	=	NOUN
ap-3105	45	5	m̃/γ	m̃/γ	NOUN
ap-3105	45	6	is	be	AUX
ap-3105	45	7	a	a	DET
ap-3105	45	8	connected	connect	VERB
ap-3105	45	9	riemannian	riemannian	NOUN
ap-3105	45	10	manifold	manifold	ADJ
ap-3105	45	11	with	with	ADP
ap-3105	45	12	an	an	DET
ap-3105	45	13	induced	induced	ADJ
ap-3105	45	14	measure	measure	NOUN
ap-3105	45	15	µ.	µ.	NOUN
ap-3105	45	16	this	this	DET
ap-3105	45	17	way	way	NOUN
ap-3105	45	18	one	one	PRON
ap-3105	45	19	gets	get	VERB
ap-3105	45	20	a	a	DET
ap-3105	45	21	principal	principal	ADJ
ap-3105	45	22	fiber	fiber	NOUN
ap-3105	45	23	bundle	bundle	NOUN
ap-3105	46	1	π	π	NOUN
ap-3105	46	2	:	:	PUNCT
ap-3105	46	3	m̃	m̃	PROPN
ap-3105	46	4	→m	→m	PUNCT
ap-3105	46	5	with	with	ADP
ap-3105	46	6	the	the	DET
ap-3105	46	7	structure	structure	NOUN
ap-3105	46	8	group	group	NOUN
ap-3105	46	9	γ	γ	PROPN
ap-3105	46	10	.	.	PROPN
ap-3105	47	1	all	all	DET
ap-3105	47	2	l2	l2	NOUN
ap-3105	47	3	spaces	space	NOUN
ap-3105	47	4	based	base	VERB
ap-3105	47	5	on	on	ADP
ap-3105	47	6	the	the	DET
ap-3105	47	7	manifolds	manifold	NOUN
ap-3105	47	8	m	m	PROPN
ap-3105	47	9	and	and	CCONJ
ap-3105	47	10	m̃	m̃	PROPN
ap-3105	47	11	are	be	AUX
ap-3105	47	12	everywhere	everywhere	ADV
ap-3105	47	13	tacitly	tacitly	ADV
ap-3105	47	14	understood	understand	VERB
ap-3105	47	15	with	with	ADP
ap-3105	47	16	the	the	DET
ap-3105	47	17	measures	measure	NOUN
ap-3105	47	18	µ	µ	X
ap-3105	47	19	and	and	CCONJ
ap-3105	47	20	µ̃	µ̃	PROPN
ap-3105	47	21	,	,	PUNCT
ap-3105	47	22	respectively	respectively	ADV
ap-3105	47	23	.	.	PUNCT
ap-3105	48	1	in	in	ADP
ap-3105	48	2	a	a	DET
ap-3105	48	3	number	number	NOUN
ap-3105	48	4	of	of	ADP
ap-3105	48	5	important	important	ADJ
ap-3105	48	6	examples	example	NOUN
ap-3105	48	7	,	,	PUNCT
ap-3105	48	8	m̃	m̃	PROPN
ap-3105	48	9	is	be	AUX
ap-3105	48	10	the	the	DET
ap-3105	48	11	universal	universal	ADJ
ap-3105	48	12	covering	covering	NOUN
ap-3105	48	13	space	space	NOUN
ap-3105	48	14	ofm	ofm	PROPN
ap-3105	48	15	and	and	CCONJ
ap-3105	48	16	γ	γ	X
ap-3105	48	17	=	=	SYM
ap-3105	48	18	π1(m	π1(m	PROPN
ap-3105	48	19	)	)	PUNCT
ap-3105	48	20	is	be	AUX
ap-3105	48	21	the	the	DET
ap-3105	48	22	fundamental	fundamental	ADJ
ap-3105	48	23	group	group	NOUN
ap-3105	48	24	of	of	ADP
ap-3105	48	25	m	m	PROPN
ap-3105	48	26	.	.	PUNCT
ap-3105	49	1	in	in	ADP
ap-3105	49	2	particular	particular	ADJ
ap-3105	49	3	,	,	PUNCT
ap-3105	49	4	this	this	PRON
ap-3105	49	5	is	be	AUX
ap-3105	49	6	the	the	DET
ap-3105	49	7	case	case	NOUN
ap-3105	49	8	when	when	SCONJ
ap-3105	49	9	one	one	PRON
ap-3105	49	10	is	be	AUX
ap-3105	49	11	considering	consider	VERB
ap-3105	49	12	the	the	DET
ap-3105	49	13	aharonov	aharonov	PROPN
ap-3105	49	14	-	-	PUNCT
ap-3105	49	15	bohm	bohm	PROPN
ap-3105	49	16	effect	effect	NOUN
ap-3105	49	17	.	.	PUNCT
ap-3105	50	1	to	to	ADP
ap-3105	50	2	a	a	DET
ap-3105	50	3	unitary	unitary	ADJ
ap-3105	50	4	representation	representation	NOUN
ap-3105	50	5	λ	λ	PROPN
ap-3105	50	6	of	of	ADP
ap-3105	50	7	γ	γ	NOUN
ap-3105	50	8	in	in	ADP
ap-3105	50	9	a	a	DET
ap-3105	50	10	separable	separable	ADJ
ap-3105	50	11	hilbert	hilbert	NOUN
ap-3105	50	12	space	space	NOUN
ap-3105	50	13	lλ	lλ	ADP
ap-3105	50	14	one	one	NOUN
ap-3105	50	15	relates	relate	VERB
ap-3105	50	16	the	the	DET
ap-3105	50	17	hilbert	hilbert	PROPN
ap-3105	50	18	space	space	NOUN
ap-3105	50	19	hλ	hλ	AUX
ap-3105	50	20	formed	form	VERB
ap-3105	50	21	by	by	ADP
ap-3105	50	22	λ	λ	PROPN
ap-3105	50	23	-	-	PUNCT
ap-3105	50	24	equivariant	equivariant	ADJ
ap-3105	50	25	vector	vector	NOUN
ap-3105	50	26	-	-	PUNCT
ap-3105	50	27	valued	value	VERB
ap-3105	50	28	functions	function	NOUN
ap-3105	50	29	on	on	ADP
ap-3105	50	30	m̃	m̃	PROPN
ap-3105	50	31	.	.	PUNCT
ap-3105	51	1	this	this	PRON
ap-3105	51	2	means	mean	VERB
ap-3105	51	3	that	that	SCONJ
ap-3105	51	4	any	any	DET
ap-3105	51	5	function	function	NOUN
ap-3105	51	6	ψ	ψ	ADP
ap-3105	51	7	∈	∈	NOUN
ap-3105	51	8	hλ	hλ	NOUN
ap-3105	51	9	is	be	AUX
ap-3105	51	10	measurable	measurable	ADJ
ap-3105	51	11	with	with	ADP
ap-3105	51	12	values	value	NOUN
ap-3105	51	13	in	in	ADP
ap-3105	51	14	lλ	lλ	NOUN
ap-3105	51	15	and	and	CCONJ
ap-3105	51	16	satisfies	satisfy	VERB
ap-3105	51	17	∀s	∀s	PROPN
ap-3105	51	18	∈	∈	PROPN
ap-3105	51	19	γ	γ	X
ap-3105	51	20	,	,	PUNCT
ap-3105	51	21	ψ(s	ψ(s	PROPN
ap-3105	51	22	·	·	PUNCT
ap-3105	51	23	y	y	X
ap-3105	51	24	)	)	PUNCT
ap-3105	51	25	=	=	SYM
ap-3105	51	26	λ(s)ψ(y	λ(s)ψ(y	X
ap-3105	51	27	)	)	PUNCT
ap-3105	51	28	almost	almost	ADV
ap-3105	51	29	everywhere	everywhere	ADV
ap-3105	51	30	on	on	ADP
ap-3105	51	31	m̃.	m̃.	PROPN
ap-3105	51	32	moreover	moreover	ADV
ap-3105	51	33	,	,	PUNCT
ap-3105	51	34	the	the	DET
ap-3105	51	35	norm	norm	NOUN
ap-3105	51	36	of	of	ADP
ap-3105	51	37	ψ	ψ	PRON
ap-3105	51	38	induced	induce	VERB
ap-3105	51	39	by	by	ADP
ap-3105	51	40	the	the	DET
ap-3105	51	41	following	follow	VERB
ap-3105	51	42	scalar	scalar	ADJ
ap-3105	51	43	product	product	NOUN
ap-3105	51	44	is	be	AUX
ap-3105	51	45	required	require	VERB
ap-3105	51	46	to	to	PART
ap-3105	51	47	be	be	AUX
ap-3105	51	48	finite	finite	ADJ
ap-3105	51	49	.	.	PUNCT
ap-3105	52	1	if	if	SCONJ
ap-3105	52	2	ψ1	ψ1	NOUN
ap-3105	52	3	,	,	PUNCT
ap-3105	52	4	ψ2	ψ2	NOUN
ap-3105	52	5	∈hλ	∈hλ	X
ap-3105	52	6	then	then	ADV
ap-3105	52	7	the	the	DET
ap-3105	52	8	function	function	NOUN
ap-3105	52	9	y	y	PROPN
ap-3105	52	10	7→	7→	PROPN
ap-3105	52	11	〈	〈	PROPN
ap-3105	52	12	ψ1(y	ψ1(y	NOUN
ap-3105	52	13	)	)	PUNCT
ap-3105	52	14	,	,	PUNCT
ap-3105	52	15	ψ2(y)〉lλ	ψ2(y)〉lλ	PROPN
ap-3105	52	16	defined	define	VERB
ap-3105	52	17	on	on	ADP
ap-3105	52	18	m̃	m̃	PROPN
ap-3105	52	19	is	be	AUX
ap-3105	52	20	γ	γ	NOUN
ap-3105	52	21	-	-	ADJ
ap-3105	52	22	invariant	invariant	ADJ
ap-3105	52	23	and	and	CCONJ
ap-3105	52	24	so	so	ADV
ap-3105	52	25	it	it	PRON
ap-3105	52	26	projects	project	VERB
ap-3105	52	27	to	to	ADP
ap-3105	52	28	a	a	DET
ap-3105	52	29	function	function	NOUN
ap-3105	52	30	sψ1,ψ2	sψ1,ψ2	ADV
ap-3105	52	31	defined	define	VERB
ap-3105	52	32	on	on	ADP
ap-3105	52	33	m	m	PROPN
ap-3105	52	34	,	,	PUNCT
ap-3105	52	35	and	and	CCONJ
ap-3105	52	36	the	the	DET
ap-3105	52	37	scalar	scalar	ADJ
ap-3105	52	38	product	product	NOUN
ap-3105	52	39	is	be	AUX
ap-3105	52	40	defined	define	VERB
ap-3105	52	41	by	by	ADP
ap-3105	52	42	〈	〈	PROPN
ap-3105	52	43	ψ1	ψ1	NOUN
ap-3105	52	44	,	,	PUNCT
ap-3105	52	45	ψ2	ψ2	VERB
ap-3105	53	1	〉	〉	NOUN
ap-3105	53	2	=	=	SYM
ap-3105	53	3	∫	∫	PROPN
ap-3105	53	4	m	m	PROPN
ap-3105	53	5	sψ1,ψ2(x)dµ(x	sψ1,ψ2(x)dµ(x	PROPN
ap-3105	53	6	)	)	PUNCT
ap-3105	53	7	.	.	PUNCT
ap-3105	54	1	our	our	PRON
ap-3105	54	2	discussion	discussion	NOUN
ap-3105	54	3	focuses	focus	VERB
ap-3105	54	4	on	on	ADP
ap-3105	54	5	γ	γ	ADJ
ap-3105	54	6	-	-	ADJ
ap-3105	54	7	periodic	periodic	ADJ
ap-3105	54	8	hamiltonians	hamiltonian	NOUN
ap-3105	54	9	on	on	ADP
ap-3105	54	10	m̃	m̃	PROPN
ap-3105	54	11	of	of	ADP
ap-3105	54	12	the	the	DET
ap-3105	54	13	form	form	NOUN
ap-3105	54	14	h	h	NOUN
ap-3105	54	15	=	=	PUNCT
ap-3105	54	16	−∆lb	−∆lb	PROPN
ap-3105	55	1	+	+	CCONJ
ap-3105	55	2	v	v	NOUN
ap-3105	55	3	where	where	SCONJ
ap-3105	55	4	∆lb	∆lb	PROPN
ap-3105	55	5	is	be	AUX
ap-3105	55	6	the	the	DET
ap-3105	55	7	laplace	laplace	NOUN
ap-3105	55	8	-	-	PUNCT
ap-3105	55	9	beltrami	beltrami	NOUN
ap-3105	55	10	operator	operator	NOUN
ap-3105	55	11	and	and	CCONJ
ap-3105	55	12	v	v	NOUN
ap-3105	55	13	is	be	AUX
ap-3105	55	14	a	a	DET
ap-3105	55	15	γ	γ	NOUN
ap-3105	55	16	-	-	ADJ
ap-3105	55	17	invariant	invariant	ADJ
ap-3105	55	18	semibounded	semibounde	VERB
ap-3105	55	19	and	and	CCONJ
ap-3105	55	20	locally	locally	ADV
ap-3105	55	21	integrable	integrable	ADJ
ap-3105	55	22	real	real	ADJ
ap-3105	55	23	function	function	NOUN
ap-3105	55	24	on	on	ADP
ap-3105	55	25	m̃	m̃	PROPN
ap-3105	55	26	.	.	PUNCT
ap-3105	56	1	clearly	clearly	ADV
ap-3105	56	2	,	,	PUNCT
ap-3105	56	3	the	the	DET
ap-3105	56	4	differential	differential	ADJ
ap-3105	56	5	operator	operator	NOUN
ap-3105	56	6	−∆lb	−∆lb	VERB
ap-3105	56	7	+	+	NOUN
ap-3105	56	8	v	v	NOUN
ap-3105	56	9	is	be	AUX
ap-3105	56	10	semibounded	semibounde	VERB
ap-3105	56	11	on	on	ADP
ap-3105	56	12	the	the	DET
ap-3105	56	13	domain	domain	NOUN
ap-3105	56	14	formed	form	VERB
ap-3105	56	15	by	by	ADP
ap-3105	56	16	test	test	NOUN
ap-3105	56	17	functions	function	NOUN
ap-3105	56	18	(	(	PUNCT
ap-3105	56	19	i.e.	i.e.	X
ap-3105	56	20	smooth	smooth	ADJ
ap-3105	56	21	and	and	CCONJ
ap-3105	56	22	compactly	compactly	ADV
ap-3105	56	23	supported	support	VERB
ap-3105	56	24	functions	function	NOUN
ap-3105	56	25	)	)	PUNCT
ap-3105	56	26	,	,	PUNCT
ap-3105	56	27	and	and	CCONJ
ap-3105	56	28	h	h	NOUN
ap-3105	56	29	is	be	AUX
ap-3105	56	30	defined	define	VERB
ap-3105	56	31	as	as	ADP
ap-3105	56	32	its	its	PRON
ap-3105	56	33	friedrichs	friedrich	NOUN
ap-3105	56	34	extension	extension	NOUN
ap-3105	56	35	.	.	PUNCT
ap-3105	57	1	the	the	DET
ap-3105	57	2	same	same	ADJ
ap-3105	57	3	choice	choice	NOUN
ap-3105	57	4	will	will	AUX
ap-3105	57	5	also	also	ADV
ap-3105	57	6	be	be	AUX
ap-3105	57	7	made	make	VERB
ap-3105	57	8	in	in	ADP
ap-3105	57	9	other	other	ADJ
ap-3105	57	10	instances	instance	NOUN
ap-3105	57	11	below	below	ADV
ap-3105	57	12	in	in	ADP
ap-3105	57	13	the	the	DET
ap-3105	57	14	paper	paper	NOUN
ap-3105	57	15	.	.	PUNCT
ap-3105	58	1	this	this	PRON
ap-3105	58	2	is	be	AUX
ap-3105	58	3	to	to	PART
ap-3105	58	4	say	say	VERB
ap-3105	58	5	that	that	SCONJ
ap-3105	58	6	in	in	ADP
ap-3105	58	7	the	the	DET
ap-3105	58	8	presented	present	VERB
ap-3105	58	9	approach	approach	NOUN
ap-3105	58	10	we	we	PRON
ap-3105	58	11	distinguish	distinguish	VERB
ap-3105	58	12	the	the	DET
ap-3105	58	13	friedrichs	friedrich	NOUN
ap-3105	58	14	extension	extension	NOUN
ap-3105	58	15	as	as	ADP
ap-3105	58	16	the	the	DET
ap-3105	58	17	preferred	preferred	ADJ
ap-3105	58	18	self	self	NOUN
ap-3105	58	19	-	-	PUNCT
ap-3105	58	20	adjoint	adjoint	NOUN
ap-3105	58	21	extension	extension	NOUN
ap-3105	58	22	of	of	ADP
ap-3105	58	23	a	a	DET
ap-3105	58	24	given	give	VERB
ap-3105	58	25	semibounded	semibounde	VERB
ap-3105	58	26	symmetric	symmetric	ADJ
ap-3105	58	27	operator	operator	NOUN
ap-3105	58	28	.	.	PUNCT
ap-3105	59	1	here	here	ADV
ap-3105	59	2	we	we	PRON
ap-3105	59	3	are	be	AUX
ap-3105	59	4	referring	refer	VERB
ap-3105	59	5	to	to	ADP
ap-3105	59	6	the	the	DET
ap-3105	59	7	widely	widely	ADV
ap-3105	59	8	used	use	VERB
ap-3105	59	9	result	result	NOUN
ap-3105	59	10	ensuring	ensure	VERB
ap-3105	59	11	the	the	DET
ap-3105	59	12	existence	existence	NOUN
ap-3105	59	13	of	of	ADP
ap-3105	59	14	an	an	DET
ap-3105	59	15	unambiguously	unambiguously	ADV
ap-3105	59	16	defined	define	VERB
ap-3105	59	17	and	and	CCONJ
ap-3105	59	18	in	in	ADP
ap-3105	59	19	some	some	DET
ap-3105	59	20	sense	sense	NOUN
ap-3105	59	21	minimal	minimal	ADJ
ap-3105	59	22	self	self	NOUN
ap-3105	59	23	-	-	PUNCT
ap-3105	59	24	adjoint	adjoint	NOUN
ap-3105	59	25	extension	extension	NOUN
ap-3105	59	26	of	of	ADP
ap-3105	59	27	a	a	DET
ap-3105	59	28	semibounded	semibounde	VERB
ap-3105	59	29	symmetric	symmetric	ADJ
ap-3105	59	30	operator	operator	NOUN
ap-3105	59	31	,	,	PUNCT
ap-3105	59	32	the	the	DET
ap-3105	59	33	so	so	ADV
ap-3105	59	34	called	call	VERB
ap-3105	59	35	friedrichs	friedrich	NOUN
ap-3105	59	36	extension	extension	NOUN
ap-3105	59	37	[	[	X
ap-3105	59	38	10	10	NUM
ap-3105	59	39	,	,	PUNCT
ap-3105	59	40	§	§	NOUN
ap-3105	59	41	vi.2	vi.2	NOUN
ap-3105	59	42	]	]	PUNCT
ap-3105	59	43	.	.	PUNCT
ap-3105	60	1	this	this	DET
ap-3105	60	2	choice	choice	NOUN
ap-3105	60	3	is	be	AUX
ap-3105	60	4	encountered	encounter	VERB
ap-3105	60	5	very	very	ADV
ap-3105	60	6	frequently	frequently	ADV
ap-3105	60	7	in	in	ADP
ap-3105	60	8	various	various	ADJ
ap-3105	60	9	applications	application	NOUN
ap-3105	60	10	and	and	CCONJ
ap-3105	60	11	it	it	PRON
ap-3105	60	12	also	also	ADV
ap-3105	60	13	makes	make	VERB
ap-3105	60	14	it	it	PRON
ap-3105	60	15	possible	possible	ADJ
ap-3105	60	16	to	to	PART
ap-3105	60	17	avoid	avoid	VERB
ap-3105	60	18	the	the	DET
ap-3105	60	19	discussion	discussion	NOUN
ap-3105	60	20	of	of	ADP
ap-3105	60	21	the	the	DET
ap-3105	60	22	domain	domain	NOUN
ap-3105	60	23	of	of	ADP
ap-3105	60	24	the	the	DET
ap-3105	60	25	self	self	NOUN
ap-3105	60	26	-	-	PUNCT
ap-3105	60	27	adjoint	adjoint	NOUN
ap-3105	60	28	operator	operator	NOUN
ap-3105	60	29	in	in	ADP
ap-3105	60	30	question	question	NOUN
ap-3105	60	31	which	which	PRON
ap-3105	60	32	sometimes	sometimes	ADV
ap-3105	60	33	may	may	AUX
ap-3105	60	34	be	be	AUX
ap-3105	60	35	quite	quite	ADV
ap-3105	60	36	tedious	tedious	ADJ
ap-3105	60	37	.	.	PUNCT
ap-3105	61	1	to	to	ADP
ap-3105	61	2	the	the	DET
ap-3105	61	3	same	same	ADJ
ap-3105	61	4	differential	differential	NOUN
ap-3105	61	5	operator	operator	NOUN
ap-3105	61	6	,	,	PUNCT
ap-3105	61	7	−∆lb	−∆lb	ADJ
ap-3105	61	8	+	+	CCONJ
ap-3105	61	9	v	v	NOUN
ap-3105	61	10	,	,	PUNCT
ap-3105	61	11	one	one	PRON
ap-3105	61	12	can	can	AUX
ap-3105	61	13	relate	relate	VERB
ap-3105	61	14	a	a	DET
ap-3105	61	15	self	self	NOUN
ap-3105	61	16	-	-	PUNCT
ap-3105	61	17	adjoint	adjoint	NOUN
ap-3105	61	18	operator	operator	NOUN
ap-3105	61	19	hλ	hλ	NOUN
ap-3105	61	20	in	in	ADP
ap-3105	61	21	the	the	DET
ap-3105	61	22	space	space	NOUN
ap-3105	61	23	hλ	hλ	NOUN
ap-3105	61	24	for	for	ADP
ap-3105	61	25	any	any	DET
ap-3105	61	26	unitary	unitary	ADJ
ap-3105	61	27	representation	representation	NOUN
ap-3105	61	28	λ	λ	PROPN
ap-3105	61	29	of	of	ADP
ap-3105	61	30	γ	γ	PROPN
ap-3105	61	31	in	in	ADP
ap-3105	61	32	lλ	lλ	PROPN
ap-3105	61	33	.	.	PUNCT
ap-3105	62	1	let	let	VERB
ap-3105	62	2	us	we	PRON
ap-3105	62	3	define	define	VERB
ap-3105	62	4	φλ	φλ	ADV
ap-3105	62	5	:	:	PUNCT
ap-3105	62	6	c∞0	c∞0	X
ap-3105	62	7	(	(	PUNCT
ap-3105	62	8	m̃)⊗lλ	m̃)⊗lλ	NOUN
ap-3105	62	9	→hλ	→hλ	PUNCT
ap-3105	62	10	by	by	ADP
ap-3105	62	11	∀ϕ	∀ϕ	PROPN
ap-3105	62	12	∈	∈	PROPN
ap-3105	62	13	c∞0	c∞0	PROPN
ap-3105	62	14	(	(	PUNCT
ap-3105	62	15	m̃),∀v	m̃),∀v	PROPN
ap-3105	62	16	∈	∈	PROPN
ap-3105	62	17	lλ	lλ	PROPN
ap-3105	62	18	,	,	PUNCT
ap-3105	62	19	(	(	PUNCT
ap-3105	62	20	φλϕ⊗	φλϕ⊗	NOUN
ap-3105	62	21	v)(y	v)(y	NOUN
ap-3105	62	22	)	)	PUNCT
ap-3105	63	1	=	=	PUNCT
ap-3105	63	2	∑	∑	PUNCT
ap-3105	63	3	s∈γ	s∈γ	PROPN
ap-3105	63	4	ϕ(s	ϕ(s	PROPN
ap-3105	63	5	·	·	PUNCT
ap-3105	63	6	y)λ(s−1)v	y)λ(s−1)v	ADJ
ap-3105	63	7	.	.	PUNCT
ap-3105	64	1	(	(	PUNCT
ap-3105	64	2	1	1	X
ap-3105	64	3	)	)	PUNCT
ap-3105	64	4	since	since	SCONJ
ap-3105	64	5	the	the	DET
ap-3105	64	6	action	action	NOUN
ap-3105	64	7	of	of	ADP
ap-3105	64	8	γ	γ	PROPN
ap-3105	64	9	is	be	AUX
ap-3105	64	10	proper	proper	ADJ
ap-3105	64	11	,	,	PUNCT
ap-3105	64	12	the	the	DET
ap-3105	64	13	vector	vector	NOUN
ap-3105	64	14	-	-	PUNCT
ap-3105	64	15	valued	value	VERB
ap-3105	64	16	function	function	NOUN
ap-3105	64	17	φλϕ⊗v	φλϕ⊗v	NOUN
ap-3105	64	18	is	be	AUX
ap-3105	64	19	smooth	smooth	ADJ
ap-3105	64	20	.	.	PUNCT
ap-3105	65	1	moreover	moreover	ADV
ap-3105	65	2	,	,	PUNCT
ap-3105	65	3	φλϕ⊗v	φλϕ⊗v	PROPN
ap-3105	65	4	is	be	AUX
ap-3105	65	5	λ	λ	NOUN
ap-3105	65	6	-	-	NOUN
ap-3105	65	7	equivariant	equivariant	ADJ
ap-3105	65	8	,	,	PUNCT
ap-3105	65	9	the	the	DET
ap-3105	65	10	norm	norm	NOUN
ap-3105	65	11	of	of	ADP
ap-3105	65	12	φλϕ⊗	φλϕ⊗	NOUN
ap-3105	65	13	v	v	NOUN
ap-3105	65	14	in	in	ADP
ap-3105	65	15	hλ	hλ	NOUN
ap-3105	65	16	is	be	AUX
ap-3105	65	17	finite	finite	ADJ
ap-3105	65	18	,	,	PUNCT
ap-3105	65	19	and	and	CCONJ
ap-3105	65	20	the	the	DET
ap-3105	65	21	range	range	NOUN
ap-3105	65	22	of	of	ADP
ap-3105	65	23	φλ	φλ	NOUN
ap-3105	65	24	is	be	AUX
ap-3105	65	25	dense	dense	ADJ
ap-3105	65	26	in	in	ADP
ap-3105	65	27	hλ	hλ	X
ap-3105	65	28	.	.	PUNCT
ap-3105	66	1	the	the	DET
ap-3105	66	2	laplace	laplace	NOUN
ap-3105	66	3	-	-	PUNCT
ap-3105	66	4	beltrami	beltrami	NOUN
ap-3105	66	5	operator	operator	NOUN
ap-3105	66	6	is	be	AUX
ap-3105	66	7	well	well	ADV
ap-3105	66	8	defined	define	VERB
ap-3105	66	9	on	on	ADP
ap-3105	66	10	ran(φλ	ran(φλ	X
ap-3105	66	11	)	)	PUNCT
ap-3105	66	12	and	and	CCONJ
ap-3105	66	13	it	it	PRON
ap-3105	66	14	holds	hold	VERB
ap-3105	66	15	∆lbφλ[ϕ⊗	∆lbφλ[ϕ⊗	X
ap-3105	66	16	v	v	NOUN
ap-3105	66	17	]	]	X
ap-3105	66	18	=	=	PUNCT
ap-3105	66	19	φλ[∆lbϕ⊗	φλ[∆lbϕ⊗	NOUN
ap-3105	66	20	v	v	ADP
ap-3105	66	21	]	]	PUNCT
ap-3105	66	22	.	.	PUNCT
ap-3105	67	1	one	one	PRON
ap-3105	67	2	can	can	AUX
ap-3105	67	3	also	also	ADV
ap-3105	67	4	verify	verify	VERB
ap-3105	67	5	that	that	SCONJ
ap-3105	67	6	the	the	DET
ap-3105	67	7	differential	differential	ADJ
ap-3105	67	8	operator	operator	NOUN
ap-3105	67	9	−∆lb	−∆lb	VERB
ap-3105	67	10	is	be	AUX
ap-3105	67	11	positive	positive	ADJ
ap-3105	67	12	on	on	ADP
ap-3105	67	13	the	the	DET
ap-3105	67	14	domain	domain	NOUN
ap-3105	67	15	ran(φλ	ran(φλ	NOUN
ap-3105	67	16	)	)	PUNCT
ap-3105	67	17	⊂hλ	⊂hλ	PROPN
ap-3105	67	18	.	.	PUNCT
ap-3105	68	1	since	since	SCONJ
ap-3105	68	2	the	the	DET
ap-3105	68	3	function	function	NOUN
ap-3105	68	4	v	v	NOUN
ap-3105	68	5	(	(	PUNCT
ap-3105	68	6	y	y	NOUN
ap-3105	68	7	)	)	PUNCT
ap-3105	68	8	is	be	AUX
ap-3105	68	9	γ	γ	X
ap-3105	68	10	-	-	PUNCT
ap-3105	68	11	invariant	invariant	ADJ
ap-3105	68	12	,	,	PUNCT
ap-3105	68	13	the	the	DET
ap-3105	68	14	multiplication	multiplication	NOUN
ap-3105	68	15	operator	operator	NOUN
ap-3105	68	16	by	by	ADP
ap-3105	68	17	v	v	NOUN
ap-3105	68	18	is	be	AUX
ap-3105	68	19	well	well	ADV
ap-3105	68	20	defined	define	VERB
ap-3105	68	21	in	in	ADP
ap-3105	68	22	the	the	DET
ap-3105	68	23	hilbert	hilbert	NOUN
ap-3105	68	24	space	space	NOUN
ap-3105	68	25	hλ	hλ	PROPN
ap-3105	68	26	.	.	PUNCT
ap-3105	69	1	the	the	DET
ap-3105	69	2	hamiltonian	hamiltonian	ADJ
ap-3105	69	3	hλ	hλ	X
ap-3105	69	4	is	be	AUX
ap-3105	69	5	defined	define	VERB
ap-3105	69	6	as	as	ADP
ap-3105	69	7	the	the	DET
ap-3105	69	8	friedrichs	friedrichs	ADJ
ap-3105	69	9	extension	extension	NOUN
ap-3105	69	10	of	of	ADP
ap-3105	69	11	the	the	DET
ap-3105	69	12	differential	differential	ADJ
ap-3105	69	13	operator	operator	NOUN
ap-3105	69	14	−∆lb	−∆lb	VERB
ap-3105	69	15	+	+	CCONJ
ap-3105	69	16	v	v	NOUN
ap-3105	69	17	considered	consider	VERB
ap-3105	69	18	on	on	ADP
ap-3105	69	19	the	the	DET
ap-3105	69	20	domain	domain	NOUN
ap-3105	69	21	ran	run	VERB
ap-3105	69	22	φλ	φλ	ADV
ap-3105	69	23	.	.	PUNCT
ap-3105	70	1	the	the	DET
ap-3105	70	2	reader	reader	NOUN
ap-3105	70	3	is	be	AUX
ap-3105	70	4	referred	refer	VERB
ap-3105	70	5	to	to	ADP
ap-3105	70	6	[	[	X
ap-3105	70	7	11	11	NUM
ap-3105	70	8	,	,	PUNCT
ap-3105	70	9	12	12	NUM
ap-3105	70	10	]	]	PUNCT
ap-3105	70	11	for	for	ADP
ap-3105	70	12	more	more	ADJ
ap-3105	70	13	details	detail	NOUN
ap-3105	70	14	.	.	PUNCT
ap-3105	71	1	225	225	NUM
ap-3105	71	2	petra	petra	PROPN
ap-3105	71	3	košťáková	košťáková	PROPN
ap-3105	71	4	,	,	PUNCT
ap-3105	71	5	pavel	pavel	PROPN
ap-3105	71	6	šťovíček	šťovíček	PROPN
ap-3105	71	7	acta	acta	PROPN
ap-3105	71	8	polytechnica	polytechnica	PROPN
ap-3105	71	9	2.2	2.2	NUM
ap-3105	71	10	.	.	PUNCT
ap-3105	72	1	a	a	DET
ap-3105	72	2	generalization	generalization	NOUN
ap-3105	72	3	of	of	ADP
ap-3105	72	4	the	the	DET
ap-3105	72	5	bloch	bloch	PROPN
ap-3105	72	6	decomposition	decomposition	NOUN
ap-3105	72	7	let	let	VERB
ap-3105	72	8	γ̂	γ̂	PRON
ap-3105	72	9	be	be	AUX
ap-3105	72	10	the	the	DET
ap-3105	72	11	dual	dual	ADJ
ap-3105	72	12	space	space	NOUN
ap-3105	72	13	to	to	ADP
ap-3105	72	14	γ	γ	PROPN
ap-3105	72	15	(	(	PUNCT
ap-3105	72	16	the	the	DET
ap-3105	72	17	quotient	quotient	NOUN
ap-3105	72	18	space	space	NOUN
ap-3105	72	19	of	of	ADP
ap-3105	72	20	the	the	DET
ap-3105	72	21	space	space	NOUN
ap-3105	72	22	of	of	ADP
ap-3105	72	23	irreducible	irreducible	ADJ
ap-3105	72	24	unitary	unitary	ADJ
ap-3105	72	25	representations	representation	NOUN
ap-3105	72	26	of	of	ADP
ap-3105	72	27	γ	γ	NOUN
ap-3105	72	28	)	)	PUNCT
ap-3105	72	29	.	.	PUNCT
ap-3105	73	1	in	in	ADP
ap-3105	73	2	the	the	DET
ap-3105	73	3	first	first	ADJ
ap-3105	73	4	step	step	NOUN
ap-3105	73	5	of	of	ADP
ap-3105	73	6	the	the	DET
ap-3105	73	7	generalized	generalized	ADJ
ap-3105	73	8	bloch	bloch	PROPN
ap-3105	73	9	analysis	analysis	NOUN
ap-3105	73	10	one	one	NUM
ap-3105	73	11	decomposes	decompose	VERB
ap-3105	73	12	h	h	NOUN
ap-3105	73	13	into	into	ADP
ap-3105	73	14	a	a	DET
ap-3105	73	15	direct	direct	ADJ
ap-3105	73	16	integral	integral	NOUN
ap-3105	73	17	over	over	ADV
ap-3105	73	18	γ̂	γ̂	PUNCT
ap-3105	73	19	with	with	ADP
ap-3105	73	20	components	component	NOUN
ap-3105	73	21	being	be	AUX
ap-3105	73	22	equal	equal	ADJ
ap-3105	73	23	to	to	ADP
ap-3105	73	24	hλ	hλ	X
ap-3105	73	25	.	.	PUNCT
ap-3105	74	1	to	to	PART
ap-3105	74	2	achieve	achieve	VERB
ap-3105	74	3	this	this	DET
ap-3105	74	4	goal	goal	NOUN
ap-3105	74	5	a	a	DET
ap-3105	74	6	well	well	ADV
ap-3105	74	7	defined	define	VERB
ap-3105	74	8	harmonic	harmonic	ADJ
ap-3105	74	9	analysis	analysis	NOUN
ap-3105	74	10	on	on	ADP
ap-3105	74	11	γ	γ	PROPN
ap-3105	74	12	is	be	AUX
ap-3105	74	13	necessary	necessary	ADJ
ap-3105	74	14	.	.	PUNCT
ap-3105	75	1	it	it	PRON
ap-3105	75	2	is	be	AUX
ap-3105	75	3	known	know	VERB
ap-3105	75	4	that	that	SCONJ
ap-3105	75	5	the	the	DET
ap-3105	75	6	harmonic	harmonic	ADJ
ap-3105	75	7	analysis	analysis	NOUN
ap-3105	75	8	is	be	AUX
ap-3105	75	9	well	well	ADV
ap-3105	75	10	established	establish	VERB
ap-3105	75	11	for	for	ADP
ap-3105	75	12	locally	locally	ADV
ap-3105	75	13	compact	compact	ADJ
ap-3105	75	14	groups	group	NOUN
ap-3105	75	15	of	of	ADP
ap-3105	75	16	type	type	NOUN
ap-3105	76	1	i	i	PRON
ap-3105	76	2	[	[	X
ap-3105	76	3	20	20	NUM
ap-3105	76	4	]	]	PUNCT
ap-3105	76	5	.	.	PUNCT
ap-3105	77	1	so	so	ADV
ap-3105	77	2	all	all	DET
ap-3105	77	3	formulas	formula	NOUN
ap-3105	77	4	presented	present	VERB
ap-3105	77	5	below	below	ADV
ap-3105	77	6	are	be	AUX
ap-3105	77	7	well	well	ADV
ap-3105	77	8	defined	define	VERB
ap-3105	77	9	provided	provide	VERB
ap-3105	77	10	γ	γ	PROPN
ap-3105	77	11	is	be	AUX
ap-3105	77	12	a	a	DET
ap-3105	77	13	type	type	NOUN
ap-3105	77	14	i	i	PRON
ap-3105	77	15	group	group	NOUN
ap-3105	77	16	.	.	PUNCT
ap-3105	78	1	as	as	SCONJ
ap-3105	78	2	shown	show	VERB
ap-3105	78	3	in	in	ADP
ap-3105	78	4	[	[	X
ap-3105	78	5	26	26	NUM
ap-3105	78	6	,	,	PUNCT
ap-3105	78	7	satz	satz	X
ap-3105	78	8	6	6	NUM
ap-3105	78	9	]	]	PUNCT
ap-3105	78	10	,	,	PUNCT
ap-3105	78	11	a	a	DET
ap-3105	78	12	countable	countable	ADJ
ap-3105	78	13	discrete	discrete	ADJ
ap-3105	78	14	group	group	NOUN
ap-3105	78	15	is	be	AUX
ap-3105	78	16	of	of	ADP
ap-3105	78	17	type	type	NOUN
ap-3105	79	1	i	i	PRON
ap-3105	79	2	if	if	SCONJ
ap-3105	79	3	and	and	CCONJ
ap-3105	79	4	only	only	ADV
ap-3105	79	5	if	if	SCONJ
ap-3105	79	6	it	it	PRON
ap-3105	79	7	has	have	VERB
ap-3105	79	8	an	an	DET
ap-3105	79	9	abelian	abelian	ADJ
ap-3105	79	10	normal	normal	ADJ
ap-3105	79	11	subgroup	subgroup	NOUN
ap-3105	79	12	of	of	ADP
ap-3105	79	13	finite	finite	PROPN
ap-3105	79	14	index	index	PROPN
ap-3105	79	15	.	.	PUNCT
ap-3105	80	1	this	this	PRON
ap-3105	80	2	means	mean	VERB
ap-3105	80	3	that	that	SCONJ
ap-3105	80	4	there	there	PRON
ap-3105	80	5	exist	exist	VERB
ap-3105	80	6	multiply	multiply	ADV
ap-3105	80	7	connected	connect	VERB
ap-3105	80	8	configuration	configuration	NOUN
ap-3105	80	9	spaces	space	NOUN
ap-3105	80	10	of	of	ADP
ap-3105	80	11	interest	interest	NOUN
ap-3105	80	12	whose	whose	DET
ap-3105	80	13	fundamental	fundamental	ADJ
ap-3105	80	14	groups	group	NOUN
ap-3105	80	15	are	be	AUX
ap-3105	80	16	not	not	PART
ap-3105	80	17	of	of	ADP
ap-3105	80	18	type	type	NOUN
ap-3105	80	19	i.	i.	NOUN
ap-3105	80	20	for	for	ADP
ap-3105	80	21	example	example	NOUN
ap-3105	80	22	,	,	PUNCT
ap-3105	80	23	the	the	DET
ap-3105	80	24	fundamental	fundamental	ADJ
ap-3105	80	25	group	group	NOUN
ap-3105	80	26	in	in	ADP
ap-3105	80	27	the	the	DET
ap-3105	80	28	case	case	NOUN
ap-3105	80	29	of	of	ADP
ap-3105	80	30	the	the	DET
ap-3105	80	31	aharonov	aharonov	PROPN
ap-3105	80	32	-	-	PUNCT
ap-3105	80	33	bohm	bohm	PROPN
ap-3105	80	34	effect	effect	NOUN
ap-3105	80	35	with	with	ADP
ap-3105	80	36	two	two	NUM
ap-3105	80	37	vortices	vortex	NOUN
ap-3105	80	38	is	be	AUX
ap-3105	80	39	the	the	DET
ap-3105	80	40	free	free	ADJ
ap-3105	80	41	group	group	NOUN
ap-3105	80	42	with	with	ADP
ap-3105	80	43	two	two	NUM
ap-3105	80	44	generators	generator	NOUN
ap-3105	80	45	,	,	PUNCT
ap-3105	80	46	and	and	CCONJ
ap-3105	80	47	it	it	PRON
ap-3105	80	48	is	be	AUX
ap-3105	80	49	not	not	PART
ap-3105	80	50	of	of	ADP
ap-3105	80	51	type	type	NOUN
ap-3105	80	52	i.	i.	NOUN
ap-3105	80	53	this	this	DET
ap-3105	80	54	problem	problem	NOUN
ap-3105	80	55	is	be	AUX
ap-3105	80	56	avoided	avoid	VERB
ap-3105	80	57	,	,	PUNCT
ap-3105	80	58	however	however	ADV
ap-3105	80	59	,	,	PUNCT
ap-3105	80	60	if	if	SCONJ
ap-3105	80	61	m̃	m̃	PROPN
ap-3105	80	62	is	be	AUX
ap-3105	80	63	the	the	DET
ap-3105	80	64	maximal	maximal	ADJ
ap-3105	80	65	abelian	abelian	NOUN
ap-3105	80	66	covering	covering	NOUN
ap-3105	80	67	of	of	ADP
ap-3105	80	68	m	m	PROPN
ap-3105	80	69	rather	rather	ADV
ap-3105	80	70	than	than	ADP
ap-3105	80	71	the	the	DET
ap-3105	80	72	universal	universal	ADJ
ap-3105	80	73	covering	covering	NOUN
ap-3105	80	74	[	[	X
ap-3105	80	75	12	12	NUM
ap-3105	80	76	,	,	PUNCT
ap-3105	80	77	24	24	NUM
ap-3105	80	78	]	]	PUNCT
ap-3105	80	79	.	.	PUNCT
ap-3105	81	1	let	let	VERB
ap-3105	81	2	us	we	PRON
ap-3105	81	3	recall	recall	VERB
ap-3105	81	4	basic	basic	ADJ
ap-3105	81	5	properties	property	NOUN
ap-3105	81	6	of	of	ADP
ap-3105	81	7	the	the	DET
ap-3105	81	8	harmonic	harmonic	ADJ
ap-3105	81	9	analysis	analysis	NOUN
ap-3105	81	10	on	on	ADP
ap-3105	81	11	discrete	discrete	ADJ
ap-3105	81	12	type	type	NOUN
ap-3105	81	13	i	i	PRON
ap-3105	81	14	groups	group	NOUN
ap-3105	81	15	[	[	X
ap-3105	81	16	20	20	NUM
ap-3105	81	17	]	]	PUNCT
ap-3105	81	18	.	.	PUNCT
ap-3105	82	1	the	the	DET
ap-3105	82	2	haar	haar	NOUN
ap-3105	82	3	measure	measure	NOUN
ap-3105	82	4	on	on	ADP
ap-3105	82	5	γ	γ	X
ap-3105	82	6	is	be	AUX
ap-3105	82	7	simply	simply	ADV
ap-3105	82	8	the	the	DET
ap-3105	82	9	counting	counting	NOUN
ap-3105	82	10	measure	measure	NOUN
ap-3105	82	11	.	.	PUNCT
ap-3105	83	1	let	let	VERB
ap-3105	83	2	dm̂	dm̂	NOUN
ap-3105	83	3	be	be	AUX
ap-3105	83	4	the	the	DET
ap-3105	83	5	plancherel	plancherel	NOUN
ap-3105	83	6	measure	measure	NOUN
ap-3105	83	7	on	on	ADP
ap-3105	83	8	γ̂.	γ̂.	NOUN
ap-3105	83	9	it	it	PRON
ap-3105	83	10	is	be	AUX
ap-3105	83	11	known	know	VERB
ap-3105	83	12	that	that	SCONJ
ap-3105	83	13	if	if	SCONJ
ap-3105	83	14	γ	γ	NOUN
ap-3105	83	15	is	be	AUX
ap-3105	83	16	a	a	DET
ap-3105	83	17	countable	countable	ADJ
ap-3105	83	18	discrete	discrete	ADJ
ap-3105	83	19	group	group	NOUN
ap-3105	83	20	of	of	ADP
ap-3105	83	21	type	type	NOUN
ap-3105	83	22	i	i	PRON
ap-3105	83	23	then	then	ADV
ap-3105	83	24	dim	dim	VERB
ap-3105	83	25	lλ	lλ	PROPN
ap-3105	83	26	,	,	PUNCT
ap-3105	83	27	the	the	DET
ap-3105	83	28	dimension	dimension	NOUN
ap-3105	83	29	of	of	ADP
ap-3105	83	30	the	the	DET
ap-3105	83	31	carrier	carrier	NOUN
ap-3105	83	32	representation	representation	NOUN
ap-3105	83	33	space	space	NOUN
ap-3105	83	34	,	,	PUNCT
ap-3105	83	35	is	be	AUX
ap-3105	83	36	a	a	DET
ap-3105	83	37	bounded	bounded	ADJ
ap-3105	83	38	function	function	NOUN
ap-3105	83	39	of	of	ADP
ap-3105	83	40	λ	λ	PROPN
ap-3105	83	41	∈	∈	PROPN
ap-3105	83	42	γ̂	γ̂	PUNCT
ap-3105	84	1	[	[	X
ap-3105	84	2	26	26	NUM
ap-3105	84	3	,	,	PUNCT
ap-3105	84	4	korollar	korollar	PROPN
ap-3105	84	5	i	i	PRON
ap-3105	84	6	]	]	PUNCT
ap-3105	84	7	.	.	PUNCT
ap-3105	85	1	denote	denote	VERB
ap-3105	85	2	by	by	ADP
ap-3105	85	3	i2(lλ	i2(lλ	NOUN
ap-3105	85	4	)	)	PUNCT
ap-3105	85	5	≡	≡	PROPN
ap-3105	86	1	lλ	lλ	INTJ
ap-3105	86	2	⊗l	⊗l	PROPN
ap-3105	86	3	∗λ	∗λ	PROPN
ap-3105	86	4	the	the	DET
ap-3105	86	5	hilbert	hilbert	PROPN
ap-3105	86	6	space	space	NOUN
ap-3105	86	7	formed	form	VERB
ap-3105	86	8	by	by	ADP
ap-3105	86	9	hilbert	hilbert	PROPN
ap-3105	86	10	-	-	PUNCT
ap-3105	86	11	schmidt	schmidt	PROPN
ap-3105	86	12	operators	operator	NOUN
ap-3105	86	13	on	on	ADP
ap-3105	86	14	lλ	lλ	PROPN
ap-3105	86	15	(	(	PUNCT
ap-3105	86	16	l	l	PROPN
ap-3105	86	17	∗λ	∗λ	PROPN
ap-3105	86	18	is	be	AUX
ap-3105	86	19	the	the	DET
ap-3105	86	20	dual	dual	ADJ
ap-3105	86	21	space	space	NOUN
ap-3105	86	22	to	to	PART
ap-3105	86	23	lλ	lλ	VERB
ap-3105	86	24	)	)	PUNCT
ap-3105	86	25	.	.	PUNCT
ap-3105	87	1	the	the	DET
ap-3105	87	2	fourier	fourier	NOUN
ap-3105	87	3	transform	transform	NOUN
ap-3105	87	4	is	be	AUX
ap-3105	87	5	defined	define	VERB
ap-3105	87	6	as	as	ADP
ap-3105	87	7	a	a	DET
ap-3105	87	8	unitary	unitary	ADJ
ap-3105	87	9	mapping	mapping	NOUN
ap-3105	87	10	f	f	NOUN
ap-3105	87	11	:	:	PUNCT
ap-3105	87	12	l2(γ)→	l2(γ)→	ADJ
ap-3105	87	13	∫	∫	PROPN
ap-3105	87	14	⊕	⊕	PROPN
ap-3105	87	15	γ̂	γ̂	PUNCT
ap-3105	88	1	i2(lλ	i2(lλ	NOUN
ap-3105	88	2	)	)	PUNCT
ap-3105	89	1	dm̂(λ	dm̂(λ	NUM
ap-3105	89	2	)	)	PUNCT
ap-3105	89	3	.	.	PUNCT
ap-3105	90	1	note	note	VERB
ap-3105	90	2	that	that	SCONJ
ap-3105	90	3	in	in	ADP
ap-3105	90	4	this	this	DET
ap-3105	90	5	situation	situation	NOUN
ap-3105	90	6	f	f	PROPN
ap-3105	90	7	∈	∈	PROPN
ap-3105	90	8	l1(γ	l1(γ	PROPN
ap-3105	90	9	)	)	PUNCT
ap-3105	90	10	just	just	ADV
ap-3105	90	11	means	mean	VERB
ap-3105	90	12	that	that	SCONJ
ap-3105	90	13	the	the	DET
ap-3105	90	14	values	value	NOUN
ap-3105	90	15	of	of	ADP
ap-3105	90	16	f	f	PROPN
ap-3105	90	17	on	on	ADP
ap-3105	90	18	γ	γ	PROPN
ap-3105	90	19	represent	represent	VERB
ap-3105	90	20	a	a	DET
ap-3105	90	21	summable	summable	ADJ
ap-3105	90	22	sequence	sequence	NOUN
ap-3105	90	23	.	.	PUNCT
ap-3105	91	1	since	since	SCONJ
ap-3105	91	2	every	every	DET
ap-3105	91	3	summable	summable	ADJ
ap-3105	91	4	sequence	sequence	NOUN
ap-3105	91	5	is	be	AUX
ap-3105	91	6	also	also	ADV
ap-3105	91	7	square	square	ADJ
ap-3105	91	8	summable	summable	ADJ
ap-3105	91	9	we	we	PRON
ap-3105	91	10	have	have	VERB
ap-3105	91	11	f	f	PROPN
ap-3105	91	12	∈	∈	PROPN
ap-3105	91	13	l1(γ	l1(γ	PROPN
ap-3105	91	14	)	)	PUNCT
ap-3105	91	15	⊂	⊂	PROPN
ap-3105	91	16	l2(γ	l2(γ	NOUN
ap-3105	91	17	)	)	PUNCT
ap-3105	91	18	,	,	PUNCT
ap-3105	91	19	and	and	CCONJ
ap-3105	91	20	then	then	ADV
ap-3105	91	21	f	f	PROPN
ap-3105	92	1	[	[	X
