id	sid	tid	token	lemma	pos
ap-2097	1	1	acta	acta	PROPN
ap-2097	1	2	polytechnica	polytechnica	PROPN
ap-2097	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2097	1	4	/	/	SYM
ap-2097	1	5	ap.2014.54.0142	ap.2014.54.0142	PROPN
ap-2097	1	6	acta	acta	PROPN
ap-2097	1	7	polytechnica	polytechnica	PROPN
ap-2097	1	8	54(2):142–148	54(2):142–148	PROPN
ap-2097	1	9	,	,	PUNCT
ap-2097	1	10	2014	2014	NUM
ap-2097	1	11	©	©	PROPN
ap-2097	1	12	czech	czech	PROPN
ap-2097	1	13	technical	technical	PROPN
ap-2097	1	14	university	university	PROPN
ap-2097	1	15	in	in	ADP
ap-2097	1	16	prague	prague	PROPN
ap-2097	1	17	,	,	PUNCT
ap-2097	1	18	2014	2014	NUM
ap-2097	1	19	available	available	ADJ
ap-2097	1	20	online	online	ADV
ap-2097	1	21	at	at	ADP
ap-2097	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2097	1	23	a	a	DET
ap-2097	1	24	simple	simple	ADJ
ap-2097	1	25	derivation	derivation	NOUN
ap-2097	1	26	of	of	ADP
ap-2097	1	27	finite	finite	ADJ
ap-2097	1	28	-	-	ADJ
ap-2097	1	29	temperature	temperature	ADJ
ap-2097	1	30	cft	cft	NOUN
ap-2097	1	31	correlators	correlator	NOUN
ap-2097	1	32	from	from	ADP
ap-2097	1	33	the	the	DET
ap-2097	1	34	btz	btz	PROPN
ap-2097	1	35	black	black	ADJ
ap-2097	1	36	hole	hole	PROPN
ap-2097	1	37	satoshi	satoshi	PROPN
ap-2097	1	38	ohyaa	ohyaa	PROPN
ap-2097	1	39	,	,	PUNCT
ap-2097	1	40	b	b	PROPN
ap-2097	1	41	a	a	DET
ap-2097	1	42	department	department	NOUN
ap-2097	1	43	of	of	ADP
ap-2097	1	44	physics	physics	PROPN
ap-2097	1	45	,	,	PUNCT
ap-2097	1	46	faculty	faculty	NOUN
ap-2097	1	47	of	of	ADP
ap-2097	1	48	nuclear	nuclear	ADJ
ap-2097	1	49	sciences	science	NOUN
ap-2097	1	50	and	and	CCONJ
ap-2097	1	51	physical	physical	ADJ
ap-2097	1	52	engineering	engineering	NOUN
ap-2097	1	53	,	,	PUNCT
ap-2097	1	54	czech	czech	PROPN
ap-2097	1	55	technical	technical	PROPN
ap-2097	1	56	university	university	PROPN
ap-2097	1	57	in	in	ADP
ap-2097	1	58	prague	prague	PROPN
ap-2097	1	59	,	,	PUNCT
ap-2097	1	60	pohraniční	pohraniční	NOUN
ap-2097	1	61	1288/1	1288/1	NUM