ap-3105	92	2	f	f	X
ap-3105	92	3	]	]	X
ap-3105	92	4	(	(	PUNCT
ap-3105	92	5	λ	λ	NOUN
ap-3105	92	6	)	)	PUNCT
ap-3105	92	7	=	=	SYM
ap-3105	92	8	∑	∑	AUX
ap-3105	92	9	s∈γ	s∈γ	PROPN
ap-3105	92	10	f(s)λ(s	f(s)λ(	NOUN
ap-3105	92	11	)	)	PUNCT
ap-3105	92	12	.	.	PUNCT
ap-3105	93	1	conversely	conversely	ADV
ap-3105	93	2	,	,	PUNCT
ap-3105	93	3	if	if	SCONJ
ap-3105	93	4	f	f	PROPN
ap-3105	93	5	is	be	AUX
ap-3105	93	6	of	of	ADP
ap-3105	93	7	the	the	DET
ap-3105	93	8	form	form	NOUN
ap-3105	93	9	f	f	NOUN
ap-3105	93	10	=	=	SYM
ap-3105	93	11	g	g	PROPN
ap-3105	93	12	∗	∗	NOUN
ap-3105	93	13	h	h	NOUN
ap-3105	93	14	(	(	PUNCT
ap-3105	93	15	the	the	DET
ap-3105	93	16	convolution	convolution	NOUN
ap-3105	93	17	)	)	PUNCT
ap-3105	93	18	where	where	SCONJ
ap-3105	93	19	g	g	NOUN
ap-3105	93	20	,	,	PUNCT
ap-3105	93	21	h	h	NOUN
ap-3105	93	22	∈	∈	PROPN
ap-3105	93	23	l1(γ	l1(γ	PROPN
ap-3105	93	24	)	)	PUNCT
ap-3105	93	25	,	,	PUNCT
ap-3105	93	26	and	and	CCONJ
ap-3105	93	27	f̂	f̂	NUM
ap-3105	93	28	=	=	SYM
ap-3105	93	29	f	f	X
ap-3105	94	1	[	[	X
ap-3105	94	2	f	f	X
ap-3105	94	3	]	]	PUNCT
ap-3105	94	4	then	then	ADV
ap-3105	94	5	f(s	f(	VERB
ap-3105	94	6	)	)	PUNCT
ap-3105	95	1	=	=	SYM
ap-3105	95	2	∫	∫	PROPN
ap-3105	95	3	γ̂	γ̂	PUNCT
ap-3105	95	4	tr	tr	PUNCT
ap-3105	95	5	[	[	PUNCT
ap-3105	95	6	λ(s)∗f̂(λ	λ(s)∗f̂(λ	PROPN
ap-3105	95	7	)	)	PUNCT
ap-3105	95	8	]	]	PUNCT
ap-3105	96	1	dm̂(λ	dm̂(λ	NUM
ap-3105	96	2	)	)	PUNCT
ap-3105	96	3	.	.	PUNCT
ap-3105	97	1	using	use	VERB
ap-3105	97	2	unitarity	unitarity	NOUN
ap-3105	97	3	of	of	ADP
ap-3105	97	4	the	the	DET
ap-3105	97	5	fourier	fourier	NOUN
ap-3105	97	6	transform	transform	NOUN
ap-3105	97	7	one	one	NUM
ap-3105	97	8	finds	find	VERB
ap-3105	97	9	that	that	DET
ap-3105	97	10	m̂(γ̂	m̂(γ̂	NOUN
ap-3105	97	11	)	)	PUNCT
ap-3105	97	12	≤	≤	NUM
ap-3105	97	13	1	1	NUM
ap-3105	97	14	.	.	PUNCT
ap-3105	98	1	the	the	DET
ap-3105	98	2	following	follow	VERB
ap-3105	98	3	rule	rule	NOUN
ap-3105	98	4	is	be	AUX
ap-3105	98	5	of	of	ADP
ap-3105	98	6	crucial	crucial	ADJ
ap-3105	98	7	importance	importance	NOUN
ap-3105	98	8	:	:	PUNCT
ap-3105	98	9	∀s	∀s	PROPN
ap-3105	98	10	∈	∈	PROPN
ap-3105	98	11	γ	γ	X
ap-3105	98	12	,	,	PUNCT
ap-3105	98	13	∀f	∀f	PROPN
ap-3105	98	14	∈	∈	PROPN
ap-3105	98	15	l2(γ	l2(γ	NOUN
ap-3105	98	16	)	)	PUNCT
ap-3105	98	17	,	,	PUNCT
ap-3105	98	18	f	f	PROPN
ap-3105	98	19	[	[	X
ap-3105	98	20	f(s	f(s	X
ap-3105	98	21	·	·	SYM
ap-3105	98	22	g)](λ	g)](λ	PROPN
ap-3105	98	23	)	)	PUNCT
ap-3105	99	1	=	=	PUNCT
ap-3105	100	1	λ(s−1)f	λ(s−1)f	PROPN
ap-3105	101	1	[	[	X
ap-3105	101	2	f(g)](λ	f(g)](λ	NUM
ap-3105	101	3	)	)	PUNCT
ap-3105	101	4	.	.	PUNCT
ap-3105	102	1	now	now	ADV
ap-3105	102	2	we	we	PRON
ap-3105	102	3	are	be	AUX
ap-3105	102	4	going	go	VERB
ap-3105	102	5	to	to	PART
ap-3105	102	6	construct	construct	VERB
ap-3105	102	7	a	a	DET
ap-3105	102	8	unitary	unitary	ADJ
ap-3105	102	9	map	map	NOUN
ap-3105	102	10	φ	φ	NOUN
ap-3105	102	11	:	:	PUNCT
ap-3105	102	12	l2(m̃)→	l2(m̃)→	PROPN
ap-3105	102	13	∫	∫	PROPN
ap-3105	102	14	⊕	⊕	PROPN
ap-3105	102	15	γ̂	γ̂	PUNCT
ap-3105	102	16	hλ	hλ	ADP
ap-3105	102	17	⊗l	⊗l	PROPN
ap-3105	102	18	∗λ	∗λ	PROPN
ap-3105	102	19	dm̂(λ	dm̂(λ	ADV
ap-3105	102	20	)	)	PUNCT
ap-3105	102	21	making	make	VERB
ap-3105	102	22	it	it	PRON
ap-3105	102	23	possible	possible	ADJ
ap-3105	102	24	to	to	PART
ap-3105	102	25	decompose	decompose	VERB
ap-3105	102	26	h.	h.	NOUN
ap-3105	102	27	observe	observe	VERB
ap-3105	102	28	that	that	SCONJ
ap-3105	102	29	the	the	DET
ap-3105	102	30	tensor	tensor	NOUN
ap-3105	102	31	product	product	NOUN
ap-3105	102	32	hλ	hλ	ADP
ap-3105	102	33	⊗l	⊗l	PROPN
ap-3105	102	34	∗λ	∗λ	PROPN
ap-3105	102	35	can	can	AUX
ap-3105	102	36	be	be	AUX
ap-3105	102	37	naturally	naturally	ADV
ap-3105	102	38	identified	identify	VERB
ap-3105	102	39	with	with	ADP
ap-3105	102	40	the	the	DET
ap-3105	102	41	hilbert	hilbert	NOUN
ap-3105	102	42	space	space	NOUN
ap-3105	102	43	of	of	ADP
ap-3105	102	44	λ	λ	NOUN
ap-3105	102	45	-	-	PUNCT
ap-3105	102	46	equivariant	equivariant	ADJ
ap-3105	102	47	operator	operator	NOUN
ap-3105	102	48	-	-	PUNCT
ap-3105	102	49	valued	value	VERB
ap-3105	102	50	functions	function	NOUN
ap-3105	102	51	on	on	ADP
ap-3105	102	52	m̃	m̃	PROPN
ap-3105	102	53	with	with	ADP
ap-3105	102	54	values	value	NOUN
ap-3105	102	55	in	in	ADP
ap-3105	102	56	i2(lλ	i2(lλ	NOUN
ap-3105	102	57	)	)	PUNCT
ap-3105	102	58	.	.	PUNCT
ap-3105	103	1	for	for	ADP
ap-3105	103	2	f	f	PROPN
ap-3105	103	3	∈	∈	PROPN
ap-3105	103	4	l2(m̃	l2(m̃	PROPN
ap-3105	103	5	)	)	PUNCT
ap-3105	103	6	and	and	CCONJ
ap-3105	103	7	y	y	PROPN
ap-3105	103	8	∈	∈	PROPN
ap-3105	103	9	m̃	m̃	PROPN
ap-3105	103	10	set	set	VERB
ap-3105	103	11	∀s	∀s	PROPN
ap-3105	103	12	∈	∈	PROPN
ap-3105	103	13	γ	γ	X
ap-3105	103	14	,	,	PUNCT
ap-3105	103	15	fy(s	fy(s	X
ap-3105	103	16	)	)	PUNCT
ap-3105	103	17	=	=	SYM
ap-3105	104	1	f(s−1	f(s−1	X
ap-3105	104	2	·	·	PUNCT
ap-3105	104	3	y	y	X
ap-3105	104	4	)	)	PUNCT
ap-3105	104	5	.	.	PUNCT
ap-3105	105	1	the	the	DET
ap-3105	105	2	norm	norm	NOUN
ap-3105	105	3	‖fy‖	‖fy‖	VERB
ap-3105	105	4	in	in	ADP
ap-3105	105	5	l2(γ	l2(γ	NOUN
ap-3105	105	6	)	)	PUNCT
ap-3105	105	7	is	be	AUX
ap-3105	105	8	a	a	DET
ap-3105	105	9	γ	γ	ADJ
ap-3105	105	10	-	-	ADJ
ap-3105	105	11	invariant	invariant	ADJ
ap-3105	105	12	function	function	NOUN
ap-3105	105	13	of	of	ADP
ap-3105	105	14	y	y	PROPN
ap-3105	105	15	∈	∈	PROPN
ap-3105	105	16	m̃	m̃	PROPN
ap-3105	105	17	whose	whose	DET
ap-3105	105	18	projection	projection	NOUN
ap-3105	105	19	onto	onto	ADP
ap-3105	105	20	m	m	PROPN
ap-3105	105	21	is	be	AUX
ap-3105	105	22	square	square	ADJ
ap-3105	105	23	integrable	integrable	ADJ
ap-3105	105	24	.	.	PUNCT
ap-3105	106	1	hence	hence	ADV
ap-3105	106	2	for	for	ADP
ap-3105	106	3	almost	almost	ADV
ap-3105	106	4	all	all	PRON
ap-3105	106	5	x	x	NOUN
ap-3105	106	6	∈m	∈m	NOUN
ap-3105	106	7	and	and	CCONJ
ap-3105	106	8	all	all	DET
ap-3105	106	9	y	y	PROPN
ap-3105	106	10	∈	∈	PROPN
ap-3105	106	11	π−1({x	π−1({x	NOUN
ap-3105	106	12	}	}	PUNCT
ap-3105	106	13	)	)	PUNCT
ap-3105	106	14	one	one	PRON
ap-3105	106	15	has	have	VERB
ap-3105	106	16	fy	fy	PROPN
ap-3105	106	17	∈	∈	PROPN
ap-3105	106	18	l2(γ	l2(γ	PROPN
ap-3105	106	19	)	)	PUNCT
ap-3105	106	20	.	.	PUNCT
ap-3105	107	1	we	we	PRON
ap-3105	107	2	define	define	VERB
ap-3105	107	3	components	component	NOUN
ap-3105	107	4	φ[f	φ[f	ADP
ap-3105	107	5	]	]	X
ap-3105	107	6	(	(	PUNCT
ap-3105	107	7	λ	λ	NOUN
ap-3105	107	8	)	)	PUNCT
ap-3105	107	9	,	,	PUNCT
ap-3105	107	10	λ	λ	PROPN
ap-3105	107	11	∈	∈	PROPN
ap-3105	107	12	γ̂	γ̂	NOUN
ap-3105	107	13	,	,	PUNCT
ap-3105	107	14	by	by	ADP
ap-3105	107	15	(	(	PUNCT
ap-3105	107	16	φ[f	φ[f	ADP
ap-3105	107	17	]	]	PUNCT
ap-3105	107	18	(	(	PUNCT
ap-3105	107	19	λ	λ	NOUN
ap-3105	107	20	)	)	PUNCT
ap-3105	107	21	)	)	PUNCT
ap-3105	108	1	(	(	PUNCT
ap-3105	108	2	y	y	X
ap-3105	108	3	)	)	PUNCT
ap-3105	108	4	=	=	PUNCT
ap-3105	109	1	f	f	X
ap-3105	110	1	[	[	X
ap-3105	110	2	fy](λ	fy](λ	X
ap-3105	110	3	)	)	PUNCT
ap-3105	110	4	∈	∈	PROPN
ap-3105	110	5	i2(lλ	i2(lλ	PROPN
ap-3105	110	6	)	)	PUNCT
ap-3105	110	7	.	.	PUNCT
ap-3105	111	1	in	in	ADP
ap-3105	111	2	particular	particular	ADJ
ap-3105	111	3	,	,	PUNCT
ap-3105	111	4	if	if	SCONJ
ap-3105	111	5	f	f	PROPN
ap-3105	111	6	∈	∈	PROPN
ap-3105	111	7	l1(m̃	l1(m̃	PROPN
ap-3105	111	8	)	)	PUNCT
ap-3105	111	9	∩	∩	PROPN
ap-3105	111	10	l2(m̃	l2(m̃	PROPN
ap-3105	111	11	)	)	PUNCT
ap-3105	111	12	then	then	ADV
ap-3105	111	13	(	(	PUNCT
ap-3105	111	14	φ[f	φ[f	ADP
ap-3105	111	15	]	]	PUNCT
ap-3105	111	16	(	(	PUNCT
ap-3105	111	17	λ	λ	NOUN
ap-3105	111	18	)	)	PUNCT
ap-3105	111	19	)	)	PUNCT
ap-3105	111	20	(	(	PUNCT
ap-3105	111	21	y	y	X
ap-3105	111	22	)	)	PUNCT
ap-3105	111	23	=	=	SYM
ap-3105	111	24	∑	∑	ADP
ap-3105	111	25	s∈γ	s∈γ	VERB
ap-3105	111	26	f(s−1	f(s−1	PROPN
ap-3105	111	27	·	·	PUNCT
ap-3105	111	28	y)λ(s	y)λ(s	PROPN
ap-3105	111	29	)	)	PUNCT
ap-3105	111	30	.	.	PUNCT
ap-3105	112	1	equivalently	equivalently	ADV
ap-3105	112	2	,	,	PUNCT
ap-3105	112	3	referring	refer	VERB
ap-3105	112	4	to	to	ADP
ap-3105	112	5	(	(	PUNCT
ap-3105	112	6	1	1	NUM
ap-3105	112	7	)	)	PUNCT
ap-3105	112	8	,	,	PUNCT
ap-3105	112	9	one	one	PRON
ap-3105	112	10	can	can	AUX
ap-3105	112	11	define	define	VERB
ap-3105	112	12	φ	φ	PROPN
ap-3105	112	13	in	in	ADP
ap-3105	112	14	the	the	DET
ap-3105	112	15	following	following	ADJ
ap-3105	112	16	way	way	NOUN
ap-3105	112	17	.	.	PUNCT
ap-3105	113	1	for	for	ADP
ap-3105	113	2	ϕ	ϕ	PROPN
ap-3105	113	3	∈	∈	PROPN
ap-3105	113	4	c∞0	c∞0	PROPN
ap-3105	113	5	(	(	PUNCT
ap-3105	113	6	m̃	m̃	PROPN
ap-3105	113	7	)	)	PUNCT
ap-3105	113	8	,	,	PUNCT
ap-3105	113	9	v	v	X
ap-3105	113	10	∈	∈	PROPN
ap-3105	113	11	lλ	lλ	NOUN
ap-3105	113	12	and	and	CCONJ
ap-3105	113	13	y	y	PROPN
ap-3105	113	14	∈	∈	PROPN
ap-3105	113	15	m̃	m̃	PROPN
ap-3105	113	16	set	set	NOUN
ap-3105	113	17	(	(	PUNCT
ap-3105	113	18	φ[ϕ](λ	φ[ϕ](λ	NOUN
ap-3105	113	19	)	)	PUNCT
ap-3105	113	20	)	)	PUNCT
ap-3105	113	21	(	(	PUNCT
ap-3105	113	22	y)v	y)v	VERB
ap-3105	113	23	=	=	SYM
ap-3105	113	24	(	(	PUNCT
ap-3105	113	25	φλϕ⊗	φλϕ⊗	NOUN
ap-3105	113	26	v)(y	v)(y	NOUN
ap-3105	113	27	)	)	PUNCT
ap-3105	113	28	.	.	PUNCT
ap-3105	114	1	(	(	PUNCT
ap-3105	114	2	2	2	X
ap-3105	114	3	)	)	PUNCT
ap-3105	114	4	then	then	ADV
ap-3105	114	5	φ	φ	PROPN
ap-3105	114	6	introduced	introduce	VERB
ap-3105	114	7	in	in	ADP
ap-3105	114	8	(	(	PUNCT
ap-3105	114	9	2	2	NUM
ap-3105	114	10	)	)	PUNCT
ap-3105	114	11	is	be	AUX
ap-3105	114	12	an	an	DET
ap-3105	114	13	isometry	isometry	NOUN
ap-3105	114	14	and	and	CCONJ
ap-3105	114	15	extends	extend	VERB
ap-3105	114	16	unambiguously	unambiguously	ADV
ap-3105	114	17	to	to	ADP
ap-3105	114	18	a	a	DET
ap-3105	114	19	unitary	unitary	ADJ
ap-3105	114	20	mapping	mapping	NOUN
ap-3105	114	21	.	.	PUNCT
ap-3105	115	1	finally	finally	ADV
ap-3105	115	2	one	one	PRON
ap-3105	115	3	can	can	AUX
ap-3105	115	4	verify	verify	VERB
ap-3105	115	5	the	the	DET
ap-3105	115	6	formula	formula	NOUN
ap-3105	115	7	φhφ−1	φhφ−1	NOUN
ap-3105	115	8	=	=	SYM
ap-3105	115	9	∫	∫	PROPN
ap-3105	115	10	⊕	⊕	PROPN
ap-3105	115	11	γ̂	γ̂	PUNCT
ap-3105	115	12	hλ	hλ	PROPN
ap-3105	115	13	⊗	⊗	PROPN
ap-3105	115	14	1	1	NUM
ap-3105	115	15	dm̂(λ	dm̂(λ	NOUN
ap-3105	115	16	)	)	PUNCT
ap-3105	115	17	which	which	PRON
ap-3105	115	18	represents	represent	VERB
ap-3105	115	19	the	the	DET
ap-3105	115	20	sought	seek	VERB
ap-3105	115	21	bloch	bloch	NOUN
ap-3105	115	22	decomposition	decomposition	NOUN
ap-3105	115	23	.	.	PUNCT
ap-3105	116	1	as	as	ADP
ap-3105	116	2	a	a	DET
ap-3105	116	3	corollary	corollary	NOUN
ap-3105	116	4	we	we	PRON
ap-3105	116	5	have	have	VERB
ap-3105	116	6	φu(t)φ−1	φu(t)φ−1	PROPN
ap-3105	116	7	=	=	SYM
ap-3105	116	8	∫	∫	PROPN
ap-3105	116	9	⊕	⊕	PROPN
ap-3105	116	10	γ̂	γ̂	PUNCT
ap-3105	116	11	uλ(t)⊗	uλ(t)⊗	ADJ
ap-3105	116	12	1	1	NUM
ap-3105	116	13	dm̂(λ	dm̂(λ	NUM
ap-3105	116	14	)	)	PUNCT
ap-3105	116	15	.	.	PUNCT
ap-3105	117	1	(	(	PUNCT
ap-3105	117	2	3	3	X
ap-3105	117	3	)	)	PUNCT
ap-3105	117	4	226	226	NUM
ap-3105	117	5	vol	vol	NOUN
ap-3105	117	6	.	.	PUNCT
ap-3105	118	1	56	56	NUM
ap-3105	118	2	no	no	NOUN
ap-3105	118	3	.	.	PUNCT
ap-3105	119	1	3/2016	3/2016	NUM
ap-3105	119	2	the	the	DET
ap-3105	119	3	aharonov	aharonov	PROPN
ap-3105	119	4	-	-	PUNCT
ap-3105	119	5	bohm	bohm	PROPN
ap-3105	119	6	hamiltonian	hamiltonian	NOUN
ap-3105	119	7	with	with	ADP
ap-3105	119	8	two	two	NUM
ap-3105	119	9	vortices	vortex	NOUN
ap-3105	119	10	revisited	revisit	VERB
ap-3105	119	11	2.3	2.3	NUM
ap-3105	119	12	.	.	PUNCT
ap-3105	120	1	propagators	propagator	NOUN
ap-3105	120	2	associated	associate	VERB
ap-3105	120	3	with	with	ADP
ap-3105	120	4	periodic	periodic	ADJ
ap-3105	120	5	hamiltonians	hamiltonian	NOUN
ap-3105	120	6	in	in	ADP
ap-3105	120	7	(	(	PUNCT
ap-3105	120	8	3	3	NUM
ap-3105	120	9	)	)	PUNCT
ap-3105	120	10	,	,	PUNCT
ap-3105	120	11	the	the	DET
ap-3105	120	12	evolution	evolution	NOUN
ap-3105	120	13	operator	operator	NOUN
ap-3105	120	14	u(t	u(t	NOUN
ap-3105	120	15	)	)	PUNCT
ap-3105	120	16	is	be	AUX
ap-3105	120	17	expressed	express	VERB
ap-3105	120	18	in	in	ADP
ap-3105	120	19	terms	term	NOUN
ap-3105	120	20	of	of	ADP
ap-3105	120	21	uλ(t	uλ(t	NOUN
ap-3105	120	22	)	)	PUNCT
ap-3105	120	23	,	,	PUNCT
ap-3105	120	24	λ	λ	PROPN
ap-3105	120	25	∈	∈	PROPN
ap-3105	120	26	γ̂.	γ̂.	NOUN
ap-3105	120	27	it	it	PRON
ap-3105	120	28	is	be	AUX
ap-3105	120	29	possible	possible	ADJ
ap-3105	120	30	to	to	PART
ap-3105	120	31	invert	invert	VERB
ap-3105	120	32	this	this	DET
ap-3105	120	33	relationship	relationship	NOUN
ap-3105	120	34	and	and	CCONJ
ap-3105	120	35	to	to	PART
ap-3105	120	36	derive	derive	VERB
ap-3105	120	37	a	a	DET
ap-3105	120	38	formula	formula	NOUN
ap-3105	120	39	for	for	ADP
ap-3105	120	40	the	the	DET
ap-3105	120	41	propagator	propagator	NOUN
ap-3105	120	42	associated	associate	VERB
ap-3105	120	43	with	with	ADP
ap-3105	120	44	hλ	hλ	NOUN
ap-3105	120	45	which	which	PRON
ap-3105	120	46	is	be	AUX
ap-3105	120	47	expressed	express	VERB
ap-3105	120	48	in	in	ADP
ap-3105	120	49	terms	term	NOUN
ap-3105	120	50	of	of	ADP
ap-3105	120	51	the	the	DET
ap-3105	120	52	propagator	propagator	NOUN
ap-3105	120	53	associated	associate	VERB
ap-3105	120	54	with	with	ADP
ap-3105	120	55	h.	h.	PROPN
ap-3105	120	56	the	the	DET
ap-3105	120	57	propagators	propagator	NOUN
ap-3105	120	58	are	be	AUX
ap-3105	120	59	regarded	regard	VERB
ap-3105	120	60	as	as	ADP
ap-3105	120	61	distributions	distribution	NOUN
ap-3105	120	62	which	which	PRON
ap-3105	120	63	are	be	AUX
ap-3105	120	64	introduced	introduce	VERB
ap-3105	120	65	as	as	ADP
ap-3105	120	66	kernels	kernel	NOUN
ap-3105	120	67	of	of	ADP
ap-3105	120	68	the	the	DET
ap-3105	120	69	corresponding	corresponding	ADJ
ap-3105	120	70	evolution	evolution	NOUN
ap-3105	120	71	operators	operator	NOUN
ap-3105	120	72	.	.	PUNCT
ap-3105	121	1	recall	recall	VERB
ap-3105	121	2	that	that	PRON
ap-3105	121	3	,	,	PUNCT
ap-3105	121	4	by	by	ADP
ap-3105	121	5	the	the	DET
ap-3105	121	6	schwartz	schwartz	PROPN
ap-3105	121	7	kernel	kernel	PROPN
ap-3105	121	8	theorem	theorem	PROPN
ap-3105	121	9	(	(	PUNCT
ap-3105	121	10	see	see	VERB
ap-3105	121	11	,	,	PUNCT
ap-3105	121	12	for	for	ADP
ap-3105	121	13	example	example	NOUN
ap-3105	121	14	,	,	PUNCT
ap-3105	121	15	[	[	X
ap-3105	121	16	8	8	NUM
ap-3105	121	17	,	,	PUNCT
ap-3105	121	18	theorem	theorem	VERB
ap-3105	121	19	5.2.1	5.2.1	NUM
ap-3105	121	20	]	]	NUM
ap-3105	121	21	)	)	PUNCT
ap-3105	121	22	,	,	PUNCT
ap-3105	121	23	to	to	ADP
ap-3105	121	24	every	every	DET
ap-3105	121	25	b	b	PROPN
ap-3105	121	26	∈	∈	PROPN
ap-3105	121	27	b(l2(m̃	b(l2(m̃	NOUN
ap-3105	121	28	)	)	PUNCT
ap-3105	121	29	)	)	PUNCT
ap-3105	122	1	there	there	PRON
ap-3105	122	2	exists	exist	VERB
ap-3105	122	3	one	one	NUM
ap-3105	122	4	and	and	CCONJ
ap-3105	122	5	only	only	ADV
ap-3105	122	6	one	one	NUM
ap-3105	122	7	β	β	NOUN
ap-3105	122	8	∈	∈	PROPN
ap-3105	123	1	d	d	X
ap-3105	123	2	′(m̃	′(m̃	PROPN
ap-3105	123	3	×	×	PROPN
ap-3105	123	4	m̃	m̃	PROPN
ap-3105	123	5	)	)	PUNCT
ap-3105	123	6	such	such	ADJ
ap-3105	123	7	that	that	SCONJ
ap-3105	123	8	∀ϕ1	∀ϕ1	PROPN
ap-3105	123	9	,	,	PUNCT
ap-3105	123	10	ϕ2	ϕ2	ADV
ap-3105	123	11	∈	∈	PROPN
ap-3105	123	12	c∞0	c∞0	PRON
ap-3105	123	13	(	(	PUNCT
ap-3105	123	14	m̃	m̃	PROPN
ap-3105	123	15	)	)	PUNCT
ap-3105	123	16	,	,	PUNCT
ap-3105	123	17	β(ϕ1	β(ϕ1	PUNCT
ap-3105	124	1	⊗	⊗	PROPN
ap-3105	124	2	ϕ2	ϕ2	ADV
ap-3105	124	3	)	)	PUNCT
ap-3105	124	4	=	=	SYM
ap-3105	125	1	〈	〈	NOUN
ap-3105	125	2	ϕ1	ϕ1	NOUN
ap-3105	125	3	,	,	PUNCT
ap-3105	125	4	bϕ2	bϕ2	PROPN
ap-3105	125	5	〉	〉	PROPN
ap-3105	125	6	.	.	PUNCT
ap-3105	126	1	one	one	NUM
ap-3105	126	2	calls	call	VERB
ap-3105	126	3	β	β	VERB
ap-3105	126	4	the	the	DET
ap-3105	126	5	kernel	kernel	PROPN
ap-3105	126	6	of	of	ADP
ap-3105	126	7	b.	b.	PROPN
ap-3105	126	8	the	the	DET
ap-3105	126	9	kernel	kernel	PROPN
ap-3105	126	10	theorem	theorem	NOUN
ap-3105	126	11	can	can	AUX
ap-3105	126	12	be	be	AUX
ap-3105	126	13	extended	extend	VERB
ap-3105	126	14	to	to	ADP
ap-3105	126	15	hilbert	hilbert	NOUN
ap-3105	126	16	spaces	space	NOUN
ap-3105	126	17	formed	form	VERB
ap-3105	126	18	by	by	ADP
ap-3105	126	19	λ	λ	PROPN
ap-3105	126	20	-	-	PUNCT
ap-3105	126	21	equivariant	equivariant	ADJ
ap-3105	126	22	vector	vector	NOUN
ap-3105	126	23	-	-	PUNCT
ap-3105	126	24	valued	value	VERB
ap-3105	126	25	functions	function	NOUN
ap-3105	126	26	.	.	PUNCT
ap-3105	127	1	in	in	ADP
ap-3105	127	2	this	this	DET
ap-3105	127	3	case	case	NOUN
ap-3105	127	4	the	the	DET
ap-3105	127	5	kernels	kernel	NOUN
ap-3105	127	6	are	be	AUX
ap-3105	127	7	operator	operator	NOUN
ap-3105	127	8	-	-	PUNCT
ap-3105	127	9	valued	value	VERB
ap-3105	127	10	distributions	distribution	NOUN
ap-3105	127	11	.	.	PUNCT
ap-3105	128	1	to	to	ADP
ap-3105	128	2	every	every	DET
ap-3105	128	3	b	b	PROPN
ap-3105	128	4	∈	∈	PROPN
ap-3105	128	5	b(hλ	b(hλ	NOUN
ap-3105	128	6	)	)	PUNCT
ap-3105	128	7	there	there	PRON
ap-3105	128	8	exists	exist	VERB
ap-3105	128	9	one	one	NUM
ap-3105	128	10	and	and	CCONJ
ap-3105	128	11	only	only	ADV
ap-3105	128	12	one	one	NUM
ap-3105	129	1	β	β	NOUN
ap-3105	129	2	∈	∈	PROPN
ap-3105	130	1	d	d	X
ap-3105	130	2	′(m̃	′(m̃	PROPN
ap-3105	130	3	×	×	NOUN
ap-3105	130	4	m̃)⊗b(lλ	m̃)⊗b(lλ	NOUN
ap-3105	130	5	)	)	PUNCT
ap-3105	130	6	such	such	ADJ
ap-3105	130	7	that	that	SCONJ
ap-3105	130	8	∀ϕ1	∀ϕ1	PROPN
ap-3105	130	9	,	,	PUNCT
ap-3105	130	10	ϕ2	ϕ2	ADV
ap-3105	130	11	∈	∈	PROPN
ap-3105	130	12	c∞0	c∞0	PRON
ap-3105	130	13	(	(	PUNCT
ap-3105	130	14	m̃	m̃	PROPN
ap-3105	130	15	)	)	PUNCT
ap-3105	130	16	,	,	PUNCT
ap-3105	130	17	∀v1	∀v1	PROPN
ap-3105	130	18	,	,	PUNCT
ap-3105	130	19	v2	v2	PROPN
ap-3105	130	20	∈	∈	PROPN
ap-3105	130	21	lλ	lλ	NOUN
ap-3105	130	22	,	,	PUNCT
ap-3105	130	23	〈	〈	PROPN
ap-3105	130	24	v1	v1	NOUN
ap-3105	130	25	,	,	PUNCT
ap-3105	130	26	β(ϕ1	β(ϕ1	X
ap-3105	131	1	⊗	⊗	PROPN
ap-3105	131	2	ϕ2)v2	ϕ2)v2	PROPN
ap-3105	131	3	〉	〉	NOUN
ap-3105	131	4	lλ	lλ	NOUN
ap-3105	131	5	=	=	SYM
ap-3105	131	6	〈	〈	PROPN
ap-3105	131	7	φλϕ1	φλϕ1	PROPN
ap-3105	131	8	⊗	⊗	PROPN
ap-3105	131	9	v1	v1	PROPN
ap-3105	131	10	,	,	PUNCT
ap-3105	131	11	bφλϕ2	bφλϕ2	PROPN
ap-3105	131	12	⊗	⊗	PROPN
ap-3105	131	13	v2	v2	PROPN
ap-3105	131	14	〉	〉	NOUN
ap-3105	131	15	.	.	PUNCT
ap-3105	132	1	the	the	DET
ap-3105	132	2	distribution	distribution	NOUN
ap-3105	132	3	β	β	X
ap-3105	132	4	is	be	AUX
ap-3105	132	5	λ	λ	NOUN
ap-3105	132	6	-	-	NOUN
ap-3105	132	7	equivariant	equivariant	ADJ
ap-3105	132	8	:	:	PUNCT
ap-3105	132	9	∀s	∀s	PROPN
ap-3105	132	10	∈	∈	PROPN
ap-3105	132	11	γ	γ	X
ap-3105	132	12	,	,	PUNCT
ap-3105	132	13	β(s	β(s	PROPN
ap-3105	132	14	·	·	PUNCT
ap-3105	132	15	y1	y1	INTJ
ap-3105	132	16	,	,	PUNCT
ap-3105	132	17	y2	y2	NOUN
ap-3105	132	18	)	)	PUNCT
ap-3105	132	19	=	=	PUNCT
ap-3105	132	20	λ(s)β(y1	λ(s)β(y1	PROPN
ap-3105	132	21	,	,	PUNCT
ap-3105	132	22	y2	y2	NOUN
ap-3105	132	23	)	)	PUNCT
ap-3105	132	24	and	and	CCONJ
ap-3105	132	25	β(y1	β(y1	NUM
ap-3105	132	26	,	,	PUNCT
ap-3105	132	27	s	s	PART
ap-3105	132	28	·	·	PUNCT
ap-3105	132	29	y2	y2	NUM
ap-3105	132	30	)	)	PUNCT
ap-3105	133	1	=	=	SYM
ap-3105	133	2	β(y1	β(y1	X
ap-3105	133	3	,	,	PUNCT
ap-3105	133	4	y2)λ(s−1	y2)λ(s−1	NOUN
ap-3105	133	5	)	)	PUNCT
ap-3105	133	6	(	(	PUNCT
ap-3105	133	7	4	4	X
ap-3105	133	8	)	)	PUNCT
ap-3105	133	9	denote	denote	NOUN
ap-3105	133	10	by	by	ADP
ap-3105	133	11	kt	kt	PROPN
ap-3105	133	12	∈	∈	PROPN
ap-3105	133	13	d	d	PROPN
ap-3105	133	14	′(m̃	′(m̃	PROPN
ap-3105	133	15	×	×	PROPN
ap-3105	133	16	m̃	m̃	PROPN
ap-3105	133	17	)	)	PUNCT
ap-3105	133	18	the	the	DET
ap-3105	133	19	kernel	kernel	NOUN
ap-3105	133	20	of	of	ADP
ap-3105	133	21	u(t	u(t	NOUN
ap-3105	133	22	)	)	PUNCT
ap-3105	133	23	∈	∈	PROPN
ap-3105	133	24	b(l2(m̃	b(l2(m̃	NOUN
ap-3105	133	25	)	)	PUNCT
ap-3105	133	26	)	)	PUNCT
ap-3105	133	27	,	,	PUNCT
ap-3105	133	28	and	and	CCONJ
ap-3105	133	29	by	by	ADP
ap-3105	133	30	kλ	kλ	PROPN
ap-3105	133	31	t	t	PROPN
ap-3105	133	32	∈	∈	PROPN
ap-3105	133	33	d	d	X
ap-3105	133	34	′(m̃	′(m̃	PROPN
ap-3105	133	35	×	×	NOUN
ap-3105	133	36	m̃)⊗b(lλ	m̃)⊗b(lλ	NOUN
ap-3105	133	37	)	)	PUNCT
ap-3105	133	38	the	the	DET
ap-3105	133	39	kernel	kernel	NOUN
ap-3105	133	40	of	of	ADP
ap-3105	133	41	uλ(t	uλ(t	ADV
ap-3105	133	42	)	)	PUNCT
ap-3105	133	43	∈	∈	PROPN
ap-3105	133	44	b(hλ	b(hλ	NOUN
ap-3105	133	45	)	)	PUNCT
ap-3105	133	46	.	.	PUNCT
ap-3105	134	1	here	here	ADV
ap-3105	134	2	and	and	CCONJ
ap-3105	134	3	everywhere	everywhere	ADV
ap-3105	134	4	in	in	ADP
ap-3105	134	5	this	this	DET
ap-3105	134	6	section	section	NOUN
ap-3105	134	7	,	,	PUNCT
ap-3105	134	8	t	t	PROPN
ap-3105	134	9	is	be	AUX
ap-3105	134	10	a	a	DET
ap-3105	134	11	real	real	ADJ
ap-3105	134	12	parameter	parameter	NOUN
ap-3105	134	13	.	.	PUNCT
ap-3105	135	1	the	the	DET
ap-3105	135	2	kernel	kernel	PROPN
ap-3105	135	3	kλ	kλ	PROPN
ap-3105	135	4	t	t	PROPN
ap-3105	135	5	is	be	AUX
ap-3105	135	6	λ	λ	NOUN
ap-3105	135	7	-	-	NOUN
ap-3105	135	8	equivariant	equivariant	ADJ
ap-3105	135	9	in	in	ADP
ap-3105	135	10	the	the	DET
ap-3105	135	11	sense	sense	NOUN
ap-3105	135	12	of	of	ADP
ap-3105	135	13	(	(	PUNCT
ap-3105	135	14	4	4	NUM
ap-3105	135	15	)	)	PUNCT
ap-3105	135	16	.	.	PUNCT
ap-3105	136	1	first	first	ADV
ap-3105	136	2	,	,	PUNCT
ap-3105	136	3	we	we	PRON
ap-3105	136	4	can	can	AUX
ap-3105	136	5	rewrite	rewrite	VERB
ap-3105	136	6	the	the	DET
ap-3105	136	7	bloch	bloch	PROPN
ap-3105	136	8	decomposition	decomposition	NOUN
ap-3105	136	9	(	(	PUNCT
ap-3105	136	10	3	3	X
ap-3105	136	11	)	)	PUNCT
ap-3105	136	12	in	in	ADP
ap-3105	136	13	terms	term	NOUN
ap-3105	136	14	of	of	ADP
ap-3105	136	15	kernels	kernel	NOUN
ap-3105	136	16	.	.	PUNCT
ap-3105	137	1	for	for	ADP
ap-3105	137	2	all	all	DET
ap-3105	137	3	ϕ1	ϕ1	NOUN
ap-3105	137	4	,	,	PUNCT
ap-3105	137	5	ϕ2	ϕ2	ADV
ap-3105	137	6	∈	∈	PROPN
ap-3105	137	7	c∞0	c∞0	PRON
ap-3105	137	8	(	(	PUNCT
ap-3105	137	9	m̃	m̃	PROPN
ap-3105	137	10	)	)	PUNCT
ap-3105	137	11	,	,	PUNCT
ap-3105	137	12	kt(ϕ1	kt(ϕ1	ADP
ap-3105	137	13	⊗	⊗	PROPN
ap-3105	137	14	ϕ2	ϕ2	ADV
ap-3105	137	15	)	)	PUNCT
ap-3105	137	16	=	=	SYM
ap-3105	138	1	∫	∫	PROPN
ap-3105	138	2	γ̂	γ̂	PUNCT
ap-3105	138	3	tr	tr	VERB
ap-3105	138	4	[	[	PUNCT
ap-3105	138	5	kλ	kλ	X
ap-3105	138	6	t	t	PROPN
ap-3105	138	7	(	(	PUNCT
ap-3105	138	8	ϕ1	ϕ1	NOUN
ap-3105	138	9	⊗	⊗	PROPN
ap-3105	138	10	ϕ2	ϕ2	ADV
ap-3105	138	11	)	)	PUNCT
ap-3105	138	12	]	]	PUNCT
ap-3105	139	1	dm̂(λ	dm̂(λ	X
ap-3105	139	2	)	)	PUNCT
ap-3105	139	3	,	,	PUNCT
ap-3105	139	4	with	with	ADP
ap-3105	139	5	the	the	DET
ap-3105	139	6	integral	integral	ADJ
ap-3105	139	7	being	being	NOUN
ap-3105	139	8	convergent	convergent	NOUN
ap-3105	139	9	.	.	PUNCT
ap-3105	140	1	an	an	DET
ap-3105	140	2	inverse	inverse	NOUN
ap-3105	140	3	relation	relation	NOUN
ap-3105	140	4	was	be	AUX
ap-3105	140	5	derived	derive	VERB
ap-3105	140	6	by	by	ADP
ap-3105	140	7	schulman	schulman	NOUN
ap-3105	140	8	in	in	ADP
ap-3105	140	9	the	the	DET
ap-3105	140	10	framework	framework	NOUN
ap-3105	140	11	of	of	ADP
ap-3105	140	12	path	path	NOUN
ap-3105	140	13	integration	integration	NOUN
ap-3105	140	14	[	[	X
ap-3105	140	15	18	18	NUM
ap-3105	140	16	,	,	PUNCT
ap-3105	140	17	19	19	NUM
ap-3105	140	18	]	]	PUNCT
ap-3105	140	19	and	and	CCONJ
ap-3105	140	20	reads	read	VERB
ap-3105	140	21	kλ	kλ	PROPN
ap-3105	140	22	t	t	PROPN
ap-3105	140	23	(	(	PUNCT
ap-3105	140	24	x	x	PROPN
ap-3105	140	25	,	,	PUNCT
ap-3105	140	26	y	y	NOUN
ap-3105	140	27	)	)	PUNCT
ap-3105	140	28	=	=	SYM
ap-3105	140	29	∑	∑	PUNCT
ap-3105	140	30	s∈γ	s∈γ	VERB
ap-3105	140	31	λ(s)kt(s−1	λ(s)kt(s−1	PROPN
ap-3105	140	32	·	·	PUNCT
ap-3105	140	33	x	x	X
ap-3105	140	34	,	,	PUNCT
ap-3105	140	35	y	y	PROPN
ap-3105	140	36	)	)	PUNCT
ap-3105	140	37	.	.	PUNCT
ap-3105	141	1	(	(	PUNCT
ap-3105	141	2	5	5	X
ap-3105	141	3	)	)	PUNCT
ap-3105	141	4	it	it	PRON
ap-3105	141	5	is	be	AUX
ap-3105	141	6	possible	possible	ADJ
ap-3105	141	7	to	to	PART
ap-3105	141	8	give	give	VERB
ap-3105	141	9	(	(	PUNCT
ap-3105	141	10	5	5	NUM
ap-3105	141	11	)	)	PUNCT
ap-3105	141	12	the	the	DET
ap-3105	141	13	following	follow	VERB
ap-3105	141	14	rigorous	rigorous	ADJ
ap-3105	141	15	interpretation	interpretation	NOUN
ap-3105	141	16	[	[	X
ap-3105	141	17	11	11	NUM
ap-3105	141	18	,	,	PUNCT
ap-3105	141	19	12	12	NUM
ap-3105	141	20	]	]	PUNCT
ap-3105	141	21	.	.	PUNCT
ap-3105	142	1	suppose	suppose	VERB
ap-3105	142	2	that	that	SCONJ
ap-3105	142	3	ϕ1	ϕ1	NOUN
ap-3105	142	4	,	,	PUNCT
ap-3105	142	5	ϕ2	ϕ2	ADV
ap-3105	142	6	∈	∈	PROPN
ap-3105	142	7	c∞0	c∞0	PRON
ap-3105	142	8	(	(	PUNCT
ap-3105	142	9	m̃	m̃	PROPN
ap-3105	142	10	)	)	PUNCT
ap-3105	142	11	are	be	AUX
ap-3105	142	12	fixed	fix	VERB
ap-3105	142	13	but	but	CCONJ
ap-3105	142	14	otherwise	otherwise	ADV
ap-3105	142	15	arbitrary	arbitrary	ADJ
ap-3105	142	16	.	.	PUNCT
ap-3105	143	1	set	set	VERB
ap-3105	143	2	ft(s	ft(s	PUNCT
ap-3105	143	3	)	)	PUNCT
ap-3105	143	4	=	=	SYM
ap-3105	144	1	kt	kt	PROPN
ap-3105	144	2	(	(	PUNCT
ap-3105	144	3	ϕ1(s−1	ϕ1(s−1	PROPN
ap-3105	144	4	·	·	PUNCT
ap-3105	144	5	y1)⊗	y1)⊗	NOUN
ap-3105	144	6	ϕ2(y2	ϕ2(y2	NOUN
ap-3105	144	7	)	)	PUNCT
ap-3105	144	8	)	)	PUNCT
ap-3105	145	1	for	for	ADP
ap-3105	145	2	s	s	PROPN
ap-3105	145	3	∈	∈	PROPN
ap-3105	145	4	γ	γ	X
ap-3105	145	5	,	,	PUNCT
ap-3105	145	6	gt(λ	gt(λ	X
ap-3105	145	7	)	)	PUNCT
ap-3105	145	8	=	=	SYM
ap-3105	145	9	kλ	kλ	PROPN
ap-3105	145	10	t	t	PROPN
ap-3105	145	11	(	(	PUNCT
ap-3105	145	12	ϕ1	ϕ1	NOUN
ap-3105	145	13	⊗	⊗	PROPN
ap-3105	145	14	ϕ2	ϕ2	ADV
ap-3105	145	15	)	)	PUNCT
ap-3105	145	16	∈	∈	PROPN
ap-3105	145	17	i2(lλ	i2(lλ	PROPN
ap-3105	145	18	)	)	PUNCT
ap-3105	145	19	for	for	ADP
ap-3105	145	20	λ	λ	PROPN
ap-3105	145	21	∈	∈	PROPN
ap-3105	145	22	γ̂.	γ̂.	NOUN
ap-3105	145	23	one	one	PRON
ap-3105	145	24	can	can	AUX
ap-3105	145	25	show	show	VERB
ap-3105	145	26	that	that	SCONJ
ap-3105	145	27	ft	ft	PROPN
ap-3105	145	28	∈	∈	PROPN
ap-3105	145	29	l2(γ	l2(γ	PROPN
ap-3105	145	30	)	)	PUNCT
ap-3105	145	31	and	and	CCONJ
ap-3105	145	32	gt	gt	PROPN
ap-3105	145	33	is	be	AUX
ap-3105	145	34	bounded	bound	VERB
ap-3105	145	35	on	on	ADP
ap-3105	145	36	γ̂	γ̂	PUNCT
ap-3105	145	37	in	in	ADP
ap-3105	145	38	the	the	DET
ap-3105	145	39	hilbert	hilbert	NOUN
ap-3105	145	40	-	-	PUNCT
ap-3105	145	41	schmidt	schmidt	PROPN
ap-3105	145	42	norm	norm	NOUN
ap-3105	145	43	.	.	PUNCT
ap-3105	146	1	recalling	recall	VERB
ap-3105	146	2	that	that	DET
ap-3105	146	3	m̂(γ̂	m̂(γ̂	NOUN
ap-3105	146	4	)	)	PUNCT
ap-3105	146	5	≤	≤	NOUN
ap-3105	146	6	1	1	NUM
ap-3105	146	7	we	we	PRON
ap-3105	146	8	have	have	VERB
ap-3105	146	9	‖gt(·)‖	‖gt(·)‖	PROPN
ap-3105	146	10	∈	∈	PROPN
ap-3105	146	11	l1(γ̂	l1(γ̂	PROPN
ap-3105	146	12	)	)	PUNCT
ap-3105	146	13	∩	∩	X
ap-3105	146	14	l2(γ̂	l2(γ̂	PROPN
ap-3105	146	15	)	)	PUNCT
ap-3105	146	16	.	.	PUNCT
ap-3105	147	1	then	then	ADV
ap-3105	147	2	ft	ft	PROPN
ap-3105	147	3	=	=	SYM
ap-3105	147	4	f−1[gt	f−1[gt	X
ap-3105	147	5	]	]	PUNCT
ap-3105	147	6	and	and	CCONJ
ap-3105	147	7	,	,	PUNCT
ap-3105	147	8	consequently	consequently	ADV
ap-3105	147	9	,	,	PUNCT
ap-3105	147	10	gt	gt	PROPN
ap-3105	147	11	=	=	SYM
ap-3105	147	12	f	f	PROPN
ap-3105	148	1	[	[	X
ap-3105	148	2	ft	ft	X
ap-3105	148	3	]	]	X
ap-3105	148	4	.	.	PUNCT
ap-3105	149	1	(	(	PUNCT
ap-3105	149	2	6	6	X
ap-3105	149	3	)	)	PUNCT
ap-3105	149	4	rewriting	rewrite	VERB
ap-3105	149	5	(	(	PUNCT
ap-3105	149	6	6	6	NUM
ap-3105	149	7	)	)	PUNCT
ap-3105	149	8	formally	formally	ADV
ap-3105	149	9	yields	yield	VERB
ap-3105	149	10	(	(	PUNCT
ap-3105	149	11	5	5	NUM
ap-3105	149	12	)	)	PUNCT
ap-3105	149	13	.	.	PUNCT
ap-3105	150	1	3	3	X
ap-3105	150	2	.	.	X
ap-3105	150	3	the	the	DET
ap-3105	150	4	propagator	propagator	NOUN
ap-3105	150	5	on	on	ADP
ap-3105	150	6	the	the	DET
ap-3105	150	7	universal	universal	ADJ
ap-3105	150	8	covering	covering	NOUN
ap-3105	150	9	space	space	NOUN
ap-3105	150	10	3.1	3.1	NUM
ap-3105	150	11	.	.	PUNCT
ap-3105	151	1	a	a	DET
ap-3105	151	2	formula	formula	NOUN
ap-3105	151	3	for	for	ADP
ap-3105	151	4	the	the	DET
ap-3105	151	5	propagator	propagator	NOUN
ap-3105	151	6	the	the	DET
ap-3105	151	7	configuration	configuration	NOUN
ap-3105	151	8	space	space	NOUN
ap-3105	151	9	for	for	ADP
ap-3105	151	10	the	the	DET
ap-3105	151	11	aharonov	aharonov	PROPN
ap-3105	151	12	-	-	PUNCT
ap-3105	151	13	bohm	bohm	PROPN
ap-3105	151	14	effect	effect	NOUN
ap-3105	151	15	with	with	ADP
ap-3105	151	16	two	two	NUM
ap-3105	151	17	vortices	vortex	NOUN
ap-3105	151	18	is	be	AUX
ap-3105	151	19	the	the	DET
ap-3105	151	20	plane	plane	NOUN
ap-3105	151	21	with	with	ADP
ap-3105	151	22	two	two	NUM
ap-3105	151	23	excluded	exclude	VERB
ap-3105	151	24	points	point	NOUN
ap-3105	151	25	,	,	PUNCT
ap-3105	151	26	m	m	VERB
ap-3105	151	27	=	=	ADJ
ap-3105	151	28	r2	r2	PROPN
ap-3105	151	29	\	\	PROPN
ap-3105	151	30	{	{	PUNCT
ap-3105	151	31	a	a	PRON
ap-3105	151	32	,	,	PUNCT
ap-3105	151	33	b	b	NOUN
ap-3105	151	34	}	}	PUNCT
ap-3105	151	35	.	.	PUNCT
ap-3105	152	1	this	this	PRON
ap-3105	152	2	is	be	AUX
ap-3105	152	3	a	a	DET
ap-3105	152	4	flat	flat	ADJ
ap-3105	152	5	riemannian	riemannian	NOUN
ap-3105	152	6	manifold	manifold	NOUN
ap-3105	152	7	and	and	CCONJ
ap-3105	152	8	the	the	DET
ap-3105	152	9	same	same	ADJ
ap-3105	152	10	is	be	AUX
ap-3105	152	11	true	true	ADJ
ap-3105	152	12	for	for	ADP
ap-3105	152	13	the	the	DET
ap-3105	152	14	universal	universal	ADJ
ap-3105	152	15	covering	covering	NOUN
ap-3105	152	16	space	space	NOUN
ap-3105	152	17	m̃	m̃	PROPN
ap-3105	152	18	.	.	PUNCT
ap-3105	153	1	let	let	VERB
ap-3105	153	2	π	π	NOUN
ap-3105	153	3	:	:	PUNCT
ap-3105	153	4	m̃	m̃	PROPN
ap-3105	153	5	→	→	PUNCT
ap-3105	153	6	m	m	AUX
ap-3105	153	7	be	be	AUX
ap-3105	153	8	the	the	DET
ap-3105	153	9	projection	projection	NOUN
ap-3105	153	10	.	.	PUNCT
ap-3105	154	1	it	it	PRON
ap-3105	154	2	is	be	AUX
ap-3105	154	3	convenient	convenient	ADJ
ap-3105	154	4	to	to	PART
ap-3105	154	5	complete	complete	VERB
ap-3105	154	6	the	the	DET
ap-3105	154	7	manifold	manifold	ADJ
ap-3105	154	8	m̃	m̃	PROPN
ap-3105	154	9	by	by	ADP
ap-3105	154	10	a	a	DET
ap-3105	154	11	countable	countable	ADJ
ap-3105	154	12	set	set	NOUN
ap-3105	154	13	of	of	ADP
ap-3105	154	14	points	point	NOUN
ap-3105	154	15	a	a	DET
ap-3105	154	16	∪	∪	NOUN
ap-3105	154	17	b	b	NOUN
ap-3105	154	18	lying	lie	VERB
ap-3105	154	19	on	on	ADP
ap-3105	154	20	the	the	DET
ap-3105	154	21	border	border	NOUN
ap-3105	154	22	of	of	ADP
ap-3105	154	23	m̃	m̃	PROPN
ap-3105	154	24	and	and	CCONJ
ap-3105	154	25	projecting	project	VERB
ap-3105	154	26	onto	onto	ADP
ap-3105	154	27	the	the	DET
ap-3105	154	28	excluded	exclude	VERB
ap-3105	154	29	points	point	NOUN
ap-3105	154	30	,	,	PUNCT
ap-3105	154	31	π(a	π(a	PROPN
ap-3105	154	32	)	)	PUNCT
ap-3105	155	1	=	=	PRON
ap-3105	155	2	{	{	PUNCT
ap-3105	155	3	a	a	NOUN
ap-3105	155	4	}	}	PUNCT
ap-3105	155	5	and	and	CCONJ
ap-3105	155	6	π(b	π(b	PROPN
ap-3105	155	7	)	)	PUNCT
ap-3105	155	8	=	=	PRON
ap-3105	155	9	{	{	PUNCT
ap-3105	155	10	b	b	NOUN
ap-3105	155	11	}	}	PUNCT
ap-3105	155	12	.	.	PUNCT
ap-3105	156	1	m̃	m̃	PROPN
ap-3105	156	2	looks	look	VERB
ap-3105	156	3	locally	locally	ADV
ap-3105	156	4	like	like	ADP
ap-3105	156	5	r2	r2	PROPN
ap-3105	156	6	but	but	CCONJ
ap-3105	156	7	differs	differ	VERB
ap-3105	156	8	from	from	ADP
ap-3105	156	9	the	the	DET
ap-3105	156	10	euclidean	euclidean	ADJ
ap-3105	156	11	space	space	NOUN
ap-3105	156	12	by	by	ADP
ap-3105	156	13	some	some	DET
ap-3105	156	14	global	global	ADJ
ap-3105	156	15	features	feature	NOUN
ap-3105	156	16	.	.	PUNCT
ap-3105	157	1	first	first	ADV
ap-3105	157	2	of	of	ADP
ap-3105	157	3	all	all	PRON
ap-3105	157	4	,	,	PUNCT
ap-3105	157	5	not	not	PART
ap-3105	157	6	every	every	DET
ap-3105	157	7	two	two	NUM
ap-3105	157	8	points	point	NOUN
ap-3105	157	9	from	from	ADP
ap-3105	157	10	m̃	m̃	PROPN
ap-3105	157	11	can	can	AUX
ap-3105	157	12	be	be	AUX
ap-3105	157	13	connected	connect	VERB
ap-3105	157	14	by	by	ADP
ap-3105	157	15	a	a	DET
ap-3105	157	16	geodesic	geodesic	ADJ
ap-3105	157	17	segment	segment	NOUN
ap-3105	157	18	.	.	PUNCT
ap-3105	158	1	fix	fix	VERB
ap-3105	158	2	a	a	DET
ap-3105	158	3	point	point	NOUN
ap-3105	158	4	x	x	PUNCT
ap-3105	158	5	∈	∈	PROPN
ap-3105	158	6	m̃	m̃	PROPN
ap-3105	158	7	.	.	PUNCT
ap-3105	159	1	the	the	DET
ap-3105	159	2	symbol	symbol	NOUN
ap-3105	159	3	d(x	d(x	PROPN
ap-3105	159	4	)	)	PUNCT
ap-3105	159	5	,	,	PUNCT
ap-3105	159	6	as	as	SCONJ
ap-3105	159	7	introduced	introduce	VERB
ap-3105	159	8	below	below	ADP
ap-3105	159	9	in	in	ADP
ap-3105	159	10	(	(	PUNCT
ap-3105	159	11	20	20	NUM
ap-3105	159	12	)	)	PUNCT
ap-3105	159	13	,	,	PUNCT
ap-3105	159	14	stands	stand	VERB
ap-3105	159	15	for	for	ADP
ap-3105	159	16	the	the	DET
ap-3105	159	17	set	set	NOUN
ap-3105	159	18	of	of	ADP
ap-3105	159	19	points	point	NOUN
ap-3105	159	20	y	y	PROPN
ap-3105	159	21	∈	∈	PROPN
ap-3105	159	22	m̃	m̃	PROPN
ap-3105	159	23	which	which	PRON
ap-3105	159	24	can	can	AUX
ap-3105	159	25	be	be	AUX
ap-3105	159	26	connected	connect	VERB
ap-3105	159	27	with	with	ADP
ap-3105	159	28	x	x	PUNCT
ap-3105	159	29	by	by	ADP
ap-3105	159	30	a	a	DET
ap-3105	159	31	segment	segment	NOUN
ap-3105	159	32	.	.	PUNCT
ap-3105	160	1	then	then	ADV
ap-3105	160	2	d(x	d(x	PROPN
ap-3105	160	3	)	)	PUNCT
ap-3105	160	4	is	be	AUX
ap-3105	160	5	a	a	DET
ap-3105	160	6	sheet	sheet	NOUN
ap-3105	160	7	of	of	ADP
ap-3105	160	8	the	the	DET
ap-3105	160	9	covering	cover	VERB
ap-3105	160	10	m̃	m̃	PROPN
ap-3105	160	11	→	→	SYM
ap-3105	160	12	m	m	VERB
ap-3105	160	13	.	.	PUNCT
ap-3105	161	1	it	it	PRON
ap-3105	161	2	can	can	AUX
ap-3105	161	3	be	be	AUX
ap-3105	161	4	identified	identify	VERB
ap-3105	161	5	with	with	ADP
ap-3105	161	6	r2	r2	PROPN
ap-3105	161	7	cut	cut	VERB
ap-3105	161	8	along	along	ADP
ap-3105	161	9	two	two	NUM
ap-3105	161	10	half	half	ADJ
ap-3105	161	11	-	-	PUNCT
ap-3105	161	12	lines	line	NOUN
ap-3105	161	13	with	with	ADP
ap-3105	161	14	the	the	DET
ap-3105	161	15	limit	limit	NOUN
ap-3105	161	16	points	point	VERB
ap-3105	161	17	a	a	PRON
ap-3105	161	18	and	and	CCONJ
ap-3105	161	19	b	b	NOUN
ap-3105	161	20	,	,	PUNCT
ap-3105	161	21	respectively	respectively	ADV
ap-3105	161	22	.	.	PUNCT
ap-3105	162	1	the	the	DET
ap-3105	162	2	border	border	NOUN
ap-3105	162	3	∂d(x	∂d(x	NOUN
ap-3105	162	4	)	)	PUNCT
ap-3105	162	5	is	be	AUX
ap-3105	162	6	formed	form	VERB
ap-3105	162	7	by	by	ADP
ap-3105	162	8	four	four	NUM
ap-3105	162	9	half	half	ADJ
ap-3105	162	10	-	-	PUNCT
ap-3105	162	11	lines	line	NOUN
ap-3105	162	12	.	.	PUNCT
ap-3105	163	1	the	the	DET
ap-3105	163	2	universal	universal	ADJ
ap-3105	163	3	covering	cover	VERB
ap-3105	163	4	space	space	NOUN
ap-3105	163	5	m̃	m̃	PROPN
ap-3105	163	6	can	can	AUX
ap-3105	163	7	be	be	AUX
ap-3105	163	8	imagined	imagine	VERB
ap-3105	163	9	as	as	ADP
ap-3105	163	10	a	a	DET
ap-3105	163	11	result	result	NOUN
ap-3105	163	12	of	of	ADP
ap-3105	163	13	an	an	DET
ap-3105	163	14	infinite	infinite	ADJ
ap-3105	163	15	process	process	NOUN
ap-3105	163	16	of	of	ADP
ap-3105	163	17	gluing	glue	VERB
ap-3105	163	18	together	together	ADV
ap-3105	163	19	countably	countably	ADV
ap-3105	163	20	many	many	ADJ
ap-3105	163	21	copies	copy	NOUN
ap-3105	163	22	of	of	ADP
ap-3105	163	23	d(x	d(x	PROPN
ap-3105	163	24	)	)	PUNCT
ap-3105	163	25	with	with	ADP
ap-3105	163	26	each	each	DET
ap-3105	163	27	copy	copy	NOUN
ap-3105	163	28	having	have	VERB
ap-3105	163	29	four	four	NUM
ap-3105	163	30	neighbors	neighbor	NOUN
ap-3105	163	31	.	.	PUNCT
ap-3105	164	1	227	227	NUM
ap-3105	164	2	petra	petra	PROPN
ap-3105	164	3	košťáková	košťáková	PROPN
ap-3105	164	4	,	,	PUNCT
ap-3105	164	5	pavel	pavel	PROPN
ap-3105	164	6	šťovíček	šťovíček	PROPN
ap-3105	164	7	acta	acta	PROPN
ap-3105	164	8	polytechnica	polytechnica	PROPN
ap-3105	164	9	the	the	DET
ap-3105	164	10	fundamental	fundamental	ADJ
ap-3105	164	11	group	group	NOUN
ap-3105	164	12	of	of	ADP
ap-3105	164	13	m	m	PROPN
ap-3105	164	14	,	,	PUNCT
ap-3105	164	15	called	call	VERB
ap-3105	164	16	γ	γ	NOUN
ap-3105	164	17	,	,	PUNCT
ap-3105	164	18	is	be	AUX
ap-3105	164	19	known	know	VERB
ap-3105	164	20	to	to	PART
ap-3105	164	21	be	be	AUX
ap-3105	164	22	the	the	DET
ap-3105	164	23	free	free	ADJ
ap-3105	164	24	group	group	NOUN
ap-3105	164	25	with	with	ADP
ap-3105	164	26	two	two	NUM
ap-3105	164	27	generators	generator	NOUN
ap-3105	164	28	ga	ga	PROPN
ap-3105	164	29	and	and	CCONJ
ap-3105	164	30	gb	gb	NOUN
ap-3105	164	31	.	.	PUNCT
ap-3105	165	1	for	for	ADP
ap-3105	165	2	the	the	DET
ap-3105	165	3	generator	generator	PROPN
ap-3105	165	4	ga	ga	PROPN
ap-3105	165	5	one	one	PRON
ap-3105	165	6	can	can	AUX
ap-3105	165	7	choose	choose	VERB
ap-3105	165	8	the	the	DET
ap-3105	165	9	homotopy	homotopy	NOUN
ap-3105	165	10	class	class	NOUN
ap-3105	165	11	of	of	ADP
ap-3105	165	12	a	a	DET
ap-3105	165	13	simple	simple	ADJ
ap-3105	165	14	positively	positively	ADV
ap-3105	165	15	oriented	orient	VERB
ap-3105	165	16	loop	loop	NOUN
ap-3105	165	17	winding	wind	VERB
ap-3105	165	18	once	once	ADV
ap-3105	165	19	around	around	ADP
ap-3105	165	20	the	the	DET
ap-3105	165	21	point	point	NOUN
ap-3105	165	22	a	a	PRON
ap-3105	165	23	and	and	CCONJ
ap-3105	165	24	leaving	leave	VERB
ap-3105	165	25	the	the	DET
ap-3105	165	26	point	point	NOUN
ap-3105	165	27	b	b	NOUN
ap-3105	165	28	in	in	ADP
ap-3105	165	29	the	the	DET
ap-3105	165	30	exterior	exterior	NOUN
ap-3105	165	31	.	.	PUNCT
ap-3105	166	1	analogously	analogously	ADV
ap-3105	166	2	one	one	PRON
ap-3105	166	3	can	can	AUX
ap-3105	166	4	choose	choose	VERB
ap-3105	166	5	gb	gb	PRON
ap-3105	166	6	by	by	ADP
ap-3105	166	7	interchanging	interchange	VERB
ap-3105	166	8	the	the	DET
ap-3105	166	9	role	role	NOUN
ap-3105	166	10	of	of	ADP
ap-3105	166	11	a	a	DET
ap-3105	166	12	and	and	CCONJ
ap-3105	166	13	b.	b.	PROPN
ap-3105	166	14	one	one	NUM
ap-3105	166	15	-	-	PUNCT
ap-3105	166	16	dimensional	dimensional	ADJ
ap-3105	166	17	unitary	unitary	ADJ
ap-3105	166	18	representations	representation	NOUN
ap-3105	166	19	λ	λ	NOUN
ap-3105	166	20	of	of	ADP
ap-3105	166	21	γ	γ	NOUN
ap-3105	166	22	are	be	AUX
ap-3105	166	23	determined	determine	VERB
ap-3105	166	24	by	by	ADP
ap-3105	166	25	two	two	NUM
ap-3105	166	26	numbers	number	NOUN
ap-3105	166	27	α	α	X
ap-3105	166	28	,	,	PUNCT
ap-3105	166	29	β	β	X
ap-3105	166	30	,	,	PUNCT
ap-3105	166	31	0	0	NUM
ap-3105	166	32	≤	≤	NUM
ap-3105	166	33	α	α	X
ap-3105	166	34	,	,	PUNCT
ap-3105	166	35	β	β	X
ap-3105	166	36	<	<	X
ap-3105	166	37	1	1	NUM
ap-3105	166	38	,	,	PUNCT
ap-3105	166	39	so	so	SCONJ
ap-3105	166	40	that	that	SCONJ
ap-3105	166	41	λ(ga	λ(ga	VERB
ap-3105	166	42	)	)	PUNCT
ap-3105	166	43	=	=	SYM
ap-3105	166	44	e2πiα	e2πiα	NOUN
ap-3105	166	45	,	,	PUNCT
ap-3105	166	46	λ(gb	λ(gb	NOUN
ap-3105	166	47	)	)	PUNCT
ap-3105	166	48	=	=	PUNCT
ap-3105	166	49	e2πiβ	e2πiβ	NOUN
ap-3105	166	50	.	.	PUNCT
ap-3105	167	1	the	the	DET
ap-3105	167	2	standard	standard	ADJ
ap-3105	167	3	way	way	NOUN
ap-3105	167	4	how	how	SCONJ
ap-3105	167	5	to	to	PART
ap-3105	167	6	define	define	VERB
ap-3105	167	7	the	the	DET
ap-3105	167	8	aharonov	aharonov	NOUN
ap-3105	167	9	-	-	PUNCT
ap-3105	167	10	bohm	bohm	PROPN
ap-3105	167	11	hamiltonian	hamiltonian	ADJ
ap-3105	167	12	hab	hab	NOUN
ap-3105	167	13	with	with	ADP
ap-3105	167	14	two	two	NUM
ap-3105	167	15	vortices	vortex	NOUN
ap-3105	167	16	is	be	AUX
ap-3105	167	17	to	to	PART
ap-3105	167	18	choose	choose	VERB
ap-3105	167	19	a	a	DET
ap-3105	167	20	vector	vector	NOUN
ap-3105	167	21	potential	potential	ADJ
ap-3105	167	22	−→a	−→a	PROPN
ap-3105	167	23	for	for	ADP
ap-3105	167	24	which	which	PRON
ap-3105	167	25	curl−→a	curl−→a	X
ap-3105	167	26	=	=	SYM
ap-3105	167	27	0	0	NUM
ap-3105	167	28	on	on	ADP
ap-3105	167	29	m	m	PROPN
ap-3105	167	30	and	and	CCONJ
ap-3105	167	31	such	such	ADJ
ap-3105	167	32	that	that	SCONJ
ap-3105	167	33	the	the	DET
ap-3105	167	34	nonintegrable	nonintegrable	ADJ
ap-3105	167	35	phase	phase	NOUN
ap-3105	167	36	factor	factor	NOUN
ap-3105	167	37	[	[	X
ap-3105	167	38	27	27	NUM
ap-3105	167	39	]	]	PUNCT
ap-3105	167	40	for	for	ADP
ap-3105	167	41	a	a	DET
ap-3105	167	42	closed	closed	ADJ
ap-3105	167	43	path	path	NOUN
ap-3105	167	44	from	from	ADP
ap-3105	167	45	the	the	DET
ap-3105	167	46	homotopy	homotopy	PROPN
ap-3105	167	47	class	class	PROPN
ap-3105	167	48	ga	ga	PROPN
ap-3105	167	49	or	or	CCONJ
ap-3105	167	50	gb	gb	PROPN
ap-3105	167	51	equals	equal	VERB
ap-3105	167	52	e2πiα	e2πiα	ADP
ap-3105	167	53	or	or	CCONJ
ap-3105	167	54	e2πiβ	e2πiβ	ADV
ap-3105	167	55	,	,	PUNCT
ap-3105	167	56	respectively	respectively	ADV
ap-3105	167	57	(	(	PUNCT
ap-3105	167	58	assuming	assume	VERB
ap-3105	167	59	that	that	SCONJ
ap-3105	167	60	0	0	NUM
ap-3105	167	61	<	<	X
ap-3105	167	62	α	α	X
ap-3105	167	63	,	,	PUNCT
ap-3105	167	64	β	β	X
ap-3105	167	65	<	<	X
ap-3105	167	66	1	1	NUM
ap-3105	167	67	)	)	PUNCT
ap-3105	167	68	.	.	PUNCT
ap-3105	168	1	hab	hab	PROPN
ap-3105	168	2	then	then	ADV
ap-3105	168	3	acts	act	VERB
ap-3105	168	4	as	as	ADP
ap-3105	168	5	the	the	DET
ap-3105	168	6	differential	differential	ADJ
ap-3105	168	7	operator	operator	NOUN
ap-3105	168	8	(	(	PUNCT
ap-3105	168	9	−i∇	−i∇	INTJ
ap-3105	168	10	−	−	PROPN
ap-3105	168	11	−→a	−→a	PROPN
ap-3105	168	12	)	)	PUNCT
ap-3105	168	13	2	2	NUM
ap-3105	168	14	in	in	ADP
ap-3105	168	15	l2(m	l2(m	NOUN
ap-3105	168	16	)	)	PUNCT
ap-3105	168	17	.	.	PUNCT
ap-3105	169	1	here	here	ADV
ap-3105	169	2	again	again	ADV
ap-3105	169	3	,	,	PUNCT
ap-3105	169	4	to	to	PART
ap-3105	169	5	be	be	AUX
ap-3105	169	6	more	more	ADV
ap-3105	169	7	rigorous	rigorous	ADJ
ap-3105	169	8	,	,	PUNCT
ap-3105	169	9	hab	hab	NOUN
ap-3105	169	10	is	be	AUX
ap-3105	169	11	the	the	DET
ap-3105	169	12	friedrichs	friedrichs	ADJ
ap-3105	169	13	extension	extension	NOUN
ap-3105	169	14	of	of	ADP
ap-3105	169	15	the	the	DET
ap-3105	169	16	positive	positive	ADJ
ap-3105	169	17	operator	operator	NOUN
ap-3105	169	18	(	(	PUNCT
ap-3105	169	19	−i∇−−→a	−i∇−−→a	X
ap-3105	169	20	)	)	PUNCT
ap-3105	169	21	2	2	NUM
ap-3105	169	22	defined	define	VERB
ap-3105	169	23	on	on	ADP
ap-3105	169	24	test	test	NOUN
ap-3105	169	25	functions	function	NOUN
ap-3105	169	26	on	on	ADP
ap-3105	169	27	m	m	PROPN
ap-3105	169	28	.	.	PUNCT
ap-3105	170	1	for	for	ADP
ap-3105	170	2	our	our	PRON
ap-3105	170	3	purposes	purpose	NOUN
ap-3105	170	4	it	it	PRON
ap-3105	170	5	would	would	AUX
ap-3105	170	6	be	be	AUX
ap-3105	170	7	more	more	ADV
ap-3105	170	8	convenient	convenient	ADJ
ap-3105	170	9	to	to	PART
ap-3105	170	10	pass	pass	VERB
ap-3105	170	11	to	to	ADP
ap-3105	170	12	a	a	DET
ap-3105	170	13	unitarily	unitarily	ADV
ap-3105	170	14	equivalent	equivalent	ADJ
ap-3105	170	15	formulation	formulation	NOUN
ap-3105	170	16	.	.	PUNCT
ap-3105	171	1	this	this	PRON
ap-3105	171	2	is	be	AUX
ap-3105	171	3	done	do	VERB
ap-3105	171	4	in	in	ADP
ap-3105	171	5	two	two	NUM
ap-3105	171	6	steps	step	NOUN
ap-3105	171	7	.	.	PUNCT
ap-3105	172	1	first	first	ADV
ap-3105	172	2	,	,	PUNCT
ap-3105	172	3	the	the	DET
ap-3105	172	4	differential	differential	ADJ
ap-3105	172	5	operator	operator	NOUN
ap-3105	172	6	(	(	PUNCT
ap-3105	172	7	−i∇−−→a	−i∇−−→a	ADJ
ap-3105	172	8	)	)	PUNCT
ap-3105	172	9	2	2	NUM
ap-3105	172	10	is	be	AUX
ap-3105	172	11	lifted	lift	VERB
ap-3105	172	12	to	to	ADP
ap-3105	172	13	m̃	m̃	PROPN
ap-3105	172	14	.	.	PUNCT
ap-3105	173	1	then	then	ADV
ap-3105	173	2	the	the	DET
ap-3105	173	3	unitarily	unitarily	ADV
ap-3105	173	4	equivalent	equivalent	ADJ
ap-3105	173	5	operator	operator	NOUN
ap-3105	173	6	is	be	AUX
ap-3105	173	7	h̃ab	h̃ab	PROPN
ap-3105	173	8	acting	act	VERB
ap-3105	173	9	as	as	ADP
ap-3105	173	10	a	a	DET
ap-3105	173	11	differential	differential	ADJ
ap-3105	173	12	operator	operator	NOUN
ap-3105	173	13	(	(	PUNCT
ap-3105	173	14	−i∇−	−i∇−	PROPN
ap-3105	173	15	−→̃	−→̃	PROPN
ap-3105	173	16	a	a	DET
ap-3105	173	17	)	)	PUNCT
ap-3105	173	18	2	2	NUM
ap-3105	173	19	in	in	ADP
ap-3105	173	20	the	the	DET
ap-3105	173	21	hilbert	hilbert	NOUN
ap-3105	173	22	space	space	NOUN
ap-3105	173	23	of	of	ADP
ap-3105	173	24	γ	γ	PROPN
ap-3105	173	25	-	-	ADJ
ap-3105	173	26	periodic	periodic	ADJ
ap-3105	173	27	functions	function	NOUN
ap-3105	173	28	on	on	ADP
ap-3105	173	29	m̃	m̃	PROPN
ap-3105	173	30	which	which	PRON
ap-3105	173	31	are	be	AUX
ap-3105	173	32	square	square	ADJ
ap-3105	173	33	integrable	integrable	ADJ
ap-3105	173	34	over	over	ADP
ap-3105	173	35	a	a	DET
ap-3105	173	36	fundamental	fundamental	ADJ
ap-3105	173	37	domain	domain	NOUN
ap-3105	173	38	of	of	ADP
ap-3105	173	39	the	the	DET
ap-3105	173	40	γ	γ	PROPN
ap-3105	173	41	action	action	NOUN
ap-3105	173	42	.	.	PUNCT
ap-3105	174	1	once	once	ADV
ap-3105	174	2	more	more	ADV
ap-3105	174	3	,	,	PUNCT
ap-3105	174	4	h̃ab	h̃ab	PROPN
ap-3105	174	5	is	be	AUX
ap-3105	174	6	rigorously	rigorously	ADV
ap-3105	174	7	introduced	introduce	VERB
ap-3105	174	8	with	with	ADP
ap-3105	174	9	the	the	DET
ap-3105	174	10	aid	aid	NOUN
ap-3105	174	11	of	of	ADP
ap-3105	174	12	the	the	DET
ap-3105	174	13	friedrichs	friedrich	NOUN
ap-3105	174	14	extension	extension	NOUN
ap-3105	174	15	.	.	PUNCT
ap-3105	175	1	second	second	ADJ
ap-3105	175	2	,	,	PUNCT
ap-3105	175	3	curl	curl	VERB
ap-3105	175	4	−→̃	−→̃	PROPN
ap-3105	175	5	a	a	DET
ap-3105	175	6	=	=	SYM
ap-3105	175	7	0	0	NUM
ap-3105	175	8	holds	hold	VERB
ap-3105	175	9	again	again	ADV
ap-3105	175	10	on	on	ADP
ap-3105	175	11	m̃	m̃	PROPN
ap-3105	175	12	.	.	PUNCT
ap-3105	176	1	but	but	CCONJ
ap-3105	176	2	this	this	DET
ap-3105	176	3	time	time	NOUN
ap-3105	176	4	m̃	m̃	PROPN
ap-3105	176	5	is	be	AUX
ap-3105	176	6	simply	simply	ADV
ap-3105	176	7	connected	connect	VERB
ap-3105	176	8	and	and	CCONJ
ap-3105	176	9	therefore	therefore	ADV
ap-3105	176	10	the	the	DET
ap-3105	176	11	vector	vector	NOUN
ap-3105	176	12	potential	potential	NOUN
ap-3105	176	13	can	can	AUX
ap-3105	176	14	be	be	AUX
ap-3105	176	15	removed	remove	VERB
ap-3105	176	16	by	by	ADP
ap-3105	176	17	a	a	DET
ap-3105	176	18	globally	globally	ADV
ap-3105	176	19	well	well	ADV
ap-3105	176	20	defined	define	VERB
ap-3105	176	21	gauge	gauge	NOUN
ap-3105	176	22	transformation	transformation	NOUN
ap-3105	176	23	.	.	PUNCT
ap-3105	177	1	this	this	DET
ap-3105	177	2	gauge	gauge	ADJ
ap-3105	177	3	transformation	transformation	NOUN
ap-3105	177	4	induces	induce	VERB
ap-3105	177	5	a	a	DET
ap-3105	177	6	unitary	unitary	ADJ
ap-3105	177	7	mapping	mapping	NOUN
ap-3105	177	8	between	between	ADP
ap-3105	177	9	the	the	DET
ap-3105	177	10	hilbert	hilbert	NOUN
ap-3105	177	11	space	space	NOUN
ap-3105	177	12	of	of	ADP
ap-3105	177	13	γ	γ	PROPN
ap-3105	177	14	-	-	ADJ
ap-3105	177	15	periodic	periodic	ADJ
ap-3105	177	16	functions	function	NOUN
ap-3105	177	17	on	on	ADP
ap-3105	177	18	m̃	m̃	PROPN
ap-3105	177	19	and	and	CCONJ
ap-3105	177	20	the	the	DET
ap-3105	177	21	hilbert	hilbert	PROPN
ap-3105	177	22	space	space	NOUN
ap-3105	177	23	hλ	hλ	NOUN
ap-3105	177	24	of	of	ADP
ap-3105	177	25	λ	λ	PROPN
ap-3105	177	26	-	-	PUNCT
ap-3105	177	27	equivariant	equivariant	ADJ
ap-3105	177	28	functions	function	NOUN
ap-3105	177	29	on	on	ADP
ap-3105	177	30	m̃	m̃	PROPN
ap-3105	177	31	,	,	PUNCT
ap-3105	177	32	as	as	SCONJ
ap-3105	177	33	introduced	introduce	VERB
ap-3105	177	34	in	in	ADP
ap-3105	177	35	subsection	subsection	NOUN
ap-3105	177	36	2.1	2.1	NUM
ap-3105	177	37	.	.	PUNCT
ap-3105	178	1	the	the	DET
ap-3105	178	2	resulting	result	VERB
ap-3105	178	3	operator	operator	NOUN
ap-3105	178	4	which	which	PRON
ap-3105	178	5	is	be	AUX
ap-3105	178	6	unitarily	unitarily	ADV
ap-3105	178	7	equivalent	equivalent	ADJ
ap-3105	178	8	to	to	ADP
ap-3105	178	9	hab	hab	NOUN
ap-3105	178	10	is	be	AUX
ap-3105	178	11	nothing	nothing	PRON
ap-3105	178	12	but	but	SCONJ
ap-3105	178	13	the	the	DET
ap-3105	178	14	hamiltonian	hamiltonian	NOUN
ap-3105	178	15	hλ	hλ	ADP
ap-3105	178	16	=	=	SYM
ap-3105	178	17	−∆	−∆	NOUN
ap-3105	178	18	acting	act	VERB
ap-3105	178	19	in	in	ADP
ap-3105	178	20	hλ	hλ	ADP
ap-3105	178	21	,	,	PUNCT
ap-3105	178	22	as	as	SCONJ
ap-3105	178	23	it	it	PRON
ap-3105	178	24	has	have	AUX
ap-3105	178	25	been	be	AUX
ap-3105	178	26	introduced	introduce	VERB
ap-3105	178	27	in	in	ADP
ap-3105	178	28	the	the	DET
ap-3105	178	29	same	same	ADJ
ap-3105	178	30	subsection	subsection	NOUN
ap-3105	178	31	.	.	PUNCT
ap-3105	179	1	remember	remember	VERB
ap-3105	179	2	that	that	SCONJ
ap-3105	179	3	simultaneously	simultaneously	ADV
ap-3105	179	4	one	one	NUM
ap-3105	179	5	considers	consider	VERB
ap-3105	179	6	the	the	DET
ap-3105	179	7	free	free	ADJ
ap-3105	179	8	hamiltonian	hamiltonian	ADJ
ap-3105	179	9	h	h	NOUN
ap-3105	179	10	=	=	PUNCT
ap-3105	179	11	−∆	−∆	PROPN
ap-3105	179	12	in	in	ADP
ap-3105	179	13	l2(m̃	l2(m̃	PROPN
ap-3105	179	14	)	)	PUNCT
ap-3105	179	15	.	.	PUNCT
ap-3105	180	1	h	h	PROPN
ap-3105	180	2	is	be	AUX
ap-3105	180	3	γ	γ	NOUN
ap-3105	180	4	-	-	NOUN
ap-3105	180	5	periodic	periodic	NOUN
ap-3105	180	6	.	.	PUNCT
ap-3105	181	1	in	in	ADP
ap-3105	181	2	order	order	NOUN
ap-3105	181	3	to	to	PART
ap-3105	181	4	apply	apply	VERB
ap-3105	181	5	(	(	PUNCT
ap-3105	181	6	5	5	NUM
ap-3105	181	7	)	)	PUNCT
ap-3105	181	8	and	and	CCONJ
ap-3105	181	9	compute	compute	VERB
ap-3105	181	10	the	the	DET
ap-3105	181	11	propagator	propagator	NOUN
ap-3105	181	12	kλ(t	kλ(t	VERB
ap-3105	181	13	,	,	PUNCT
ap-3105	181	14	x	x	NOUN
ap-3105	181	15	,	,	PUNCT
ap-3105	181	16	y	y	NOUN
ap-3105	181	17	)	)	PUNCT
ap-3105	181	18	associated	associate	VERB
ap-3105	181	19	with	with	ADP
ap-3105	181	20	hλ	hλ	NOUN
ap-3105	181	21	one	one	PRON
ap-3105	181	22	has	have	VERB
ap-3105	181	23	to	to	PART
ap-3105	181	24	rely	rely	VERB
ap-3105	181	25	on	on	ADP
ap-3105	181	26	a	a	DET
ap-3105	181	27	known	know	VERB
ap-3105	181	28	formula	formula	NOUN
ap-3105	181	29	for	for	ADP
ap-3105	181	30	the	the	DET
ap-3105	181	31	free	free	ADJ
ap-3105	181	32	propagator	propagator	NOUN
ap-3105	181	33	k(t	k(t	PROPN
ap-3105	181	34	,	,	PUNCT
ap-3105	181	35	x	x	X
ap-3105	181	36	,	,	PUNCT
ap-3105	181	37	y	y	NOUN
ap-3105	181	38	)	)	PUNCT
ap-3105	181	39	on	on	ADP
ap-3105	181	40	m̃	m̃	PROPN
ap-3105	181	41	.	.	PUNCT
ap-3105	182	1	let	let	VERB
ap-3105	182	2	us	we	PRON
ap-3105	182	3	recall	recall	VERB
ap-3105	182	4	a	a	DET
ap-3105	182	5	formula	formula	NOUN
ap-3105	182	6	for	for	ADP
ap-3105	182	7	k(t	k(t	PROPN
ap-3105	182	8	,	,	PUNCT
ap-3105	182	9	x	x	X
ap-3105	182	10	,	,	PUNCT
ap-3105	182	11	y	y	PROPN
ap-3105	182	12	)	)	PUNCT
ap-3105	182	13	,	,	PUNCT
ap-3105	182	14	as	as	SCONJ
ap-3105	182	15	presented	present	VERB
ap-3105	182	16	in	in	ADP
ap-3105	182	17	[	[	X
ap-3105	182	18	21	21	NUM
ap-3105	182	19	]	]	PUNCT
ap-3105	182	20	.	.	PUNCT
ap-3105	183	1	let	let	VERB
ap-3105	183	2	ϑ	ϑ	PRON
ap-3105	183	3	stand	stand	VERB
ap-3105	183	4	for	for	ADP
ap-3105	183	5	the	the	DET
ap-3105	183	6	heaviside	heaviside	ADJ
ap-3105	183	7	step	step	NOUN
ap-3105	183	8	function	function	NOUN
ap-3105	183	9	.	.	PUNCT
ap-3105	184	1	for	for	ADP
ap-3105	184	2	x	x	SYM
ap-3105	184	3	,	,	PUNCT
ap-3105	184	4	y	y	PROPN
ap-3105	184	5	∈	∈	PROPN
ap-3105	184	6	m̃	m̃	PROPN
ap-3105	184	7	∪	∪	VERB
ap-3105	184	8	a	a	DET
ap-3105	184	9	∪	∪	X
ap-3105	184	10	b	b	NOUN
ap-3105	184	11	set	set	NOUN
ap-3105	184	12	χ(x	χ(x	PROPN
ap-3105	184	13	,	,	PUNCT
ap-3105	184	14	y	y	PROPN
ap-3105	184	15	)	)	PUNCT
ap-3105	184	16	=	=	SYM
ap-3105	184	17	1	1	NUM
ap-3105	184	18	if	if	SCONJ
ap-3105	184	19	the	the	DET
ap-3105	184	20	points	point	NOUN
ap-3105	184	21	x	x	X
ap-3105	184	22	,	,	PUNCT
ap-3105	184	23	y	y	PROPN
ap-3105	184	24	can	can	AUX
ap-3105	184	25	be	be	AUX
ap-3105	184	26	connected	connect	VERB
ap-3105	184	27	by	by	ADP
ap-3105	184	28	a	a	DET
ap-3105	184	29	geodesic	geodesic	ADJ
ap-3105	184	30	segment	segment	NOUN
ap-3105	184	31	,	,	PUNCT
ap-3105	184	32	and	and	CCONJ
ap-3105	184	33	χ(x	χ(x	PROPN
ap-3105	184	34	,	,	PUNCT
ap-3105	184	35	y	y	PROPN
ap-3105	184	36	)	)	PUNCT
ap-3105	185	1	=	=	SYM
ap-3105	185	2	0	0	NUM
ap-3105	186	1	otherwise	otherwise	ADV
ap-3105	186	2	.	.	PUNCT
ap-3105	187	1	given	give	VERB
ap-3105	187	2	t	t	PROPN
ap-3105	187	3	∈	∈	NOUN
ap-3105	188	1	r	r	NOUN
ap-3105	189	1	we	we	PRON
ap-3105	189	2	define	define	VERB
ap-3105	189	3	z(t	z(t	NOUN
ap-3105	189	4	,	,	PUNCT
ap-3105	189	5	x	x	X
ap-3105	189	6	,	,	PUNCT
ap-3105	189	7	y	y	NOUN
ap-3105	189	8	)	)	PUNCT
ap-3105	189	9	=	=	SYM
ap-3105	189	10	ϑ(t)χ(x	ϑ(t)χ(x	PROPN
ap-3105	189	11	,	,	PUNCT
ap-3105	189	12	y	y	NOUN
ap-3105	189	13	)	)	PUNCT
ap-3105	189	14	1	1	NUM
ap-3105	189	15	4πit	4πit	NUM
ap-3105	189	16	exp	exp	NOUN
ap-3105	189	17	(	(	PUNCT
ap-3105	189	18	i	i	NOUN
ap-3105	189	19	4	4	NUM
ap-3105	189	20	t	t	NOUN
ap-3105	189	21	dist2(x	dist2(x	PROPN
ap-3105	189	22	,	,	PUNCT
ap-3105	189	23	y	y	NOUN
ap-3105	189	24	)	)	PUNCT
ap-3105	189	25	)	)	PUNCT
ap-3105	189	26	,	,	PUNCT
ap-3105	189	27	(	(	PUNCT
ap-3105	189	28	7	7	X
ap-3105	189	29	)	)	PUNCT
ap-3105	189	30	furthermore	furthermore	ADV
ap-3105	189	31	,	,	PUNCT
ap-3105	189	32	for	for	ADP
ap-3105	189	33	x1	x1	PROPN
ap-3105	189	34	,	,	PUNCT
ap-3105	189	35	x3	x3	PROPN
ap-3105	189	36	∈	∈	PROPN
ap-3105	189	37	m̃	m̃	PROPN
ap-3105	189	38	∪a∪b	∪a∪b	PUNCT
ap-3105	189	39	and	and	CCONJ
ap-3105	189	40	x2	x2	PROPN
ap-3105	189	41	∈	∈	PROPN
ap-3105	189	42	a∪b	a∪b	ADJ
ap-3105	189	43	obeying	obey	VERB
ap-3105	189	44	χ(x1	χ(x1	NOUN
ap-3105	189	45	,	,	PUNCT
ap-3105	189	46	x2	x2	NUM
ap-3105	189	47	)	)	PUNCT
ap-3105	189	48	=	=	SYM
ap-3105	189	49	χ(x2	χ(x2	NOUN
ap-3105	189	50	,	,	PUNCT
ap-3105	189	51	x3	x3	ADJ
ap-3105	189	52	)	)	PUNCT
ap-3105	189	53	=	=	SYM
ap-3105	189	54	1	1	NUM
ap-3105	189	55	,	,	PUNCT
ap-3105	189	56	and	and	CCONJ
ap-3105	189	57	for	for	ADP
ap-3105	189	58	t1	t1	NOUN
ap-3105	189	59	,	,	PUNCT
ap-3105	189	60	t2	t2	PROPN
ap-3105	189	61	>	>	X
ap-3105	189	62	0	0	NUM
ap-3105	189	63	,	,	PUNCT
ap-3105	189	64	we	we	PRON
ap-3105	189	65	set	set	VERB
ap-3105	189	66	v	v	NOUN
ap-3105	189	67	(	(	PUNCT
ap-3105	189	68	x3	x3	ADJ
ap-3105	189	69	,	,	PUNCT
ap-3105	189	70	x2	x2	PROPN
ap-3105	189	71	,	,	PUNCT
ap-3105	189	72	x1	x1	PROPN
ap-3105	189	73	t2	t2	NOUN
ap-3105	189	74	,	,	PUNCT
ap-3105	189	75	t1	t1	NOUN
ap-3105	189	76	)	)	PUNCT
ap-3105	190	1	=	=	SYM
ap-3105	190	2	2i	2i	NOUN
ap-3105	190	3	(	(	PUNCT
ap-3105	190	4	(	(	PUNCT
ap-3105	190	5	θ	θ	NOUN
ap-3105	190	6	−	−	PROPN
ap-3105	191	1	π	π	X
ap-3105	192	1	+	+	CCONJ
ap-3105	192	2	i	i	PRON
ap-3105	192	3	ln	ln	VERB
ap-3105	192	4	t2r1	t2r1	PRON
ap-3105	192	5	t1r2	t1r2	X
ap-3105	192	6	)	)	PUNCT
ap-3105	192	7	−1	−1	NOUN
ap-3105	192	8	−	−	PROPN
ap-3105	192	9	(	(	PUNCT
ap-3105	192	10	θ	θ	PROPN
ap-3105	193	1	+	+	PUNCT
ap-3105	193	2	π	π	PUNCT
ap-3105	194	1	+	+	CCONJ
ap-3105	194	2	i	i	PRON
ap-3105	194	3	ln	ln	VERB
ap-3105	194	4	t2r1	t2r1	PRON
ap-3105	194	5	t1r2	t1r2	X
ap-3105	194	6	)	)	PUNCT
ap-3105	194	7	−1	−1	NOUN
ap-3105	194	8	)	)	PUNCT
ap-3105	194	9	(	(	PUNCT
ap-3105	194	10	8)	8)	NUM
ap-3105	194	11	where	where	SCONJ
ap-3105	194	12	θ	θ	PROPN
ap-3105	194	13	=	=	SYM
ap-3105	194	14	∠x1	∠x1	PROPN
ap-3105	194	15	,	,	PUNCT
ap-3105	194	16	x2	x2	PROPN
ap-3105	194	17	,	,	PUNCT
ap-3105	194	18	x3	x3	PROPN
ap-3105	194	19	∈	∈	NOUN
ap-3105	194	20	r	r	NOUN
ap-3105	194	21	is	be	AUX
ap-3105	194	22	the	the	DET
ap-3105	194	23	oriented	orient	VERB
ap-3105	194	24	angle	angle	NOUN
ap-3105	194	25	and	and	CCONJ
ap-3105	194	26	r1	r1	NOUN
ap-3105	194	27	=	=	PUNCT
ap-3105	194	28	dist(x1	dist(x1	PROPN
ap-3105	194	29	,	,	PUNCT
ap-3105	194	30	x2	x2	PROPN
ap-3105	194	31	)	)	PUNCT
ap-3105	194	32	,	,	PUNCT
ap-3105	194	33	r2	r2	NOUN
ap-3105	194	34	=	=	PUNCT
ap-3105	194	35	dist(x2	dist(x2	NOUN
ap-3105	194	36	,	,	PUNCT
ap-3105	194	37	x3	x3	ADJ
ap-3105	194	38	)	)	PUNCT
ap-3105	194	39	.	.	PUNCT
ap-3105	195	1	note	note	VERB
ap-3105	195	2	that	that	SCONJ
ap-3105	195	3	θ	θ	PROPN
ap-3105	195	4	can	can	AUX
ap-3105	195	5	take	take	VERB
ap-3105	195	6	any	any	DET
ap-3105	195	7	real	real	ADJ
ap-3105	195	8	value	value	NOUN
ap-3105	195	9	.	.	PUNCT
ap-3105	196	1	we	we	PRON
ap-3105	196	2	claim	claim	VERB
ap-3105	196	3	that	that	SCONJ
ap-3105	196	4	the	the	DET
ap-3105	196	5	free	free	ADJ
ap-3105	196	6	propagator	propagator	NOUN
ap-3105	196	7	on	on	ADP
ap-3105	196	8	m̃	m̃	PROPN
ap-3105	196	9	equals	equal	VERB
ap-3105	196	10	k(t	k(t	PROPN
ap-3105	196	11	,	,	PUNCT
ap-3105	196	12	x	x	PRON
ap-3105	196	13	,	,	PUNCT
ap-3105	196	14	x0	x0	PROPN
ap-3105	196	15	)	)	PUNCT
ap-3105	197	1	=	=	PUNCT
ap-3105	197	2	∑	∑	PROPN
ap-3105	197	3	γ∈c	γ∈c	PROPN
ap-3105	197	4	(	(	PUNCT
ap-3105	197	5	x	x	NOUN
ap-3105	197	6	,	,	PUNCT
ap-3105	197	7	x0	x0	NUM
ap-3105	197	8	)	)	PUNCT
ap-3105	197	9	kγ(t	kγ(t	PROPN
ap-3105	197	10	,	,	PUNCT
ap-3105	197	11	x	x	PRON
ap-3105	197	12	,	,	PUNCT
ap-3105	197	13	x0	x0	PROPN
ap-3105	197	14	)	)	PUNCT
ap-3105	197	15	,	,	PUNCT
ap-3105	197	16	(	(	PUNCT
ap-3105	197	17	9	9	X
ap-3105	197	18	)	)	PUNCT
ap-3105	197	19	where	where	SCONJ
ap-3105	197	20	c	c	X
ap-3105	197	21	(	(	PUNCT
ap-3105	197	22	x	x	NOUN
ap-3105	197	23	,	,	PUNCT
ap-3105	197	24	x0	x0	PROPN
ap-3105	197	25	)	)	PUNCT
ap-3105	197	26	stands	stand	VERB
ap-3105	197	27	for	for	ADP
ap-3105	197	28	the	the	DET
ap-3105	197	29	set	set	NOUN
ap-3105	197	30	of	of	ADP
ap-3105	197	31	all	all	DET
ap-3105	197	32	piecewise	piecewise	NOUN
ap-3105	197	33	geodesic	geodesic	ADJ
ap-3105	197	34	curves	curve	NOUN
ap-3105	197	35	γ	γ	NOUN
ap-3105	197	36	:	:	PUNCT
ap-3105	197	37	x0	x0	PROPN
ap-3105	197	38	→	→	SYM
ap-3105	197	39	c1	c1	PROPN
ap-3105	197	40	→	→	SYM
ap-3105	197	41	·	·	PUNCT
ap-3105	197	42	·	·	PUNCT
ap-3105	197	43	·	·	PUNCT
ap-3105	198	1	→	→	SYM
ap-3105	198	2	cn	cn	PROPN
ap-3105	198	3	→	→	SYM
ap-3105	198	4	x	x	X
ap-3105	198	5	with	with	ADP
ap-3105	198	6	the	the	DET
ap-3105	198	7	inner	inner	ADJ
ap-3105	198	8	vortices	vortex	NOUN
ap-3105	198	9	cj	cj	X
ap-3105	198	10	,	,	PUNCT
ap-3105	198	11	1	1	NUM
ap-3105	198	12	≤	≤	NUM
ap-3105	198	13	j	j	PROPN
ap-3105	198	14	≤	≤	PROPN
ap-3105	198	15	n	n	CCONJ
ap-3105	198	16	,	,	PUNCT
ap-3105	198	17	belonging	belong	VERB
ap-3105	198	18	to	to	ADP
ap-3105	198	19	the	the	DET
ap-3105	198	20	set	set	NOUN
ap-3105	198	21	of	of	ADP
ap-3105	198	22	extreme	extreme	ADJ
ap-3105	198	23	points	point	NOUN
ap-3105	198	24	a	a	DET
ap-3105	198	25	∪	∪	X
ap-3105	198	26	b.	b.	NOUN
ap-3105	198	27	this	this	PRON
ap-3105	198	28	means	mean	VERB
ap-3105	198	29	that	that	SCONJ
ap-3105	198	30	it	it	PRON
ap-3105	198	31	should	should	AUX
ap-3105	198	32	hold	hold	VERB
ap-3105	198	33	χ(x0	χ(x0	NOUN
ap-3105	198	34	,	,	PUNCT
ap-3105	198	35	c1	c1	PROPN
ap-3105	198	36	)	)	PUNCT
ap-3105	198	37	=	=	SYM
ap-3105	198	38	χ(c1	χ(c1	PROPN
ap-3105	198	39	,	,	PUNCT
ap-3105	198	40	c2	c2	PROPN
ap-3105	198	41	)	)	PUNCT
ap-3105	198	42	=	=	SYM
ap-3105	198	43	·	·	PUNCT
ap-3105	198	44	·	·	PUNCT
ap-3105	198	45	·	·	PUNCT
ap-3105	198	46	=	=	SYM
ap-3105	198	47	χ(cn	χ(cn	PROPN
ap-3105	198	48	,	,	PUNCT
ap-3105	198	49	x	x	NOUN
ap-3105	198	50	)	)	PUNCT
ap-3105	198	51	=	=	SYM
ap-3105	199	1	1	1	X
ap-3105	199	2	.	.	PUNCT
ap-3105	200	1	let	let	VERB
ap-3105	200	2	us	we	PRON
ap-3105	200	3	denote	denote	VERB
ap-3105	200	4	by	by	ADP
ap-3105	200	5	|γ|	|γ|	PROPN
ap-3105	200	6	=	=	SYM
ap-3105	200	7	n	n	CCONJ
ap-3105	200	8	the	the	DET
ap-3105	200	9	length	length	NOUN
ap-3105	200	10	of	of	ADP
ap-3105	200	11	the	the	DET
ap-3105	200	12	sequence	sequence	NOUN
ap-3105	200	13	(	(	PUNCT
ap-3105	200	14	c1	c1	PROPN
ap-3105	200	15	,	,	PUNCT
ap-3105	200	16	c2	c2	PROPN
ap-3105	200	17	,	,	PUNCT
ap-3105	200	18	.	.	PUNCT
ap-3105	200	19	.	.	PUNCT
ap-3105	201	1	.	.	PUNCT
ap-3105	202	1	,	,	PUNCT
ap-3105	202	2	cn	cn	PROPN
ap-3105	202	3	)	)	PUNCT
ap-3105	202	4	.	.	PUNCT
ap-3105	203	1	in	in	ADP
ap-3105	203	2	particular	particular	ADJ
ap-3105	203	3	,	,	PUNCT
ap-3105	203	4	if	if	SCONJ
ap-3105	203	5	|γ|	|γ|	PROPN
ap-3105	203	6	=	=	NOUN
ap-3105	203	7	0	0	PUNCT
ap-3105	204	1	then	then	ADV
ap-3105	204	2	γ	γ	PROPN
ap-3105	204	3	designates	designate	VERB
ap-3105	204	4	the	the	DET
ap-3105	204	5	geodesic	geodesic	ADJ
ap-3105	204	6	segment	segment	NOUN
ap-3105	204	7	x0	x0	PROPN
ap-3105	204	8	→	→	PUNCT
ap-3105	204	9	x.	x.	NOUN
ap-3105	204	10	to	to	PART
ap-3105	204	11	simplify	simplify	VERB
ap-3105	204	12	notation	notation	NOUN
ap-3105	204	13	we	we	PRON
ap-3105	204	14	set	set	VERB
ap-3105	204	15	everywhere	everywhere	ADV
ap-3105	204	16	where	where	SCONJ
ap-3105	204	17	convenient	convenient	ADJ
ap-3105	204	18	c0	c0	NOUN
ap-3105	204	19	=	=	PUNCT
ap-3105	204	20	x0	x0	PROPN
ap-3105	204	21	and	and	CCONJ
ap-3105	204	22	cn+1	cn+1	VERB
ap-3105	204	23	=	=	SYM
ap-3105	204	24	x.	x.	NOUN
ap-3105	204	25	with	with	ADP
ap-3105	204	26	this	this	DET
ap-3105	204	27	convention	convention	NOUN
ap-3105	204	28	,	,	PUNCT
ap-3105	204	29	the	the	DET
ap-3105	204	30	terms	term	NOUN
ap-3105	204	31	in	in	ADP
ap-3105	204	32	(	(	PUNCT
ap-3105	204	33	9	9	X
ap-3105	204	34	)	)	PUNCT
ap-3105	204	35	equal	equal	ADJ
ap-3105	204	36	kγ(t	kγ(t	NOUN
ap-3105	204	37	,	,	PUNCT
ap-3105	204	38	x	x	PRON
ap-3105	204	39	,	,	PUNCT
ap-3105	204	40	x0	x0	PROPN
ap-3105	204	41	)	)	PUNCT
ap-3105	205	1	=	=	SYM
ap-3105	205	2	∫	∫	PROPN
ap-3105	205	3	rn+1	rn+1	X
ap-3105	205	4	dtn	dtn	PROPN
ap-3105	205	5	·	·	PUNCT
ap-3105	205	6	·	·	PUNCT
ap-3105	205	7	·	·	PUNCT
ap-3105	205	8	dt0	dt0	ADP
ap-3105	205	9	δ(tn	δ(tn	PROPN
ap-3105	205	10	+	+	CCONJ
ap-3105	205	11	·	·	PUNCT
ap-3105	205	12	·	·	PUNCT
ap-3105	205	13	·	·	PUNCT
ap-3105	205	14	+	+	NUM
ap-3105	205	15	t0	t0	PROPN
ap-3105	205	16	−	−	PROPN
ap-3105	205	17	t	t	PROPN
ap-3105	205	18	)	)	PUNCT
ap-3105	205	19	n−1∏	n−1∏	PROPN
ap-3105	205	20	j=0	j=0	PROPN
ap-3105	205	21	v	v	PROPN
ap-3105	205	22	(	(	PUNCT
ap-3105	205	23	cj+2	cj+2	NUM
ap-3105	205	24	,	,	PUNCT
ap-3105	205	25	cj+1	cj+1	NUM
ap-3105	205	26	,	,	PUNCT
ap-3105	205	27	cj	cj	NOUN
ap-3105	205	28	tj+1	tj+1	PROPN
ap-3105	205	29	,	,	PUNCT
ap-3105	205	30	tj	tj	NOUN
ap-3105	205	31	)	)	PUNCT
ap-3105	205	32	n∏	n∏	PROPN
ap-3105	205	33	j=0	j=0	PROPN
ap-3105	205	34	z(tj	z(tj	PROPN
ap-3105	205	35	,	,	PUNCT
ap-3105	205	36	cj+1	cj+1	NUM
ap-3105	205	37	,	,	PUNCT
ap-3105	205	38	cj	cj	NOUN
ap-3105	205	39	)	)	PUNCT
ap-3105	205	40	.	.	PUNCT
ap-3105	206	1	(	(	PUNCT
ap-3105	206	2	10	10	NUM
ap-3105	206	3	)	)	PUNCT
ap-3105	206	4	in	in	ADP
ap-3105	206	5	particular	particular	ADJ
ap-3105	206	6	,	,	PUNCT
ap-3105	206	7	if	if	SCONJ
ap-3105	206	8	|γ|	|γ|	PROPN
ap-3105	206	9	=	=	SYM
ap-3105	206	10	0	0	PUNCT
ap-3105	206	11	then	then	ADV
ap-3105	206	12	kγ(t	kγ(t	NOUN
ap-3105	206	13	,	,	PUNCT
ap-3105	206	14	x	x	PRON
ap-3105	206	15	,	,	PUNCT
ap-3105	206	16	x0	x0	PROPN
ap-3105	206	17	)	)	PUNCT
ap-3105	206	18	=	=	PUNCT
ap-3105	207	1	z(t	z(t	NOUN
ap-3105	207	2	,	,	PUNCT
ap-3105	207	3	x	x	X
ap-3105	207	4	,	,	PUNCT
ap-3105	207	5	x0	x0	PROPN
ap-3105	207	6	)	)	PUNCT
ap-3105	207	7	,	,	PUNCT
ap-3105	207	8	and	and	CCONJ
ap-3105	207	9	if	if	SCONJ
ap-3105	207	10	|γ|	|γ|	PROPN
ap-3105	207	11	=	=	NOUN
ap-3105	207	12	1	1	NUM
ap-3105	207	13	then	then	ADV
ap-3105	207	14	γ	γ	PROPN
ap-3105	207	15	designates	designate	VERB
ap-3105	207	16	a	a	DET
ap-3105	207	17	path	path	NOUN
ap-3105	207	18	composed	compose	VERB
ap-3105	207	19	of	of	ADP
ap-3105	207	20	two	two	NUM
ap-3105	207	21	geodesic	geodesic	ADJ
ap-3105	207	22	segments	segment	NOUN
ap-3105	207	23	x0	x0	PROPN
ap-3105	207	24	→	→	SYM
ap-3105	207	25	c	c	PROPN
ap-3105	207	26	→	→	SYM
ap-3105	207	27	x	x	SYM
ap-3105	207	28	,	,	PUNCT
ap-3105	207	29	with	with	ADP
ap-3105	207	30	c	c	PROPN
ap-3105	207	31	∈	∈	PROPN
ap-3105	207	32	a	a	DET
ap-3105	207	33	∪	∪	ADJ
ap-3105	207	34	b	b	NOUN
ap-3105	207	35	,	,	PUNCT
ap-3105	207	36	and	and	CCONJ
ap-3105	207	37	kγ(t	kγ(t	PROPN
ap-3105	207	38	,	,	PUNCT
ap-3105	207	39	x	x	PRON
ap-3105	207	40	,	,	PUNCT
ap-3105	207	41	x0	x0	PROPN
ap-3105	207	42	)	)	PUNCT
ap-3105	207	43	=	=	SYM
ap-3105	207	44	ϑ(t	ϑ(t	X
ap-3105	207	45	)	)	PUNCT
ap-3105	208	1	∫	∫	PROPN
ap-3105	208	2	t	t	PROPN
ap-3105	208	3	0	0	NUM
ap-3105	208	4	v	v	PROPN
ap-3105	208	5	(	(	PUNCT
ap-3105	208	6	x	x	X
ap-3105	208	7	,	,	PUNCT
ap-3105	208	8	c	c	X
ap-3105	208	9	,	,	PUNCT
ap-3105	208	10	x0	x0	PROPN
ap-3105	208	11	t−	t−	PROPN
ap-3105	208	12	s	s	PROPN
ap-3105	208	13	,	,	PUNCT
ap-3105	208	14	s	s	PART
ap-3105	208	15	)	)	PUNCT
ap-3105	208	16	z(t−	z(t−	PROPN
ap-3105	208	17	s	s	NOUN
ap-3105	208	18	,	,	PUNCT
ap-3105	208	19	x	x	PRON
ap-3105	208	20	,	,	PUNCT
ap-3105	208	21	c)z(s	c)z(s	PROPN
ap-3105	208	22	,	,	PUNCT
ap-3105	208	23	c	c	NOUN
ap-3105	208	24	,	,	PUNCT
ap-3105	208	25	x0	x0	PROPN
ap-3105	208	26	)	)	PUNCT
ap-3105	208	27	ds	ds	NOUN
ap-3105	208	28	.	.	NOUN
ap-3105	209	1	in	in	ADP
ap-3105	209	2	what	what	PRON
ap-3105	209	3	follows	follow	VERB
ap-3105	209	4	we	we	PRON
ap-3105	209	5	aim	aim	VERB
ap-3105	209	6	to	to	PART
ap-3105	209	7	provide	provide	VERB
ap-3105	209	8	a	a	DET
ap-3105	209	9	detailed	detailed	ADJ
ap-3105	209	10	verification	verification	NOUN
ap-3105	209	11	of	of	ADP
ap-3105	209	12	formulas	formula	NOUN
ap-3105	209	13	(	(	PUNCT
ap-3105	209	14	9	9	NUM
ap-3105	209	15	)	)	PUNCT
ap-3105	209	16	,	,	PUNCT
ap-3105	209	17	(	(	PUNCT
ap-3105	209	18	10	10	NUM
ap-3105	209	19	)	)	PUNCT
ap-3105	209	20	.	.	PUNCT
ap-3105	210	1	228	228	NUM
ap-3105	210	2	vol	vol	NOUN
ap-3105	210	3	.	.	PUNCT
ap-3105	211	1	56	56	NUM
ap-3105	211	2	no	no	NOUN
ap-3105	211	3	.	.	PUNCT
ap-3105	212	1	3/2016	3/2016	NUM
ap-3105	212	2	the	the	DET
ap-3105	212	3	aharonov	aharonov	PROPN
ap-3105	212	4	-	-	PUNCT
ap-3105	212	5	bohm	bohm	PROPN
ap-3105	212	6	hamiltonian	hamiltonian	NOUN
ap-3105	212	7	with	with	ADP
ap-3105	212	8	two	two	NUM
ap-3105	212	9	vortices	vortex	NOUN
ap-3105	212	10	revisited	revisit	VERB
ap-3105	212	11	3.2	3.2	NUM
ap-3105	212	12	.	.	PUNCT
ap-3105	213	1	auxiliary	auxiliary	ADJ
ap-3105	213	2	relations	relation	NOUN
ap-3105	213	3	in	in	ADP
ap-3105	213	4	r2	r2	PROPN
ap-3105	213	5	,	,	PUNCT
ap-3105	213	6	it	it	PRON
ap-3105	213	7	holds	hold	VERB
ap-3105	213	8	true	true	ADJ
ap-3105	213	9	that	that	SCONJ
ap-3105	213	10	(	(	PUNCT
ap-3105	213	11	∂	∂	NUM
ap-3105	213	12	∂x	∂x	NOUN
ap-3105	214	1	+	+	CCONJ
ap-3105	214	2	i	i	PRON
ap-3105	214	3	∂	∂	NOUN
ap-3105	214	4	∂y	∂y	X
ap-3105	214	5	)	)	PUNCT
ap-3105	214	6	1	1	NUM
ap-3105	214	7	x+	x+	PROPN
ap-3105	214	8	iy	iy	NOUN
ap-3105	214	9	=	=	PUNCT
ap-3105	214	10	2πδ(x)δ(y	2πδ(x)δ(y	NUM
ap-3105	214	11	)	)	PUNCT
ap-3105	214	12	and	and	CCONJ
ap-3105	214	13	∆	∆	PROPN
ap-3105	214	14	1	1	NUM
ap-3105	214	15	x+	x+	PROPN
ap-3105	214	16	iy	iy	NOUN
ap-3105	214	17	=	=	PUNCT
ap-3105	214	18	2π	2π	PROPN
ap-3105	214	19	(	(	PUNCT
ap-3105	214	20	δ(y)δ′(x)−	δ(y)δ′(x)−	NOUN
ap-3105	214	21	iδ(x)δ′(y	iδ(x)δ′(y	PROPN
ap-3105	214	22	)	)	PUNCT
ap-3105	214	23	)	)	PUNCT
ap-3105	214	24	.	.	PUNCT
ap-3105	215	1	it	it	PRON
ap-3105	215	2	follows	follow	VERB
ap-3105	215	3	that	that	SCONJ
ap-3105	215	4	(	(	PUNCT
ap-3105	215	5	∂2	∂2	NUM
ap-3105	215	6	∂r2	∂r2	NOUN
ap-3105	215	7	+	+	CCONJ
ap-3105	215	8	1	1	NUM
ap-3105	215	9	r	r	NOUN
ap-3105	215	10	∂	∂	NOUN
ap-3105	215	11	∂r	∂r	NOUN
ap-3105	215	12	+	+	CCONJ
ap-3105	215	13	1	1	NUM
ap-3105	215	14	r2	r2	NOUN
ap-3105	215	15	∂2	∂2	PROPN
ap-3105	215	16	∂θ2	∂θ2	PROPN
ap-3105	215	17	)	)	PUNCT
ap-3105	215	18	(	(	PUNCT
ap-3105	215	19	θ	θ	X
ap-3105	216	1	+	+	PUNCT
ap-3105	216	2	i	i	PRON
ap-3105	216	3	ln	ln	NOUN
ap-3105	216	4	t	t	PROPN
ap-3105	216	5	r	r	NOUN
ap-3105	216	6	)	)	PUNCT
ap-3105	216	7	−1	−1	NOUN
ap-3105	216	8	=	=	SYM
ap-3105	216	9	2πt	2πt	ADJ
ap-3105	216	10	r2	r2	PROPN
ap-3105	216	11	(	(	PUNCT
ap-3105	216	12	δ(t−	δ(t−	PROPN
ap-3105	216	13	r)δ′(θ)−	r)δ′(θ)−	PROPN
ap-3105	216	14	irδ′(t−	irδ′(t−	PROPN
ap-3105	216	15	r)δ(θ	r)δ(θ	NOUN
ap-3105	216	16	)	)	PUNCT
ap-3105	216	17	)	)	PUNCT
ap-3105	217	1	(	(	PUNCT
ap-3105	217	2	11	11	NUM
ap-3105	217	3	)	)	PUNCT
ap-3105	217	4	holds	hold	VERB
ap-3105	217	5	on	on	ADP
ap-3105	217	6	the	the	DET
ap-3105	217	7	domain	domain	NOUN
ap-3105	217	8	t	t	X
ap-3105	217	9	>	>	X
ap-3105	217	10	0	0	NUM
ap-3105	217	11	,	,	PUNCT
ap-3105	217	12	r	r	NOUN
ap-3105	217	13	>	>	X
ap-3105	217	14	0	0	NUM
ap-3105	217	15	,	,	PUNCT
ap-3105	217	16	θ	θ	PROPN
ap-3105	217	17	∈	∈	PROPN
ap-3105	217	18	r.	r.	PROPN
ap-3105	217	19	on	on	ADP
ap-3105	217	20	the	the	DET
ap-3105	217	21	same	same	ADJ
ap-3105	217	22	domain	domain	NOUN
ap-3105	217	23	,	,	PUNCT
ap-3105	217	24	(	(	PUNCT
ap-3105	217	25	r	r	NOUN
ap-3105	217	26	∂	∂	NOUN
ap-3105	217	27	∂r	∂r	NOUN
ap-3105	217	28	+	+	PROPN
ap-3105	217	29	t	t	PROPN
ap-3105	217	30	∂	∂	NOUN
ap-3105	217	31	∂t	∂t	PROPN
ap-3105	217	32	)	)	PUNCT
ap-3105	217	33	(	(	PUNCT
ap-3105	217	34	θ	θ	X
ap-3105	218	1	+	+	PUNCT
ap-3105	218	2	i	i	PRON
ap-3105	218	3	ln	ln	NOUN
ap-3105	218	4	t	t	PROPN
ap-3105	218	5	r	r	NOUN
ap-3105	218	6	)	)	PUNCT
ap-3105	218	7	−1	−1	NOUN
ap-3105	218	8	=	=	SYM
ap-3105	218	9	0	0	PROPN
ap-3105	218	10	.	.	PUNCT
ap-3105	219	1	(	(	PUNCT
ap-3105	219	2	12	12	X
ap-3105	219	3	)	)	PUNCT
ap-3105	219	4	combining	combine	VERB
ap-3105	219	5	(	(	PUNCT
ap-3105	219	6	11	11	NUM
ap-3105	219	7	)	)	PUNCT
ap-3105	219	8	and	and	CCONJ
ap-3105	219	9	(	(	PUNCT
ap-3105	219	10	12	12	NUM
ap-3105	219	11	)	)	PUNCT
ap-3105	219	12	one	one	NUM
ap-3105	219	13	finds	find	VERB
ap-3105	219	14	that	that	PRON
ap-3105	219	15	(	(	PUNCT
ap-3105	219	16	i	i	PRON
ap-3105	219	17	∂	∂	VERB
ap-3105	219	18	∂t	∂t	PROPN
ap-3105	219	19	+	+	CCONJ
ap-3105	219	20	∂2	∂2	ADJ
ap-3105	219	21	∂r2	∂r2	NOUN
ap-3105	219	22	+	+	CCONJ
ap-3105	219	23	1	1	NUM
ap-3105	219	24	r	r	NOUN
ap-3105	219	25	∂	∂	NOUN
ap-3105	219	26	∂r	∂r	NOUN
ap-3105	220	1	+	+	CCONJ
ap-3105	220	2	1	1	NUM
ap-3105	220	3	r2	r2	NOUN
ap-3105	220	4	∂2	∂2	PROPN
ap-3105	220	5	∂θ2	∂θ2	PROPN
ap-3105	220	6	)	)	PUNCT
ap-3105	220	7	(	(	PUNCT
ap-3105	220	8	θ	θ	X
ap-3105	221	1	+	+	PUNCT
ap-3105	221	2	i	i	PRON
ap-3105	221	3	ln	ln	NOUN
ap-3105	221	4	t	t	PROPN
ap-3105	221	5	r	r	NOUN
ap-3105	221	6	)	)	PUNCT
ap-3105	221	7	−1	−1	NOUN
ap-3105	221	8	1	1	NUM
ap-3105	221	9	t	t	NOUN
ap-3105	221	10	exp	exp	NOUN
ap-3105	221	11	(	(	PUNCT
ap-3105	221	12	i	i	PRON
ap-3105	221	13	r2	r2	PROPN
ap-3105	221	14	4	4	NUM
ap-3105	221	15	t	t	NOUN
ap-3105	221	16	)	)	PUNCT
ap-3105	222	1	=	=	PUNCT
ap-3105	222	2	2π	2π	NUM
ap-3105	222	3	r2	r2	PROPN
ap-3105	222	4	exp	exp	PROPN
ap-3105	222	5	(	(	PUNCT
ap-3105	222	6	i	i	PRON
ap-3105	222	7	r2	r2	PROPN
ap-3105	222	8	4	4	NUM
ap-3105	222	9	t	t	NOUN
ap-3105	222	10	)	)	PUNCT
ap-3105	222	11	(	(	PUNCT
ap-3105	222	12	δ(t−	δ(t−	PROPN
ap-3105	222	13	r)δ′(θ)−	r)δ′(θ)−	PROPN
ap-3105	222	14	irδ′(t−	irδ′(t−	PROPN
ap-3105	222	15	r)δ(θ	r)δ(θ	NOUN
ap-3105	222	16	)	)	PUNCT
ap-3105	222	17	)	)	PUNCT
ap-3105	222	18	.	.	PUNCT
ap-3105	223	1	(	(	PUNCT
ap-3105	223	2	13	13	X
ap-3105	223	3	)	)	PUNCT
ap-3105	223	4	equipped	equip	VERB
ap-3105	223	5	with	with	ADP
ap-3105	223	6	(	(	PUNCT
ap-3105	223	7	13	13	NUM
ap-3105	223	8	)	)	PUNCT
ap-3105	223	9	one	one	NOUN
ap-3105	223	10	can	can	AUX
ap-3105	223	11	prove	prove	VERB
ap-3105	223	12	the	the	DET
ap-3105	223	13	identity	identity	NOUN
ap-3105	223	14	(	(	PUNCT
ap-3105	223	15	i	i	NOUN
ap-3105	223	16	∂	∂	NOUN
ap-3105	223	17	∂t	∂t	PROPN
ap-3105	223	18	+	+	CCONJ
ap-3105	223	19	∂2	∂2	ADJ
ap-3105	223	20	∂r2	∂r2	NOUN
ap-3105	223	21	+	+	CCONJ
ap-3105	223	22	1	1	NUM
ap-3105	223	23	r	r	NOUN
ap-3105	223	24	∂	∂	NOUN
ap-3105	223	25	∂r	∂r	NOUN
ap-3105	223	26	+	+	CCONJ
ap-3105	223	27	1	1	NUM
ap-3105	223	28	r2	r2	NOUN
ap-3105	223	29	∂2	∂2	PROPN
ap-3105	223	30	∂θ2	∂θ2	PROPN
ap-3105	223	31	)	)	PUNCT
ap-3105	223	32	∫	∫	PROPN
ap-3105	223	33	t	t	PROPN
ap-3105	223	34	0	0	NUM
ap-3105	224	1	(	(	PUNCT
ap-3105	224	2	θ	θ	X
ap-3105	225	1	+	+	CCONJ
ap-3105	225	2	i	i	PRON
ap-3105	225	3	ln	ln	NOUN
ap-3105	225	4	(	(	PUNCT
ap-3105	225	5	t−	t−	PROPN
ap-3105	225	6	s)r0	s)r0	PROPN
ap-3105	225	7	sr	sr	PROPN
ap-3105	225	8	)	)	PUNCT
ap-3105	225	9	−1	−1	NOUN
ap-3105	225	10	1	1	NUM
ap-3105	225	11	t−	t−	PROPN
ap-3105	225	12	s	s	NOUN
ap-3105	225	13	exp	exp	NOUN
ap-3105	225	14	(	(	PUNCT
ap-3105	225	15	i	i	NOUN
ap-3105	225	16	r2	r2	PROPN
ap-3105	225	17	4(t−	4(t−	PROPN
ap-3105	225	18	s	s	NOUN
ap-3105	225	19	)	)	PUNCT
ap-3105	225	20	)	)	PUNCT
ap-3105	225	21	f(s	f(	VERB
ap-3105	225	22	)	)	PUNCT
ap-3105	225	23	ds	ds	PROPN
ap-3105	225	24	=	=	SYM
ap-3105	225	25	2πr0	2πr0	NUM
ap-3105	225	26	r2(r	r2(r	PROPN
ap-3105	225	27	+	+	CCONJ
ap-3105	225	28	r0	r0	NOUN
ap-3105	225	29	)	)	PUNCT
ap-3105	225	30	exp	exp	NOUN
ap-3105	225	31	(	(	PUNCT
ap-3105	225	32	i	i	PRON
ap-3105	225	33	(	(	PUNCT
ap-3105	226	1	r	r	NOUN
ap-3105	226	2	+	+	CCONJ
ap-3105	226	3	r0)r	r0)r	VERB
ap-3105	226	4	4	4	NUM
ap-3105	226	5	t	t	NOUN
ap-3105	226	6	)	)	PUNCT
ap-3105	227	1	[	[	PUNCT
ap-3105	227	2	f	f	X
ap-3105	227	3	(	(	PUNCT
ap-3105	227	4	tr0	tr0	INTJ
ap-3105	227	5	r	r	NOUN
ap-3105	227	6	+	+	NUM
ap-3105	227	7	r0	r0	NOUN
ap-3105	227	8	)	)	PUNCT
ap-3105	227	9	δ′(θ	δ′(θ	NOUN
ap-3105	227	10	)	)	PUNCT
ap-3105	228	1	−	−	NOUN
ap-3105	229	1	i	i	PRON
ap-3105	229	2	r	r	NOUN
ap-3105	229	3	r	r	NOUN
ap-3105	229	4	+	+	NUM
ap-3105	229	5	r0	r0	NOUN
ap-3105	229	6	(	(	PUNCT
ap-3105	229	7	(	(	PUNCT
ap-3105	229	8	1	1	X
ap-3105	229	9	+	+	CCONJ
ap-3105	229	10	i	i	PRON
ap-3105	229	11	r0(r	r0(r	NOUN
ap-3105	229	12	+	+	NUM
ap-3105	229	13	r0	r0	NOUN
ap-3105	229	14	)	)	PUNCT
ap-3105	229	15	4	4	NUM
ap-3105	229	16	t	t	NOUN
ap-3105	229	17	)	)	PUNCT
ap-3105	230	1	f	f	PROPN
ap-3105	230	2	(	(	PUNCT
ap-3105	230	3	tr0	tr0	INTJ
ap-3105	230	4	r	r	NOUN
ap-3105	230	5	+	+	NUM
ap-3105	230	6	r0	r0	NOUN
ap-3105	230	7	)	)	PUNCT
ap-3105	231	1	+	+	CCONJ
ap-3105	232	1	tr0	tr0	PRON
ap-3105	232	2	r	r	NOUN
ap-3105	232	3	+	+	NUM
ap-3105	232	4	r0	r0	NOUN
ap-3105	232	5	f	f	NOUN
ap-3105	232	6	′	′	NUM
ap-3105	233	1	(	(	PUNCT
ap-3105	233	2	tr0	tr0	INTJ
ap-3105	233	3	r	r	NOUN
ap-3105	233	4	+	+	NUM
ap-3105	233	5	r0	r0	NOUN
ap-3105	233	6	)	)	PUNCT
ap-3105	233	7	)	)	PUNCT
ap-3105	234	1	δ(θ	δ(θ	PROPN
ap-3105	234	2	)	)	PUNCT
ap-3105	234	3	]	]	PUNCT
ap-3105	234	4	,	,	PUNCT
ap-3105	234	5	(	(	PUNCT
ap-3105	234	6	14	14	NUM
ap-3105	234	7	)	)	PUNCT
ap-3105	234	8	which	which	PRON
ap-3105	234	9	is	be	AUX
ap-3105	234	10	true	true	ADJ
ap-3105	234	11	in	in	ADP
ap-3105	234	12	the	the	DET
ap-3105	234	13	sense	sense	NOUN
ap-3105	234	14	of	of	ADP
ap-3105	234	15	distributions	distribution	NOUN
ap-3105	234	16	for	for	ADP
ap-3105	234	17	any	any	DET
ap-3105	234	18	r0	r0	NOUN
ap-3105	234	19	>	>	X
ap-3105	234	20	0	0	PUNCT
ap-3105	235	1	and	and	CCONJ
ap-3105	235	2	f	f	PROPN
ap-3105	235	3	∈	∈	PROPN
ap-3105	235	4	c1([0,+∞	c1([0,+∞	PROPN
ap-3105	235	5	[	[	X
ap-3105	235	6	)	)	PUNCT
ap-3105	235	7	,	,	PUNCT
ap-3105	235	8	again	again	ADV
ap-3105	235	9	on	on	ADP
ap-3105	235	10	the	the	DET
ap-3105	235	11	domain	domain	NOUN
ap-3105	235	12	t	t	X
ap-3105	235	13	>	>	X
ap-3105	235	14	0	0	NUM
ap-3105	235	15	,	,	PUNCT
ap-3105	235	16	r	r	NOUN
ap-3105	235	17	>	>	X
ap-3105	235	18	0	0	NUM
ap-3105	235	19	,	,	PUNCT
ap-3105	235	20	θ	θ	PROPN
ap-3105	235	21	∈	∈	PROPN
ap-3105	235	22	r.	r.	PROPN
ap-3105	235	23	note	note	VERB
ap-3105	235	24	that	that	SCONJ
ap-3105	235	25	1	1	NUM
ap-3105	235	26	ε	ε	PROPN
ap-3105	235	27	exp	exp	NOUN
ap-3105	235	28	(	(	PUNCT
ap-3105	235	29	i	i	PRON
ap-3105	235	30	r2	r2	PROPN
ap-3105	235	31	4ε	4ε	PROPN
ap-3105	235	32	)	)	PUNCT
ap-3105	235	33	→	→	SYM
ap-3105	235	34	0	0	X
ap-3105	235	35	as	as	ADP
ap-3105	235	36	ε→	ε→	NUM
ap-3105	235	37	0	0	NUM
ap-3105	236	1	+	+	CCONJ
ap-3105	236	2	in	in	ADP
ap-3105	236	3	d	d	PROPN
ap-3105	236	4	′(]0,+∞	′(]0,+∞	NOUN
ap-3105	236	5	[	[	X
ap-3105	236	6	)	)	PUNCT
ap-3105	236	7	.	.	PUNCT
ap-3105	237	1	in	in	ADP
ap-3105	237	2	particular	particular	ADJ
ap-3105	237	3	,	,	PUNCT
ap-3105	237	4	letting	let	VERB
ap-3105	237	5	f(s	f(	NOUN
ap-3105	237	6	)	)	PUNCT
ap-3105	238	1	=	=	SYM
ap-3105	238	2	(	(	PUNCT
ap-3105	238	3	1	1	NUM
ap-3105	238	4	/	/	SYM
ap-3105	238	5	s	s	PART
ap-3105	238	6	)	)	PUNCT
ap-3105	238	7	exp(ir	exp(ir	VERB
ap-3105	238	8	2	2	NUM
ap-3105	238	9	0	0	NUM
ap-3105	238	10	/(4s	/(4s	NOUN
ap-3105	238	11	)	)	PUNCT
ap-3105	238	12	)	)	PUNCT
ap-3105	239	1	one	one	PRON
ap-3105	239	2	derives	derive	VERB
ap-3105	239	3	the	the	DET
ap-3105	239	4	identity	identity	NOUN
ap-3105	239	5	(	(	PUNCT
ap-3105	239	6	i	i	NOUN
ap-3105	239	7	∂	∂	NOUN
ap-3105	239	8	∂t	∂t	PROPN
ap-3105	239	9	+	+	CCONJ
ap-3105	239	10	∂2	∂2	ADJ
ap-3105	239	11	∂r2	∂r2	NOUN
ap-3105	239	12	+	+	CCONJ
ap-3105	239	13	1	1	NUM
ap-3105	239	14	r	r	NOUN
ap-3105	239	15	∂	∂	NOUN
ap-3105	239	16	∂r	∂r	NOUN
ap-3105	239	17	+	+	CCONJ
ap-3105	239	18	1	1	NUM
ap-3105	239	19	r2	r2	NOUN
ap-3105	239	20	∂2	∂2	PROPN
ap-3105	239	21	∂θ2	∂θ2	PROPN
ap-3105	239	22	)	)	PUNCT
ap-3105	239	23	∫	∫	PROPN
ap-3105	239	24	t	t	PROPN
ap-3105	239	25	0	0	NUM
ap-3105	240	1	(	(	PUNCT
ap-3105	240	2	θ	θ	X
ap-3105	241	1	+	+	CCONJ
ap-3105	241	2	i	i	PRON
ap-3105	241	3	ln	ln	NOUN
ap-3105	241	4	(	(	PUNCT
ap-3105	241	5	t−	t−	PROPN
ap-3105	241	6	s)r0	s)r0	PROPN
ap-3105	241	7	sr	sr	PROPN
ap-3105	241	8	)	)	PUNCT
ap-3105	241	9	−1	−1	NOUN
ap-3105	241	10	1	1	NUM
ap-3105	241	11	(	(	PUNCT
ap-3105	241	12	t−	t−	PROPN
ap-3105	241	13	s)s	s)s	X
ap-3105	241	14	exp	exp	NOUN
ap-3105	241	15	(	(	PUNCT
ap-3105	241	16	i	i	PRON
ap-3105	241	17	(	(	PUNCT
ap-3105	241	18	r2	r2	PROPN
ap-3105	241	19	4(t−	4(t−	PROPN
ap-3105	241	20	s	s	PART
ap-3105	241	21	)	)	PUNCT
ap-3105	241	22	+	+	CCONJ
ap-3105	241	23	r	r	NOUN
ap-3105	241	24	2	2	NUM
ap-3105	241	25	0	0	NUM
ap-3105	241	26	4s	4s	NUM
ap-3105	241	27	)	)	PUNCT
ap-3105	241	28	)	)	PUNCT
ap-3105	241	29	ds	ds	NOUN
ap-3105	241	30	=	=	PUNCT
ap-3105	241	31	2π	2π	NOUN
ap-3105	241	32	tr2	tr2	VERB
ap-3105	241	33	exp	exp	NOUN
ap-3105	241	34	(	(	PUNCT
ap-3105	241	35	i	i	PRON
ap-3105	241	36	(	(	PUNCT
ap-3105	241	37	r	r	NOUN
ap-3105	241	38	+	+	NOUN
ap-3105	241	39	r0)2	r0)2	NUM
ap-3105	241	40	4	4	NUM
ap-3105	241	41	t	t	NOUN
ap-3105	241	42	)	)	PUNCT
ap-3105	241	43	δ′(θ	δ′(θ	NOUN
ap-3105	241	44	)	)	PUNCT
ap-3105	241	45	.	.	PUNCT
ap-3105	242	1	(	(	PUNCT
ap-3105	242	2	15	15	X
ap-3105	242	3	)	)	PUNCT
ap-3105	242	4	let	let	VERB
ap-3105	242	5	us	we	PRON
ap-3105	242	6	further	far	ADV
ap-3105	242	7	recall	recall	VERB
ap-3105	242	8	a	a	DET
ap-3105	242	9	basic	basic	ADJ
ap-3105	242	10	fact	fact	NOUN
ap-3105	242	11	concerning	concern	VERB
ap-3105	242	12	the	the	DET
ap-3105	242	13	generalized	generalize	VERB
ap-3105	242	14	laplacian	laplacian	NOUN
ap-3105	242	15	.	.	PUNCT
ap-3105	243	1	if	if	SCONJ
ap-3105	243	2	g	g	PROPN
ap-3105	243	3	⊂	⊂	PROPN
ap-3105	243	4	m̃	m̃	PROPN
ap-3105	243	5	is	be	AUX
ap-3105	243	6	an	an	DET
ap-3105	243	7	open	open	ADJ
ap-3105	243	8	set	set	NOUN
ap-3105	243	9	with	with	ADP
ap-3105	243	10	a	a	DET
ap-3105	243	11	piecewise	piecewise	NOUN
ap-3105	243	12	smooth	smooth	ADJ
ap-3105	243	13	boundary	boundary	NOUN
ap-3105	243	14	,	,	PUNCT
ap-3105	243	15	χg	χg	NOUN
ap-3105	243	16	is	be	AUX
ap-3105	243	17	the	the	DET
ap-3105	243	18	characteristic	characteristic	ADJ
ap-3105	243	19	function	function	NOUN
ap-3105	243	20	of	of	ADP
ap-3105	243	21	g	g	NOUN
ap-3105	243	22	,	,	PUNCT
ap-3105	243	23	−→n	−→n	VERB
ap-3105	243	24	is	be	AUX
ap-3105	243	25	the	the	DET
ap-3105	243	26	normalized	normalize	VERB
ap-3105	243	27	outer	outer	ADJ
ap-3105	243	28	normal	normal	ADJ
ap-3105	243	29	vector	vector	NOUN
ap-3105	243	30	field	field	NOUN
ap-3105	243	31	on	on	ADP
ap-3105	243	32	∂g	∂g	PROPN
ap-3105	243	33	and	and	CCONJ
ap-3105	243	34	η	η	PROPN
ap-3105	243	35	is	be	AUX
ap-3105	243	36	a	a	DET
ap-3105	243	37	smooth	smooth	ADJ
ap-3105	243	38	function	function	NOUN
ap-3105	243	39	on	on	ADP
ap-3105	243	40	m̃	m̃	PROPN
ap-3105	243	41	then	then	ADV
ap-3105	243	42	,	,	PUNCT
ap-3105	243	43	in	in	ADP
ap-3105	243	44	the	the	DET
ap-3105	243	45	sense	sense	NOUN
ap-3105	243	46	of	of	ADP
ap-3105	243	47	distributions	distribution	NOUN
ap-3105	243	48	,	,	PUNCT
ap-3105	243	49	∆(ηχg	∆(ηχg	NOUN
ap-3105	243	50	)	)	PUNCT
ap-3105	243	51	=	=	PUNCT
ap-3105	244	1	(	(	PUNCT
ap-3105	244	2	∆η)χg	∆η)χg	PROPN
ap-3105	244	3	−	−	PROPN
ap-3105	244	4	∂η	∂η	PROPN
ap-3105	244	5	∂−→n	∂−→n	PROPN
ap-3105	244	6	δ∂g	δ∂g	NOUN
ap-3105	244	7	−	−	NOUN
ap-3105	244	8	∂	∂	NOUN
ap-3105	244	9	∂−→n	∂−→n	PROPN
ap-3105	244	10	(	(	PUNCT
ap-3105	244	11	ηδ∂g	ηδ∂g	PROPN
ap-3105	244	12	)	)	PUNCT
ap-3105	244	13	.	.	PUNCT
ap-3105	245	1	(	(	PUNCT
ap-3105	245	2	16	16	NUM
ap-3105	245	3	)	)	PUNCT
ap-3105	245	4	the	the	DET
ap-3105	245	5	distribution	distribution	NOUN
ap-3105	245	6	δ∂g	δ∂g	NOUN
ap-3105	245	7	is	be	AUX
ap-3105	245	8	a	a	DET
ap-3105	245	9	single	single	ADJ
ap-3105	245	10	layer	layer	NOUN
ap-3105	245	11	supported	support	VERB
ap-3105	245	12	on	on	ADP
ap-3105	245	13	the	the	DET
ap-3105	245	14	curve	curve	NOUN
ap-3105	245	15	∂g	∂g	PROPN
ap-3105	245	16	and	and	CCONJ
ap-3105	245	17	fulfilling	fulfil	VERB
ap-3105	245	18	∀ϕ	∀ϕ	PROPN
ap-3105	245	19	∈	∈	PROPN
ap-3105	245	20	c∞0	c∞0	PROPN
ap-3105	245	21	(	(	PUNCT
ap-3105	245	22	m̃	m̃	PROPN
ap-3105	245	23	)	)	PUNCT
ap-3105	245	24	,	,	PUNCT
ap-3105	245	25	δ∂g(ϕ	δ∂g(ϕ	NOUN
ap-3105	245	26	)	)	PUNCT
ap-3105	245	27	=	=	SYM
ap-3105	246	1	∫	∫	PROPN
ap-3105	247	1	∂g	∂g	PROPN
ap-3105	247	2	ϕd	ϕd	X
ap-3105	247	3	`	`	PUNCT
ap-3105	247	4	.	.	PUNCT
ap-3105	248	1	the	the	DET
ap-3105	248	2	double	double	ADJ
ap-3105	248	3	layer	layer	NOUN
ap-3105	248	4	∂/∂−→n	∂/∂−→n	NOUN
ap-3105	248	5	(	(	PUNCT
ap-3105	248	6	ηδ∂g	ηδ∂g	PROPN
ap-3105	248	7	)	)	PUNCT
ap-3105	248	8	is	be	AUX
ap-3105	248	9	defined	define	VERB
ap-3105	248	10	by	by	ADP
ap-3105	248	11	∀ϕ	∀ϕ	PROPN
ap-3105	248	12	∈	∈	PROPN
ap-3105	248	13	c∞0	c∞0	PROPN
ap-3105	248	14	(	(	PUNCT
ap-3105	248	15	m̃	m̃	PROPN
ap-3105	248	16	)	)	PUNCT
ap-3105	248	17	,	,	PUNCT
ap-3105	248	18	(	(	PUNCT
ap-3105	248	19	∂	∂	NUM
ap-3105	248	20	∂−→n	∂−→n	PROPN
ap-3105	248	21	(	(	PUNCT
ap-3105	248	22	ηδ∂g	ηδ∂g	PROPN
ap-3105	248	23	)	)	PUNCT
ap-3105	248	24	)	)	PUNCT
ap-3105	249	1	(	(	PUNCT
ap-3105	249	2	ϕ	ϕ	NOUN
ap-3105	249	3	)	)	PUNCT
ap-3105	249	4	=	=	PUNCT
ap-3105	250	1	−	−	NOUN
ap-3105	250	2	∫	∫	PROPN
ap-3105	251	1	∂g	∂g	PROPN
ap-3105	251	2	∂ϕ	∂ϕ	PROPN
ap-3105	252	1	∂−→n	∂−→n	PROPN
ap-3105	252	2	d	d	PROPN
ap-3105	252	3	`	`	PUNCT
ap-3105	252	4	.	.	PUNCT
ap-3105	253	1	229	229	NUM
ap-3105	253	2	petra	petra	PROPN
ap-3105	253	3	košťáková	košťáková	PROPN
ap-3105	253	4	,	,	PUNCT
ap-3105	253	5	pavel	pavel	PROPN
ap-3105	253	6	šťovíček	šťovíček	PROPN
ap-3105	253	7	acta	acta	PROPN
ap-3105	253	8	polytechnica	polytechnica	PROPN
ap-3105	253	9	3.3	3.3	NUM
ap-3105	253	10	.	.	PUNCT
ap-3105	254	1	verification	verification	NOUN
ap-3105	254	2	of	of	ADP
ap-3105	254	3	the	the	DET
ap-3105	254	4	propagator	propagator	NOUN
ap-3105	254	5	formula	formula	NOUN
ap-3105	254	6	we	we	PRON
ap-3105	254	7	have	have	VERB
ap-3105	254	8	to	to	PART
ap-3105	254	9	show	show	VERB
ap-3105	254	10	that	that	SCONJ
ap-3105	254	11	,	,	PUNCT
ap-3105	254	12	for	for	ADP
ap-3105	254	13	x0	x0	PROPN
ap-3105	254	14	∈	∈	PROPN
ap-3105	254	15	m̃	m̃	PROPN
ap-3105	254	16	fixed	fix	VERB
ap-3105	254	17	,	,	PUNCT
ap-3105	254	18	the	the	DET
ap-3105	254	19	propagator	propagator	NOUN
ap-3105	254	20	k(t	k(t	PROPN
ap-3105	254	21	,	,	PUNCT
ap-3105	254	22	x	x	PRON
ap-3105	254	23	,	,	PUNCT
ap-3105	254	24	x0	x0	PROPN
ap-3105	254	25	)	)	PUNCT
ap-3105	254	26	defined	define	VERB
ap-3105	254	27	in	in	ADP
ap-3105	254	28	(	(	PUNCT
ap-3105	254	29	9	9	NUM
ap-3105	254	30	)	)	PUNCT
ap-3105	254	31	,	,	PUNCT
ap-3105	254	32	(	(	PUNCT
ap-3105	254	33	10	10	X
ap-3105	254	34	)	)	PUNCT
ap-3105	254	35	verifies	verifie	NOUN
ap-3105	254	36	the	the	DET
ap-3105	254	37	condition	condition	NOUN
ap-3105	254	38	(	(	PUNCT
ap-3105	254	39	i	i	NOUN
ap-3105	254	40	∂	∂	NOUN
ap-3105	254	41	∂t	∂t	PROPN
ap-3105	254	42	+	+	CCONJ
ap-3105	254	43	∆	∆	X
ap-3105	254	44	)	)	PUNCT
ap-3105	255	1	k(t	k(t	ADJ
ap-3105	255	2	,	,	PUNCT
ap-3105	255	3	x	x	X
ap-3105	255	4	,	,	PUNCT
ap-3105	255	5	x0	x0	PROPN
ap-3105	255	6	)	)	PUNCT
ap-3105	255	7	=	=	PUNCT
ap-3105	255	8	iδ(t)δ(x	iδ(t)δ(x	ADJ
ap-3105	255	9	,	,	PUNCT
ap-3105	255	10	x0	x0	PROPN
ap-3105	255	11	)	)	PUNCT
ap-3105	255	12	on	on	ADP
ap-3105	255	13	r×	r×	PROPN
ap-3105	255	14	m̃.	m̃.	PROPN
ap-3105	255	15	(	(	PUNCT
ap-3105	255	16	17	17	NUM
ap-3105	255	17	)	)	PUNCT
ap-3105	255	18	this	this	PRON
ap-3105	255	19	is	be	AUX
ap-3105	255	20	equivalent	equivalent	ADJ
ap-3105	255	21	to	to	ADP
ap-3105	255	22	showing	show	VERB
ap-3105	255	23	that	that	SCONJ
ap-3105	255	24	lim	lim	PROPN
ap-3105	255	25	t→0	t→0	AUX
ap-3105	255	26	+	+	CCONJ
ap-3105	255	27	k(t	k(t	PROPN
ap-3105	255	28	,	,	PUNCT
ap-3105	255	29	x	x	X
ap-3105	255	30	,	,	PUNCT
ap-3105	255	31	x0	x0	PROPN
ap-3105	255	32	)	)	PUNCT
ap-3105	256	1	=	=	SYM
ap-3105	256	2	δ(x	δ(x	PROPN
ap-3105	256	3	,	,	PUNCT
ap-3105	256	4	x0	x0	PROPN
ap-3105	256	5	)	)	PUNCT
ap-3105	256	6	(	(	PUNCT
ap-3105	256	7	18	18	NUM
ap-3105	256	8	)	)	PUNCT
ap-3105	256	9	and	and	CCONJ
ap-3105	256	10	(	(	PUNCT
ap-3105	256	11	i	i	NOUN
ap-3105	256	12	∂	∂	NOUN
ap-3105	256	13	∂t	∂t	PROPN
ap-3105	256	14	+	+	CCONJ
ap-3105	256	15	∆	∆	X
ap-3105	256	16	)	)	PUNCT
ap-3105	257	1	k(t	k(t	ADJ
ap-3105	257	2	,	,	PUNCT
ap-3105	257	3	x	x	X
ap-3105	257	4	,	,	PUNCT
ap-3105	257	5	x0	x0	PROPN
ap-3105	257	6	)	)	PUNCT
ap-3105	258	1	=	=	SYM
ap-3105	258	2	0	0	NUM
ap-3105	259	1	for	for	ADP
ap-3105	259	2	t	t	PROPN
ap-3105	259	3	>	>	X
ap-3105	259	4	0	0	PROPN
ap-3105	259	5	,	,	PUNCT
ap-3105	259	6	x	x	SYM
ap-3105	259	7	∈	∈	PROPN
ap-3105	259	8	m̃.	m̃.	NOUN
ap-3105	259	9	(	(	PUNCT
ap-3105	259	10	19	19	NUM
ap-3105	259	11	)	)	PUNCT
ap-3105	259	12	equation	equation	NOUN
ap-3105	259	13	(	(	PUNCT
ap-3105	259	14	18	18	NUM
ap-3105	259	15	)	)	PUNCT
ap-3105	259	16	is	be	AUX
ap-3105	259	17	obvious	obvious	ADJ
ap-3105	259	18	.	.	PUNCT
ap-3105	260	1	in	in	ADP
ap-3105	260	2	fact	fact	NOUN
ap-3105	260	3	,	,	PUNCT
ap-3105	260	4	since	since	SCONJ
ap-3105	260	5	the	the	DET
ap-3105	260	6	form	form	NOUN
ap-3105	260	7	of	of	ADP
ap-3105	260	8	z(t	z(t	NOUN
ap-3105	260	9	,	,	PUNCT
ap-3105	260	10	x	x	PRON
ap-3105	260	11	,	,	PUNCT
ap-3105	260	12	x0	x0	PROPN
ap-3105	260	13	)	)	PUNCT
ap-3105	260	14	on	on	ADP
ap-3105	260	15	the	the	DET
ap-3105	260	16	sheet	sheet	NOUN
ap-3105	260	17	{	{	PUNCT
ap-3105	260	18	x;χ(x	x;χ(x	PROPN
ap-3105	260	19	,	,	PUNCT
ap-3105	260	20	x0	x0	PROPN
ap-3105	260	21	)	)	PUNCT
ap-3105	260	22	=	=	SYM
ap-3105	260	23	1	1	X
ap-3105	260	24	}	}	PUNCT
ap-3105	260	25	is	be	AUX
ap-3105	260	26	that	that	PRON
ap-3105	260	27	of	of	ADP
ap-3105	260	28	the	the	DET
ap-3105	260	29	free	free	ADJ
ap-3105	260	30	propagator	propagator	NOUN
ap-3105	260	31	on	on	ADP
ap-3105	260	32	r2	r2	PROPN
ap-3105	260	33	we	we	PRON
ap-3105	260	34	have	have	VERB
ap-3105	260	35	lim	lim	NOUN
ap-3105	260	36	t→0	t→0	PROPN
ap-3105	260	37	+	+	CCONJ
ap-3105	260	38	z(t	z(t	NOUN
ap-3105	260	39	,	,	PUNCT
ap-3105	260	40	x	x	PRON
ap-3105	260	41	,	,	PUNCT
ap-3105	260	42	x0	x0	PROPN
ap-3105	260	43	)	)	PUNCT
ap-3105	261	1	=	=	SYM
ap-3105	261	2	δ(x	δ(x	PROPN
ap-3105	261	3	,	,	PUNCT
ap-3105	261	4	x0	x0	PROPN
ap-3105	261	5	)	)	PUNCT
ap-3105	261	6	.	.	PUNCT
ap-3105	262	1	by	by	ADP
ap-3105	262	2	a	a	DET
ap-3105	262	3	similar	similar	ADJ
ap-3105	262	4	reasoning	reasoning	NOUN
ap-3105	262	5	,	,	PUNCT
ap-3105	262	6	limt→0	limt→0	PROPN
ap-3105	262	7	+	+	X
ap-3105	262	8	z(t	z(t	PROPN
ap-3105	262	9	,	,	PUNCT
ap-3105	262	10	x	x	X
ap-3105	262	11	,	,	PUNCT
ap-3105	262	12	c	c	NOUN
ap-3105	262	13	)	)	PUNCT
ap-3105	262	14	=	=	SYM
ap-3105	262	15	0	0	PUNCT
ap-3105	263	1	if	if	SCONJ
ap-3105	263	2	c	c	PROPN
ap-3105	263	3	∈	∈	VERB
ap-3105	263	4	a	a	DET
ap-3105	263	5	∪	∪	NOUN
ap-3105	263	6	b	b	NOUN
ap-3105	263	7	and	and	CCONJ
ap-3105	263	8	x	x	NOUN
ap-3105	263	9	runs	run	NOUN
ap-3105	263	10	over	over	ADP
ap-3105	263	11	m̃	m̃	PROPN
ap-3105	263	12	.	.	PUNCT
ap-3105	264	1	hence	hence	ADV
ap-3105	264	2	lim	lim	PROPN
ap-3105	264	3	t→0	t→0	PROPN
ap-3105	264	4	+	+	CCONJ
ap-3105	264	5	kγ(t	kγ(t	NOUN
ap-3105	264	6	,	,	PUNCT
ap-3105	264	7	x	x	PRON
ap-3105	264	8	,	,	PUNCT
ap-3105	264	9	x0	x0	PROPN
ap-3105	264	10	)	)	PUNCT
ap-3105	265	1	=	=	SYM
ap-3105	265	2	0	0	PUNCT
ap-3105	265	3	if	if	SCONJ
ap-3105	265	4	|γ|	|γ|	PROPN
ap-3105	265	5	≥	≥	NOUN
ap-3105	265	6	1	1	NUM
ap-3105	265	7	.	.	PUNCT
ap-3105	266	1	concerning	concern	VERB
ap-3105	266	2	(	(	PUNCT
ap-3105	266	3	19	19	NUM
ap-3105	266	4	)	)	PUNCT
ap-3105	266	5	,	,	PUNCT
ap-3105	266	6	we	we	PRON
ap-3105	266	7	first	first	ADV
ap-3105	266	8	introduce	introduce	VERB
ap-3105	266	9	some	some	DET
ap-3105	266	10	notation	notation	NOUN
ap-3105	266	11	related	relate	VERB
ap-3105	266	12	to	to	ADP
ap-3105	266	13	the	the	DET
ap-3105	266	14	geometry	geometry	NOUN
ap-3105	266	15	of	of	ADP
ap-3105	266	16	the	the	DET
ap-3105	266	17	universal	universal	ADJ
ap-3105	266	18	covering	covering	NOUN
ap-3105	266	19	space	space	NOUN
ap-3105	266	20	.	.	PUNCT
ap-3105	267	1	denote	denote	VERB
ap-3105	267	2	by	by	ADP
ap-3105	267	3	%	%	NOUN
ap-3105	267	4	the	the	DET
ap-3105	267	5	distance	distance	NOUN
ap-3105	267	6	dist(a	dist(a	PROPN
ap-3105	267	7	,	,	PUNCT
ap-3105	267	8	b	b	NOUN
ap-3105	267	9	)	)	PUNCT
ap-3105	267	10	.	.	PUNCT
ap-3105	268	1	observe	observe	VERB
ap-3105	268	2	that	that	SCONJ
ap-3105	268	3	if	if	SCONJ
ap-3105	268	4	c1	c1	PROPN
ap-3105	268	5	,	,	PUNCT
ap-3105	268	6	c2	c2	PROPN
ap-3105	268	7	∈	∈	PROPN
ap-3105	268	8	a	a	DET
ap-3105	268	9	∪	∪	NOUN
ap-3105	268	10	b	b	NOUN
ap-3105	268	11	then	then	ADV
ap-3105	268	12	χ(c1	χ(c1	NOUN
ap-3105	268	13	,	,	PUNCT
ap-3105	268	14	c2	c2	PROPN
ap-3105	268	15	)	)	PUNCT
ap-3105	268	16	=	=	PUNCT
ap-3105	268	17	1	1	NUM
ap-3105	268	18	if	if	SCONJ
ap-3105	268	19	and	and	CCONJ
ap-3105	268	20	only	only	ADV
ap-3105	268	21	if	if	SCONJ
ap-3105	268	22	dist(c1	dist(c1	NOUN
ap-3105	268	23	,	,	PUNCT
ap-3105	268	24	c2	c2	PROPN
ap-3105	268	25	)	)	PUNCT
ap-3105	269	1	=	=	PUNCT
ap-3105	269	2	%	%	INTJ
ap-3105	269	3	.	.	PUNCT
ap-3105	270	1	if	if	SCONJ
ap-3105	270	2	this	this	PRON
ap-3105	270	3	is	be	AUX
ap-3105	270	4	the	the	DET
ap-3105	270	5	case	case	NOUN
ap-3105	270	6	then	then	ADV
ap-3105	270	7	necessarily	necessarily	ADV
ap-3105	270	8	c1	c1	PROPN
ap-3105	270	9	∈	∈	PROPN
ap-3105	270	10	a	a	PRON
ap-3105	270	11	and	and	CCONJ
ap-3105	270	12	c2	c2	PROPN
ap-3105	270	13	∈	∈	PROPN
ap-3105	270	14	b	b	PROPN
ap-3105	270	15	or	or	CCONJ
ap-3105	270	16	vice	vice	NOUN
ap-3105	270	17	versa	versa	ADV
ap-3105	270	18	.	.	PUNCT
ap-3105	271	1	for	for	ADP
ap-3105	271	2	x	x	PROPN
ap-3105	271	3	∈	∈	PROPN
ap-3105	271	4	m̃	m̃	PROPN
ap-3105	271	5	∪	∪	VERB
ap-3105	271	6	a	a	DET
ap-3105	271	7	∪	∪	X
ap-3105	271	8	b	b	NOUN
ap-3105	271	9	set	set	NOUN
ap-3105	271	10	d(x	d(x	NOUN
ap-3105	271	11	)	)	PUNCT
ap-3105	272	1	=	=	PRON
ap-3105	272	2	{	{	PUNCT
ap-3105	272	3	y	y	PROPN
ap-3105	272	4	∈	∈	PROPN
ap-3105	272	5	m̃	m̃	PROPN
ap-3105	272	6	;	;	PUNCT
ap-3105	272	7	χ(x	χ(x	PROPN
ap-3105	272	8	,	,	PUNCT
ap-3105	272	9	y	y	PROPN
ap-3105	272	10	)	)	PUNCT
ap-3105	272	11	=	=	SYM
ap-3105	272	12	1	1	NUM
ap-3105	272	13	}	}	PUNCT
ap-3105	272	14	.	.	PUNCT
ap-3105	273	1	(	(	PUNCT
ap-3105	273	2	20	20	NUM
ap-3105	273	3	)	)	PUNCT
ap-3105	273	4	if	if	SCONJ
ap-3105	273	5	x	x	PROPN
ap-3105	273	6	∈	∈	PROPN
ap-3105	273	7	m̃	m̃	PROPN
ap-3105	273	8	then	then	ADV
ap-3105	273	9	d(x	d(x	PROPN
ap-3105	273	10	)	)	PUNCT
ap-3105	273	11	can	can	AUX
ap-3105	273	12	be	be	AUX
ap-3105	273	13	identified	identify	VERB
ap-3105	273	14	with	with	ADP
ap-3105	273	15	the	the	DET
ap-3105	273	16	plane	plane	NOUN
ap-3105	273	17	cut	cut	VERB
ap-3105	273	18	along	along	ADP
ap-3105	273	19	two	two	NUM
ap-3105	273	20	half	half	ADJ
ap-3105	273	21	-	-	PUNCT
ap-3105	273	22	lines	line	NOUN
ap-3105	273	23	with	with	ADP
ap-3105	273	24	the	the	DET
ap-3105	273	25	limit	limit	NOUN
ap-3105	273	26	points	point	VERB
ap-3105	273	27	a	a	PRON
ap-3105	273	28	and	and	CCONJ
ap-3105	273	29	b	b	NOUN
ap-3105	273	30	,	,	PUNCT
ap-3105	273	31	respectively	respectively	ADV
ap-3105	273	32	.	.	PUNCT
ap-3105	274	1	the	the	DET
ap-3105	274	2	border	border	NOUN
ap-3105	274	3	of	of	ADP
ap-3105	274	4	d(x	d(x	PROPN
ap-3105	274	5	)	)	PUNCT
ap-3105	274	6	consists	consist	VERB
ap-3105	274	7	of	of	ADP
ap-3105	274	8	two	two	NUM
ap-3105	274	9	pairs	pair	NOUN
ap-3105	274	10	of	of	ADP
ap-3105	274	11	half	half	ADJ
ap-3105	274	12	-	-	PUNCT
ap-3105	274	13	lines	line	NOUN
ap-3105	274	14	.	.	PUNCT
ap-3105	275	1	one	one	NUM
ap-3105	275	2	pair	pair	NOUN
ap-3105	275	3	has	have	VERB
ap-3105	275	4	a	a	DET
ap-3105	275	5	common	common	ADJ
ap-3105	275	6	limit	limit	NOUN
ap-3105	275	7	point	point	NOUN
ap-3105	275	8	a	a	DET
ap-3105	275	9	∈	∈	PROPN
ap-3105	275	10	a	a	PRON
ap-3105	275	11	and	and	CCONJ
ap-3105	275	12	is	be	AUX
ap-3105	275	13	denoted	denote	VERB
ap-3105	275	14	∂d(x;a	∂d(x;a	PROPN
ap-3105	275	15	)	)	PUNCT
ap-3105	275	16	,	,	PUNCT
ap-3105	275	17	the	the	DET
ap-3105	275	18	other	other	ADJ
ap-3105	275	19	pair	pair	NOUN
ap-3105	275	20	has	have	VERB
ap-3105	275	21	a	a	DET
ap-3105	275	22	common	common	ADJ
ap-3105	275	23	limit	limit	NOUN
ap-3105	275	24	point	point	NOUN
ap-3105	275	25	b	b	PROPN
ap-3105	275	26	∈	∈	PROPN
ap-3105	275	27	b	b	NOUN
ap-3105	275	28	and	and	CCONJ
ap-3105	275	29	is	be	AUX
ap-3105	275	30	denoted	denote	VERB
ap-3105	275	31	∂d(x;b	∂d(x;b	NUM
ap-3105	275	32	)	)	PUNCT
ap-3105	275	33	.	.	PUNCT
ap-3105	276	1	we	we	PRON
ap-3105	276	2	have	have	VERB
ap-3105	276	3	∂d(x	∂d(x	NOUN
ap-3105	276	4	)	)	PUNCT
ap-3105	276	5	=	=	SYM
ap-3105	277	1	∂d(x;a	∂d(x;a	PROPN
ap-3105	277	2	)	)	PUNCT
ap-3105	277	3	∪	∪	ADP
ap-3105	277	4	∂d(x;b	∂d(x;b	NUM
ap-3105	277	5	)	)	PUNCT
ap-3105	277	6	.	.	PUNCT
ap-3105	278	1	(	(	PUNCT
ap-3105	278	2	21	21	NUM
ap-3105	278	3	)	)	PUNCT
ap-3105	278	4	if	if	SCONJ
ap-3105	278	5	c	c	PROPN
ap-3105	278	6	∈	∈	PROPN
ap-3105	278	7	a∪b	a∪b	NOUN
ap-3105	278	8	then	then	ADV
ap-3105	278	9	d(c	d(c	PROPN
ap-3105	278	10	)	)	PUNCT
ap-3105	278	11	resembles	resemble	VERB
ap-3105	278	12	the	the	DET
ap-3105	278	13	universal	universal	ADJ
ap-3105	278	14	covering	covering	NOUN
ap-3105	278	15	space	space	NOUN
ap-3105	278	16	in	in	ADP
ap-3105	278	17	the	the	DET
ap-3105	278	18	one	one	NUM
ap-3105	278	19	-	-	PUNCT
ap-3105	278	20	vortex	vortex	NOUN
ap-3105	278	21	case	case	NOUN
ap-3105	278	22	.	.	PUNCT
ap-3105	279	1	it	it	PRON
ap-3105	279	2	can	can	AUX
ap-3105	279	3	be	be	AUX
ap-3105	279	4	viewed	view	VERB
ap-3105	279	5	as	as	ADP
ap-3105	279	6	a	a	DET
ap-3105	279	7	union	union	NOUN
ap-3105	279	8	of	of	ADP
ap-3105	279	9	countably	countably	ADV
ap-3105	279	10	many	many	ADJ
ap-3105	279	11	sheets	sheet	NOUN
ap-3105	279	12	glued	glue	VERB
ap-3105	279	13	together	together	ADV
ap-3105	279	14	in	in	ADP
ap-3105	279	15	a	a	DET
ap-3105	279	16	staircase	staircase	NOUN
ap-3105	279	17	-	-	PUNCT
ap-3105	279	18	like	like	ADJ
ap-3105	279	19	way	way	NOUN
ap-3105	279	20	.	.	PUNCT
ap-3105	280	1	each	each	DET
ap-3105	280	2	sheet	sheet	NOUN
ap-3105	280	3	contributes	contribute	VERB
ap-3105	280	4	to	to	ADP
ap-3105	280	5	the	the	DET
ap-3105	280	6	border	border	NOUN
ap-3105	280	7	of	of	ADP
ap-3105	280	8	d(c	d(c	PROPN
ap-3105	280	9	)	)	PUNCT
ap-3105	280	10	by	by	ADP
ap-3105	280	11	a	a	DET
ap-3105	280	12	pair	pair	NOUN
ap-3105	280	13	of	of	ADP
ap-3105	280	14	half	half	ADJ
ap-3105	280	15	-	-	PUNCT
ap-3105	280	16	lines	line	NOUN
ap-3105	280	17	with	with	ADP
ap-3105	280	18	a	a	DET
ap-3105	280	19	common	common	ADJ
ap-3105	280	20	limit	limit	NOUN
ap-3105	280	21	point	point	NOUN
ap-3105	280	22	c	c	NOUN
ap-3105	280	23	′.	′.	NOUN
ap-3105	280	24	thus	thus	ADV
ap-3105	280	25	the	the	DET
ap-3105	280	26	border	border	NOUN
ap-3105	280	27	∂d(c	∂d(c	NOUN
ap-3105	280	28	)	)	PUNCT
ap-3105	280	29	is	be	AUX
ap-3105	280	30	formed	form	VERB
ap-3105	280	31	by	by	ADP
ap-3105	280	32	a	a	DET
ap-3105	280	33	countable	countable	ADJ
ap-3105	280	34	union	union	NOUN
ap-3105	280	35	of	of	ADP
ap-3105	280	36	pairs	pair	NOUN
ap-3105	280	37	of	of	ADP
ap-3105	280	38	half	half	ADJ
ap-3105	280	39	-	-	PUNCT
ap-3105	280	40	lines	line	NOUN
ap-3105	280	41	:	:	PUNCT
ap-3105	280	42	∂d(c	∂d(c	NUM
ap-3105	280	43	)	)	PUNCT
ap-3105	280	44	=	=	SYM
ap-3105	280	45	⋃	⋃	NOUN
ap-3105	280	46	c′∈d	c′∈d	NOUN
ap-3105	280	47	,	,	PUNCT
ap-3105	280	48	dist(c	dist(c	ADJ
ap-3105	280	49	,	,	PUNCT
ap-3105	280	50	c′)=%	c′)=%	PROPN
ap-3105	280	51	∂d(c;c	∂d(c;c	PROPN
ap-3105	280	52	′	′	NUM
ap-3105	280	53	)	)	PUNCT
ap-3105	280	54	,	,	PUNCT
ap-3105	280	55	(	(	PUNCT
ap-3105	280	56	22	22	NUM
ap-3105	280	57	)	)	PUNCT
ap-3105	281	1	where	where	SCONJ
ap-3105	281	2	d	d	NOUN
ap-3105	281	3	=	=	SYM
ap-3105	281	4	b	b	PROPN
ap-3105	281	5	if	if	SCONJ
ap-3105	281	6	c	c	PROPN
ap-3105	281	7	∈	∈	PROPN
ap-3105	281	8	a	a	PRON
ap-3105	281	9	and	and	CCONJ
ap-3105	281	10	d	d	NOUN
ap-3105	281	11	=	=	PUNCT
ap-3105	281	12	a	a	PRON
ap-3105	281	13	if	if	SCONJ
ap-3105	281	14	c	c	PROPN
ap-3105	281	15	∈	∈	PROPN
ap-3105	281	16	b.	b.	PROPN
ap-3105	281	17	let	let	VERB
ap-3105	281	18	us	we	PRON
ap-3105	281	19	first	first	ADV
ap-3105	281	20	examine	examine	VERB
ap-3105	281	21	the	the	DET
ap-3105	281	22	case	case	NOUN
ap-3105	281	23	|γ|	|γ|	PROPN
ap-3105	281	24	=	=	SYM
ap-3105	281	25	0	0	X
ap-3105	281	26	.	.	PUNCT
ap-3105	282	1	one	one	PRON
ap-3105	282	2	has	have	VERB
ap-3105	282	3	(	(	PUNCT
ap-3105	282	4	i	i	NOUN
ap-3105	282	5	∂	∂	NOUN
ap-3105	282	6	∂t	∂t	PROPN
ap-3105	282	7	+	+	CCONJ
ap-3105	282	8	∆	∆	X
ap-3105	282	9	)	)	PUNCT
ap-3105	283	1	z(t	z(t	NOUN
ap-3105	283	2	,	,	PUNCT
ap-3105	283	3	x	x	PRON
ap-3105	283	4	,	,	PUNCT
ap-3105	283	5	x0	x0	PROPN
ap-3105	283	6	)	)	PUNCT
ap-3105	284	1	=	=	SYM
ap-3105	284	2	0	0	NUM
ap-3105	285	1	for	for	ADP
ap-3105	285	2	t	t	PROPN
ap-3105	285	3	>	>	X
ap-3105	285	4	0	0	PUNCT
ap-3105	286	1	and	and	CCONJ
ap-3105	286	2	x	x	PROPN
ap-3105	286	3	∈	∈	PROPN
ap-3105	286	4	d(x0	d(x0	NOUN
ap-3105	286	5	)	)	PUNCT
ap-3105	286	6	.	.	PUNCT
ap-3105	287	1	observe	observe	VERB
ap-3105	287	2	also	also	ADV
ap-3105	287	3	that	that	SCONJ
ap-3105	287	4	∂	∂	NUM
ap-3105	287	5	∂−→n	∂−→n	PROPN
ap-3105	287	6	z(t	z(t	PROPN
ap-3105	287	7	,	,	PUNCT
ap-3105	287	8	x	x	PRON
ap-3105	287	9	,	,	PUNCT
ap-3105	287	10	x0	x0	PROPN
ap-3105	287	11	)	)	PUNCT
ap-3105	288	1	=	=	SYM
ap-3105	288	2	0	0	NUM
ap-3105	289	1	for	for	ADP
ap-3105	289	2	x	x	PROPN
ap-3105	289	3	∈	∈	PROPN
ap-3105	289	4	∂d(x0	∂d(x0	NOUN
ap-3105	289	5	)	)	PUNCT
ap-3105	289	6	.	.	PUNCT
ap-3105	290	1	this	this	PRON
ap-3105	290	2	is	be	AUX
ap-3105	290	3	so	so	ADV
ap-3105	290	4	since	since	SCONJ
ap-3105	290	5	,	,	PUNCT
ap-3105	290	6	in	in	ADP
ap-3105	290	7	polar	polar	ADJ
ap-3105	290	8	coordinates	coordinate	NOUN
ap-3105	290	9	centered	center	VERB
ap-3105	290	10	at	at	ADP
ap-3105	290	11	x0	x0	PROPN
ap-3105	290	12	,	,	PUNCT
ap-3105	290	13	z(t	z(t	PROPN
ap-3105	290	14	,	,	PUNCT
ap-3105	290	15	x	x	PRON
ap-3105	290	16	,	,	PUNCT
ap-3105	290	17	x0	x0	PROPN
ap-3105	290	18	)	)	PUNCT
ap-3105	290	19	does	do	AUX
ap-3105	290	20	not	not	PART
ap-3105	290	21	depend	depend	VERB
ap-3105	290	22	on	on	ADP
ap-3105	290	23	the	the	DET
ap-3105	290	24	angle	angle	NOUN
ap-3105	290	25	variable	variable	NOUN
ap-3105	290	26	.	.	PUNCT
ap-3105	291	1	let	let	VERB
ap-3105	291	2	us	we	PRON
ap-3105	291	3	also	also	ADV
ap-3105	291	4	note	note	VERB
ap-3105	291	5	that	that	SCONJ
ap-3105	291	6	z(t	z(t	NOUN
ap-3105	291	7	,	,	PUNCT
ap-3105	291	8	x	x	PRON
ap-3105	291	9	,	,	PUNCT
ap-3105	291	10	x0	x0	PROPN
ap-3105	291	11	)	)	PUNCT
ap-3105	291	12	can	can	AUX
ap-3105	291	13	be	be	AUX
ap-3105	291	14	continued	continue	VERB
ap-3105	291	15	smoothly	smoothly	ADV
ap-3105	291	16	in	in	ADP
ap-3105	291	17	the	the	DET
ap-3105	291	18	variable	variable	NOUN
ap-3105	291	19	x	x	NOUN
ap-3105	291	20	over	over	ADP
ap-3105	291	21	the	the	DET
ap-3105	291	22	borderline	borderline	NOUN
ap-3105	291	23	of	of	ADP
ap-3105	291	24	the	the	DET
ap-3105	291	25	domain	domain	NOUN
ap-3105	291	26	d(x0	d(x0	NOUN
ap-3105	291	27	)	)	PUNCT
ap-3105	291	28	.	.	PUNCT
ap-3105	292	1	thus	thus	ADV
ap-3105	292	2	,	,	PUNCT
ap-3105	292	3	in	in	ADP
ap-3105	292	4	virtue	virtue	NOUN
ap-3105	292	5	of	of	ADP
ap-3105	292	6	(	(	PUNCT
ap-3105	292	7	16	16	NUM
ap-3105	292	8	)	)	PUNCT
ap-3105	292	9	,	,	PUNCT
ap-3105	292	10	for	for	ADP
ap-3105	292	11	t	t	PROPN
ap-3105	292	12	>	>	X
ap-3105	292	13	0	0	PUNCT
ap-3105	292	14	and	and	CCONJ
ap-3105	292	15	x	x	SYM
ap-3105	292	16	∈	∈	PROPN
ap-3105	292	17	m̃	m̃	PROPN
ap-3105	292	18	,	,	PUNCT
ap-3105	292	19	(	(	PUNCT
ap-3105	292	20	i	i	NOUN
ap-3105	292	21	∂	∂	NOUN
ap-3105	292	22	∂t	∂t	PROPN
ap-3105	292	23	+	+	CCONJ
ap-3105	292	24	∆	∆	X
ap-3105	292	25	)	)	PUNCT
ap-3105	293	1	z(t	z(t	NOUN
ap-3105	293	2	,	,	PUNCT
ap-3105	293	3	x	x	PRON
ap-3105	293	4	,	,	PUNCT
ap-3105	293	5	x0	x0	PROPN
ap-3105	293	6	)	)	PUNCT
ap-3105	293	7	=	=	SYM
ap-3105	293	8	−	−	PROPN
ap-3105	293	9	∂	∂	NOUN
ap-3105	293	10	∂−→n	∂−→n	PROPN
ap-3105	293	11	(	(	PUNCT
ap-3105	293	12	z(t	z(t	PROPN
ap-3105	293	13	,	,	PUNCT
ap-3105	293	14	x	x	X
ap-3105	293	15	,	,	PUNCT
ap-3105	293	16	x0)δ∂d(x0	x0)δ∂d(x0	NUM
ap-3105	293	17	)	)	PUNCT
ap-3105	293	18	)	)	PUNCT
ap-3105	293	19	.	.	PUNCT
ap-3105	294	1	(	(	PUNCT
ap-3105	294	2	23	23	X
ap-3105	294	3	)	)	PUNCT
ap-3105	294	4	remark	remark	NOUN
ap-3105	294	5	.	.	PUNCT
ap-3105	295	1	in	in	ADP
ap-3105	295	2	(	(	PUNCT
ap-3105	295	3	23	23	NUM
ap-3105	295	4	)	)	PUNCT
ap-3105	295	5	as	as	ADV
ap-3105	295	6	well	well	ADV
ap-3105	295	7	as	as	ADP
ap-3105	295	8	everywhere	everywhere	ADV
ap-3105	295	9	in	in	ADP
ap-3105	295	10	this	this	DET
ap-3105	295	11	section	section	NOUN
ap-3105	295	12	we	we	PRON
ap-3105	295	13	use	use	VERB
ap-3105	295	14	the	the	DET
ap-3105	295	15	following	follow	VERB
ap-3105	295	16	convention	convention	NOUN
ap-3105	295	17	.	.	PUNCT
ap-3105	296	1	the	the	DET
ap-3105	296	2	value	value	NOUN
ap-3105	296	3	of	of	ADP
ap-3105	296	4	a	a	DET
ap-3105	296	5	density	density	NOUN
ap-3105	296	6	(	(	PUNCT
ap-3105	296	7	which	which	PRON
ap-3105	296	8	is	be	AUX
ap-3105	296	9	in	in	ADP
ap-3105	296	10	this	this	DET
ap-3105	296	11	case	case	NOUN
ap-3105	296	12	z(t	z(t	NOUN
ap-3105	296	13	,	,	PUNCT
ap-3105	296	14	x	x	X
ap-3105	296	15	,	,	PUNCT
ap-3105	296	16	x0	x0	PROPN
ap-3105	296	17	)	)	PUNCT
ap-3105	296	18	)	)	PUNCT
ap-3105	296	19	on	on	ADP
ap-3105	296	20	the	the	DET
ap-3105	296	21	border	border	NOUN
ap-3105	296	22	∂d(x0	∂d(x0	NOUN
ap-3105	296	23	)	)	PUNCT
ap-3105	296	24	is	be	AUX
ap-3105	296	25	understood	understand	VERB
ap-3105	296	26	as	as	ADP
ap-3105	296	27	the	the	DET
ap-3105	296	28	limit	limit	NOUN
ap-3105	296	29	value	value	NOUN
ap-3105	296	30	taken	take	VERB
ap-3105	296	31	from	from	ADP
ap-3105	296	32	the	the	DET
ap-3105	296	33	interior	interior	NOUN
ap-3105	296	34	of	of	ADP
ap-3105	296	35	the	the	DET
ap-3105	296	36	domain	domain	NOUN
ap-3105	296	37	d(x0	d(x0	NOUN
ap-3105	296	38	)	)	PUNCT
ap-3105	296	39	.	.	PUNCT
ap-3105	297	1	230	230	NUM
ap-3105	297	2	vol	vol	NOUN
ap-3105	297	3	.	.	PUNCT
ap-3105	298	1	56	56	NUM
ap-3105	298	2	no	no	NOUN
ap-3105	298	3	.	.	PUNCT
ap-3105	299	1	3/2016	3/2016	NUM
ap-3105	299	2	the	the	DET
ap-3105	299	3	aharonov	aharonov	PROPN
ap-3105	299	4	-	-	PUNCT
ap-3105	299	5	bohm	bohm	PROPN
ap-3105	299	6	hamiltonian	hamiltonian	NOUN
ap-3105	299	7	with	with	ADP
ap-3105	299	8	two	two	NUM
ap-3105	299	9	vortices	vortex	NOUN
ap-3105	299	10	revisited	revisit	VERB
ap-3105	299	11	next	next	ADV
ap-3105	299	12	we	we	PRON
ap-3105	299	13	discuss	discuss	VERB
ap-3105	299	14	the	the	DET
ap-3105	299	15	case	case	NOUN
ap-3105	299	16	|γ|	|γ|	ADV
ap-3105	299	17	=	=	SYM
ap-3105	299	18	1	1	X
ap-3105	299	19	.	.	PUNCT
ap-3105	300	1	then	then	ADV
ap-3105	300	2	γ	γ	PROPN
ap-3105	300	3	designates	designate	VERB
ap-3105	300	4	a	a	DET
ap-3105	300	5	piecewise	piecewise	NOUN
ap-3105	300	6	geodesic	geodesic	NOUN
ap-3105	300	7	curve	curve	NOUN
ap-3105	300	8	x0	x0	PROPN
ap-3105	300	9	→	→	SYM
ap-3105	300	10	c	c	PROPN
ap-3105	300	11	→	→	SYM
ap-3105	300	12	x	x	SYM
ap-3105	300	13	,	,	PUNCT
ap-3105	300	14	with	with	ADP
ap-3105	300	15	c	c	PROPN
ap-3105	300	16	∈	∈	PROPN
ap-3105	300	17	a∪b	a∪b	NOUN
ap-3105	300	18	.	.	PUNCT
ap-3105	301	1	denote	denote	VERB
ap-3105	301	2	by	by	ADP
ap-3105	301	3	γ′	γ′	PROPN
ap-3105	301	4	the	the	DET
ap-3105	301	5	geodesic	geodesic	ADJ
ap-3105	301	6	segment	segment	NOUN
ap-3105	301	7	x0	x0	PROPN
ap-3105	301	8	→	→	PUNCT
ap-3105	301	9	x	x	PUNCT
ap-3105	301	10	provided	provide	VERB
ap-3105	301	11	x	x	PROPN
ap-3105	301	12	∈	∈	PROPN
ap-3105	301	13	d(x0	d(x0	NOUN
ap-3105	301	14	)	)	PUNCT
ap-3105	301	15	.	.	PUNCT
ap-3105	302	1	we	we	PRON
ap-3105	302	2	have	have	VERB
ap-3105	302	3	kγ(t	kγ(t	NOUN
ap-3105	302	4	,	,	PUNCT
ap-3105	302	5	x	x	PRON
ap-3105	302	6	,	,	PUNCT
ap-3105	302	7	x0	x0	PROPN
ap-3105	302	8	)	)	PUNCT
ap-3105	303	1	=	=	SYM
ap-3105	303	2	1	1	NUM
ap-3105	303	3	8π2i	8π2i	NUM
ap-3105	303	4	χ(x	χ(x	PROPN
ap-3105	303	5	,	,	PUNCT
ap-3105	303	6	c)χ(c	c)χ(c	X
ap-3105	303	7	,	,	PUNCT
ap-3105	303	8	x0	x0	NUM
ap-3105	303	9	)	)	PUNCT
ap-3105	303	10	×	×	NOUN
ap-3105	303	11	∫	∫	PROPN
ap-3105	303	12	t	t	PROPN
ap-3105	303	13	0	0	NUM
ap-3105	304	1	(	(	PUNCT
ap-3105	304	2	(	(	PUNCT
ap-3105	304	3	θ	θ	NOUN
ap-3105	304	4	−	−	PROPN
ap-3105	304	5	π	π	X
ap-3105	305	1	+	+	CCONJ
ap-3105	305	2	i	i	PRON
ap-3105	305	3	ln	ln	NOUN
ap-3105	305	4	(	(	PUNCT
ap-3105	305	5	t−	t−	PROPN
ap-3105	305	6	s)r0	s)r0	PROPN
ap-3105	305	7	sr	sr	PROPN
ap-3105	305	8	)	)	PUNCT
ap-3105	305	9	−1	−1	NOUN
ap-3105	305	10	−	−	PROPN
ap-3105	306	1	(	(	PUNCT
ap-3105	306	2	θ	θ	PROPN
ap-3105	306	3	+	+	PUNCT
ap-3105	307	1	π	π	PUNCT
ap-3105	308	1	+	+	CCONJ
ap-3105	309	1	i	i	PRON
ap-3105	309	2	ln	ln	NOUN
ap-3105	309	3	(	(	PUNCT
ap-3105	309	4	t−	t−	PROPN
ap-3105	309	5	s)r0	s)r0	PROPN
ap-3105	309	6	sr	sr	PROPN
ap-3105	309	7	)	)	PUNCT
ap-3105	309	8	−1	−1	NOUN
ap-3105	309	9	)	)	PUNCT
ap-3105	309	10	1	1	NUM
ap-3105	309	11	(	(	PUNCT
ap-3105	309	12	t−	t−	PROPN
ap-3105	309	13	s)s	s)s	X
ap-3105	309	14	exp	exp	NOUN
ap-3105	309	15	(	(	PUNCT
ap-3105	309	16	i	i	PRON
ap-3105	309	17	(	(	PUNCT
ap-3105	309	18	r2	r2	PROPN
ap-3105	309	19	4(t−	4(t−	PROPN
ap-3105	309	20	s	s	PART
ap-3105	309	21	)	)	PUNCT
ap-3105	310	1	+	+	NUM
ap-3105	310	2	r2	r2	PROPN
ap-3105	310	3	0	0	NUM
ap-3105	310	4	4s	4s	NUM
ap-3105	310	5	)	)	PUNCT
ap-3105	310	6	)	)	PUNCT
ap-3105	311	1	ds	ds	INTJ
ap-3105	311	2	(	(	PUNCT
ap-3105	311	3	24	24	NUM
ap-3105	311	4	)	)	PUNCT
ap-3105	311	5	where	where	SCONJ
ap-3105	311	6	r	r	NOUN
ap-3105	311	7	=	=	SYM
ap-3105	311	8	dist(x	dist(x	PROPN
ap-3105	311	9	,	,	PUNCT
ap-3105	311	10	c	c	NOUN
ap-3105	311	11	)	)	PUNCT
ap-3105	311	12	,	,	PUNCT
ap-3105	311	13	r0	r0	NOUN
ap-3105	311	14	=	=	SYM
ap-3105	311	15	dist(c	dist(c	PROPN
ap-3105	311	16	,	,	PUNCT
ap-3105	311	17	x0	x0	NUM
ap-3105	311	18	)	)	PUNCT
ap-3105	311	19	and	and	CCONJ
ap-3105	311	20	θ	θ	PROPN
ap-3105	311	21	=	=	SYM
ap-3105	311	22	∠x0	∠x0	PROPN
ap-3105	311	23	,	,	PUNCT
ap-3105	311	24	c	c	X
ap-3105	311	25	,	,	PUNCT
ap-3105	311	26	x.	x.	NOUN
ap-3105	311	27	application	application	NOUN
ap-3105	311	28	of	of	ADP
ap-3105	311	29	the	the	DET
ap-3105	311	30	differential	differential	ADJ
ap-3105	311	31	operator	operator	NOUN
ap-3105	311	32	(	(	PUNCT
ap-3105	311	33	i∂t	i∂t	NOUN
ap-3105	311	34	+	+	CCONJ
ap-3105	311	35	∆	∆	X
ap-3105	311	36	)	)	PUNCT
ap-3105	311	37	to	to	ADP
ap-3105	311	38	the	the	DET
ap-3105	311	39	rhs	rhs	PROPN
ap-3105	311	40	of	of	ADP
ap-3105	311	41	(	(	PUNCT
ap-3105	311	42	24	24	NUM
ap-3105	311	43	)	)	PUNCT
ap-3105	311	44	in	in	ADP
ap-3105	311	45	the	the	DET
ap-3105	311	46	sense	sense	NOUN
ap-3105	311	47	of	of	ADP
ap-3105	311	48	distributions	distribution	NOUN
ap-3105	311	49	results	result	NOUN
ap-3105	311	50	in	in	ADP
ap-3105	311	51	several	several	ADJ
ap-3105	311	52	singular	singular	ADJ
ap-3105	311	53	terms	term	NOUN
ap-3105	311	54	supported	support	VERB
ap-3105	311	55	on	on	ADP
ap-3105	311	56	one	one	NUM
ap-3105	311	57	-	-	PUNCT
ap-3105	311	58	dimensional	dimensional	ADJ
ap-3105	311	59	submanifolds	submanifold	NOUN
ap-3105	311	60	.	.	PUNCT
ap-3105	312	1	first	first	ADV
ap-3105	312	2	,	,	PUNCT
ap-3105	312	3	due	due	ADP
ap-3105	312	4	to	to	ADP
ap-3105	312	5	the	the	DET
ap-3105	312	6	discontinuity	discontinuity	NOUN
ap-3105	312	7	of	of	ADP
ap-3105	312	8	the	the	DET
ap-3105	312	9	characteristic	characteristic	ADJ
ap-3105	312	10	function	function	NOUN
ap-3105	312	11	χ(x	χ(x	PROPN
ap-3105	312	12	,	,	PUNCT
ap-3105	312	13	c	c	NOUN
ap-3105	312	14	)	)	PUNCT
ap-3105	312	15	,	,	PUNCT
ap-3105	312	16	the	the	DET
ap-3105	312	17	application	application	NOUN
ap-3105	312	18	of	of	ADP
ap-3105	312	19	∆	∆	PROPN
ap-3105	312	20	leads	lead	VERB
ap-3105	312	21	to	to	ADP
ap-3105	312	22	two	two	NUM
ap-3105	312	23	terms	term	NOUN
ap-3105	312	24	supported	support	VERB
ap-3105	312	25	on	on	ADP
ap-3105	312	26	the	the	DET
ap-3105	312	27	boundary	boundary	ADJ
ap-3105	312	28	∂d(c	∂d(c	PROPN
ap-3105	312	29	)	)	PUNCT
ap-3105	312	30	(	(	PUNCT
ap-3105	312	31	see	see	VERB
ap-3105	312	32	(	(	PUNCT
ap-3105	312	33	16	16	NUM
ap-3105	312	34	)	)	PUNCT
ap-3105	312	35	)	)	PUNCT
ap-3105	312	36	.	.	PUNCT
ap-3105	313	1	second	second	ADJ
ap-3105	313	2	,	,	PUNCT
ap-3105	313	3	as	as	SCONJ
ap-3105	313	4	it	it	PRON
ap-3105	313	5	follows	follow	VERB
ap-3105	313	6	from	from	ADP
ap-3105	313	7	(	(	PUNCT
ap-3105	313	8	15	15	NUM
ap-3105	313	9	)	)	PUNCT
ap-3105	313	10	,	,	PUNCT
ap-3105	313	11	the	the	DET
ap-3105	313	12	singularity	singularity	NOUN
ap-3105	313	13	of	of	ADP
ap-3105	313	14	the	the	DET
ap-3105	313	15	integrand	integrand	NOUN
ap-3105	313	16	for	for	ADP
ap-3105	313	17	the	the	DET
ap-3105	313	18	values	value	NOUN
ap-3105	313	19	θ	θ	X
ap-3105	313	20	=	=	SYM
ap-3105	313	21	±π	±π	PROPN
ap-3105	313	22	and	and	CCONJ
ap-3105	313	23	r0	r0	NOUN
ap-3105	313	24	/	/	SYM
ap-3105	313	25	s	s	PART
ap-3105	313	26	=	=	PUNCT
ap-3105	313	27	r/(t−	r/(t−	NOUN
ap-3105	313	28	s	s	NOUN
ap-3105	313	29	)	)	PUNCT
ap-3105	313	30	produces	produce	VERB
ap-3105	313	31	terms	term	NOUN
ap-3105	313	32	supported	support	VERB
ap-3105	313	33	on	on	ADP
ap-3105	313	34	the	the	DET
ap-3105	313	35	submanifold	submanifold	NOUN
ap-3105	313	36	determined	determine	VERB
ap-3105	313	37	by	by	ADP
ap-3105	313	38	θ	θ	X
ap-3105	313	39	=	=	SYM
ap-3105	313	40	±π	±π	PROPN
ap-3105	313	41	,	,	PUNCT
ap-3105	313	42	and	and	CCONJ
ap-3105	313	43	this	this	DET
ap-3105	313	44	set	set	NOUN
ap-3105	313	45	is	be	AUX
ap-3105	313	46	nothing	nothing	PRON
ap-3105	313	47	but	but	SCONJ
ap-3105	313	48	a	a	DET
ap-3105	313	49	part	part	NOUN
ap-3105	313	50	of	of	ADP
ap-3105	313	51	the	the	DET
ap-3105	313	52	boundary	boundary	NOUN
ap-3105	313	53	of	of	ADP
ap-3105	313	54	the	the	DET
ap-3105	313	55	domain	domain	NOUN
ap-3105	313	56	d(x0	d(x0	NOUN
ap-3105	313	57	)	)	PUNCT
ap-3105	313	58	,	,	PUNCT
ap-3105	313	59	namely	namely	ADV
ap-3105	313	60	∂d(x0;c	∂d(x0;c	NOUN
ap-3105	313	61	)	)	PUNCT
ap-3105	313	62	.	.	PUNCT
ap-3105	314	1	notice	notice	VERB
ap-3105	314	2	that	that	SCONJ
ap-3105	314	3	for	for	ADP
ap-3105	314	4	θ	θ	X
ap-3105	314	5	=	=	SYM
ap-3105	314	6	±π	±π	NOUN
ap-3105	314	7	it	it	PRON
ap-3105	314	8	holds	hold	VERB
ap-3105	314	9	r	r	NOUN
ap-3105	314	10	+	+	NUM
ap-3105	314	11	r0	r0	NOUN
ap-3105	314	12	=	=	SYM
ap-3105	314	13	dist(x	dist(x	PROPN
ap-3105	314	14	,	,	PUNCT
ap-3105	314	15	x0	x0	PROPN
ap-3105	314	16	)	)	PUNCT
ap-3105	314	17	and	and	CCONJ
ap-3105	314	18	∂/∂−→n	∂/∂−→n	ADJ
ap-3105	314	19	=	=	PROPN
ap-3105	314	20	±r−1∂/∂θ	±r−1∂/∂θ	PROPN
ap-3105	314	21	.	.	PUNCT
ap-3105	315	1	moreover	moreover	ADV
ap-3105	315	2	,	,	PUNCT
ap-3105	315	3	in	in	ADP
ap-3105	315	4	polar	polar	ADJ
ap-3105	315	5	coordinates	coordinate	NOUN
ap-3105	315	6	centered	center	VERB
ap-3105	315	7	at	at	ADP
ap-3105	315	8	c	c	NOUN
ap-3105	315	9	,	,	PUNCT
ap-3105	315	10	δ∂d(x0;c	δ∂d(x0;c	NOUN
ap-3105	315	11	)	)	PUNCT
ap-3105	315	12	=	=	SYM
ap-3105	315	13	1	1	NUM
ap-3105	315	14	r	r	NOUN
ap-3105	315	15	(	(	PUNCT
ap-3105	315	16	δ(θ	δ(θ	PROPN
ap-3105	315	17	−	−	PROPN
ap-3105	315	18	π	π	PROPN
ap-3105	315	19	)	)	PUNCT
ap-3105	316	1	+	+	NUM
ap-3105	316	2	δ(θ	δ(θ	PROPN
ap-3105	316	3	+	+	CCONJ
ap-3105	316	4	π	π	NOUN
ap-3105	316	5	)	)	PUNCT
ap-3105	316	6	)	)	PUNCT
ap-3105	316	7	.	.	PUNCT
ap-3105	317	1	thus	thus	ADV
ap-3105	317	2	the	the	DET
ap-3105	317	3	latter	latter	ADJ
ap-3105	317	4	contribution	contribution	NOUN
ap-3105	317	5	takes	take	VERB
ap-3105	317	6	the	the	DET
ap-3105	317	7	form	form	NOUN
ap-3105	317	8	1	1	NUM
ap-3105	317	9	4πitr2	4πitr2	NUM
ap-3105	317	10	∂	∂	NUM
ap-3105	318	1	∂θ	∂θ	PROPN
ap-3105	318	2	(	(	PUNCT
ap-3105	318	3	exp	exp	X
ap-3105	318	4	(	(	PUNCT
ap-3105	318	5	i	i	NOUN
ap-3105	318	6	4	4	NUM
ap-3105	318	7	t	t	NOUN
ap-3105	318	8	dist(x	dist(x	PROPN
ap-3105	318	9	,	,	PUNCT
ap-3105	318	10	x0)2	x0)2	PROPN
ap-3105	318	11	)	)	PUNCT
ap-3105	318	12	(	(	PUNCT
ap-3105	318	13	δ(θ	δ(θ	PROPN
ap-3105	318	14	−	−	PROPN
ap-3105	318	15	π)−	π)−	PROPN
ap-3105	318	16	δ(θ	δ(θ	PROPN
ap-3105	318	17	+	+	CCONJ
ap-3105	318	18	π	π	NOUN
ap-3105	318	19	)	)	PUNCT
ap-3105	318	20	)	)	PUNCT
ap-3105	318	21	)	)	PUNCT
ap-3105	319	1	=	=	SYM
ap-3105	319	2	∂	∂	NUM
ap-3105	320	1	∂−→n	∂−→n	PROPN
ap-3105	320	2	(	(	PUNCT
ap-3105	320	3	kγ′(t	kγ′(t	PROPN
ap-3105	320	4	,	,	PUNCT
ap-3105	320	5	x	x	X
ap-3105	320	6	,	,	PUNCT
ap-3105	320	7	x0)δ∂d(x0,c	x0)δ∂d(x0,c	NUM
ap-3105	320	8	)	)	PUNCT
ap-3105	320	9	)	)	PUNCT
ap-3105	320	10	,	,	PUNCT
ap-3105	320	11	where	where	SCONJ
ap-3105	320	12	kγ′(t	kγ′(t	NOUN
ap-3105	320	13	,	,	PUNCT
ap-3105	320	14	x	x	X
ap-3105	320	15	,	,	PUNCT
ap-3105	320	16	x0	x0	PROPN
ap-3105	320	17	)	)	PUNCT
ap-3105	320	18	=	=	PUNCT
ap-3105	321	1	z(t	z(t	NOUN
ap-3105	321	2	,	,	PUNCT
ap-3105	321	3	x	x	X
ap-3105	321	4	,	,	PUNCT
ap-3105	321	5	x0	x0	PROPN
ap-3105	321	6	)	)	PUNCT
ap-3105	321	7	.	.	PUNCT
ap-3105	322	1	in	in	ADP
ap-3105	322	2	summary	summary	NOUN
ap-3105	322	3	,	,	PUNCT
ap-3105	322	4	we	we	PRON
ap-3105	322	5	obtain	obtain	VERB
ap-3105	322	6	(	(	PUNCT
ap-3105	322	7	i	i	NOUN
ap-3105	322	8	∂	∂	NOUN
ap-3105	322	9	∂t	∂t	PROPN
ap-3105	322	10	+	+	CCONJ
ap-3105	322	11	∆	∆	X
ap-3105	322	12	)	)	PUNCT
ap-3105	323	1	kγ(t	kγ(t	PROPN
ap-3105	323	2	,	,	PUNCT
ap-3105	323	3	x	x	AUX
ap-3105	323	4	,	,	PUNCT
ap-3105	323	5	x0	x0	PROPN
ap-3105	323	6	)	)	PUNCT
ap-3105	324	1	=	=	SYM
ap-3105	324	2	−	−	PROPN
ap-3105	324	3	(	(	PUNCT
ap-3105	324	4	∂	∂	NOUN
ap-3105	324	5	∂−→n	∂−→n	PROPN
ap-3105	324	6	kγ(t	kγ(t	NOUN
ap-3105	324	7	,	,	PUNCT
ap-3105	324	8	x	x	PRON
ap-3105	324	9	,	,	PUNCT
ap-3105	324	10	x0	x0	PROPN
ap-3105	324	11	)	)	PUNCT
ap-3105	324	12	)	)	PUNCT
ap-3105	324	13	δ∂d(c	δ∂d(c	NOUN
ap-3105	324	14	)	)	PUNCT
ap-3105	324	15	−	−	PROPN
ap-3105	324	16	∂	∂	NOUN
ap-3105	325	1	∂−→n	∂−→n	PROPN
ap-3105	325	2	(	(	PUNCT
ap-3105	325	3	kγ(t	kγ(t	X
ap-3105	325	4	,	,	PUNCT
ap-3105	325	5	x	x	X
ap-3105	325	6	,	,	PUNCT
ap-3105	325	7	x0)δ∂d(c	x0)δ∂d(c	NUM
ap-3105	325	8	)	)	PUNCT
ap-3105	325	9	)	)	PUNCT
ap-3105	326	1	+	+	NUM
ap-3105	326	2	∂	∂	NUM
ap-3105	326	3	∂−→n	∂−→n	PROPN
ap-3105	326	4	(	(	PUNCT
ap-3105	326	5	kγ′(t	kγ′(t	PROPN
ap-3105	326	6	,	,	PUNCT
ap-3105	326	7	x	x	X
ap-3105	326	8	,	,	PUNCT
ap-3105	326	9	x0)δ∂d(x0,c	x0)δ∂d(x0,c	NUM
ap-3105	326	10	)	)	PUNCT
ap-3105	326	11	)	)	PUNCT
ap-3105	326	12	.	.	PUNCT
ap-3105	327	1	(	(	PUNCT
ap-3105	327	2	25	25	NUM
ap-3105	327	3	)	)	PUNCT
ap-3105	327	4	finally	finally	ADV
ap-3105	327	5	,	,	PUNCT
ap-3105	327	6	let	let	VERB
ap-3105	327	7	us	we	PRON
ap-3105	327	8	consider	consider	VERB
ap-3105	327	9	the	the	DET
ap-3105	327	10	case	case	NOUN
ap-3105	327	11	|γ|	|γ|	PRON
ap-3105	327	12	≥	≥	NOUN
ap-3105	327	13	2	2	NUM
ap-3105	327	14	.	.	PUNCT
ap-3105	328	1	thus	thus	ADV
ap-3105	328	2	γ	γ	X
ap-3105	328	3	is	be	AUX
ap-3105	328	4	a	a	DET
ap-3105	328	5	piecewise	piecewise	NOUN
ap-3105	328	6	geodesic	geodesic	NOUN
ap-3105	328	7	curve	curve	NOUN
ap-3105	328	8	x0	x0	PROPN
ap-3105	328	9	→	→	SYM
ap-3105	328	10	c1	c1	PROPN
ap-3105	328	11	→	→	SYM
ap-3105	328	12	·	·	PUNCT
ap-3105	328	13	·	·	PUNCT
ap-3105	328	14	·	·	PUNCT
ap-3105	328	15	→	→	SYM
ap-3105	328	16	cn	cn	PROPN
ap-3105	328	17	→	→	SYM
ap-3105	328	18	x	x	PROPN
ap-3105	328	19	,	,	PUNCT
ap-3105	328	20	n	n	PRON
ap-3105	328	21	≥	≥	NOUN
ap-3105	328	22	2	2	NUM
ap-3105	328	23	.	.	PUNCT
ap-3105	328	24	denote	denote	VERB
ap-3105	328	25	by	by	ADP
ap-3105	328	26	γ′	γ′	PROPN
ap-3105	328	27	the	the	DET
ap-3105	328	28	truncated	truncated	ADJ
ap-3105	328	29	geodesic	geodesic	NOUN
ap-3105	328	30	curve	curve	NOUN
ap-3105	328	31	x0	x0	PROPN
ap-3105	328	32	→	→	SYM
ap-3105	328	33	c1	c1	PROPN
ap-3105	328	34	→	→	SYM
ap-3105	328	35	·	·	PUNCT
ap-3105	328	36	·	·	PUNCT
ap-3105	328	37	·	·	PUNCT
ap-3105	329	1	→	→	PUNCT
ap-3105	329	2	cn−1	cn−1	PROPN
ap-3105	329	3	→	→	SYM
ap-3105	329	4	x	x	PUNCT
ap-3105	329	5	provided	provide	VERB
ap-3105	329	6	x	x	PROPN
ap-3105	329	7	∈	∈	PROPN
ap-3105	329	8	d(cn−1	d(cn−1	NUM
ap-3105	329	9	)	)	PUNCT
ap-3105	329	10	.	.	PUNCT
ap-3105	330	1	recalling	recall	VERB
ap-3105	330	2	(	(	PUNCT
ap-3105	330	3	7	7	NUM
ap-3105	330	4	)	)	PUNCT
ap-3105	330	5	,	,	PUNCT
ap-3105	330	6	(	(	PUNCT
ap-3105	330	7	8)	8)	NUM
ap-3105	330	8	,	,	PUNCT
ap-3105	330	9	one	one	PRON
ap-3105	330	10	can	can	AUX
ap-3105	330	11	express	express	VERB
ap-3105	330	12	kγ(t	kγ(t	NOUN
ap-3105	330	13	,	,	PUNCT
ap-3105	330	14	x	x	PRON
ap-3105	330	15	,	,	PUNCT
ap-3105	330	16	x0	x0	PROPN
ap-3105	330	17	)	)	PUNCT
ap-3105	331	1	=	=	SYM
ap-3105	331	2	∫	∫	PROPN
ap-3105	332	1	rn	rn	PROPN
ap-3105	332	2	dtn−1	dtn−1	PROPN
ap-3105	332	3	.	.	PUNCT
ap-3105	332	4	.	.	PUNCT
ap-3105	332	5	.	.	PUNCT
ap-3105	333	1	dt0v	dt0v	PROPN
ap-3105	333	2	(	(	PUNCT
ap-3105	333	3	x	x	X
ap-3105	333	4	,	,	PUNCT
ap-3105	333	5	cn	cn	INTJ
ap-3105	333	6	,	,	PUNCT
ap-3105	333	7	cn−1	cn−1	PROPN
ap-3105	333	8	t−	t−	PROPN
ap-3105	333	9	τ	τ	PROPN
ap-3105	333	10	,	,	PUNCT
ap-3105	333	11	tn−1	tn−1	PROPN
ap-3105	333	12	)	)	PUNCT
ap-3105	333	13	z(t−	z(t−	PROPN
ap-3105	333	14	τ	τ	PROPN
ap-3105	333	15	,	,	PUNCT
ap-3105	333	16	x	x	PROPN
ap-3105	333	17	,	,	PUNCT
ap-3105	333	18	cn)fγ(t0	cn)fγ(t0	PROPN
ap-3105	333	19	,	,	PUNCT
ap-3105	333	20	.	.	PUNCT
ap-3105	333	21	.	.	PUNCT
ap-3105	333	22	.	.	PUNCT
ap-3105	334	1	,	,	PUNCT
ap-3105	334	2	tn−1	tn−1	ADJ
ap-3105	334	3	,	,	PUNCT
ap-3105	334	4	x0	x0	PROPN
ap-3105	334	5	)	)	PUNCT
ap-3105	335	1	=	=	PUNCT
ap-3105	335	2	1	1	NUM
ap-3105	335	3	2πχ(x	2πχ(x	NUM
ap-3105	335	4	,	,	PUNCT
ap-3105	335	5	cn	cn	NOUN
ap-3105	335	6	)	)	PUNCT
ap-3105	335	7	∫	∫	PROPN
ap-3105	335	8	rn−1	rn−1	PROPN
ap-3105	335	9	dtn−2	dtn−2	PROPN
ap-3105	335	10	.	.	PUNCT
ap-3105	335	11	.	.	PUNCT
ap-3105	335	12	.	.	PUNCT
ap-3105	336	1	dt0	dt0	PROPN
ap-3105	336	2	∫	∫	PROPN
ap-3105	336	3	t−τ	t−τ	NOUN
ap-3105	337	1	′	′	NOUN
ap-3105	337	2	0	0	PUNCT
ap-3105	338	1	dtn−1	dtn−1	ADJ
ap-3105	338	2	(	(	PUNCT
ap-3105	338	3	(	(	PUNCT
ap-3105	338	4	θ	θ	NOUN
ap-3105	338	5	−	−	PROPN
ap-3105	339	1	π	π	X
ap-3105	340	1	+	+	CCONJ
ap-3105	340	2	i	i	PRON
ap-3105	340	3	ln	ln	NOUN
ap-3105	340	4	(	(	PUNCT
ap-3105	340	5	t−	t−	PROPN
ap-3105	340	6	τ	τ	PROPN
ap-3105	340	7	′	′	NUM
ap-3105	341	1	−	−	PROPN
ap-3105	341	2	tn−1)%	tn−1)%	PROPN
ap-3105	341	3	tn−1r	tn−1r	PROPN
ap-3105	341	4	)	)	PUNCT
ap-3105	341	5	−1	−1	NOUN
ap-3105	341	6	−	−	PROPN
ap-3105	341	7	(	(	PUNCT
ap-3105	341	8	θ	θ	PROPN
ap-3105	342	1	+	+	PUNCT
ap-3105	342	2	π	π	PUNCT
ap-3105	343	1	+	+	CCONJ
ap-3105	343	2	i	i	PRON
ap-3105	343	3	ln	ln	NOUN
ap-3105	343	4	(	(	PUNCT
ap-3105	343	5	t−	t−	PROPN
ap-3105	343	6	τ	τ	PROPN
ap-3105	343	7	′	′	NUM
ap-3105	344	1	−	−	PROPN
ap-3105	344	2	tn−1)%	tn−1)%	PROPN
ap-3105	344	3	tn−1r	tn−1r	PROPN
ap-3105	344	4	)	)	PUNCT
ap-3105	344	5	−1	−1	NOUN
ap-3105	344	6	)	)	PUNCT
ap-3105	344	7	1	1	NUM
ap-3105	345	1	t−	t−	PROPN
ap-3105	345	2	τ	τ	PROPN
ap-3105	346	1	′	′	NUM
ap-3105	347	1	−	−	PROPN
ap-3105	347	2	tn−1	tn−1	ADJ
ap-3105	347	3	exp	exp	NOUN
ap-3105	347	4	(	(	PUNCT
ap-3105	347	5	i	i	NOUN
ap-3105	347	6	r2	r2	PROPN
ap-3105	347	7	4(t−	4(t−	PROPN
ap-3105	347	8	τ	τ	X
ap-3105	347	9	′	′	NUM
ap-3105	347	10	−	−	PROPN
ap-3105	348	1	tn−1	tn−1	PROPN
ap-3105	348	2	)	)	PUNCT
ap-3105	348	3	)	)	PUNCT
ap-3105	349	1	fγ(t0	fγ(t0	NOUN
ap-3105	349	2	,	,	PUNCT
ap-3105	349	3	.	.	PUNCT
ap-3105	349	4	.	.	PUNCT
ap-3105	350	1	.	.	PUNCT
ap-3105	351	1	,	,	PUNCT
ap-3105	351	2	tn−1	tn−1	ADJ
ap-3105	351	3	,	,	PUNCT
ap-3105	351	4	x0	x0	PROPN
ap-3105	351	5	)	)	PUNCT
ap-3105	351	6	,	,	PUNCT
ap-3105	351	7	(	(	PUNCT
ap-3105	351	8	26	26	NUM
ap-3105	351	9	)	)	PUNCT
ap-3105	351	10	where	where	SCONJ
ap-3105	351	11	τ	τ	X
ap-3105	351	12	=	=	SYM
ap-3105	351	13	t0	t0	PROPN
ap-3105	351	14	+	+	CCONJ
ap-3105	351	15	·	·	PUNCT
ap-3105	351	16	·	·	PUNCT
ap-3105	351	17	·	·	PUNCT
ap-3105	352	1	+	+	NUM
ap-3105	352	2	tn−2	tn−2	ADV
ap-3105	352	3	+	+	PROPN
ap-3105	352	4	tn−1	tn−1	ADJ
ap-3105	352	5	,	,	PUNCT
ap-3105	352	6	τ	τ	X
ap-3105	352	7	′	′	NUM
ap-3105	352	8	=	=	PUNCT
ap-3105	352	9	t0	t0	PROPN
ap-3105	352	10	+	+	CCONJ
ap-3105	352	11	·	·	PUNCT
ap-3105	352	12	·	·	PUNCT
ap-3105	352	13	·	·	PUNCT
ap-3105	353	1	+	+	CCONJ
ap-3105	353	2	tn−2	tn−2	ADV
ap-3105	353	3	,	,	PUNCT
ap-3105	353	4	r	r	NOUN
ap-3105	353	5	=	=	SYM
ap-3105	353	6	dist(cn	dist(cn	PROPN
ap-3105	353	7	,	,	PUNCT
ap-3105	353	8	x	x	NOUN
ap-3105	353	9	)	)	PUNCT
ap-3105	353	10	,	,	PUNCT
ap-3105	353	11	θ	θ	X
ap-3105	353	12	=	=	SYM
ap-3105	353	13	∠cn−1	∠cn−1	PROPN
ap-3105	353	14	,	,	PUNCT
ap-3105	353	15	cn	cn	PROPN
ap-3105	353	16	,	,	PUNCT
ap-3105	353	17	x	x	NOUN
ap-3105	353	18	,	,	PUNCT
ap-3105	353	19	and	and	CCONJ
ap-3105	353	20	fγ(t0	fγ(t0	NOUN
ap-3105	353	21	,	,	PUNCT
ap-3105	353	22	.	.	PUNCT
ap-3105	353	23	.	.	PUNCT
ap-3105	354	1	.	.	PUNCT
ap-3105	355	1	,	,	PUNCT
ap-3105	355	2	tn−1	tn−1	ADJ
ap-3105	355	3	,	,	PUNCT
ap-3105	355	4	x0	x0	PROPN
ap-3105	355	5	)	)	PUNCT
ap-3105	356	1	=	=	SYM
ap-3105	356	2	n−2∏	n−2∏	NUM
ap-3105	356	3	j=0	j=0	PROPN
ap-3105	356	4	v	v	PROPN
ap-3105	356	5	(	(	PUNCT
ap-3105	356	6	cj+2	cj+2	NUM
ap-3105	356	7	,	,	PUNCT
ap-3105	356	8	cj+1	cj+1	NUM
ap-3105	356	9	,	,	PUNCT
ap-3105	356	10	cj	cj	NOUN
ap-3105	356	11	tj+1	tj+1	PROPN
ap-3105	356	12	,	,	PUNCT
ap-3105	356	13	tj	tj	NOUN
ap-3105	356	14	)	)	PUNCT
ap-3105	356	15	n−1∏	n−1∏	PROPN
ap-3105	356	16	j=0	j=0	PROPN
ap-3105	356	17	ztj	ztj	PROPN
ap-3105	356	18	(	(	PUNCT
ap-3105	356	19	cj+1	cj+1	PROPN
ap-3105	356	20	,	,	PUNCT
ap-3105	356	21	cj	cj	NOUN
ap-3105	356	22	)	)	PUNCT
ap-3105	356	23	.	.	PUNCT
ap-3105	357	1	application	application	NOUN
ap-3105	357	2	of	of	ADP
ap-3105	357	3	(	(	PUNCT
ap-3105	357	4	i∂t	i∂t	NOUN
ap-3105	357	5	+	+	CCONJ
ap-3105	357	6	∆	∆	NOUN
ap-3105	357	7	)	)	PUNCT
ap-3105	357	8	to	to	ADP
ap-3105	357	9	the	the	DET
ap-3105	357	10	rhs	rhs	PROPN
ap-3105	357	11	of	of	ADP
ap-3105	357	12	(	(	PUNCT
ap-3105	357	13	26	26	NUM
ap-3105	357	14	)	)	PUNCT
ap-3105	357	15	in	in	ADP
ap-3105	357	16	the	the	DET
ap-3105	357	17	sense	sense	NOUN
ap-3105	357	18	of	of	ADP
ap-3105	357	19	distributions	distribution	NOUN
ap-3105	357	20	again	again	ADV
ap-3105	357	21	produces	produce	VERB
ap-3105	357	22	several	several	ADJ
ap-3105	357	23	singular	singular	ADJ
ap-3105	357	24	terms	term	NOUN
ap-3105	357	25	.	.	PUNCT
ap-3105	358	1	as	as	ADP
ap-3105	358	2	a	a	DET
ap-3105	358	3	consequence	consequence	NOUN
ap-3105	358	4	of	of	ADP
ap-3105	358	5	the	the	DET
ap-3105	358	6	discontinuity	discontinuity	NOUN
ap-3105	358	7	of	of	ADP
ap-3105	358	8	the	the	DET
ap-3105	358	9	characteristic	characteristic	ADJ
ap-3105	358	10	function	function	NOUN
ap-3105	358	11	χ(x	χ(x	PROPN
ap-3105	358	12	,	,	PUNCT
ap-3105	358	13	cn	cn	PROPN
ap-3105	358	14	)	)	PUNCT
ap-3105	358	15	a	a	DET
ap-3105	358	16	single	single	ADJ
ap-3105	358	17	and	and	CCONJ
ap-3105	358	18	a	a	DET
ap-3105	358	19	double	double	ADJ
ap-3105	358	20	layer	layer	NOUN
ap-3105	358	21	supported	support	VERB
ap-3105	358	22	on	on	ADP
ap-3105	358	23	the	the	DET
ap-3105	358	24	boundary	boundary	ADJ
ap-3105	358	25	∂d(cn	∂d(cn	PROPN
ap-3105	358	26	)	)	PUNCT
ap-3105	358	27	occur	occur	VERB
ap-3105	358	28	(	(	PUNCT
ap-3105	358	29	see	see	VERB
ap-3105	358	30	(	(	PUNCT
ap-3105	358	31	16	16	NUM
ap-3105	358	32	)	)	PUNCT
ap-3105	358	33	)	)	PUNCT
ap-3105	358	34	.	.	PUNCT
ap-3105	359	1	the	the	DET
ap-3105	359	2	singularity	singularity	NOUN
ap-3105	359	3	of	of	ADP
ap-3105	359	4	the	the	DET
ap-3105	359	5	integrand	integrand	NOUN
ap-3105	359	6	for	for	ADP
ap-3105	359	7	the	the	DET
ap-3105	359	8	values	value	NOUN
ap-3105	359	9	θ	θ	X
ap-3105	359	10	=	=	SYM
ap-3105	359	11	±π	±π	PROPN
ap-3105	359	12	and	and	CCONJ
ap-3105	359	13	%	%	INTJ
ap-3105	359	14	/tn−1	/tn−1	PUNCT
ap-3105	359	15	=	=	PUNCT
ap-3105	360	1	r/(t−	r/(t−	NOUN
ap-3105	360	2	τ	τ	X
ap-3105	360	3	′	′	NUM
ap-3105	361	1	−	−	NOUN
ap-3105	361	2	tn−1	tn−1	ADJ
ap-3105	361	3	)	)	PUNCT
ap-3105	361	4	produces	produce	VERB
ap-3105	361	5	terms	term	NOUN
ap-3105	361	6	supported	support	VERB
ap-3105	361	7	on	on	ADP
ap-3105	361	8	the	the	DET
ap-3105	361	9	part	part	NOUN
ap-3105	361	10	of	of	ADP
ap-3105	361	11	the	the	DET
ap-3105	361	12	boundary	boundary	NOUN
ap-3105	361	13	of	of	ADP
ap-3105	361	14	the	the	DET
ap-3105	361	15	domain	domain	NOUN
ap-3105	361	16	d(cn−1	d(cn−1	NUM
ap-3105	361	17	)	)	PUNCT
ap-3105	361	18	,	,	PUNCT
ap-3105	361	19	namely	namely	ADV
ap-3105	361	20	on	on	ADP
ap-3105	361	21	∂d(cn−1;cn	∂d(cn−1;cn	PROPN
ap-3105	361	22	)	)	PUNCT
ap-3105	361	23	.	.	PUNCT
ap-3105	362	1	this	this	DET
ap-3105	362	2	time	time	NOUN
ap-3105	362	3	one	one	PRON
ap-3105	362	4	can	can	AUX
ap-3105	362	5	apply	apply	VERB
ap-3105	362	6	identity	identity	NOUN
ap-3105	362	7	(	(	PUNCT
ap-3105	362	8	14	14	NUM
ap-3105	362	9	)	)	PUNCT
ap-3105	362	10	.	.	PUNCT
ap-3105	363	1	in	in	ADP
ap-3105	363	2	order	order	NOUN
ap-3105	363	3	to	to	PART
ap-3105	363	4	treat	treat	VERB
ap-3105	363	5	the	the	DET
ap-3105	363	6	resulting	result	VERB
ap-3105	363	7	terms	term	NOUN
ap-3105	363	8	the	the	DET
ap-3105	363	9	following	follow	VERB
ap-3105	363	10	equations	equation	NOUN
ap-3105	363	11	are	be	AUX
ap-3105	363	12	useful	useful	ADJ
ap-3105	363	13	.	.	PUNCT
ap-3105	364	1	suppose	suppose	VERB
ap-3105	364	2	that	that	SCONJ
ap-3105	364	3	θ	θ	PROPN
ap-3105	364	4	=	=	SYM
ap-3105	364	5	±π	±π	PROPN
ap-3105	364	6	and	and	CCONJ
ap-3105	364	7	so	so	ADV
ap-3105	364	8	x	x	SYM
ap-3105	364	9	∈	∈	PROPN
ap-3105	364	10	∂d(cn−1;cn	∂d(cn−1;cn	PROPN
ap-3105	364	11	)	)	PUNCT
ap-3105	364	12	.	.	PUNCT
ap-3105	365	1	set	set	VERB
ap-3105	365	2	r′	r′	NOUN
ap-3105	365	3	=	=	SYM
ap-3105	365	4	r	r	NOUN
ap-3105	365	5	+	+	NUM
ap-3105	365	6	%	%	NOUN
ap-3105	365	7	=	=	SYM
ap-3105	365	8	dist(cn−1	dist(cn−1	ADJ
ap-3105	365	9	,	,	PUNCT
ap-3105	365	10	x	x	NOUN
ap-3105	365	11	)	)	PUNCT
ap-3105	365	12	,	,	PUNCT
ap-3105	365	13	θ′	θ′	NOUN
ap-3105	365	14	=	=	SYM
ap-3105	365	15	∠cn−2	∠cn−2	PROPN
ap-3105	365	16	,	,	PUNCT
ap-3105	365	17	cn−1	cn−1	PROPN
ap-3105	365	18	,	,	PUNCT
ap-3105	365	19	x.	x.	VERB
ap-3105	366	1	if	if	SCONJ
ap-3105	366	2	%	%	INTJ
ap-3105	366	3	/tn−1	/tn−1	PUNCT
ap-3105	367	1	=	=	PUNCT
ap-3105	368	1	r/(t−	r/(t−	NOUN
ap-3105	368	2	τ	τ	X
ap-3105	368	3	′	′	NUM
ap-3105	369	1	−	−	PROPN
ap-3105	369	2	tn−1	tn−1	PROPN
ap-3105	369	3	)	)	PUNCT
ap-3105	369	4	then	then	ADV
ap-3105	369	5	tn−1	tn−1	PROPN
ap-3105	369	6	=	=	SYM
ap-3105	369	7	%	%	NOUN
ap-3105	369	8	(	(	PUNCT
ap-3105	369	9	t−	t−	PROPN
ap-3105	369	10	τ	τ	PROPN
ap-3105	369	11	′	′	NUM
ap-3105	369	12	)	)	PUNCT
ap-3105	369	13	r′	r′	PROPN
ap-3105	369	14	and	and	CCONJ
ap-3105	369	15	t−	t−	PROPN
ap-3105	369	16	τ	τ	PROPN
ap-3105	369	17	′	′	NUM
ap-3105	369	18	−	−	X
ap-3105	370	1	tn−1	tn−1	ADJ
ap-3105	370	2	r	r	NOUN
ap-3105	370	3	=	=	PUNCT
ap-3105	370	4	t−	t−	PROPN
ap-3105	370	5	τ	τ	PROPN
ap-3105	370	6	′	′	NUM
ap-3105	370	7	r′	r′	NOUN
ap-3105	370	8	.	.	PUNCT
ap-3105	371	1	231	231	NUM
ap-3105	371	2	petra	petra	PROPN
ap-3105	371	3	košťáková	košťáková	PROPN
ap-3105	371	4	,	,	PUNCT
ap-3105	371	5	pavel	pavel	PROPN
ap-3105	371	6	šťovíček	šťovíček	PROPN
ap-3105	371	7	acta	acta	PROPN
ap-3105	371	8	polytechnica	polytechnica	PROPN
ap-3105	371	9	moreover	moreover	ADV
ap-3105	371	10	,	,	PUNCT
ap-3105	371	11	%	%	INTJ
ap-3105	371	12	r′	r′	X
ap-3105	371	13	exp	exp	NOUN
ap-3105	371	14	(	(	PUNCT
ap-3105	371	15	ir2	ir2	PROPN
ap-3105	371	16	4(t−	4(t−	PROPN
ap-3105	371	17	τ	τ	NOUN
ap-3105	371	18	)	)	PUNCT
ap-3105	371	19	)	)	PUNCT
ap-3105	371	20	z(tn−1	z(tn−1	PROPN
ap-3105	371	21	,	,	PUNCT
ap-3105	371	22	cn	cn	PROPN
ap-3105	371	23	,	,	PUNCT
ap-3105	371	24	cn−1	cn−1	PROPN
ap-3105	371	25	)	)	PUNCT
ap-3105	371	26	=	=	SYM
ap-3105	372	1	z(t−	z(t−	PROPN
ap-3105	372	2	τ	τ	X
ap-3105	372	3	′	′	NUM
ap-3105	372	4	,	,	PUNCT
ap-3105	372	5	x	x	X
ap-3105	372	6	,	,	PUNCT
ap-3105	372	7	cn−1	cn−1	PROPN
ap-3105	372	8	)	)	PUNCT
ap-3105	372	9	and	and	CCONJ
ap-3105	372	10	v	v	X
ap-3105	372	11	(	(	PUNCT
ap-3105	372	12	cn	cn	PROPN
ap-3105	372	13	,	,	PUNCT
ap-3105	372	14	cn−1	cn−1	PROPN
ap-3105	372	15	,	,	PUNCT
ap-3105	372	16	cn−2	cn−2	PROPN
ap-3105	372	17	%	%	NOUN
ap-3105	372	18	s2	s2	PROPN
ap-3105	372	19	/	/	SYM
ap-3105	372	20	r	r	NOUN
ap-3105	372	21	′	′	NOUN
ap-3105	372	22	,	,	PUNCT
ap-3105	372	23	s1	s1	NOUN
ap-3105	372	24	)	)	PUNCT
ap-3105	373	1	=	=	SYM
ap-3105	373	2	v	v	X
ap-3105	373	3	(	(	PUNCT
ap-3105	373	4	x	x	NOUN
ap-3105	373	5	,	,	PUNCT
ap-3105	373	6	cn−1	cn−1	PROPN
ap-3105	373	7	,	,	PUNCT
ap-3105	373	8	cn−2	cn−2	PROPN
ap-3105	373	9	s2	s2	PROPN
ap-3105	373	10	,	,	PUNCT
ap-3105	373	11	s1	s1	PROPN
ap-3105	373	12	)	)	PUNCT
ap-3105	373	13	.	.	PUNCT
ap-3105	374	1	observe	observe	VERB
ap-3105	374	2	also	also	ADV
ap-3105	374	3	that	that	SCONJ
ap-3105	374	4	∂	∂	NUM
ap-3105	375	1	∂s	∂s	PROPN
ap-3105	375	2	(	(	PUNCT
ap-3105	375	3	exp	exp	PROPN
ap-3105	375	4	(	(	PUNCT
ap-3105	375	5	ir2	ir2	PROPN
ap-3105	375	6	4(t−	4(t−	PROPN
ap-3105	375	7	τ	τ	X
ap-3105	375	8	′	′	NUM
ap-3105	375	9	−	−	PROPN
ap-3105	375	10	s	s	NOUN
ap-3105	375	11	)	)	PUNCT
ap-3105	375	12	)	)	PUNCT
ap-3105	375	13	exp	exp	NOUN
ap-3105	375	14	(	(	PUNCT
ap-3105	375	15	i%2	i%2	NOUN
ap-3105	375	16	4s	4s	NUM
ap-3105	375	17	)	)	PUNCT
ap-3105	375	18	)	)	PUNCT
ap-3105	375	19	∣∣∣∣	∣∣∣∣	NOUN
ap-3105	375	20	s=%(t−τ	s=%(t−τ	NOUN
ap-3105	375	21	′)/r′	′)/r′	PUNCT
ap-3105	375	22	=	=	SYM
ap-3105	375	23	0	0	NUM
ap-3105	375	24	,	,	PUNCT
ap-3105	375	25	exp	exp	NOUN
ap-3105	375	26	(	(	PUNCT
ap-3105	375	27	ir2	ir2	PROPN
ap-3105	375	28	4(t−	4(t−	PROPN
ap-3105	375	29	τ	τ	X
ap-3105	375	30	′	′	NUM
ap-3105	375	31	−	−	PROPN
ap-3105	375	32	s	s	NOUN
ap-3105	375	33	)	)	PUNCT
ap-3105	375	34	)	)	PUNCT
ap-3105	375	35	exp	exp	NOUN
ap-3105	375	36	(	(	PUNCT
ap-3105	375	37	i%2	i%2	NOUN
ap-3105	375	38	4s	4s	NUM
ap-3105	375	39	)	)	PUNCT
ap-3105	375	40	∣∣∣∣	∣∣∣∣	NOUN
ap-3105	375	41	s=%(t−τ	s=%(t−τ	NOUN
ap-3105	375	42	′)/r′	′)/r′	PART
ap-3105	375	43	=	=	SYM
ap-3105	375	44	exp	exp	X
ap-3105	375	45	(	(	PUNCT
ap-3105	375	46	ir′	ir′	PROPN
ap-3105	375	47	2	2	NUM
ap-3105	375	48	4(t−	4(t−	PROPN
ap-3105	375	49	τ	τ	X
ap-3105	375	50	′	′	NUM
ap-3105	375	51	)	)	PUNCT
ap-3105	375	52	)	)	PUNCT
ap-3105	375	53	,	,	PUNCT
ap-3105	375	54	and	and	CCONJ
ap-3105	375	55	for	for	ADP
ap-3105	375	56	θ	θ	PROPN
ap-3105	375	57	=	=	SYM
ap-3105	375	58	π	π	PROPN
ap-3105	375	59	,	,	PUNCT
ap-3105	375	60	∂	∂	NUM
ap-3105	375	61	∂s	∂s	PROPN
ap-3105	375	62	v	v	NOUN
ap-3105	375	63	(	(	PUNCT
ap-3105	375	64	cn	cn	PROPN
ap-3105	375	65	,	,	PUNCT
ap-3105	375	66	cn−1	cn−1	PROPN
ap-3105	375	67	,	,	PUNCT
ap-3105	375	68	cn−2	cn−2	PROPN
ap-3105	375	69	s	s	PROPN
ap-3105	375	70	,	,	PUNCT
ap-3105	375	71	tn−2	tn−2	ADV
ap-3105	375	72	)	)	PUNCT
ap-3105	375	73	∣∣∣∣	∣∣∣∣	NOUN
ap-3105	375	74	s=%(t−τ	s=%(t−τ	NOUN
ap-3105	375	75	′)/r′	′)/r′	PART
ap-3105	375	76	=	=	SYM
ap-3105	375	77	ir′	ir′	NUM
ap-3105	375	78	%	%	NOUN
ap-3105	375	79	(	(	PUNCT
ap-3105	375	80	t−	t−	PROPN
ap-3105	375	81	τ	τ	PROPN
ap-3105	375	82	′	′	NUM
ap-3105	375	83	)	)	PUNCT
ap-3105	375	84	∂	∂	NOUN
ap-3105	375	85	∂θ′	∂θ′	NUM
ap-3105	375	86	v	v	NOUN
ap-3105	375	87	(	(	PUNCT
ap-3105	375	88	x	x	NOUN
ap-3105	375	89	,	,	PUNCT
ap-3105	375	90	cn−1	cn−1	PROPN
ap-3105	375	91	,	,	PUNCT
ap-3105	375	92	cn−2	cn−2	PROPN
ap-3105	375	93	t−	t−	PROPN
ap-3105	375	94	τ	τ	PROPN
ap-3105	375	95	′	′	NUM
ap-3105	375	96	,	,	PUNCT
ap-3105	375	97	tn−2	tn−2	ADV
ap-3105	375	98	)	)	PUNCT
ap-3105	375	99	.	.	PUNCT
ap-3105	376	1	a	a	DET
ap-3105	376	2	similar	similar	ADJ
ap-3105	376	3	relation	relation	NOUN
ap-3105	376	4	holds	hold	VERB
ap-3105	376	5	for	for	ADP
ap-3105	376	6	θ	θ	PROPN
ap-3105	376	7	=	=	SYM
ap-3105	376	8	−π	−π	PROPN
ap-3105	376	9	.	.	PUNCT
ap-3105	377	1	after	after	ADP
ap-3105	377	2	a	a	DET
ap-3105	377	3	bit	bit	NOUN
ap-3105	377	4	tedious	tedious	ADJ
ap-3105	377	5	but	but	CCONJ
ap-3105	377	6	quite	quite	ADV
ap-3105	377	7	straightforward	straightforward	ADJ
ap-3105	377	8	manipulations	manipulation	NOUN
ap-3105	377	9	one	one	PRON
ap-3105	377	10	arrives	arrive	VERB
ap-3105	377	11	at	at	ADP
ap-3105	377	12	the	the	DET
ap-3105	377	13	final	final	ADJ
ap-3105	377	14	identity	identity	NOUN
ap-3105	377	15	(	(	PUNCT
ap-3105	377	16	i	i	NOUN
ap-3105	377	17	∂	∂	NOUN
ap-3105	377	18	∂t	∂t	PROPN
ap-3105	377	19	+	+	CCONJ
ap-3105	377	20	∆	∆	X
ap-3105	377	21	)	)	PUNCT
ap-3105	378	1	kγ(t	kγ(t	PROPN
ap-3105	378	2	,	,	PUNCT
ap-3105	378	3	x	x	AUX
ap-3105	378	4	,	,	PUNCT
ap-3105	378	5	x0	x0	PROPN
ap-3105	378	6	)	)	PUNCT
ap-3105	379	1	=	=	SYM
ap-3105	379	2	−	−	PROPN
ap-3105	379	3	(	(	PUNCT
ap-3105	379	4	∂	∂	NOUN
ap-3105	379	5	∂−→n	∂−→n	PROPN
ap-3105	379	6	kγ(t	kγ(t	NOUN
ap-3105	379	7	,	,	PUNCT
ap-3105	379	8	x	x	PRON
ap-3105	379	9	,	,	PUNCT
ap-3105	379	10	x0	x0	PROPN
ap-3105	379	11	)	)	PUNCT
ap-3105	379	12	)	)	PUNCT
ap-3105	380	1	δ∂d(cn	δ∂d(cn	X
ap-3105	380	2	)	)	PUNCT
ap-3105	380	3	−	−	PROPN
ap-3105	380	4	∂	∂	NOUN
ap-3105	381	1	∂−→n	∂−→n	PROPN
ap-3105	381	2	(	(	PUNCT
ap-3105	381	3	kγ(t	kγ(t	X
ap-3105	381	4	,	,	PUNCT
ap-3105	381	5	x	x	X
ap-3105	381	6	,	,	PUNCT
ap-3105	381	7	x0)δ∂d(cn	x0)δ∂d(cn	NUM
ap-3105	381	8	)	)	PUNCT
ap-3105	381	9	)	)	PUNCT
ap-3105	382	1	+	+	CCONJ
ap-3105	382	2	(	(	PUNCT
ap-3105	382	3	∂	∂	NUM
ap-3105	382	4	∂−→n	∂−→n	PROPN
ap-3105	382	5	kγ′(t	kγ′(t	PROPN
ap-3105	382	6	,	,	PUNCT
ap-3105	382	7	x	x	X
ap-3105	382	8	,	,	PUNCT
ap-3105	382	9	x0	x0	PROPN
ap-3105	382	10	)	)	PUNCT
ap-3105	382	11	)	)	PUNCT
ap-3105	382	12	δ∂d(cn−1;cn	δ∂d(cn−1;cn	PROPN
ap-3105	382	13	)	)	PUNCT
ap-3105	382	14	+	+	NUM
ap-3105	382	15	∂	∂	NUM
ap-3105	382	16	∂−→n	∂−→n	PROPN
ap-3105	382	17	(	(	PUNCT
ap-3105	382	18	kγ′(t	kγ′(t	PROPN
ap-3105	382	19	,	,	PUNCT
ap-3105	382	20	x	x	X
ap-3105	382	21	,	,	PUNCT
ap-3105	382	22	x0)δ∂d(cn−1;cn	x0)δ∂d(cn−1;cn	PROPN
ap-3105	382	23	)	)	PUNCT
ap-3105	382	24	)	)	PUNCT
ap-3105	382	25	.	.	PUNCT
ap-3105	383	1	(	(	PUNCT
ap-3105	383	2	27	27	NUM
ap-3105	383	3	)	)	PUNCT
ap-3105	383	4	now	now	ADV
ap-3105	383	5	we	we	PRON
ap-3105	383	6	can	can	AUX
ap-3105	383	7	show	show	VERB
ap-3105	383	8	(	(	PUNCT
ap-3105	383	9	19	19	NUM
ap-3105	383	10	)	)	PUNCT
ap-3105	383	11	when	when	SCONJ
ap-3105	383	12	taking	take	VERB
ap-3105	383	13	into	into	ADP
ap-3105	383	14	account	account	NOUN
ap-3105	383	15	(	(	PUNCT
ap-3105	383	16	23	23	NUM
ap-3105	383	17	)	)	PUNCT
ap-3105	383	18	,	,	PUNCT
ap-3105	383	19	(	(	PUNCT
ap-3105	383	20	25	25	NUM
ap-3105	383	21	)	)	PUNCT
ap-3105	383	22	and	and	CCONJ
ap-3105	383	23	(	(	PUNCT
ap-3105	383	24	27	27	NUM
ap-3105	383	25	)	)	PUNCT
ap-3105	383	26	.	.	PUNCT
ap-3105	384	1	it	it	PRON
ap-3105	384	2	is	be	AUX
ap-3105	384	3	true	true	ADJ
ap-3105	384	4	that	that	SCONJ
ap-3105	384	5	(	(	PUNCT
ap-3105	384	6	i	i	PRON
ap-3105	384	7	∂	∂	VERB
ap-3105	384	8	∂t	∂t	PROPN
ap-3105	384	9	+	+	CCONJ
ap-3105	384	10	∆	∆	X
ap-3105	384	11	)	)	PUNCT
ap-3105	385	1	k(t	k(t	ADJ
ap-3105	385	2	,	,	PUNCT
ap-3105	385	3	x	x	X
ap-3105	385	4	,	,	PUNCT
ap-3105	385	5	x0	x0	PROPN
ap-3105	385	6	)	)	PUNCT
ap-3105	386	1	=	=	PUNCT
ap-3105	386	2	∑	∑	PUNCT
ap-3105	386	3	|γ|≥2	|γ|≥2	PROPN
ap-3105	386	4	[	[	PUNCT
ap-3105	386	5	−	−	PROPN
ap-3105	386	6	(	(	PUNCT
ap-3105	386	7	∂	∂	NOUN
ap-3105	386	8	∂−→n	∂−→n	PROPN
ap-3105	386	9	kγ(t	kγ(t	NOUN
ap-3105	386	10	,	,	PUNCT
ap-3105	386	11	x	x	PRON
ap-3105	386	12	,	,	PUNCT
ap-3105	386	13	x0	x0	PROPN
ap-3105	386	14	)	)	PUNCT
ap-3105	386	15	)	)	PUNCT
ap-3105	387	1	δ∂d(cn	δ∂d(cn	X
ap-3105	387	2	)	)	PUNCT
ap-3105	387	3	−	−	PROPN
ap-3105	387	4	∂	∂	NOUN
ap-3105	388	1	∂−→n	∂−→n	PROPN
ap-3105	388	2	(	(	PUNCT
ap-3105	388	3	kγ(t	kγ(t	X
ap-3105	388	4	,	,	PUNCT
ap-3105	388	5	x	x	X
ap-3105	388	6	,	,	PUNCT
ap-3105	388	7	x0)δ∂d(cn	x0)δ∂d(cn	NUM
ap-3105	388	8	)	)	PUNCT
ap-3105	388	9	)	)	PUNCT
ap-3105	389	1	+	+	CCONJ
ap-3105	389	2	(	(	PUNCT
ap-3105	389	3	∂	∂	NUM
ap-3105	389	4	∂−→n	∂−→n	PROPN
ap-3105	389	5	kγ′(t	kγ′(t	PROPN
ap-3105	389	6	,	,	PUNCT
ap-3105	389	7	x	x	X
ap-3105	389	8	,	,	PUNCT
ap-3105	389	9	x0	x0	PROPN
ap-3105	389	10	)	)	PUNCT
ap-3105	389	11	)	)	PUNCT
ap-3105	389	12	δ∂d(cn−1;cn	δ∂d(cn−1;cn	PROPN
ap-3105	389	13	)	)	PUNCT
ap-3105	389	14	+	+	NUM
ap-3105	389	15	∂	∂	NUM
ap-3105	389	16	∂−→n	∂−→n	PROPN
ap-3105	389	17	(	(	PUNCT
ap-3105	389	18	kγ′(t	kγ′(t	PROPN
ap-3105	389	19	,	,	PUNCT
ap-3105	389	20	x	x	X
ap-3105	389	21	,	,	PUNCT
ap-3105	389	22	x0)δ∂d(cn−1;cn	x0)δ∂d(cn−1;cn	PROPN
ap-3105	389	23	)	)	PUNCT
ap-3105	389	24	)	)	PUNCT
ap-3105	389	25	]	]	PUNCT
ap-3105	390	1	+	+	CCONJ
ap-3105	390	2	∑	∑	NOUN
ap-3105	390	3	|γ|=1	|γ|=1	NOUN
ap-3105	390	4	[	[	PUNCT
ap-3105	390	5	−	−	PROPN
ap-3105	390	6	(	(	PUNCT
ap-3105	390	7	∂	∂	NOUN
ap-3105	390	8	∂−→n	∂−→n	PROPN
ap-3105	390	9	kγ(t	kγ(t	NOUN
ap-3105	390	10	,	,	PUNCT
ap-3105	390	11	x	x	PRON
ap-3105	390	12	,	,	PUNCT
ap-3105	390	13	x0	x0	PROPN
ap-3105	390	14	)	)	PUNCT
ap-3105	390	15	)	)	PUNCT
ap-3105	390	16	δ∂d(c	δ∂d(c	NOUN
ap-3105	390	17	)	)	PUNCT
ap-3105	390	18	−	−	PROPN
ap-3105	390	19	∂	∂	NOUN
ap-3105	391	1	∂−→n	∂−→n	PROPN
ap-3105	391	2	(	(	PUNCT
ap-3105	391	3	kγ(t	kγ(t	X
ap-3105	391	4	,	,	PUNCT
ap-3105	391	5	x	x	X
ap-3105	391	6	,	,	PUNCT
ap-3105	391	7	x0)δ∂d(c	x0)δ∂d(c	NUM
ap-3105	391	8	)	)	PUNCT
ap-3105	391	9	)	)	PUNCT
ap-3105	392	1	+	+	NUM
ap-3105	392	2	∂	∂	NUM
ap-3105	392	3	∂−→n	∂−→n	PROPN
ap-3105	392	4	(	(	PUNCT
ap-3105	392	5	z(t	z(t	PROPN
ap-3105	392	6	,	,	PUNCT
ap-3105	392	7	x	x	X
ap-3105	392	8	,	,	PUNCT
ap-3105	392	9	x0)δ∂d(x0;c	x0)δ∂d(x0;c	PROPN
ap-3105	392	10	)	)	PUNCT
ap-3105	392	11	)	)	PUNCT
ap-3105	392	12	]	]	PUNCT
ap-3105	393	1	−	−	PROPN
ap-3105	393	2	∂	∂	NOUN
ap-3105	393	3	∂−→n	∂−→n	PROPN
ap-3105	393	4	(	(	PUNCT
ap-3105	393	5	z(t	z(t	PROPN
ap-3105	393	6	,	,	PUNCT
ap-3105	393	7	x	x	X
ap-3105	393	8	,	,	PUNCT
ap-3105	393	9	x0)δ∂d(x0	x0)δ∂d(x0	NUM
ap-3105	393	10	)	)	PUNCT
ap-3105	393	11	)	)	PUNCT
ap-3105	394	1	=	=	PUNCT
ap-3105	394	2	0	0	NUM
ap-3105	394	3	,	,	PUNCT
ap-3105	394	4	where	where	SCONJ
ap-3105	394	5	we	we	PRON
ap-3105	394	6	have	have	AUX
ap-3105	394	7	used	use	VERB
ap-3105	394	8	(	(	PUNCT
ap-3105	394	9	21	21	NUM
ap-3105	394	10	)	)	PUNCT
ap-3105	394	11	and	and	CCONJ
ap-3105	394	12	(	(	PUNCT
ap-3105	394	13	22	22	NUM
ap-3105	394	14	)	)	PUNCT
ap-3105	394	15	.	.	PUNCT
ap-3105	395	1	4	4	X
ap-3105	395	2	.	.	X
ap-3105	395	3	conclusion	conclusion	NOUN
ap-3105	395	4	.	.	PUNCT
ap-3105	396	1	the	the	DET
ap-3105	396	2	propagator	propagator	NOUN
ap-3105	396	3	for	for	ADP
ap-3105	396	4	two	two	NUM
ap-3105	396	5	aharonov	aharonov	NOUN
ap-3105	396	6	-	-	PUNCT
ap-3105	396	7	bohm	bohm	PROPN
ap-3105	396	8	vortices	vortex	NOUN
ap-3105	396	9	in	in	ADP
ap-3105	396	10	conclusion	conclusion	NOUN
ap-3105	396	11	we	we	PRON
ap-3105	396	12	present	present	VERB
ap-3105	396	13	a	a	DET
ap-3105	396	14	formula	formula	NOUN
ap-3105	396	15	for	for	ADP
ap-3105	396	16	the	the	DET
ap-3105	396	17	propagator	propagator	NOUN
ap-3105	396	18	of	of	ADP
ap-3105	396	19	a	a	DET
ap-3105	396	20	charged	charge	VERB
ap-3105	396	21	particle	particle	NOUN
ap-3105	396	22	on	on	ADP
ap-3105	396	23	the	the	DET
ap-3105	396	24	plane	plane	NOUN
ap-3105	396	25	pierced	pierce	VERB
ap-3105	396	26	by	by	ADP
ap-3105	396	27	two	two	NUM
ap-3105	396	28	aharonov	aharonov	NOUN
ap-3105	396	29	-	-	PUNCT
ap-3105	396	30	bohm	bohm	PROPN
ap-3105	396	31	magnetic	magnetic	ADJ
ap-3105	396	32	fluxes	flux	NOUN
ap-3105	396	33	.	.	PUNCT
ap-3105	397	1	without	without	ADP
ap-3105	397	2	loss	loss	NOUN
ap-3105	397	3	of	of	ADP
ap-3105	397	4	generality	generality	NOUN
ap-3105	397	5	we	we	PRON
ap-3105	397	6	can	can	AUX
ap-3105	397	7	suppose	suppose	VERB
ap-3105	397	8	that	that	SCONJ
ap-3105	397	9	the	the	DET
ap-3105	397	10	vortices	vortex	NOUN
ap-3105	397	11	are	be	AUX
ap-3105	397	12	located	locate	VERB
ap-3105	397	13	at	at	ADP
ap-3105	397	14	the	the	DET
ap-3105	397	15	points	point	NOUN
ap-3105	398	1	a	a	PRON
ap-3105	398	2	=	=	X
ap-3105	398	3	(	(	PUNCT
ap-3105	398	4	0	0	NUM
ap-3105	398	5	,	,	PUNCT
ap-3105	398	6	0	0	NUM
ap-3105	398	7	)	)	PUNCT
ap-3105	398	8	and	and	CCONJ
ap-3105	398	9	b	b	X
ap-3105	398	10	=	=	SYM
ap-3105	398	11	(	(	PUNCT
ap-3105	398	12	%	%	INTJ
ap-3105	398	13	,	,	PUNCT
ap-3105	398	14	0	0	NUM
ap-3105	398	15	)	)	PUNCT
ap-3105	398	16	.	.	PUNCT
ap-3105	399	1	in	in	ADP
ap-3105	399	2	order	order	NOUN
ap-3105	399	3	to	to	PART
ap-3105	399	4	express	express	VERB
ap-3105	399	5	the	the	DET
ap-3105	399	6	propagator	propagator	NOUN
ap-3105	399	7	for	for	ADP
ap-3105	399	8	the	the	DET
ap-3105	399	9	aharonov	aharonov	PROPN
ap-3105	399	10	-	-	PUNCT
ap-3105	399	11	bohm	bohm	PROPN
ap-3105	399	12	hamiltonian	hamiltonian	ADJ
ap-3105	399	13	hab	hab	NOUN
ap-3105	399	14	we	we	PRON
ap-3105	399	15	again	again	ADV
ap-3105	399	16	pass	pass	VERB
ap-3105	399	17	to	to	ADP
ap-3105	399	18	a	a	DET
ap-3105	399	19	unitarily	unitarily	ADV
ap-3105	399	20	equivalent	equivalent	ADJ
ap-3105	399	21	formulation	formulation	NOUN
ap-3105	399	22	.	.	PUNCT
ap-3105	400	1	let	let	VERB
ap-3105	400	2	us	we	PRON
ap-3105	400	3	cut	cut	VERB
ap-3105	400	4	the	the	DET
ap-3105	400	5	plane	plane	NOUN
ap-3105	400	6	along	along	ADP
ap-3105	400	7	two	two	NUM
ap-3105	400	8	half	half	ADJ
ap-3105	400	9	-	-	PUNCT
ap-3105	400	10	lines	line	NOUN
ap-3105	400	11	,	,	PUNCT
ap-3105	400	12	la	la	X
ap-3105	400	13	=	=	PUNCT
ap-3105	400	14	]	]	X
ap-3105	400	15	−∞	−∞	NOUN
ap-3105	400	16	,	,	PUNCT
ap-3105	400	17	0[×	0[×	ADJ
ap-3105	400	18	{	{	PUNCT
ap-3105	400	19	0	0	NUM
ap-3105	400	20	}	}	PUNCT
ap-3105	400	21	and	and	CCONJ
ap-3105	400	22	lb	lb	NOUN
ap-3105	400	23	=	=	SYM
ap-3105	400	24	]	]	X
ap-3105	400	25	%	%	INTJ
ap-3105	400	26	,	,	PUNCT
ap-3105	401	1	+	+	PROPN
ap-3105	401	2	∞[×	∞[×	NOUN
ap-3105	401	3	{	{	PUNCT
ap-3105	401	4	0	0	NUM
ap-3105	401	5	}	}	PUNCT
ap-3105	401	6	.	.	PUNCT
ap-3105	402	1	let	let	VERB
ap-3105	402	2	(	(	PUNCT
ap-3105	402	3	ra	ra	PROPN
ap-3105	402	4	,	,	PUNCT
ap-3105	402	5	θa	θa	NUM
ap-3105	402	6	)	)	PUNCT
ap-3105	402	7	be	be	VERB
ap-3105	402	8	polar	polar	ADJ
ap-3105	402	9	coordinates	coordinate	NOUN
ap-3105	402	10	centered	center	VERB
ap-3105	402	11	at	at	ADP
ap-3105	402	12	the	the	DET
ap-3105	402	13	point	point	NOUN
ap-3105	402	14	a	a	PRON
ap-3105	402	15	and	and	CCONJ
ap-3105	402	16	(	(	PUNCT
ap-3105	402	17	rb	rb	PROPN
ap-3105	402	18	,	,	PUNCT
ap-3105	402	19	θb	θb	NOUN
ap-3105	402	20	)	)	PUNCT
ap-3105	402	21	be	be	VERB
ap-3105	402	22	polar	polar	ADJ
ap-3105	402	23	coordinates	coordinate	NOUN
ap-3105	402	24	centered	center	VERB
ap-3105	402	25	at	at	ADP
ap-3105	402	26	the	the	DET
ap-3105	402	27	point	point	NOUN
ap-3105	402	28	b.	b.	PROPN
ap-3105	403	1	the	the	DET
ap-3105	403	2	angle	angle	NOUN
ap-3105	403	3	variables	variable	NOUN
ap-3105	403	4	are	be	AUX
ap-3105	403	5	chosen	choose	VERB
ap-3105	403	6	so	so	SCONJ
ap-3105	403	7	that	that	SCONJ
ap-3105	403	8	the	the	DET
ap-3105	403	9	values	value	NOUN
ap-3105	403	10	θa	θa	NUM
ap-3105	403	11	=	=	SYM
ap-3105	403	12	±π	±π	X
ap-3105	403	13	correspond	correspond	VERB
ap-3105	403	14	to	to	ADP
ap-3105	403	15	the	the	DET
ap-3105	403	16	two	two	NUM
ap-3105	403	17	sides	side	NOUN
ap-3105	403	18	of	of	ADP
ap-3105	403	19	the	the	DET
ap-3105	403	20	cut	cut	NOUN
ap-3105	403	21	la	la	NOUN
ap-3105	403	22	,	,	PUNCT
ap-3105	403	23	and	and	CCONJ
ap-3105	403	24	similarly	similarly	ADV
ap-3105	403	25	for	for	ADP
ap-3105	403	26	θb	θb	NOUN
ap-3105	403	27	and	and	CCONJ
ap-3105	403	28	lb	lb	NOUN
ap-3105	403	29	.	.	PUNCT
ap-3105	404	1	then	then	ADV
ap-3105	404	2	an	an	DET
ap-3105	404	3	explicit	explicit	ADJ
ap-3105	404	4	and	and	CCONJ
ap-3105	404	5	commonly	commonly	ADV
ap-3105	404	6	used	use	VERB
ap-3105	404	7	choice	choice	NOUN
ap-3105	404	8	of	of	ADP
ap-3105	404	9	the	the	DET
ap-3105	404	10	aharonov	aharonov	PROPN
ap-3105	404	11	-	-	PUNCT
ap-3105	404	12	bohm	bohm	PROPN
ap-3105	404	13	vector	vector	NOUN
ap-3105	404	14	potential	potential	NOUN
ap-3105	404	15	reads	read	VERB
ap-3105	404	16	−→	−→	ADV
ap-3105	404	17	a	a	DET
ap-3105	404	18	=	=	SYM
ap-3105	404	19	α∇θa	α∇θa	PROPN
ap-3105	404	20	+	+	NUM
ap-3105	404	21	β∇θb	β∇θb	X
ap-3105	404	22	.	.	PUNCT
ap-3105	405	1	denote	denote	VERB
ap-3105	405	2	by	by	ADP
ap-3105	405	3	u	u	PRON
ap-3105	405	4	a	a	DET
ap-3105	405	5	unitary	unitary	ADJ
ap-3105	405	6	operator	operator	NOUN
ap-3105	405	7	in	in	ADP
ap-3105	405	8	l2(r2,d2x	l2(r2,d2x	PROPN
ap-3105	405	9	)	)	PUNCT
ap-3105	405	10	acting	act	VERB
ap-3105	405	11	as	as	ADP
ap-3105	405	12	the	the	DET
ap-3105	405	13	multiplication	multiplication	NOUN
ap-3105	405	14	operator	operator	NOUN
ap-3105	405	15	uψ	uψ	ADP
ap-3105	405	16	=	=	SYM
ap-3105	405	17	ei(αθa+βθb)ψ	ei(αθa+βθb)ψ	PROPN
ap-3105	405	18	,	,	PUNCT
ap-3105	405	19	232	232	NUM
ap-3105	405	20	vol	vol	NOUN
ap-3105	405	21	.	.	PUNCT
ap-3105	406	1	56	56	NUM
ap-3105	406	2	no	no	NOUN
ap-3105	406	3	.	.	PUNCT
ap-3105	407	1	3/2016	3/2016	NUM
ap-3105	407	2	the	the	DET
ap-3105	407	3	aharonov	aharonov	PROPN
ap-3105	407	4	-	-	PUNCT
ap-3105	407	5	bohm	bohm	PROPN
ap-3105	407	6	hamiltonian	hamiltonian	NOUN
ap-3105	407	7	with	with	ADP
ap-3105	407	8	two	two	NUM
ap-3105	407	9	vortices	vortex	NOUN
ap-3105	407	10	revisited	revisit	VERB
ap-3105	407	11	and	and	CCONJ
ap-3105	407	12	let	let	VERB
ap-3105	407	13	h	h	NOUN
ap-3105	407	14	′λ	′λ	NOUN
ap-3105	407	15	=	=	SYM
ap-3105	407	16	u−1habu	u−1habu	ADJ
ap-3105	407	17	.	.	PUNCT
ap-3105	408	1	then	then	ADV
ap-3105	408	2	h	h	PROPN
ap-3105	408	3	′λ	′λ	PROPN
ap-3105	408	4	acts	act	VERB
ap-3105	408	5	as	as	ADP
ap-3105	408	6	−∆	−∆	NOUN
ap-3105	408	7	in	in	ADP
ap-3105	408	8	l2(r2,d2x	l2(r2,d2x	PROPN
ap-3105	408	9	)	)	PUNCT
ap-3105	408	10	,	,	PUNCT
ap-3105	408	11	and	and	CCONJ
ap-3105	408	12	its	its	PRON
ap-3105	408	13	domain	domain	NOUN
ap-3105	408	14	is	be	AUX
ap-3105	408	15	determined	determine	VERB
ap-3105	408	16	by	by	ADP
ap-3105	408	17	the	the	DET
ap-3105	408	18	boundary	boundary	ADJ
ap-3105	408	19	conditions	condition	NOUN
ap-3105	408	20	along	along	ADP
ap-3105	408	21	the	the	DET
ap-3105	408	22	cut	cut	NOUN
ap-3105	409	1	la	la	NOUN
ap-3105	409	2	∪	∪	ADJ
ap-3105	409	3	lb	lb	NOUN
ap-3105	409	4	:	:	PUNCT
ap-3105	409	5	ψ(ra	ψ(ra	PROPN
ap-3105	409	6	,	,	PUNCT
ap-3105	409	7	θa	θa	NUM
ap-3105	409	8	=	=	SYM
ap-3105	409	9	π	π	X
ap-3105	409	10	)	)	PUNCT
ap-3105	409	11	=	=	PUNCT
ap-3105	409	12	e2πiαψ(ra	e2πiαψ(ra	PROPN
ap-3105	409	13	,	,	PUNCT
ap-3105	409	14	θa	θa	NUM
ap-3105	409	15	=	=	SYM
ap-3105	409	16	−π	−π	PROPN
ap-3105	409	17	)	)	PUNCT
ap-3105	409	18	,	,	PUNCT
ap-3105	409	19	∂θaψ(ra	∂θaψ(ra	PROPN
ap-3105	409	20	,	,	PUNCT
ap-3105	409	21	θa	θa	NUM
ap-3105	409	22	=	=	SYM
ap-3105	409	23	π	π	X
ap-3105	409	24	)	)	PUNCT
ap-3105	409	25	=	=	PUNCT
ap-3105	409	26	e2πiα∂θaψ(ra	e2πiα∂θaψ(ra	PROPN
ap-3105	409	27	,	,	PUNCT
ap-3105	409	28	θa	θa	NUM
ap-3105	409	29	=	=	SYM
ap-3105	409	30	−π	−π	PROPN
ap-3105	409	31	)	)	PUNCT
ap-3105	409	32	,	,	PUNCT
ap-3105	409	33	ψ(rb	ψ(rb	PROPN
ap-3105	409	34	,	,	PUNCT
ap-3105	409	35	θb	θb	ADP
ap-3105	409	36	=	=	SYM
ap-3105	409	37	π	π	X
ap-3105	409	38	)	)	PUNCT
ap-3105	409	39	=	=	SYM
ap-3105	409	40	e2πiβψ(rb	e2πiβψ(rb	NOUN
ap-3105	409	41	,	,	PUNCT
ap-3105	409	42	θb	θb	ADP
ap-3105	409	43	=	=	SYM
ap-3105	409	44	−π	−π	PROPN
ap-3105	409	45	)	)	PUNCT
ap-3105	409	46	,	,	PUNCT
ap-3105	409	47	∂θb	∂θb	PROPN
ap-3105	409	48	ψ(rb	ψ(rb	PROPN
ap-3105	409	49	,	,	PUNCT
ap-3105	409	50	θb	θb	ADP
ap-3105	409	51	=	=	SYM
ap-3105	409	52	π	π	X
ap-3105	409	53	)	)	PUNCT
ap-3105	409	54	=	=	PUNCT
ap-3105	409	55	e2πiβ∂θb	e2πiβ∂θb	X
ap-3105	409	56	ψ(rb	ψ(rb	PROPN
ap-3105	409	57	,	,	PUNCT
ap-3105	409	58	θb	θb	ADP
ap-3105	409	59	=	=	SYM
ap-3105	409	60	−π	−π	ADJ
ap-3105	409	61	)	)	PUNCT
ap-3105	409	62	.	.	PUNCT
ap-3105	410	1	in	in	ADP
ap-3105	410	2	addition	addition	NOUN
ap-3105	410	3	,	,	PUNCT
ap-3105	410	4	one	one	PRON
ap-3105	410	5	imposes	impose	VERB
ap-3105	410	6	the	the	DET
ap-3105	410	7	regular	regular	ADJ
ap-3105	410	8	boundary	boundary	ADJ
ap-3105	410	9	condition	condition	NOUN
ap-3105	410	10	at	at	ADP
ap-3105	410	11	the	the	DET
ap-3105	410	12	vortices	vortex	NOUN
ap-3105	410	13	,	,	PUNCT
ap-3105	410	14	namely	namely	ADV
ap-3105	410	15	ψ(a	ψ(a	PROPN
ap-3105	410	16	)	)	PUNCT
ap-3105	410	17	=	=	SYM
ap-3105	410	18	ψ(b	ψ(b	NOUN
ap-3105	410	19	)	)	PUNCT
ap-3105	410	20	=	=	SYM
ap-3105	411	1	0	0	X
ap-3105	411	2	.	.	PUNCT
ap-3105	412	1	we	we	PRON
ap-3105	412	2	wish	wish	VERB
ap-3105	412	3	to	to	PART
ap-3105	412	4	find	find	VERB
ap-3105	412	5	a	a	DET
ap-3105	412	6	formula	formula	NOUN
ap-3105	412	7	for	for	ADP
ap-3105	412	8	the	the	DET
ap-3105	412	9	propagator	propagator	NOUN
ap-3105	412	10	kab(t	kab(t	PROPN
ap-3105	412	11	,	,	PUNCT
ap-3105	412	12	x	x	PRON
ap-3105	412	13	,	,	PUNCT
ap-3105	412	14	x0	x0	PROPN
ap-3105	412	15	)	)	PUNCT
ap-3105	412	16	associated	associate	VERB
ap-3105	412	17	with	with	ADP
ap-3105	412	18	the	the	DET
ap-3105	412	19	hamiltonian	hamiltonian	ADJ
ap-3105	412	20	hab	hab	NOUN
ap-3105	412	21	.	.	PUNCT
ap-3105	413	1	note	note	VERB
ap-3105	413	2	that	that	SCONJ
ap-3105	413	3	kab(t	kab(t	PROPN
ap-3105	413	4	,	,	PUNCT
ap-3105	413	5	x	x	X
ap-3105	413	6	,	,	PUNCT
ap-3105	413	7	x0	x0	PROPN
ap-3105	413	8	)	)	PUNCT
ap-3105	414	1	=	=	NOUN
ap-3105	414	2	expi(αθa(x)+βθb(x))k′λ(t	expi(αθa(x)+βθb(x))k′λ(t	NOUN
ap-3105	414	3	,	,	PUNCT
ap-3105	414	4	x	x	NOUN
ap-3105	414	5	,	,	PUNCT
ap-3105	414	6	x0)e−i(αθa(x0)+βθb(x0	x0)e−i(αθa(x0)+βθb(x0	PROPN
ap-3105	414	7	)	)	PUNCT
ap-3105	414	8	)	)	PUNCT
ap-3105	414	9	where	where	SCONJ
ap-3105	414	10	k′λ(t	k′λ(t	NOUN
ap-3105	414	11	,	,	PUNCT
ap-3105	414	12	x	x	PRON
ap-3105	414	13	,	,	PUNCT
ap-3105	414	14	x0	x0	PROPN
ap-3105	414	15	)	)	PUNCT
ap-3105	414	16	is	be	AUX
ap-3105	414	17	the	the	DET
ap-3105	414	18	propagator	propagator	NOUN
ap-3105	414	19	associated	associate	VERB
ap-3105	414	20	with	with	ADP
ap-3105	414	21	h	h	NOUN
ap-3105	414	22	′λ	′λ	PROPN
ap-3105	414	23	.	.	PUNCT
ap-3105	415	1	let	let	VERB
ap-3105	415	2	us	we	PRON
ap-3105	415	3	denote	denote	VERB
ap-3105	415	4	d	d	PROPN
ap-3105	415	5	=	=	PUNCT
ap-3105	415	6	r2	r2	PROPN
ap-3105	415	7	\	\	PROPN
ap-3105	416	1	(	(	PUNCT
ap-3105	416	2	la	la	ADV
ap-3105	416	3	∪	∪	ADJ
ap-3105	416	4	lb	lb	NOUN
ap-3105	416	5	)	)	PUNCT
ap-3105	416	6	.	.	PUNCT
ap-3105	417	1	then	then	ADV
ap-3105	417	2	one	one	PRON
ap-3105	417	3	can	can	AUX
ap-3105	417	4	embed	embed	VERB
ap-3105	417	5	d	d	PROPN
ap-3105	417	6	⊂	⊂	PROPN
ap-3105	417	7	m̃	m̃	PROPN
ap-3105	417	8	as	as	ADP
ap-3105	417	9	a	a	DET
ap-3105	417	10	fundamental	fundamental	ADJ
ap-3105	417	11	domain	domain	NOUN
ap-3105	417	12	.	.	PUNCT
ap-3105	418	1	k′λ(t	k′λ(t	NOUN
ap-3105	418	2	,	,	PUNCT
ap-3105	418	3	x	x	PRON
ap-3105	418	4	,	,	PUNCT
ap-3105	418	5	x0	x0	PROPN
ap-3105	418	6	)	)	PUNCT
ap-3105	418	7	is	be	AUX
ap-3105	418	8	simply	simply	ADV
ap-3105	418	9	obtained	obtain	VERB
ap-3105	418	10	as	as	ADP
ap-3105	418	11	the	the	DET
ap-3105	418	12	restriction	restriction	NOUN
ap-3105	418	13	to	to	ADP
ap-3105	418	14	d	d	PROPN
ap-3105	418	15	of	of	ADP
ap-3105	418	16	the	the	DET
ap-3105	418	17	propagator	propagator	NOUN
ap-3105	418	18	kλ(t	kλ(t	VERB
ap-3105	418	19	,	,	PUNCT
ap-3105	418	20	x	x	PRON
ap-3105	418	21	,	,	PUNCT
ap-3105	418	22	x0	x0	PROPN
ap-3105	418	23	)	)	PUNCT
ap-3105	418	24	associated	associate	VERB
ap-3105	418	25	with	with	ADP
ap-3105	418	26	the	the	DET
ap-3105	418	27	hamiltonian	hamiltonian	PROPN
ap-3105	418	28	hλ	hλ	NOUN
ap-3105	418	29	.	.	PROPN
ap-3105	419	1	on	on	ADP
ap-3105	419	2	the	the	DET
ap-3105	419	3	other	other	ADJ
ap-3105	419	4	hand	hand	NOUN
ap-3105	419	5	,	,	PUNCT
ap-3105	419	6	to	to	PART
ap-3105	419	7	construct	construct	VERB
ap-3105	419	8	kλ(t	kλ(t	NOUN
ap-3105	419	9	,	,	PUNCT
ap-3105	419	10	x	x	PRON
ap-3105	419	11	,	,	PUNCT
ap-3105	419	12	x0	x0	PROPN
ap-3105	419	13	)	)	PUNCT
ap-3105	419	14	one	one	PRON
ap-3105	419	15	can	can	AUX
ap-3105	419	16	apply	apply	VERB
ap-3105	419	17	formula	formula	NOUN
ap-3105	419	18	(	(	PUNCT
ap-3105	419	19	5	5	NUM
ap-3105	419	20	)	)	PUNCT
ap-3105	419	21	and	and	CCONJ
ap-3105	419	22	the	the	DET
ap-3105	419	23	knowledge	knowledge	NOUN
ap-3105	419	24	of	of	ADP
ap-3105	419	25	the	the	DET
ap-3105	419	26	free	free	ADJ
ap-3105	419	27	propagator	propagator	NOUN
ap-3105	419	28	on	on	ADP
ap-3105	419	29	m̃	m̃	PROPN
ap-3105	419	30	,	,	PUNCT
ap-3105	419	31	see	see	VERB
ap-3105	419	32	(	(	PUNCT
ap-3105	419	33	9	9	NUM
ap-3105	419	34	)	)	PUNCT
ap-3105	419	35	,	,	PUNCT
ap-3105	419	36	(	(	PUNCT
ap-3105	419	37	10	10	NUM
ap-3105	419	38	)	)	PUNCT
ap-3105	419	39	.	.	PUNCT
ap-3105	420	1	thus	thus	ADV
ap-3105	420	2	we	we	PRON
ap-3105	420	3	get	get	VERB
ap-3105	420	4	kλ(t	kλ(t	NOUN
ap-3105	420	5	,	,	PUNCT
ap-3105	420	6	x	x	PRON
ap-3105	420	7	,	,	PUNCT
ap-3105	420	8	x0	x0	PROPN
ap-3105	420	9	)	)	PUNCT
ap-3105	421	1	=	=	PUNCT
ap-3105	421	2	∑	∑	PUNCT
ap-3105	421	3	g∈γ	g∈γ	VERB
ap-3105	421	4	∑	∑	PROPN
ap-3105	421	5	γ∈c	γ∈c	PROPN
ap-3105	421	6	(	(	PUNCT
ap-3105	421	7	g·x	g·x	PROPN
ap-3105	421	8	,	,	PUNCT
ap-3105	421	9	x0	x0	PROPN
ap-3105	421	10	)	)	PUNCT
ap-3105	422	1	λ(g−1)kγ(t	λ(g−1)kγ(t	PROPN
ap-3105	422	2	,	,	PUNCT
ap-3105	422	3	g	g	NOUN
ap-3105	422	4	·	·	PUNCT
ap-3105	422	5	x	x	X
ap-3105	422	6	,	,	PUNCT
ap-3105	422	7	x0	x0	PROPN
ap-3105	422	8	)	)	PUNCT
ap-3105	422	9	.	.	PUNCT
ap-3105	423	1	(	(	PUNCT
ap-3105	423	2	28	28	X
ap-3105	423	3	)	)	PUNCT
ap-3105	423	4	fix	fix	NOUN
ap-3105	423	5	t	t	X
ap-3105	423	6	>	>	X
ap-3105	423	7	0	0	PUNCT
ap-3105	424	1	and	and	CCONJ
ap-3105	424	2	x0	x0	NUM
ap-3105	424	3	,	,	PUNCT
ap-3105	424	4	x	x	PROPN
ap-3105	424	5	∈	∈	PROPN
ap-3105	424	6	d.	d.	PROPN
ap-3105	424	7	one	one	NOUN
ap-3105	424	8	can	can	AUX
ap-3105	424	9	classify	classify	VERB
ap-3105	424	10	piecewise	piecewise	NOUN
ap-3105	424	11	geodesic	geodesic	ADJ
ap-3105	424	12	paths	path	NOUN
ap-3105	424	13	in	in	ADP
ap-3105	424	14	m̃	m̃	PROPN
ap-3105	424	15	,	,	PUNCT
ap-3105	424	16	γ	γ	X
ap-3105	424	17	:	:	PUNCT
ap-3105	424	18	x0	x0	PROPN
ap-3105	424	19	→	→	SYM
ap-3105	424	20	c1	c1	PROPN
ap-3105	424	21	→	→	SYM
ap-3105	424	22	·	·	PUNCT
ap-3105	424	23	·	·	PUNCT
ap-3105	424	24	·	·	PUNCT
ap-3105	424	25	→	→	SYM
ap-3105	424	26	cn	cn	PROPN
ap-3105	424	27	→	→	SYM
ap-3105	424	28	g	g	PROPN
ap-3105	424	29	·	·	PUNCT
ap-3105	424	30	x	x	SYM
ap-3105	424	31	,	,	PUNCT
ap-3105	424	32	(	(	PUNCT
ap-3105	424	33	29	29	NUM
ap-3105	424	34	)	)	PUNCT
ap-3105	424	35	with	with	ADP
ap-3105	424	36	cj	cj	NOUN
ap-3105	424	37	∈	∈	PROPN
ap-3105	424	38	a	a	DET
ap-3105	424	39	∪	∪	NOUN
ap-3105	424	40	b	b	NOUN
ap-3105	424	41	and	and	CCONJ
ap-3105	424	42	g	g	PROPN
ap-3105	424	43	∈	∈	PROPN
ap-3105	424	44	γ	γ	PROPN
ap-3105	424	45	,	,	PUNCT
ap-3105	424	46	according	accord	VERB
ap-3105	424	47	to	to	ADP
ap-3105	424	48	their	their	PRON
ap-3105	424	49	projections	projection	NOUN
ap-3105	424	50	to	to	ADP
ap-3105	424	51	m	m	PROPN
ap-3105	424	52	.	.	PUNCT
ap-3105	425	1	let	let	VERB
ap-3105	425	2	γ	γ	X
ap-3105	425	3	be	be	AUX
ap-3105	425	4	a	a	DET
ap-3105	425	5	finite	finite	ADJ
ap-3105	425	6	alternating	alternate	VERB
ap-3105	425	7	sequence	sequence	NOUN
ap-3105	425	8	of	of	ADP
ap-3105	425	9	points	point	NOUN
ap-3105	425	10	a	a	PRON
ap-3105	425	11	and	and	CCONJ
ap-3105	425	12	b	b	NOUN
ap-3105	425	13	,	,	PUNCT
ap-3105	425	14	i.e.	i.e.	X
ap-3105	425	15	γ	γ	X
ap-3105	425	16	=	=	SYM
ap-3105	425	17	(	(	PUNCT
ap-3105	425	18	c1	c1	PROPN
ap-3105	425	19	,	,	PUNCT
ap-3105	425	20	.	.	PUNCT
ap-3105	425	21	.	.	PUNCT
ap-3105	426	1	.	.	PUNCT
ap-3105	427	1	,	,	PUNCT
ap-3105	427	2	cn	cn	PROPN
ap-3105	427	3	)	)	PUNCT
ap-3105	427	4	,	,	PUNCT
ap-3105	427	5	cj	cj	PROPN
ap-3105	427	6	∈	∈	PROPN
ap-3105	427	7	{	{	PUNCT
ap-3105	427	8	a	a	PROPN
ap-3105	427	9	,	,	PUNCT
ap-3105	427	10	b	b	NOUN
ap-3105	427	11	}	}	PUNCT
ap-3105	427	12	and	and	CCONJ
ap-3105	427	13	cj	cj	X
ap-3105	427	14	6=	6=	NUM
ap-3105	427	15	cj+1	cj+1	PROPN
ap-3105	427	16	.	.	PUNCT
ap-3105	428	1	the	the	DET
ap-3105	428	2	empty	empty	ADJ
ap-3105	428	3	sequence	sequence	NOUN
ap-3105	428	4	γ	γ	X
ap-3105	428	5	=	=	X
ap-3105	428	6	(	(	PUNCT
ap-3105	428	7	)	)	PUNCT
ap-3105	428	8	is	be	AUX
ap-3105	428	9	admissible	admissible	ADJ
ap-3105	428	10	.	.	PUNCT
ap-3105	429	1	relate	relate	VERB
ap-3105	429	2	to	to	ADP
ap-3105	429	3	γ	γ	PROPN
ap-3105	429	4	a	a	DET
ap-3105	429	5	piecewise	piecewise	NOUN
ap-3105	429	6	geodesic	geodesic	ADJ
ap-3105	429	7	path	path	NOUN
ap-3105	429	8	in	in	ADP
ap-3105	429	9	m	m	PROPN
ap-3105	429	10	,	,	PUNCT
ap-3105	429	11	namely	namely	ADV
ap-3105	429	12	x0	x0	PROPN
ap-3105	429	13	→	→	SYM
ap-3105	429	14	c1	c1	PROPN
ap-3105	429	15	→	→	SYM
ap-3105	429	16	·	·	PUNCT
ap-3105	429	17	·	·	PUNCT
ap-3105	429	18	·	·	PUNCT
ap-3105	430	1	→	→	SYM
ap-3105	430	2	cn	cn	PROPN
ap-3105	430	3	→	→	PROPN
ap-3105	430	4	x.	x.	NOUN
ap-3105	430	5	suppose	suppose	VERB
ap-3105	430	6	that	that	SCONJ
ap-3105	430	7	this	this	DET
ap-3105	430	8	path	path	NOUN
ap-3105	430	9	is	be	AUX
ap-3105	430	10	covered	cover	VERB
ap-3105	430	11	by	by	ADP
ap-3105	430	12	a	a	DET
ap-3105	430	13	path	path	NOUN
ap-3105	430	14	γ	γ	NOUN
ap-3105	430	15	in	in	ADP
ap-3105	430	16	m̃	m̃	PROPN
ap-3105	430	17	,	,	PUNCT
ap-3105	430	18	as	as	SCONJ
ap-3105	430	19	given	give	VERB
ap-3105	430	20	in	in	ADP
ap-3105	430	21	(	(	PUNCT
ap-3105	430	22	29	29	NUM
ap-3105	430	23	)	)	PUNCT
ap-3105	430	24	.	.	PUNCT
ap-3105	431	1	then	then	ADV
ap-3105	431	2	cj	cj	VERB
ap-3105	431	3	∈	∈	PROPN
ap-3105	431	4	a	a	DET
ap-3105	431	5	iff	iff	PROPN
ap-3105	431	6	cj	cj	PROPN
ap-3105	432	1	=	=	PUNCT
ap-3105	432	2	a	a	PROPN
ap-3105	432	3	and	and	CCONJ
ap-3105	432	4	cj	cj	NOUN
ap-3105	432	5	∈	∈	PROPN
ap-3105	433	1	b	b	PROPN
ap-3105	433	2	iff	iff	PROPN
ap-3105	433	3	cj	cj	PROPN
ap-3105	433	4	=	=	PROPN
ap-3105	433	5	b.	b.	PROPN
ap-3105	433	6	denote	denote	VERB
ap-3105	433	7	the	the	DET
ap-3105	433	8	angles	angle	NOUN
ap-3105	433	9	∠x0	∠x0	PROPN
ap-3105	433	10	,	,	PUNCT
ap-3105	433	11	c1	c1	NOUN
ap-3105	433	12	,	,	PUNCT
ap-3105	433	13	c2	c2	PROPN
ap-3105	433	14	=	=	SYM
ap-3105	433	15	θ0	θ0	PROPN
ap-3105	433	16	and	and	CCONJ
ap-3105	433	17	∠	∠	PROPN
ap-3105	433	18	cn−1	cn−1	PROPN
ap-3105	433	19	,	,	PUNCT
ap-3105	433	20	cn	cn	PROPN
ap-3105	433	21	,	,	PUNCT
ap-3105	433	22	x	x	X
ap-3105	433	23	=	=	SYM
ap-3105	433	24	θ	θ	PROPN
ap-3105	433	25	.	.	PUNCT
ap-3105	434	1	then	then	ADV
ap-3105	434	2	the	the	DET
ap-3105	434	3	angles	angle	NOUN
ap-3105	434	4	in	in	ADP
ap-3105	434	5	the	the	DET
ap-3105	434	6	path	path	NOUN
ap-3105	434	7	γ	γ	X
ap-3105	434	8	in	in	ADP
ap-3105	434	9	(	(	PUNCT
ap-3105	434	10	29	29	NUM
ap-3105	434	11	)	)	PUNCT
ap-3105	434	12	take	take	VERB
ap-3105	434	13	the	the	DET
ap-3105	434	14	values	value	NOUN
ap-3105	434	15	∠x0	∠x0	PROPN
ap-3105	434	16	,	,	PUNCT
ap-3105	434	17	c1	c1	NOUN
ap-3105	434	18	,	,	PUNCT
ap-3105	434	19	c2	c2	PROPN
ap-3105	434	20	=	=	SYM
ap-3105	434	21	θ0	θ0	PROPN
ap-3105	434	22	+	+	CCONJ
ap-3105	434	23	2πk1	2πk1	NUM
ap-3105	434	24	,	,	PUNCT
ap-3105	434	25	∠cn−1	∠cn−1	PROPN
ap-3105	434	26	,	,	PUNCT
ap-3105	434	27	cn	cn	PROPN
ap-3105	434	28	,	,	PUNCT
ap-3105	434	29	g	g	NOUN
ap-3105	434	30	·	·	PUNCT
ap-3105	434	31	x	x	PUNCT
ap-3105	435	1	=	=	PUNCT
ap-3105	435	2	θ	θ	PROPN
ap-3105	435	3	+	+	CCONJ
ap-3105	435	4	2πkn	2πkn	NUM
ap-3105	435	5	and	and	CCONJ
ap-3105	435	6	∠cj	∠cj	NOUN
ap-3105	435	7	,	,	PUNCT
ap-3105	435	8	cj+1	cj+1	NUM
ap-3105	435	9	,	,	PUNCT
ap-3105	435	10	cj+2	cj+2	NOUN
ap-3105	435	11	=	=	SYM
ap-3105	435	12	2πkj+1	2πkj+1	NUM
ap-3105	435	13	for	for	ADP
ap-3105	435	14	1	1	NUM
ap-3105	435	15	≤	≤	NUM
ap-3105	435	16	j	j	PROPN
ap-3105	435	17	≤	≤	PROPN
ap-3105	435	18	n	n	CCONJ
ap-3105	435	19	−	−	PROPN
ap-3105	435	20	2	2	NUM
ap-3105	435	21	(	(	PUNCT
ap-3105	435	22	if	if	SCONJ
ap-3105	435	23	n	n	PRON
ap-3105	435	24	≥	≥	NOUN
ap-3105	435	25	3	3	NUM
ap-3105	435	26	)	)	PUNCT
ap-3105	435	27	,	,	PUNCT
ap-3105	435	28	where	where	SCONJ
ap-3105	435	29	k1	k1	NOUN
ap-3105	435	30	,	,	PUNCT
ap-3105	435	31	.	.	PUNCT
ap-3105	435	32	.	.	PUNCT
ap-3105	436	1	.	.	PUNCT
ap-3105	437	1	,	,	PUNCT
ap-3105	437	2	kn	kn	PROPN
ap-3105	437	3	are	be	AUX
ap-3105	437	4	integers	integer	NOUN
ap-3105	437	5	.	.	PUNCT
ap-3105	438	1	any	any	DET
ap-3105	438	2	values	value	NOUN
ap-3105	438	3	k1	k1	NOUN
ap-3105	438	4	,	,	PUNCT
ap-3105	438	5	.	.	PUNCT
ap-3105	438	6	.	.	PUNCT
ap-3105	438	7	.	.	PUNCT
ap-3105	439	1	,	,	PUNCT
ap-3105	439	2	kn	kn	PROPN
ap-3105	439	3	∈	∈	PROPN
ap-3105	439	4	z	z	NOUN
ap-3105	439	5	are	be	AUX
ap-3105	439	6	possible	possible	ADJ
ap-3105	439	7	.	.	PUNCT
ap-3105	440	1	in	in	ADP
ap-3105	440	2	that	that	DET
ap-3105	440	3	case	case	NOUN
ap-3105	440	4	the	the	DET
ap-3105	440	5	representation	representation	NOUN
ap-3105	440	6	λ	λ	PROPN
ap-3105	440	7	applied	apply	VERB
ap-3105	440	8	to	to	ADP
ap-3105	440	9	the	the	DET
ap-3105	440	10	group	group	NOUN
ap-3105	440	11	element	element	NOUN
ap-3105	440	12	g	g	PROPN
ap-3105	440	13	occurring	occur	VERB
ap-3105	440	14	in	in	ADP
ap-3105	440	15	(	(	PUNCT
ap-3105	440	16	29	29	NUM
ap-3105	440	17	)	)	PUNCT
ap-3105	440	18	takes	take	VERB
ap-3105	440	19	the	the	DET
ap-3105	440	20	value	value	NOUN
ap-3105	440	21	λ(g	λ(g	PROPN
ap-3105	440	22	)	)	PUNCT
ap-3105	441	1	=	=	NOUN
ap-3105	441	2	exp	exp	NOUN
ap-3105	441	3	(	(	PUNCT
ap-3105	441	4	2πi(k1σ1	2πi(k1σ1	NUM
ap-3105	441	5	+	+	NUM
ap-3105	441	6	·	·	PUNCT
ap-3105	441	7	·	·	PUNCT
ap-3105	441	8	·	·	PUNCT
ap-3105	441	9	+	+	NUM
ap-3105	441	10	knσn	knσn	NOUN
ap-3105	441	11	)	)	PUNCT
ap-3105	441	12	)	)	PUNCT
ap-3105	441	13	where	where	SCONJ
ap-3105	441	14	σj	σj	ADP
ap-3105	441	15	∈	∈	PROPN
ap-3105	441	16	{	{	PUNCT
ap-3105	441	17	α	α	NOUN
ap-3105	441	18	,	,	PUNCT
ap-3105	441	19	β	β	NOUN
ap-3105	441	20	}	}	PUNCT
ap-3105	441	21	and	and	CCONJ
ap-3105	441	22	σj	σj	VERB
ap-3105	441	23	=	=	SYM
ap-3105	441	24	α	α	PROPN
ap-3105	441	25	if	if	SCONJ
ap-3105	441	26	cj	cj	X
ap-3105	441	27	=	=	SYM
ap-3105	441	28	a	a	PRON
ap-3105	441	29	,	,	PUNCT
ap-3105	441	30	and	and	CCONJ
ap-3105	441	31	σj	σj	VERB
ap-3105	441	32	=	=	VERB
ap-3105	441	33	β	β	X
ap-3105	441	34	if	if	SCONJ
ap-3105	441	35	cj	cj	X
ap-3105	441	36	=	=	SYM
ap-3105	441	37	b.	b.	PROPN
ap-3105	441	38	using	use	VERB
ap-3105	441	39	the	the	DET
ap-3105	441	40	equation∑	equation∑	NOUN
ap-3105	441	41	k∈z	k∈z	NOUN
ap-3105	441	42	e−2πiαk	e−2πiαk	VERB
ap-3105	441	43	(	(	PUNCT
ap-3105	441	44	1	1	NUM
ap-3105	441	45	θ	θ	NOUN
ap-3105	441	46	+	+	CCONJ
ap-3105	442	1	2πk	2πk	ADJ
ap-3105	442	2	−	−	PROPN
ap-3105	442	3	π	π	X
ap-3105	442	4	+	+	CCONJ
ap-3105	442	5	is	be	AUX
ap-3105	442	6	−	−	PROPN
ap-3105	442	7	1	1	NUM
ap-3105	442	8	θ	θ	PROPN
ap-3105	442	9	+	+	CCONJ
ap-3105	442	10	2πk	2πk	ADJ
ap-3105	443	1	+	+	CCONJ
ap-3105	443	2	π	π	X
ap-3105	443	3	+	+	CCONJ
ap-3105	443	4	is	be	AUX
ap-3105	443	5	)	)	PUNCT
ap-3105	444	1	=	=	SYM
ap-3105	444	2	−2	−2	NOUN
ap-3105	444	3	sin(πα	sin(πα	ADJ
ap-3105	444	4	)	)	PUNCT
ap-3105	444	5	e−α(s−iθ	e−α(s−iθ	PROPN
ap-3105	444	6	)	)	PUNCT
ap-3105	444	7	1	1	NUM
ap-3105	445	1	+	+	SYM
ap-3105	445	2	e−s+iθ	e−s+iθ	NOUN
ap-3105	445	3	which	which	PRON
ap-3105	445	4	is	be	AUX
ap-3105	445	5	valid	valid	ADJ
ap-3105	445	6	for	for	ADP
ap-3105	445	7	0	0	NUM
ap-3105	445	8	<	<	X
ap-3105	445	9	α	α	X
ap-3105	445	10	<	<	X
ap-3105	445	11	1	1	NUM
ap-3105	445	12	,	,	PUNCT
ap-3105	445	13	|θ|	|θ|	ADV
ap-3105	445	14	<	<	X
ap-3105	445	15	π	π	PROPN
ap-3105	445	16	,	,	PUNCT
ap-3105	445	17	one	one	PRON
ap-3105	445	18	can	can	AUX
ap-3105	445	19	carry	carry	VERB
ap-3105	445	20	out	out	ADP
ap-3105	445	21	a	a	DET
ap-3105	445	22	partial	partial	ADJ
ap-3105	445	23	summation	summation	NOUN
ap-3105	445	24	in	in	ADP
ap-3105	445	25	(	(	PUNCT
ap-3105	445	26	28	28	NUM
ap-3105	445	27	)	)	PUNCT
ap-3105	445	28	over	over	ADP
ap-3105	445	29	the	the	DET
ap-3105	445	30	integers	integer	NOUN
ap-3105	445	31	k1	k1	NOUN
ap-3105	445	32	,	,	PUNCT
ap-3105	445	33	.	.	PUNCT
ap-3105	445	34	.	.	PUNCT
ap-3105	446	1	.	.	PUNCT
ap-3105	447	1	,	,	PUNCT
ap-3105	447	2	kn	kn	PROPN
ap-3105	447	3	.	.	PUNCT
ap-3105	448	1	this	this	DET
ap-3105	448	2	way	way	NOUN
ap-3105	448	3	the	the	DET
ap-3105	448	4	double	double	ADJ
ap-3105	448	5	sum	sum	NOUN
ap-3105	448	6	in	in	ADP
ap-3105	448	7	(	(	PUNCT
ap-3105	448	8	28	28	NUM
ap-3105	448	9	)	)	PUNCT
ap-3105	448	10	reduces	reduce	VERB
ap-3105	448	11	to	to	ADP
ap-3105	448	12	a	a	DET
ap-3105	448	13	sum	sum	NOUN
ap-3105	448	14	over	over	ADP
ap-3105	448	15	finite	finite	NOUN
ap-3105	448	16	alternating	alternate	VERB
ap-3105	448	17	sequences	sequence	NOUN
ap-3105	448	18	γ	γ	NOUN
ap-3105	448	19	.	.	PUNCT
ap-3105	448	20	here	here	ADV
ap-3105	448	21	is	be	AUX
ap-3105	448	22	the	the	DET
ap-3105	448	23	resulting	result	VERB
ap-3105	448	24	formula	formula	NOUN
ap-3105	448	25	for	for	ADP
ap-3105	448	26	k′λ(t	k′λ(t	NOUN
ap-3105	448	27	,	,	PUNCT
ap-3105	448	28	x	x	PRON
ap-3105	448	29	,	,	PUNCT
ap-3105	448	30	x0	x0	PROPN
ap-3105	448	31	)	)	PUNCT
ap-3105	448	32	.	.	PUNCT
ap-3105	449	1	we	we	PRON
ap-3105	449	2	set	set	VERB
ap-3105	449	3	ζa	ζa	NOUN
ap-3105	449	4	=	=	SYM
ap-3105	449	5	1	1	NUM
ap-3105	449	6	or	or	CCONJ
ap-3105	449	7	ζa	ζa	NOUN
ap-3105	449	8	=	=	PUNCT
ap-3105	449	9	e2πiα	e2πiα	NOUN
ap-3105	449	10	or	or	CCONJ
ap-3105	449	11	ζa	ζa	VERB
ap-3105	449	12	=	=	SYM
ap-3105	449	13	e−2πiα	e−2πiα	PROPN
ap-3105	449	14	depending	depend	VERB
ap-3105	449	15	on	on	ADP
ap-3105	449	16	whether	whether	SCONJ
ap-3105	449	17	the	the	DET
ap-3105	449	18	segment	segment	NOUN
ap-3105	449	19	x0x	x0x	PROPN
ap-3105	449	20	does	do	AUX
ap-3105	449	21	not	not	PART
ap-3105	449	22	intersect	intersect	VERB
ap-3105	449	23	la	la	PROPN
ap-3105	449	24	,	,	PUNCT
ap-3105	449	25	or	or	CCONJ
ap-3105	449	26	x0x	x0x	PROPN
ap-3105	449	27	intersects	intersect	NOUN
ap-3105	449	28	la	la	PROPN
ap-3105	449	29	and	and	CCONJ
ap-3105	449	30	x0	x0	PROPN
ap-3105	449	31	lies	lie	VERB
ap-3105	449	32	in	in	ADP
ap-3105	449	33	the	the	DET
ap-3105	449	34	lower	low	ADJ
ap-3105	449	35	half	half	ADJ
ap-3105	449	36	-	-	PUNCT
ap-3105	449	37	plane	plane	NOUN
ap-3105	449	38	,	,	PUNCT
ap-3105	449	39	or	or	CCONJ
ap-3105	449	40	x0x	x0x	PROPN
ap-3105	449	41	intersects	intersect	NOUN
ap-3105	449	42	la	la	PROPN
ap-3105	450	1	and	and	CCONJ
ap-3105	450	2	x0	x0	PROPN
ap-3105	450	3	lies	lie	VERB
ap-3105	450	4	in	in	ADP
ap-3105	450	5	the	the	DET
ap-3105	450	6	upper	upper	ADJ
ap-3105	450	7	half	half	ADJ
ap-3105	450	8	-	-	PUNCT
ap-3105	450	9	plane	plane	NOUN
ap-3105	450	10	.	.	PUNCT
ap-3105	451	1	analogously	analogously	ADV
ap-3105	451	2	,	,	PUNCT
ap-3105	451	3	ζb	ζb	NOUN
ap-3105	451	4	=	=	SYM
ap-3105	451	5	1	1	NUM
ap-3105	451	6	or	or	CCONJ
ap-3105	451	7	ζb	ζb	NOUN
ap-3105	451	8	=	=	PUNCT
ap-3105	451	9	e2πiβ	e2πiβ	NOUN
ap-3105	451	10	or	or	CCONJ
ap-3105	451	11	ζb	ζb	NOUN
ap-3105	451	12	=	=	PUNCT
ap-3105	451	13	e−2πiβ	e−2πiβ	PROPN
ap-3105	451	14	depending	depend	VERB
ap-3105	451	15	on	on	ADP
ap-3105	451	16	whether	whether	SCONJ
ap-3105	451	17	the	the	DET
ap-3105	451	18	segment	segment	NOUN
ap-3105	451	19	x0x	x0x	PROPN
ap-3105	451	20	does	do	AUX
ap-3105	451	21	not	not	PART
ap-3105	451	22	intersect	intersect	VERB
ap-3105	451	23	lb	lb	ADP
ap-3105	451	24	,	,	PUNCT
ap-3105	451	25	or	or	CCONJ
ap-3105	451	26	x0x	x0x	PROPN
ap-3105	451	27	intersects	intersect	VERB
ap-3105	451	28	lb	lb	NOUN
ap-3105	452	1	and	and	CCONJ
ap-3105	452	2	x0	x0	PROPN
ap-3105	452	3	lies	lie	VERB
ap-3105	452	4	in	in	ADP
ap-3105	452	5	the	the	DET
ap-3105	452	6	upper	upper	ADJ
ap-3105	452	7	half	half	ADJ
ap-3105	452	8	-	-	PUNCT
ap-3105	452	9	plane	plane	NOUN
ap-3105	452	10	,	,	PUNCT
ap-3105	452	11	or	or	CCONJ
ap-3105	452	12	x0x	x0x	PROPN
ap-3105	452	13	intersects	intersect	VERB
ap-3105	452	14	lb	lb	NOUN
ap-3105	453	1	and	and	CCONJ
ap-3105	453	2	x0	x0	PROPN
ap-3105	453	3	lies	lie	VERB
ap-3105	453	4	in	in	ADP
ap-3105	453	5	the	the	DET
ap-3105	453	6	lower	low	ADJ
ap-3105	453	7	half	half	ADJ
ap-3105	453	8	-	-	PUNCT
ap-3105	453	9	plane	plane	NOUN
ap-3105	453	10	.	.	PUNCT
ap-3105	454	1	furthermore	furthermore	ADV
ap-3105	454	2	,	,	PUNCT
ap-3105	454	3	let	let	VERB
ap-3105	454	4	us	we	PRON
ap-3105	454	5	write	write	VERB
ap-3105	454	6	ζa	ζa	NOUN
ap-3105	454	7	=	=	PUNCT
ap-3105	454	8	eiαηa	eiαηa	NOUN
ap-3105	454	9	,	,	PUNCT
ap-3105	454	10	ζb	ζb	NOUN
ap-3105	454	11	=	=	NOUN
ap-3105	454	12	eiβηb	eiβηb	NOUN
ap-3105	454	13	,	,	PUNCT
ap-3105	454	14	where	where	SCONJ
ap-3105	454	15	ηa	ηa	X
ap-3105	454	16	,	,	PUNCT
ap-3105	454	17	ηb	ηb	PROPN
ap-3105	454	18	∈	∈	PROPN
ap-3105	454	19	{	{	PUNCT
ap-3105	454	20	0	0	NUM
ap-3105	454	21	,	,	PUNCT
ap-3105	454	22	2π,−2π	2π,−2π	NOUN
ap-3105	454	23	}	}	PUNCT
ap-3105	454	24	.	.	PUNCT
ap-3105	455	1	then	then	ADV
ap-3105	455	2	one	one	PRON
ap-3105	455	3	has	have	VERB
ap-3105	455	4	k′λ(t	k′λ(t	NOUN
ap-3105	455	5	,	,	PUNCT
ap-3105	455	6	x	x	PRON
ap-3105	455	7	,	,	PUNCT
ap-3105	455	8	x0	x0	PROPN
ap-3105	455	9	)	)	PUNCT
ap-3105	456	1	=	=	PUNCT
ap-3105	456	2	ζaζb	ζaζb	ADJ
ap-3105	456	3	1	1	NUM
ap-3105	456	4	4πit	4πit	NUM
ap-3105	456	5	exp	exp	NOUN
ap-3105	456	6	(	(	PUNCT
ap-3105	456	7	i	i	PROPN
ap-3105	456	8	|x−	|x−	X
ap-3105	456	9	x0|2	x0|2	PUNCT
ap-3105	456	10	4	4	NUM
ap-3105	456	11	t	t	NOUN
ap-3105	456	12	)	)	PUNCT
ap-3105	456	13	−	−	PROPN
ap-3105	456	14	∑	∑	PUNCT
ap-3105	456	15	c∈{a	c∈{a	PROPN
ap-3105	456	16	,	,	PUNCT
ap-3105	456	17	b	b	NOUN
ap-3105	456	18	}	}	PUNCT
ap-3105	456	19	ζc	ζc	ADP
ap-3105	456	20	sin(πσ	sin(πσ	NUM
ap-3105	456	21	)	)	PUNCT
ap-3105	456	22	4π2i	4π2i	NUM
ap-3105	456	23	∫	∫	PROPN
ap-3105	456	24	∞	∞	NOUN
ap-3105	456	25	0	0	NUM
ap-3105	457	1	dt1	dt1	PROPN
ap-3105	457	2	t1	t1	PROPN
ap-3105	457	3	∫	∫	PROPN
ap-3105	458	1	∞	∞	PROPN
ap-3105	458	2	0	0	NUM
ap-3105	458	3	dt0	dt0	NOUN
ap-3105	458	4	t0	t0	NOUN
ap-3105	458	5	δ(t1	δ(t1	X
ap-3105	459	1	+	+	CCONJ
ap-3105	459	2	t0	t0	PROPN
ap-3105	459	3	−	−	PROPN
ap-3105	459	4	t	t	PROPN
ap-3105	459	5	)	)	PUNCT
ap-3105	459	6	exp	exp	NOUN
ap-3105	459	7	(	(	PUNCT
ap-3105	459	8	i	i	PRON
ap-3105	459	9	(	(	PUNCT
ap-3105	459	10	r	r	NOUN
ap-3105	459	11	2	2	NUM
ap-3105	459	12	c	c	NOUN
ap-3105	459	13	4t1	4t1	NUM
ap-3105	460	1	+	+	CCONJ
ap-3105	460	2	r	r	NOUN
ap-3105	460	3	2	2	NUM
ap-3105	460	4	0c	0c	NOUN
ap-3105	460	5	4t0	4t0	NUM
ap-3105	460	6	)	)	PUNCT
ap-3105	460	7	)	)	PUNCT
ap-3105	461	1	exp[−σ(sc	exp[−σ(sc	PROPN
ap-3105	461	2	−	−	PROPN
ap-3105	461	3	i(θc	i(θc	PROPN
ap-3105	461	4	−	−	PROPN
ap-3105	461	5	θ0c	θ0c	VERB
ap-3105	461	6	−	−	PROPN
ap-3105	461	7	ηc	ηc	NOUN
ap-3105	461	8	)	)	PUNCT
ap-3105	461	9	]	]	PUNCT
ap-3105	461	10	1	1	NUM
ap-3105	462	1	+	+	CCONJ
ap-3105	462	2	exp(−sc	exp(−sc	NOUN
ap-3105	462	3	+	+	CCONJ
ap-3105	462	4	iθc	iθc	NOUN
ap-3105	462	5	−	−	PROPN
ap-3105	462	6	iθ0c	iθ0c	NOUN
ap-3105	462	7	)	)	PUNCT
ap-3105	462	8	+	+	CCONJ
ap-3105	462	9	1	1	NUM
ap-3105	462	10	4πi	4πi	NOUN
ap-3105	462	11	∑	∑	PUNCT
ap-3105	462	12	γ	γ	X
ap-3105	462	13	,	,	PUNCT
ap-3105	462	14	n≥2	n≥2	PROPN
ap-3105	462	15	(	(	PUNCT
ap-3105	462	16	−1)n	−1)n	PROPN
ap-3105	462	17	∫	∫	PROPN
ap-3105	462	18	∞	∞	PROPN
ap-3105	462	19	0	0	PROPN
ap-3105	462	20	dtn	dtn	PROPN
ap-3105	462	21	tn	tn	PROPN
ap-3105	462	22	.	.	PUNCT
ap-3105	462	23	.	.	PUNCT
ap-3105	462	24	.	.	PUNCT
ap-3105	463	1	∫	∫	PROPN
ap-3105	464	1	∞	∞	PROPN
ap-3105	464	2	0	0	NUM
ap-3105	464	3	dt0	dt0	PROPN
ap-3105	464	4	t0	t0	PROPN
ap-3105	464	5	δ(tn	δ(tn	X
ap-3105	464	6	+	+	CCONJ
ap-3105	464	7	·	·	PUNCT
ap-3105	464	8	·	·	PUNCT
ap-3105	464	9	·	·	PUNCT
ap-3105	464	10	+	+	NUM
ap-3105	464	11	t0	t0	PROPN
ap-3105	464	12	−	−	PROPN
ap-3105	464	13	t	t	PROPN
ap-3105	464	14	)	)	PUNCT
ap-3105	464	15	exp	exp	NOUN
ap-3105	464	16	(	(	PUNCT
ap-3105	464	17	i	i	NOUN
ap-3105	464	18	4	4	NUM
ap-3105	464	19	(	(	PUNCT
ap-3105	464	20	r2	r2	PROPN
ap-3105	464	21	tn	tn	PROPN
ap-3105	465	1	+	+	CCONJ
ap-3105	465	2	%	%	NOUN
ap-3105	465	3	2	2	X
ap-3105	465	4	tn−1	tn−1	PROPN
ap-3105	465	5	+	+	CCONJ
ap-3105	465	6	·	·	PUNCT
ap-3105	465	7	·	·	PUNCT
ap-3105	465	8	·	·	PUNCT
ap-3105	466	1	+	+	NUM
ap-3105	466	2	%	%	NOUN
ap-3105	466	3	2	2	NUM
ap-3105	466	4	t1	t1	NOUN
ap-3105	466	5	+	+	X
ap-3105	466	6	r2	r2	PROPN
ap-3105	466	7	0	0	NUM
ap-3105	466	8	t0	t0	PROPN
ap-3105	466	9	)	)	PUNCT
ap-3105	466	10	)	)	PUNCT
ap-3105	467	1	sγ(s	sγ(s	NUM
ap-3105	467	2	,	,	PUNCT
ap-3105	467	3	θ	θ	NOUN
ap-3105	467	4	,	,	PUNCT
ap-3105	467	5	θ0	θ0	PROPN
ap-3105	467	6	)	)	PUNCT
ap-3105	467	7	,	,	PUNCT
ap-3105	467	8	233	233	NUM
ap-3105	467	9	petra	petra	PROPN
ap-3105	467	10	košťáková	košťáková	PROPN
ap-3105	467	11	,	,	PUNCT
ap-3105	467	12	pavel	pavel	PROPN
ap-3105	467	13	šťovíček	šťovíček	PROPN
ap-3105	467	14	acta	acta	PROPN
ap-3105	467	15	polytechnica	polytechnica	PROPN
ap-3105	467	16	where	where	SCONJ
ap-3105	467	17	sγ(s	sγ(s	ADV
ap-3105	467	18	,	,	PUNCT
ap-3105	467	19	θ	θ	NOUN
ap-3105	467	20	,	,	PUNCT
ap-3105	467	21	θ0	θ0	PROPN
ap-3105	467	22	)	)	PUNCT
ap-3105	467	23	=	=	SYM
ap-3105	467	24	sin(πσn	sin(πσn	NOUN
ap-3105	467	25	)	)	PUNCT
ap-3105	468	1	π	π	PROPN
ap-3105	468	2	exp[−σn(sn	exp[−σn(sn	NOUN
ap-3105	468	3	−	−	PROPN
ap-3105	468	4	iθ	iθ	NOUN
ap-3105	468	5	)	)	PUNCT
ap-3105	468	6	]	]	PUNCT
ap-3105	469	1	1	1	NUM
ap-3105	469	2	+	+	NUM
ap-3105	469	3	exp(−sn	exp(−sn	NUM
ap-3105	469	4	+	+	CCONJ
ap-3105	469	5	iθ	iθ	NOUN
ap-3105	469	6	)	)	PUNCT
ap-3105	469	7	sin(πσn−1	sin(πσn−1	PROPN
ap-3105	469	8	)	)	PUNCT
ap-3105	470	1	π	π	PROPN
ap-3105	470	2	exp(−σn−1sn−1	exp(−σn−1sn−1	X
ap-3105	470	3	)	)	PUNCT
ap-3105	470	4	1	1	NUM
ap-3105	471	1	+	+	CCONJ
ap-3105	471	2	exp(−sn−1	exp(−sn−1	ADJ
ap-3105	471	3	)	)	PUNCT
ap-3105	471	4	×	×	NOUN
ap-3105	471	5	·	·	PUNCT
ap-3105	471	6	·	·	PUNCT
ap-3105	471	7	·	·	PUNCT
ap-3105	471	8	×	×	PROPN
ap-3105	471	9	sin(πσ1	sin(πσ1	NOUN
ap-3105	471	10	)	)	PUNCT
ap-3105	471	11	π	π	PROPN
ap-3105	471	12	exp[−σ1(s1	exp[−σ1(s1	ADJ
ap-3105	471	13	−	−	PROPN
ap-3105	471	14	iθ0	iθ0	PROPN
ap-3105	471	15	)	)	PUNCT
ap-3105	471	16	]	]	PUNCT
ap-3105	472	1	1	1	NUM
ap-3105	472	2	+	+	CCONJ
ap-3105	472	3	exp(−s1	exp(−s1	NOUN
ap-3105	472	4	+	+	CCONJ
ap-3105	472	5	iθ0	iθ0	NOUN
ap-3105	472	6	)	)	PUNCT
ap-3105	472	7	,	,	PUNCT
ap-3105	472	8	and	and	CCONJ
ap-3105	472	9	sa	sa	X
ap-3105	472	10	=	=	PUNCT
ap-3105	472	11	ln	ln	ADJ
ap-3105	472	12	t1r0a	t1r0a	NUM
ap-3105	472	13	t0ra	t0ra	NOUN
ap-3105	472	14	,	,	PUNCT
ap-3105	472	15	sb	sb	PROPN
ap-3105	472	16	=	=	NOUN
ap-3105	472	17	ln	ln	ADJ
ap-3105	472	18	t1r0b	t1r0b	NUM
ap-3105	473	1	t0rb	t0rb	PUNCT
ap-3105	473	2	,	,	PUNCT
ap-3105	473	3	sj	sj	INTJ
ap-3105	473	4	=	=	NOUN
ap-3105	473	5	ln	ln	ADJ
ap-3105	473	6	tjrj−1	tjrj−1	NOUN
ap-3105	473	7	tj−1rj	tj−1rj	NUM
ap-3105	473	8	for	for	ADP
ap-3105	473	9	1	1	NUM
ap-3105	473	10	≤	≤	NUM
ap-3105	473	11	j	j	PROPN
ap-3105	473	12	≤	≤	PROPN
ap-3105	473	13	n.	n.	NOUN
ap-3105	473	14	furthermore	furthermore	ADV
ap-3105	473	15	,	,	PUNCT
ap-3105	473	16	in	in	ADP
ap-3105	473	17	the	the	DET
ap-3105	473	18	first	first	ADJ
ap-3105	473	19	sum	sum	NOUN
ap-3105	473	20	on	on	ADP
ap-3105	473	21	the	the	DET
ap-3105	473	22	rhs	rhs	PROPN
ap-3105	473	23	,	,	PUNCT
ap-3105	473	24	(	(	PUNCT
ap-3105	473	25	rc	rc	NOUN
ap-3105	473	26	,	,	PUNCT
ap-3105	473	27	θc	θc	NOUN
ap-3105	473	28	)	)	PUNCT
ap-3105	473	29	and	and	CCONJ
ap-3105	473	30	(	(	PUNCT
ap-3105	473	31	r0c	r0c	NOUN
ap-3105	473	32	,	,	PUNCT
ap-3105	473	33	θ0c	θ0c	NOUN
ap-3105	473	34	)	)	PUNCT
ap-3105	473	35	are	be	AUX
ap-3105	473	36	the	the	DET
ap-3105	473	37	polar	polar	ADJ
ap-3105	473	38	coordinates	coordinate	NOUN
ap-3105	473	39	of	of	ADP
ap-3105	473	40	x	x	X
ap-3105	473	41	and	and	CCONJ
ap-3105	473	42	x0	x0	PROPN
ap-3105	473	43	with	with	ADP
ap-3105	473	44	respect	respect	NOUN
ap-3105	473	45	to	to	ADP
ap-3105	473	46	the	the	DET
ap-3105	473	47	center	center	NOUN
ap-3105	473	48	c	c	NOUN
ap-3105	473	49	,	,	PUNCT
ap-3105	473	50	respectively	respectively	ADV
ap-3105	473	51	,	,	PUNCT
ap-3105	473	52	and	and	CCONJ
ap-3105	473	53	σ	σ	X
ap-3105	473	54	=	=	SYM
ap-3105	473	55	α	α	PROPN
ap-3105	473	56	(	(	PUNCT
ap-3105	473	57	resp	resp	NOUN
ap-3105	473	58	.	.	PUNCT
ap-3105	474	1	β	β	X
ap-3105	474	2	)	)	PUNCT
ap-3105	474	3	if	if	SCONJ
ap-3105	474	4	c	c	NOUN
ap-3105	474	5	=	=	SYM
ap-3105	474	6	a	a	PRON
ap-3105	474	7	(	(	PUNCT
ap-3105	474	8	resp	resp	NOUN
ap-3105	474	9	.	.	PUNCT
ap-3105	475	1	b	b	X
ap-3105	475	2	)	)	PUNCT
ap-3105	475	3	.	.	PUNCT
ap-3105	476	1	the	the	DET
ap-3105	476	2	second	second	ADJ
ap-3105	476	3	sum	sum	NOUN
ap-3105	476	4	,	,	PUNCT
ap-3105	476	5	∑	∑	ADV
ap-3105	476	6	γ	γ	PROPN
ap-3105	476	7	,	,	PUNCT
ap-3105	476	8	n≥2	n≥2	PROPN
ap-3105	476	9	,	,	PUNCT
ap-3105	476	10	runs	run	VERB
ap-3105	476	11	over	over	ADP
ap-3105	476	12	all	all	DET
ap-3105	476	13	finite	finite	NOUN
ap-3105	476	14	alternating	alternate	VERB
ap-3105	476	15	sequences	sequence	NOUN
ap-3105	476	16	of	of	ADP
ap-3105	476	17	length	length	NOUN
ap-3105	476	18	at	at	ADV
ap-3105	476	19	least	least	ADV
ap-3105	476	20	two	two	NUM
ap-3105	476	21	,	,	PUNCT
ap-3105	476	22	γ	γ	X
ap-3105	476	23	=	=	SYM
ap-3105	476	24	(	(	PUNCT
ap-3105	476	25	c1	c1	PROPN
ap-3105	476	26	,	,	PUNCT
ap-3105	476	27	.	.	PUNCT
ap-3105	476	28	.	.	PUNCT
ap-3105	477	1	.	.	PUNCT
ap-3105	478	1	,	,	PUNCT
ap-3105	478	2	cn	cn	PROPN
ap-3105	478	3	)	)	PUNCT
ap-3105	478	4	,	,	PUNCT
ap-3105	478	5	and	and	CCONJ
ap-3105	478	6	(	(	PUNCT
ap-3105	478	7	r	r	NOUN
ap-3105	478	8	,	,	PUNCT
ap-3105	478	9	θ	θ	NOUN
ap-3105	478	10	)	)	PUNCT
ap-3105	478	11	are	be	AUX
ap-3105	478	12	the	the	DET
ap-3105	478	13	polar	polar	ADJ
ap-3105	478	14	coordinates	coordinate	NOUN
ap-3105	478	15	of	of	ADP
ap-3105	478	16	x	x	PUNCT
ap-3105	478	17	with	with	ADP
ap-3105	478	18	respect	respect	NOUN
ap-3105	478	19	to	to	ADP
ap-3105	478	20	cn	cn	PROPN
ap-3105	478	21	,	,	PUNCT
ap-3105	478	22	(	(	PUNCT
ap-3105	478	23	r0	r0	NOUN
ap-3105	478	24	,	,	PUNCT
ap-3105	478	25	θ0	θ0	PROPN
ap-3105	478	26	)	)	PUNCT
ap-3105	478	27	are	be	AUX
ap-3105	478	28	the	the	DET
ap-3105	478	29	polar	polar	ADJ
ap-3105	478	30	coordinates	coordinate	NOUN
ap-3105	478	31	of	of	ADP
ap-3105	478	32	x0	x0	PROPN
ap-3105	478	33	with	with	ADP
ap-3105	478	34	respect	respect	NOUN
ap-3105	478	35	to	to	ADP
ap-3105	478	36	c1	c1	NOUN
ap-3105	478	37	,	,	PUNCT
ap-3105	478	38	and	and	CCONJ
ap-3105	478	39	σj	σj	VERB
ap-3105	478	40	=	=	SYM
ap-3105	478	41	α	α	PROPN
ap-3105	478	42	(	(	PUNCT
ap-3105	478	43	resp	resp	NOUN
ap-3105	478	44	.	.	PUNCT
ap-3105	479	1	β	β	X
ap-3105	479	2	)	)	PUNCT
ap-3105	479	3	depending	depend	VERB
ap-3105	479	4	on	on	ADP
ap-3105	479	5	whether	whether	SCONJ
ap-3105	479	6	cj	cj	NOUN
ap-3105	479	7	=	=	PUNCT
ap-3105	479	8	a	a	PRON
ap-3105	479	9	(	(	PUNCT
ap-3105	479	10	resp	resp	NOUN
ap-3105	479	11	.	.	PUNCT
ap-3105	480	1	b	b	X
ap-3105	480	2	)	)	PUNCT
ap-3105	480	3	.	.	PUNCT
ap-3105	481	1	acknowledgements	acknowledgement	NOUN
ap-3105	481	2	one	one	NUM
ap-3105	481	3	of	of	ADP
ap-3105	481	4	the	the	DET
ap-3105	481	5	authors	author	NOUN
ap-3105	481	6	(	(	PUNCT
ap-3105	481	7	p.š	p.š	PROPN
ap-3105	481	8	.	.	PUNCT
ap-3105	481	9	)	)	PUNCT
ap-3105	481	10	wishes	wish	VERB
ap-3105	481	11	to	to	PART
ap-3105	481	12	acknowledge	acknowledge	VERB
ap-3105	481	13	gratefully	gratefully	ADV
ap-3105	481	14	partial	partial	ADJ
ap-3105	481	15	support	support	NOUN
ap-3105	481	16	from	from	ADP
ap-3105	481	17	grant	grant	NOUN
ap-3105	481	18	ga13	ga13	PROPN
ap-3105	481	19	-	-	PUNCT
ap-3105	481	20	11058s	11058	NOUN
ap-3105	481	21	of	of	ADP
ap-3105	481	22	the	the	DET
ap-3105	481	23	czech	czech	PROPN
ap-3105	481	24	science	science	PROPN
ap-3105	481	25	foundation	foundation	PROPN
ap-3105	481	26	.	.	PUNCT
ap-3105	482	1	references	reference	NOUN
ap-3105	482	2	[	[	X
ap-3105	482	3	1	1	NUM
ap-3105	482	4	]	]	PUNCT
ap-3105	482	5	i.	i.	PROPN
ap-3105	482	6	alexandrova	alexandrova	PROPN
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ap-3105	482	8	h.	h.	PROPN
ap-3105	482	9	tamura	tamura	PROPN
ap-3105	482	10	.	.	PROPN
ap-3105	482	11	resonance	resonance	NOUN
ap-3105	482	12	free	free	ADJ
ap-3105	482	13	regions	region	NOUN
ap-3105	482	14	in	in	ADP
ap-3105	482	15	magnetic	magnetic	ADJ
ap-3105	482	16	scattering	scattering	NOUN
ap-3105	482	17	by	by	ADP
ap-3105	482	18	two	two	NUM
ap-3105	482	19	solenoidal	solenoidal	ADJ
ap-3105	482	20	fields	field	NOUN
ap-3105	482	21	at	at	ADP
ap-3105	482	22	large	large	ADJ
ap-3105	482	23	separation	separation	NOUN
ap-3105	482	24	.	.	PUNCT
ap-3105	483	1	j.	j.	PROPN
ap-3105	483	2	funct	funct	PROPN
ap-3105	483	3	.	.	PUNCT
ap-3105	484	1	anal	anal	ADJ
ap-3105	484	2	.	.	PUNCT
ap-3105	485	1	260:1836	260:1836	NUM
ap-3105	485	2	-	-	SYM
ap-3105	485	3	1885	1885	NUM
ap-3105	485	4	,	,	PUNCT
ap-3105	485	5	2011	2011	NUM
ap-3105	485	6	.	.	PUNCT
ap-3105	486	1	doi:10.1016	doi:10.1016	PROPN
ap-3105	486	2	/	/	SYM
ap-3105	486	3	j.jfa.2010.12.005	j.jfa.2010.12.005	PROPN
ap-3105	486	4	[	[	X
ap-3105	486	5	2	2	NUM
ap-3105	486	6	]	]	PUNCT
ap-3105	486	7	i.	i.	PROPN
ap-3105	486	8	alexandrova	alexandrova	PROPN
ap-3105	486	9	,	,	PUNCT
ap-3105	486	10	h.	h.	PROPN
ap-3105	486	11	tamura	tamura	PROPN
ap-3105	486	12	.	.	PROPN
ap-3105	486	13	resonances	resonance	NOUN
ap-3105	486	14	in	in	ADP
ap-3105	486	15	scattering	scatter	VERB
ap-3105	486	16	by	by	ADP
ap-3105	486	17	two	two	NUM
ap-3105	486	18	magnetic	magnetic	ADJ
ap-3105	486	19	fields	field	NOUN
ap-3105	486	20	at	at	ADP
ap-3105	486	21	large	large	ADJ
ap-3105	486	22	separation	separation	NOUN
ap-3105	486	23	and	and	CCONJ
ap-3105	486	24	a	a	DET
ap-3105	486	25	complex	complex	ADJ
ap-3105	486	26	scaling	scaling	NOUN
ap-3105	486	27	method	method	NOUN
ap-3105	486	28	.	.	PUNCT
ap-3105	487	1	adv	adv	PROPN
ap-3105	487	2	.	.	PUNCT
ap-3105	487	3	math	math	NOUN
ap-3105	487	4	.	.	PUNCT
ap-3105	488	1	256:398	256:398	X
ap-3105	488	2	-	-	SYM
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ap-3105	488	4	,	,	PUNCT
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ap-3105	488	6	.	.	PUNCT
ap-3105	489	1	doi:10.1016	doi:10.1016	PROPN
ap-3105	489	2	/	/	SYM
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ap-3105	490	1	[	[	X
ap-3105	490	2	3	3	X
ap-3105	490	3	]	]	X
ap-3105	490	4	j.	j.	PROPN
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ap-3105	490	6	,	,	PUNCT
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ap-3105	490	9	,	,	PUNCT
ap-3105	490	10	r.	r.	PROPN
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ap-3105	490	12	.	.	PUNCT
ap-3105	491	1	magnetic	magnetic	PROPN
ap-3105	491	2	bloch	bloch	PROPN
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ap-3105	491	5	bochner	bochn	ADJ
ap-3105	491	6	laplacians	laplacian	NOUN
ap-3105	491	7	.	.	PUNCT
ap-3105	492	1	j.	j.	PROPN
ap-3105	492	2	geom	geom	PROPN
ap-3105	492	3	.	.	PUNCT
ap-3105	493	1	phys	phy	NOUN
ap-3105	493	2	.	.	PUNCT
ap-3105	494	1	13:275	13:275	NUM
ap-3105	494	2	-	-	SYM
ap-3105	494	3	288	288	NUM
ap-3105	494	4	,	,	PUNCT
ap-3105	494	5	1994	1994	NUM
ap-3105	494	6	.	.	PUNCT
ap-3105	495	1	doi:10.1016/0393	doi:10.1016/0393	ADJ
ap-3105	495	2	-	-	PUNCT
ap-3105	495	3	0440(94)90035	0440(94)90035	NOUN
ap-3105	495	4	-	-	PUNCT
ap-3105	495	5	3	3	NUM
ap-3105	495	6	[	[	X
ap-3105	495	7	4	4	NUM
ap-3105	495	8	]	]	PUNCT
ap-3105	495	9	m.	m.	PROPN
ap-3105	495	10	f.	f.	PROPN
ap-3105	495	11	atiyah	atiyah	PROPN
ap-3105	495	12	.	.	PUNCT
ap-3105	496	1	elliptic	elliptic	ADJ
ap-3105	496	2	operators	operator	NOUN
ap-3105	496	3	,	,	PUNCT
ap-3105	496	4	discrete	discrete	ADJ
ap-3105	496	5	groups	group	NOUN
ap-3105	496	6	and	and	CCONJ
ap-3105	496	7	von	von	PROPN
ap-3105	496	8	neumann	neumann	PROPN
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ap-3105	496	10	.	.	PUNCT
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ap-3105	497	3	-	-	SYM
ap-3105	497	4	33:43	33:43	NUM
ap-3105	497	5	-	-	SYM
ap-3105	497	6	72	72	NUM
ap-3105	497	7	,	,	PUNCT
ap-3105	497	8	1976	1976	NUM
ap-3105	497	9	.	.	PUNCT
ap-3105	498	1	[	[	X
ap-3105	498	2	5	5	NUM
ap-3105	498	3	]	]	PUNCT
ap-3105	498	4	o.	o.	PROPN
ap-3105	498	5	giraud	giraud	PROPN
ap-3105	498	6	,	,	PUNCT
ap-3105	498	7	a.	a.	PROPN
ap-3105	498	8	thain	thain	PROPN
ap-3105	498	9	,	,	PUNCT
ap-3105	498	10	j.	j.	PROPN
ap-3105	498	11	h.	h.	PROPN
ap-3105	498	12	hannay	hannay	PROPN
ap-3105	498	13	.	.	PUNCT
ap-3105	498	14	shrunk	shrunk	PROPN
ap-3105	498	15	loop	loop	NOUN
ap-3105	498	16	theorem	theorem	NOUN
ap-3105	498	17	for	for	ADP
ap-3105	498	18	the	the	DET
ap-3105	498	19	topology	topology	NOUN
ap-3105	498	20	probabilities	probability	NOUN
ap-3105	498	21	of	of	ADP
ap-3105	498	22	closed	closed	ADJ
ap-3105	498	23	brownian	brownian	ADJ
ap-3105	498	24	(	(	PUNCT
ap-3105	498	25	or	or	CCONJ
ap-3105	498	26	feynman	feynman	PROPN
ap-3105	498	27	)	)	PUNCT
ap-3105	498	28	paths	path	NOUN
ap-3105	498	29	on	on	ADP
ap-3105	498	30	the	the	DET
ap-3105	498	31	twice	twice	ADJ
ap-3105	498	32	punctured	punctured	ADJ
ap-3105	498	33	plane	plane	NOUN
ap-3105	498	34	.	.	PUNCT
ap-3105	499	1	j.	j.	PROPN
ap-3105	499	2	phys	phys	PROPN
ap-3105	499	3	.	.	PUNCT
ap-3105	500	1	a	a	DET
ap-3105	500	2	:	:	PUNCT
ap-3105	500	3	math	math	NOUN
ap-3105	500	4	.	.	PUNCT
ap-3105	501	1	gen	gen	PROPN
ap-3105	501	2	.	.	PROPN
ap-3105	501	3	37:2913	37:2913	PROPN
ap-3105	501	4	-	-	SYM
ap-3105	501	5	2935	2935	NUM
ap-3105	501	6	,	,	PUNCT
ap-3105	501	7	2004	2004	NUM
ap-3105	501	8	.	.	PUNCT
ap-3105	502	1	doi:10.1088/0305	doi:10.1088/0305	NOUN
ap-3105	502	2	-	-	PUNCT
ap-3105	502	3	4470/37/8/005	4470/37/8/005	PRON
ap-3105	502	4	[	[	X
ap-3105	502	5	6	6	NUM
ap-3105	502	6	]	]	PUNCT
ap-3105	502	7	m.	m.	NOUN
ap-3105	502	8	j.	j.	PROPN
ap-3105	502	9	gruber	gruber	PROPN
ap-3105	502	10	.	.	PUNCT
ap-3105	503	1	bloch	bloch	PROPN
ap-3105	503	2	theory	theory	NOUN
ap-3105	503	3	and	and	CCONJ
ap-3105	503	4	quantization	quantization	NOUN
ap-3105	503	5	of	of	ADP
ap-3105	503	6	magnetic	magnetic	ADJ
ap-3105	503	7	systems	system	NOUN
ap-3105	503	8	.	.	PUNCT
ap-3105	504	1	j.	j.	PROPN
ap-3105	504	2	geom	geom	PROPN
ap-3105	504	3	.	.	PUNCT
ap-3105	505	1	phys	phy	NOUN
ap-3105	505	2	.	.	PUNCT
ap-3105	506	1	34:137	34:137	NUM
ap-3105	506	2	-	-	SYM
ap-3105	506	3	154	154	NUM
ap-3105	506	4	,	,	PUNCT
ap-3105	506	5	2000	2000	NUM
ap-3105	506	6	.	.	PUNCT
ap-3105	507	1	doi:10.1016	doi:10.1016	PROPN
ap-3105	507	2	/	/	SYM
ap-3105	507	3	s0393	s0393	PROPN
ap-3105	507	4	-	-	PUNCT
ap-3105	507	5	0440(99)00059	0440(99)00059	NOUN
ap-3105	507	6	-	-	PUNCT
ap-3105	507	7	5	5	NUM
ap-3105	507	8	[	[	X
ap-3105	507	9	7	7	X
ap-3105	507	10	]	]	PUNCT
ap-3105	507	11	j.	j.	PROPN
ap-3105	507	12	h.	h.	PROPN
ap-3105	507	13	hannay	hannay	PROPN
ap-3105	507	14	,	,	PUNCT
ap-3105	507	15	a.	a.	PROPN
ap-3105	507	16	thain	thain	PROPN
ap-3105	507	17	.	.	PUNCT
ap-3105	508	1	exact	exact	ADJ
ap-3105	508	2	scattering	scattering	NOUN
ap-3105	508	3	theory	theory	NOUN
ap-3105	508	4	for	for	ADP
ap-3105	508	5	any	any	DET
ap-3105	508	6	straight	straight	ADJ
ap-3105	508	7	reflectors	reflector	NOUN
ap-3105	508	8	in	in	ADP
ap-3105	508	9	two	two	NUM
ap-3105	508	10	dimensions	dimension	NOUN
ap-3105	508	11	.	.	PUNCT
ap-3105	509	1	j.	j.	PROPN
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ap-3105	509	3	.	.	PUNCT
ap-3105	510	1	a	a	DET
ap-3105	510	2	:	:	PUNCT
ap-3105	510	3	math	math	NOUN
ap-3105	510	4	.	.	PUNCT
ap-3105	511	1	gen	gen	PROPN
ap-3105	511	2	.	.	PROPN
ap-3105	511	3	36:4063	36:4063	NUM
ap-3105	511	4	-	-	SYM
ap-3105	511	5	4080	4080	NUM
ap-3105	511	6	,	,	PUNCT
ap-3105	511	7	2003	2003	NUM
ap-3105	511	8	.	.	PUNCT
ap-3105	512	1	doi:10.1088/0305	doi:10.1088/0305	ADJ
ap-3105	512	2	-	-	PUNCT
ap-3105	512	3	4470/36/14/310	4470/36/14/310	PROPN
ap-3105	512	4	[	[	X
ap-3105	512	5	8	8	NUM
ap-3105	512	6	]	]	X
ap-3105	512	7	l.	l.	NOUN
ap-3105	512	8	hörmander	hörmander	PROPN
ap-3105	512	9	.	.	PUNCT
ap-3105	513	1	the	the	DET
ap-3105	513	2	analysis	analysis	NOUN
ap-3105	513	3	of	of	ADP
ap-3105	513	4	linear	linear	ADJ
ap-3105	513	5	partial	partial	ADJ
ap-3105	513	6	differential	differential	NOUN
ap-3105	513	7	operators	operator	NOUN
ap-3105	513	8	i.	i.	PROPN
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ap-3105	513	12	,	,	PUNCT
ap-3105	513	13	2003	2003	NUM
ap-3105	513	14	.	.	PUNCT
ap-3105	514	1	[	[	X
ap-3105	514	2	9	9	NUM
ap-3105	514	3	]	]	PUNCT
ap-3105	514	4	h.	h.	PROPN
ap-3105	514	5	t.	t.	PROPN
ap-3105	514	6	ito	ito	PROPN
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ap-3105	514	8	h.	h.	PROPN
ap-3105	514	9	tamura	tamura	PROPN
ap-3105	514	10	.	.	PROPN
ap-3105	514	11	aharonov	aharonov	PROPN
ap-3105	514	12	-	-	PUNCT
ap-3105	514	13	bohm	bohm	PROPN
ap-3105	514	14	effect	effect	NOUN
ap-3105	514	15	in	in	ADP
ap-3105	514	16	scattering	scatter	VERB
ap-3105	514	17	by	by	ADP
ap-3105	514	18	point	point	NOUN
ap-3105	514	19	-	-	PUNCT
ap-3105	514	20	like	like	ADJ
ap-3105	514	21	magnetic	magnetic	ADJ
ap-3105	514	22	fields	field	NOUN
ap-3105	514	23	at	at	ADP
ap-3105	514	24	large	large	ADJ
ap-3105	514	25	separation	separation	NOUN
ap-3105	514	26	.	.	PUNCT
ap-3105	515	1	ann	ann	PROPN
ap-3105	515	2	.	.	PUNCT
ap-3105	516	1	h.	h.	PROPN
ap-3105	516	2	poincaré	poincaré	PROPN
ap-3105	516	3	2:309	2:309	PROPN
ap-3105	516	4	-	-	PUNCT
ap-3105	516	5	359	359	NUM
ap-3105	516	6	,	,	PUNCT
ap-3105	516	7	2001	2001	NUM
ap-3105	516	8	.	.	PUNCT
ap-3105	517	1	doi:10.1007	doi:10.1007	PROPN
ap-3105	517	2	/	/	SYM
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ap-3105	518	1	[	[	X
ap-3105	518	2	10	10	NUM
ap-3105	518	3	]	]	PUNCT
ap-3105	518	4	t.	t.	PROPN
ap-3105	518	5	kato	kato	PROPN
ap-3105	518	6	:	:	PUNCT
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ap-3105	518	12	.	.	PUNCT
ap-3105	519	1	new	new	PROPN
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ap-3105	519	3	:	:	PUNCT
ap-3105	519	4	springer	springer	NOUN
ap-3105	519	5	-	-	PUNCT
ap-3105	519	6	verlag	verlag	PROPN
ap-3105	519	7	,	,	PUNCT
ap-3105	519	8	1966	1966	NUM
ap-3105	519	9	.	.	PUNCT
ap-3105	520	1	[	[	X
ap-3105	520	2	11	11	NUM
ap-3105	520	3	]	]	PUNCT
ap-3105	520	4	p.	p.	NOUN
ap-3105	520	5	kocábová	kocábová	PROPN
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ap-3105	520	7	p.	p.	PROPN
ap-3105	520	8	šťovíček	šťovíček	PROPN
ap-3105	520	9	.	.	PUNCT
ap-3105	521	1	generalized	generalize	VERB
ap-3105	521	2	bloch	bloch	PROPN
ap-3105	521	3	analysis	analysis	NOUN
ap-3105	521	4	and	and	CCONJ
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ap-3105	521	6	on	on	ADP
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ap-3105	521	8	manifolds	manifold	NOUN
ap-3105	521	9	with	with	ADP
ap-3105	521	10	a	a	DET
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ap-3105	522	1	j.	j.	PROPN
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ap-3105	523	2	.	.	PUNCT
ap-3105	524	1	49	49	NUM
ap-3105	524	2	:	:	PUNCT
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ap-3105	524	4	.	.	PUNCT
ap-3105	525	1	no	no	INTJ
ap-3105	525	2	.	.	NOUN
ap-3105	525	3	033518	033518	NUM
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ap-3105	525	6	.	.	PUNCT
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ap-3105	527	1	[	[	X
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ap-3105	528	1	,	,	PUNCT
ap-3105	528	2	p.	p.	PROPN
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ap-3105	529	8	nonvanishing	nonvanishing	ADJ
ap-3105	529	9	gauge	gauge	NOUN
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ap-3105	530	1	j.	j.	PROPN
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ap-3105	531	1	phys	phy	NOUN
ap-3105	531	2	.	.	PUNCT
ap-3105	532	1	61:727	61:727	NUM
ap-3105	532	2	-	-	PUNCT
ap-3105	532	3	744	744	NUM
ap-3105	532	4	,	,	PUNCT
ap-3105	532	5	2011	2011	NUM
ap-3105	532	6	.	.	PUNCT
ap-3105	533	1	doi:10.1016	doi:10.1016	PROPN
ap-3105	533	2	/	/	SYM
ap-3105	533	3	j.geomphys.2010.12.004	j.geomphys.2010.12.004	PROPN
ap-3105	534	1	[	[	X
ap-3105	534	2	13	13	NUM
ap-3105	534	3	]	]	X
ap-3105	534	4	j.	j.	PROPN
ap-3105	534	5	m.	m.	PROPN
ap-3105	534	6	lee	lee	PROPN
ap-3105	534	7	.	.	PROPN
ap-3105	534	8	introduction	introduction	NOUN
ap-3105	534	9	to	to	ADP
ap-3105	534	10	topological	topological	ADJ
ap-3105	534	11	manifolds	manifold	NOUN
ap-3105	534	12	.	.	PUNCT
ap-3105	535	1	berlin	berlin	ADJ
ap-3105	535	2	:	:	PUNCT
ap-3105	535	3	springer	springer	NOUN
ap-3105	535	4	-	-	PUNCT
ap-3105	535	5	verlag	verlag	PROPN
ap-3105	535	6	,	,	PUNCT
ap-3105	535	7	2000	2000	NUM
ap-3105	535	8	.	.	PUNCT
ap-3105	536	1	[	[	X
ap-3105	536	2	14	14	NUM
ap-3105	536	3	]	]	X
ap-3105	536	4	s.	s.	PROPN
ap-3105	536	5	mashkevich	mashkevich	PROPN
ap-3105	536	6	,	,	PUNCT
ap-3105	536	7	j.	j.	PROPN
ap-3105	536	8	myrheim	myrheim	PROPN
ap-3105	536	9	,	,	PUNCT
ap-3105	536	10	s.	s.	PROPN
ap-3105	536	11	ouvry	ouvry	PROPN
ap-3105	536	12	.	.	PUNCT
ap-3105	537	1	quantum	quantum	ADJ
ap-3105	537	2	mechanics	mechanic	NOUN
ap-3105	537	3	of	of	ADP
ap-3105	537	4	a	a	DET
ap-3105	537	5	particle	particle	NOUN
ap-3105	537	6	with	with	ADP
ap-3105	537	7	two	two	NUM
ap-3105	537	8	magnetic	magnetic	ADJ
ap-3105	537	9	impurities	impurity	NOUN
ap-3105	537	10	.	.	PUNCT
ap-3105	538	1	phys	phy	NOUN
ap-3105	538	2	.	.	PUNCT
ap-3105	539	1	lett	lett	PROPN
ap-3105	539	2	.	.	PUNCT
ap-3105	540	1	a	a	DET
ap-3105	540	2	330:41	330:41	PROPN
ap-3105	540	3	-	-	SYM
ap-3105	540	4	47	47	NUM
ap-3105	540	5	,	,	PUNCT
ap-3105	540	6	2004	2004	NUM
ap-3105	540	7	.	.	PUNCT
ap-3105	541	1	doi:10.1016	doi:10.1016	PROPN
ap-3105	541	2	/	/	SYM
ap-3105	541	3	j.physleta.2004.07.040	j.physleta.2004.07.040	PROPN
ap-3105	542	1	[	[	X
ap-3105	542	2	15	15	NUM
ap-3105	542	3	]	]	PUNCT
ap-3105	542	4	m.	m.	NOUN
ap-3105	542	5	melgaard	melgaard	NOUN
ap-3105	542	6	,	,	PUNCT
ap-3105	542	7	e.	e.	PROPN
ap-3105	542	8	ouhabaz	ouhabaz	PROPN
ap-3105	542	9	,	,	PUNCT
ap-3105	542	10	g.	g.	PROPN
ap-3105	542	11	rozenblum	rozenblum	PROPN
ap-3105	542	12	.	.	PUNCT
ap-3105	543	1	negative	negative	ADJ
ap-3105	543	2	discrete	discrete	ADJ
ap-3105	543	3	spectrum	spectrum	NOUN
ap-3105	543	4	of	of	ADP
ap-3105	543	5	perturbed	perturb	VERB
ap-3105	543	6	multivortex	multivortex	ADJ
ap-3105	543	7	aharonov	aharonov	PROPN
ap-3105	543	8	-	-	PUNCT
ap-3105	543	9	bohm	bohm	PROPN
ap-3105	543	10	hamiltonians	hamiltonian	NOUN
ap-3105	543	11	.	.	PUNCT
ap-3105	544	1	ann	ann	PROPN
ap-3105	544	2	.	.	PUNCT
ap-3105	545	1	h.	h.	PROPN
ap-3105	545	2	poincaré	poincaré	PROPN
ap-3105	545	3	5:979	5:979	NUM
ap-3105	545	4	-	-	SYM
ap-3105	545	5	1012	1012	NUM
ap-3105	545	6	,	,	PUNCT
ap-3105	545	7	2004	2004	NUM
ap-3105	545	8	.	.	PUNCT
ap-3105	546	1	doi:10.1007	doi:10.1007	VERB
ap-3105	546	2	/	/	SYM
ap-3105	546	3	s00023	s00023	NUM
ap-3105	546	4	-	-	PUNCT
ap-3105	546	5	004	004	NOUN
ap-3105	546	6	-	-	PUNCT
ap-3105	546	7	0187	0187	NUM
ap-3105	546	8	-	-	SYM
ap-3105	546	9	3	3	NUM
ap-3105	547	1	[	[	X
ap-3105	547	2	16	16	NUM
ap-3105	547	3	]	]	PUNCT
ap-3105	547	4	t.	t.	PROPN
ap-3105	547	5	mine	mine	PROPN
ap-3105	547	6	.	.	PUNCT
ap-3105	548	1	periodic	periodic	ADJ
ap-3105	548	2	aharonov	aharonov	PROPN
ap-3105	548	3	-	-	PUNCT
ap-3105	548	4	bohm	bohm	PROPN
ap-3105	548	5	solenoids	solenoid	NOUN
ap-3105	548	6	in	in	ADP
ap-3105	548	7	a	a	DET
ap-3105	548	8	constant	constant	ADJ
ap-3105	548	9	magnetic	magnetic	ADJ
ap-3105	548	10	field	field	NOUN
ap-3105	548	11	.	.	PUNCT
ap-3105	549	1	ann	ann	PROPN
ap-3105	549	2	.	.	PUNCT
ap-3105	550	1	h.	h.	PROPN
ap-3105	550	2	poincaré	poincaré	PROPN
ap-3105	550	3	6:125	6:125	PROPN
ap-3105	550	4	-	-	PUNCT
ap-3105	550	5	154	154	NUM
ap-3105	550	6	,	,	PUNCT
ap-3105	550	7	2005	2005	NUM
ap-3105	550	8	.	.	PUNCT
ap-3105	551	1	doi:10.1007	doi:10.1007	VERB
ap-3105	551	2	/	/	SYM
ap-3105	551	3	s00023	s00023	NUM
ap-3105	551	4	-	-	PUNCT
ap-3105	551	5	005	005	NUM
ap-3105	551	6	-	-	PUNCT
ap-3105	551	7	0201	0201	NUM
ap-3105	551	8	-	-	SYM
ap-3105	551	9	4	4	NUM
ap-3105	552	1	[	[	SYM
ap-3105	552	2	17	17	NUM
ap-3105	552	3	]	]	PUNCT
ap-3105	552	4	t.	t.	NOUN
ap-3105	552	5	mine	mine	PROPN
ap-3105	552	6	,	,	PUNCT
ap-3105	552	7	y.	y.	PROPN
ap-3105	552	8	nomura	nomura	PROPN
ap-3105	552	9	.	.	PUNCT
ap-3105	553	1	periodic	periodic	ADJ
ap-3105	553	2	aharonov	aharonov	PROPN
ap-3105	553	3	-	-	PUNCT
ap-3105	553	4	bohm	bohm	PROPN
ap-3105	553	5	solenoids	solenoid	NOUN
ap-3105	553	6	in	in	ADP
ap-3105	553	7	a	a	DET
ap-3105	553	8	constant	constant	ADJ
ap-3105	553	9	magnetic	magnetic	ADJ
ap-3105	553	10	field	field	NOUN
ap-3105	553	11	.	.	PUNCT
ap-3105	554	1	rev	rev	PROPN
ap-3105	554	2	.	.	PROPN
ap-3105	554	3	math	math	NOUN
ap-3105	554	4	.	.	PUNCT
ap-3105	555	1	phys	phy	NOUN
ap-3105	555	2	.	.	PUNCT
ap-3105	556	1	18:913	18:913	NUM
ap-3105	556	2	-	-	SYM
ap-3105	556	3	934	934	NUM
ap-3105	556	4	,	,	PUNCT
ap-3105	556	5	2006	2006	NUM
ap-3105	556	6	.	.	PUNCT
ap-3105	557	1	doi:10.1142	doi:10.1142	NOUN
ap-3105	557	2	/	/	SYM
ap-3105	557	3	s0129055x06002826	s0129055x06002826	PROPN
ap-3105	557	4	[	[	X
ap-3105	557	5	18	18	NUM
ap-3105	557	6	]	]	PUNCT
ap-3105	557	7	j.	j.	PROPN
ap-3105	557	8	s.	s.	PROPN
ap-3105	557	9	schulman	schulman	PROPN
ap-3105	557	10	.	.	PROPN
ap-3105	558	1	approximate	approximate	PROPN
ap-3105	558	2	topologies	topology	NOUN
ap-3105	558	3	.	.	PUNCT
ap-3105	559	1	j.	j.	PROPN
ap-3105	559	2	math	math	PROPN
ap-3105	559	3	.	.	PUNCT
ap-3105	560	1	phys	phy	NOUN
ap-3105	560	2	.	.	PUNCT
ap-3105	561	1	12:304	12:304	NUM
ap-3105	561	2	-	-	SYM
ap-3105	561	3	308	308	NUM
ap-3105	561	4	,	,	PUNCT
ap-3105	561	5	1971	1971	NUM
ap-3105	561	6	.	.	PUNCT
ap-3105	562	1	doi:10.1063/1.1665592	doi:10.1063/1.1665592	NOUN
ap-3105	562	2	[	[	X
ap-3105	562	3	19	19	NUM
ap-3105	562	4	]	]	PUNCT
ap-3105	562	5	j.	j.	PROPN
ap-3105	562	6	s.	s.	PROPN
ap-3105	562	7	schulman	schulman	PROPN
ap-3105	562	8	.	.	PUNCT
ap-3105	563	1	techniques	technique	NOUN
ap-3105	563	2	and	and	CCONJ
ap-3105	563	3	applications	application	NOUN
ap-3105	563	4	of	of	ADP
ap-3105	563	5	path	path	NOUN
ap-3105	563	6	integration	integration	NOUN
ap-3105	563	7	.	.	PUNCT
ap-3105	564	1	new	new	PROPN
ap-3105	564	2	york	york	PROPN
ap-3105	564	3	:	:	PUNCT
ap-3105	564	4	wiley	wiley	PROPN
ap-3105	564	5	,	,	PUNCT
ap-3105	564	6	1981	1981	NUM
ap-3105	564	7	.	.	PUNCT
ap-3105	565	1	[	[	X
ap-3105	565	2	20	20	NUM
ap-3105	565	3	]	]	PUNCT
ap-3105	565	4	a.	a.	NOUN
ap-3105	565	5	j.	j.	PROPN
ap-3105	565	6	shtern	shtern	PROPN
ap-3105	565	7	.	.	PUNCT
ap-3105	566	1	unitary	unitary	ADJ
ap-3105	566	2	representation	representation	NOUN
ap-3105	566	3	of	of	ADP
ap-3105	566	4	a	a	DET
ap-3105	566	5	topological	topological	ADJ
ap-3105	566	6	group	group	NOUN
ap-3105	566	7	the	the	DET
ap-3105	566	8	online	online	ADJ
ap-3105	566	9	encyclopaedia	encyclopaedia	NOUN
ap-3105	566	10	of	of	ADP
ap-3105	566	11	mathematics	mathematic	NOUN
ap-3105	566	12	.	.	PUNCT
ap-3105	567	1	berlin	berlin	PROPN
ap-3105	567	2	:	:	PUNCT
ap-3105	567	3	springer	springer	NOUN
ap-3105	567	4	,	,	PUNCT
ap-3105	567	5	2001	2001	NUM
ap-3105	567	6	.	.	PUNCT
ap-3105	568	1	online	online	ADJ
ap-3105	568	2	:	:	PUNCT
ap-3105	568	3	http://eom.springer.de/	http://eom.springer.de/	X
ap-3105	569	1	[	[	X
ap-3105	569	2	21	21	NUM
ap-3105	569	3	]	]	X
ap-3105	569	4	p.	p.	NOUN
ap-3105	569	5	šťovíček	šťovíček	PROPN
ap-3105	569	6	.	.	PUNCT
ap-3105	570	1	the	the	DET
ap-3105	570	2	green	green	ADJ
ap-3105	570	3	function	function	NOUN
ap-3105	570	4	for	for	ADP
ap-3105	570	5	the	the	DET
ap-3105	570	6	two	two	NUM
ap-3105	570	7	-	-	PUNCT
ap-3105	570	8	solenoid	solenoid	NOUN
ap-3105	570	9	aharonov	aharonov	NOUN
ap-3105	570	10	-	-	PUNCT
ap-3105	570	11	bohm	bohm	PROPN
ap-3105	570	12	effect	effect	NOUN
ap-3105	570	13	.	.	PUNCT
ap-3105	571	1	phys	phy	NOUN
ap-3105	571	2	.	.	PUNCT
ap-3105	572	1	lett	lett	PROPN
ap-3105	572	2	.	.	PUNCT
ap-3105	573	1	a	a	DET
ap-3105	573	2	142:5	142:5	NUM
ap-3105	573	3	-	-	SYM
ap-3105	573	4	10	10	NUM
ap-3105	573	5	,	,	PUNCT
ap-3105	573	6	1989	1989	NUM
ap-3105	573	7	.	.	PUNCT
ap-3105	574	1	doi:10.1016/0375	doi:10.1016/0375	VERB
ap-3105	574	2	-	-	PUNCT
ap-3105	574	3	9601(89)90702	9601(89)90702	NUM
ap-3105	574	4	-	-	SYM
ap-3105	574	5	0	0	NUM
ap-3105	574	6	234	234	NUM
ap-3105	574	7	http://dx.doi.org/10.1016/j.jfa.2010.12.005	http://dx.doi.org/10.1016/j.jfa.2010.12.005	NOUN
ap-3105	574	8	http://dx.doi.org/10.1016/j.aim.2014.01.022	http://dx.doi.org/10.1016/j.aim.2014.01.022	NOUN
ap-3105	574	9	http://dx.doi.org/10.1016/0393-0440(94)90035-3	http://dx.doi.org/10.1016/0393-0440(94)90035-3	NOUN
ap-3105	575	1	http://dx.doi.org/10.1088/0305-4470/37/8/005	http://dx.doi.org/10.1088/0305-4470/37/8/005	PROPN
ap-3105	575	2	http://dx.doi.org/10.1016/s0393-0440(99)00059-5	http://dx.doi.org/10.1016/s0393-0440(99)00059-5	PROPN
ap-3105	575	3	http://dx.doi.org/10.1088/0305-4470/36/14/310	http://dx.doi.org/10.1088/0305-4470/36/14/310	NOUN
ap-3105	575	4	http://dx.doi.org/10.1007/pl00001036	http://dx.doi.org/10.1007/pl00001036	NOUN
ap-3105	575	5	http://dx.doi.org/10.1063/1.2898484	http://dx.doi.org/10.1063/1.2898484	VERB
ap-3105	576	1	http://dx.doi.org/10.1016/j.geomphys.2010.12.004	http://dx.doi.org/10.1016/j.geomphys.2010.12.004	PRON
ap-3105	576	2	http://dx.doi.org/10.1016/j.physleta.2004.07.040	http://dx.doi.org/10.1016/j.physleta.2004.07.040	ADJ
ap-3105	576	3	http://dx.doi.org/10.1007/s00023-004-0187-3	http://dx.doi.org/10.1007/s00023-004-0187-3	PROPN
ap-3105	576	4	http://dx.doi.org/10.1007/s00023-005-0201-4	http://dx.doi.org/10.1007/s00023-005-0201-4	NUM
ap-3105	576	5	http://dx.doi.org/10.1142/s0129055x06002826	http://dx.doi.org/10.1142/s0129055x06002826	PROPN
ap-3105	576	6	http://dx.doi.org/10.1063/1.1665592	http://dx.doi.org/10.1063/1.1665592	X
ap-3105	576	7	http://dx.doi.org/10.1016/0375-9601(89)90702-0	http://dx.doi.org/10.1016/0375-9601(89)90702-0	PROPN
ap-3105	576	8	vol	vol	NOUN
ap-3105	576	9	.	.	PUNCT
ap-3105	577	1	56	56	NUM
ap-3105	577	2	no	no	NOUN
ap-3105	577	3	.	.	PUNCT
ap-3105	578	1	3/2016	3/2016	NUM
ap-3105	578	2	the	the	DET
ap-3105	578	3	aharonov	aharonov	PROPN
ap-3105	578	4	-	-	PUNCT
ap-3105	578	5	bohm	bohm	PROPN
ap-3105	578	6	hamiltonian	hamiltonian	NOUN
ap-3105	578	7	with	with	ADP
ap-3105	578	8	two	two	NUM
ap-3105	578	9	vortices	vortex	NOUN
ap-3105	578	10	revisited	revisit	VERB
ap-3105	578	11	[	[	X
ap-3105	578	12	22	22	NUM
ap-3105	578	13	]	]	PUNCT
ap-3105	578	14	p.	p.	NOUN
ap-3105	578	15	šťovíček	šťovíček	PROPN
ap-3105	578	16	.	.	PUNCT
ap-3105	579	1	scattering	scatter	VERB
ap-3105	579	2	on	on	ADP
ap-3105	579	3	a	a	DET
ap-3105	579	4	finite	finite	ADJ
ap-3105	579	5	chain	chain	NOUN
ap-3105	579	6	of	of	ADP
ap-3105	579	7	vortices	vortex	NOUN
ap-3105	579	8	.	.	PUNCT
ap-3105	580	1	duke	duke	PROPN
ap-3105	580	2	math	math	PROPN
ap-3105	580	3	.	.	PUNCT
ap-3105	581	1	j.	j.	PROPN
ap-3105	581	2	76:303	76:303	NUM
ap-3105	581	3	-	-	SYM
ap-3105	581	4	332	332	NUM
ap-3105	581	5	,	,	PUNCT
ap-3105	581	6	1994	1994	NUM
ap-3105	581	7	.	.	PUNCT
ap-3105	581	8	doi:10.1215	doi:10.1215	PROPN
ap-3105	581	9	/	/	SYM
ap-3105	581	10	s0012	s0012	NOUN
ap-3105	581	11	-	-	PUNCT
ap-3105	581	12	7094	7094	NUM
ap-3105	581	13	-	-	PUNCT
ap-3105	581	14	94	94	NUM
ap-3105	581	15	-	-	PUNCT
ap-3105	581	16	07611	07611	NUM
ap-3105	581	17	-	-	SYM
ap-3105	581	18	4	4	NUM
ap-3105	582	1	[	[	NOUN
ap-3105	582	2	23	23	NUM
ap-3105	582	3	]	]	PUNCT
ap-3105	582	4	t.	t.	PROPN
ap-3105	582	5	sunada	sunada	PROPN
ap-3105	582	6	.	.	PUNCT
ap-3105	583	1	fundamental	fundamental	ADJ
ap-3105	583	2	groups	group	NOUN
ap-3105	583	3	and	and	CCONJ
ap-3105	583	4	laplacians	laplacian	NOUN
ap-3105	583	5	.	.	PUNCT
ap-3105	584	1	in	in	ADP
ap-3105	584	2	:	:	PUNCT
ap-3105	584	3	geometry	geometry	NOUN
ap-3105	584	4	and	and	CCONJ
ap-3105	584	5	analysis	analysis	NOUN
ap-3105	584	6	on	on	ADP
ap-3105	584	7	manifolds	manifold	NOUN
ap-3105	584	8	.	.	PUNCT
ap-3105	585	1	lect	lect	PROPN
ap-3105	585	2	.	.	PUNCT
ap-3105	586	1	notes	note	VERB
ap-3105	586	2	math	math	PROPN
ap-3105	586	3	.	.	PUNCT
ap-3105	587	1	1339	1339	NUM
ap-3105	587	2	.	.	PUNCT
ap-3105	588	1	berlin	berlin	ADJ
ap-3105	588	2	:	:	PUNCT
ap-3105	588	3	springer	springer	NOUN
ap-3105	588	4	,	,	PUNCT
ap-3105	588	5	1988	1988	NUM
ap-3105	588	6	,	,	PUNCT
ap-3105	588	7	pp	pp	ADV
ap-3105	588	8	.	.	PUNCT
ap-3105	589	1	248	248	NUM
ap-3105	589	2	-	-	SYM
ap-3105	589	3	277	277	NUM
ap-3105	589	4	.	.	PUNCT
ap-3105	590	1	[	[	X
ap-3105	590	2	24	24	NUM
ap-3105	590	3	]	]	PUNCT
ap-3105	590	4	t.	t.	PROPN
ap-3105	590	5	sunada	sunada	PROPN
ap-3105	590	6	.	.	PUNCT
ap-3105	591	1	a	a	DET
ap-3105	591	2	periodic	periodic	ADJ
ap-3105	591	3	schrödinger	schrödinger	ADJ
ap-3105	591	4	operator	operator	NOUN
ap-3105	591	5	in	in	ADP
ap-3105	591	6	an	an	DET
ap-3105	591	7	abelian	abelian	ADJ
ap-3105	591	8	cover	cover	NOUN
ap-3105	591	9	,	,	PUNCT
ap-3105	591	10	j.	j.	PROPN
ap-3105	591	11	fac	fac	PROPN
ap-3105	591	12	.	.	PUNCT
ap-3105	592	1	sci	sci	PROPN
ap-3105	592	2	.	.	PROPN
ap-3105	592	3	univ	univ	PROPN
ap-3105	592	4	.	.	PUNCT
ap-3105	593	1	tokyo	tokyo	PROPN
ap-3105	593	2	sect	sect	NOUN
ap-3105	593	3	.	.	PUNCT
ap-3105	593	4	,	,	PUNCT
ap-3105	593	5	1a	1a	PROPN
ap-3105	593	6	math	math	NOUN
ap-3105	593	7	.	.	PUNCT
ap-3105	594	1	37:575	37:575	NUM
ap-3105	594	2	-	-	PUNCT
ap-3105	594	3	583	583	NUM
ap-3105	594	4	,	,	PUNCT
ap-3105	594	5	1990	1990	NUM
ap-3105	594	6	.	.	PUNCT
ap-3105	595	1	[	[	X
ap-3105	595	2	25	25	NUM
ap-3105	595	3	]	]	X
ap-3105	595	4	h.	h.	PROPN
ap-3105	595	5	tamura	tamura	PROPN
ap-3105	595	6	.	.	PUNCT
ap-3105	596	1	semiclassical	semiclassical	ADJ
ap-3105	596	2	analysis	analysis	NOUN
ap-3105	596	3	for	for	ADP
ap-3105	596	4	magnetic	magnetic	ADJ
ap-3105	596	5	scattering	scattering	NOUN
ap-3105	596	6	by	by	ADP
ap-3105	596	7	two	two	NUM
ap-3105	596	8	solenoidal	solenoidal	ADJ
ap-3105	596	9	fields	field	NOUN
ap-3105	596	10	:	:	PUNCT
ap-3105	596	11	total	total	PROPN
ap-3105	596	12	cross	cross	PROPN
ap-3105	596	13	sections	section	NOUN
ap-3105	596	14	.	.	PUNCT
ap-3105	597	1	ann	ann	PROPN
ap-3105	597	2	.	.	PUNCT
ap-3105	598	1	h.	h.	PROPN
ap-3105	598	2	poincaré	poincaré	PROPN
ap-3105	598	3	8:1071	8:1071	PROPN
ap-3105	598	4	-	-	SYM
ap-3105	598	5	1114	1114	NUM
ap-3105	598	6	,	,	PUNCT
ap-3105	598	7	2007	2007	NUM
ap-3105	598	8	.	.	PUNCT
ap-3105	599	1	doi:10.1007	doi:10.1007	VERB
ap-3105	599	2	/	/	SYM
ap-3105	599	3	s00023	s00023	NUM
ap-3105	599	4	-	-	PUNCT
ap-3105	599	5	007	007	NUM
ap-3105	599	6	-	-	PUNCT
ap-3105	599	7	0329	0329	NUM
ap-3105	599	8	-	-	SYM
ap-3105	599	9	5	5	NUM
ap-3105	599	10	[	[	SYM
ap-3105	599	11	26	26	NUM
ap-3105	599	12	]	]	PUNCT
ap-3105	599	13	e.	e.	PROPN
ap-3105	599	14	thoma	thoma	PROPN
ap-3105	599	15	.	.	PUNCT
ap-3105	600	1	über	über	PROPN
ap-3105	600	2	unitäre	unitäre	PROPN
ap-3105	600	3	darstellungen	darstellungen	PROPN
ap-3105	600	4	abzälbarer	abzälbarer	PROPN
ap-3105	600	5	,	,	PUNCT
ap-3105	600	6	diskreter	diskreter	NOUN
ap-3105	600	7	gruppen	gruppen	NOUN
ap-3105	600	8	.	.	PUNCT
ap-3105	601	1	math	math	NOUN
ap-3105	601	2	.	.	PUNCT
ap-3105	602	1	annalen	annalen	PROPN
ap-3105	602	2	153:111	153:111	PROPN
ap-3105	602	3	-	-	PUNCT
ap-3105	602	4	138	138	NUM
ap-3105	602	5	,	,	PUNCT
ap-3105	602	6	1964	1964	NUM
ap-3105	602	7	.	.	PUNCT
ap-3105	603	1	[	[	X
ap-3105	603	2	27	27	NUM
ap-3105	603	3	]	]	PUNCT
ap-3105	603	4	t.	t.	PROPN
ap-3105	603	5	t.	t.	PROPN
ap-3105	603	6	wu	wu	PROPN
ap-3105	603	7	,	,	PUNCT
ap-3105	603	8	c.	c.	PROPN
ap-3105	603	9	n.	n.	PROPN
ap-3105	603	10	yang	yang	PROPN
ap-3105	603	11	.	.	PUNCT
ap-3105	604	1	concept	concept	NOUN
ap-3105	604	2	of	of	ADP
ap-3105	604	3	nonintegrable	nonintegrable	ADJ
ap-3105	604	4	phase	phase	NOUN
ap-3105	604	5	factors	factor	NOUN
ap-3105	604	6	and	and	CCONJ
ap-3105	604	7	global	global	ADJ
ap-3105	604	8	formulation	formulation	NOUN
ap-3105	604	9	of	of	ADP
ap-3105	604	10	gauge	gauge	NOUN
ap-3105	604	11	fields	field	NOUN
ap-3105	604	12	.	.	PUNCT
ap-3105	605	1	phys	phy	NOUN
ap-3105	605	2	.	.	PUNCT
ap-3105	606	1	rev	rev	PROPN
ap-3105	606	2	.	.	PUNCT
ap-3105	607	1	d	d	PROPN
ap-3105	607	2	12:3845	12:3845	PROPN
ap-3105	607	3	-	-	SYM
ap-3105	607	4	3857	3857	NUM
ap-3105	607	5	,	,	PUNCT
ap-3105	607	6	1978	1978	NUM
ap-3105	607	7	.	.	PUNCT
ap-3105	607	8	doi:10.1103	doi:10.1103	SYM
ap-3105	607	9	/	/	SYM
ap-3105	607	10	physrevd.12.3845	physrevd.12.3845	ADJ
ap-3105	607	11	235	235	NUM
ap-3105	607	12	http://dx.doi.org/10.1215/s0012-7094-94-07611-4	http://dx.doi.org/10.1215/s0012-7094-94-07611-4	PROPN
ap-3105	607	13	http://dx.doi.org/10.1007/s00023-007-0329-5	http://dx.doi.org/10.1007/s00023-007-0329-5	PUNCT
ap-3105	607	14	http://dx.doi.org/10.1103/physrevd.12.3845	http://dx.doi.org/10.1103/physrevd.12.3845	PROPN
ap-3105	607	15	acta	acta	PROPN
ap-3105	607	16	polytechnica	polytechnica	PROPN
ap-3105	607	17	56(3):224–235	56(3):224–235	PROPN
ap-3105	607	18	,	,	PUNCT
ap-3105	607	19	2016	2016	NUM
ap-3105	607	20	1	1	NUM
ap-3105	607	21	introduction	introduction	NOUN
ap-3105	607	22	2	2	NUM
ap-3105	607	23	a	a	DET
ap-3105	607	24	summary	summary	NOUN
ap-3105	607	25	of	of	ADP
ap-3105	607	26	the	the	DET
ap-3105	607	27	general	general	ADJ
ap-3105	607	28	approach	approach	NOUN
ap-3105	607	29	2.1	2.1	NUM
ap-3105	607	30	periodic	periodic	ADJ
ap-3105	607	31	hamiltonians	hamiltonian	NOUN
ap-3105	607	32	2.2	2.2	NUM
ap-3105	607	33	a	a	DET
ap-3105	607	34	generalization	generalization	NOUN
ap-3105	607	35	of	of	ADP
ap-3105	607	36	the	the	DET
ap-3105	607	37	bloch	bloch	PROPN
ap-3105	607	38	decomposition	decomposition	NOUN
ap-3105	607	39	2.3	2.3	NUM
ap-3105	607	40	propagators	propagator	NOUN
ap-3105	607	41	associated	associate	VERB
ap-3105	607	42	with	with	ADP
ap-3105	607	43	periodic	periodic	ADJ
ap-3105	607	44	hamiltonians	hamiltonian	NOUN
ap-3105	607	45	3	3	NUM
ap-3105	607	46	the	the	DET
ap-3105	607	47	propagator	propagator	NOUN
ap-3105	607	48	on	on	ADP
ap-3105	607	49	the	the	DET
ap-3105	607	50	universal	universal	ADJ
ap-3105	607	51	covering	covering	NOUN
ap-3105	607	52	space	space	NOUN
ap-3105	607	53	3.1	3.1	NUM
ap-3105	607	54	a	a	DET
ap-3105	607	55	formula	formula	NOUN
ap-3105	607	56	for	for	ADP
ap-3105	607	57	the	the	DET
ap-3105	607	58	propagator	propagator	NOUN
ap-3105	607	59	3.2	3.2	NUM
ap-3105	607	60	auxiliary	auxiliary	NOUN
ap-3105	607	61	relations	relation	NOUN
ap-3105	607	62	3.3	3.3	NUM
ap-3105	607	63	verification	verification	NOUN
ap-3105	607	64	of	of	ADP
ap-3105	607	65	the	the	DET
ap-3105	607	66	propagator	propagator	NOUN
ap-3105	607	67	formula	formula	VERB
ap-3105	607	68	4	4	NUM
ap-3105	607	69	conclusion	conclusion	NOUN
ap-3105	607	70	.	.	PUNCT
ap-3105	608	1	the	the	DET
ap-3105	608	2	propagator	propagator	NOUN
ap-3105	608	3	for	for	ADP
ap-3105	608	4	two	two	NUM
ap-3105	608	5	aharonov	aharonov	NOUN
ap-3105	608	6	-	-	PUNCT
ap-3105	608	7	bohm	bohm	PROPN
ap-3105	608	8	vortices	vortex	NOUN
ap-3105	608	9	acknowledgements	acknowledgement	NOUN
ap-3105	608	10	references	reference	NOUN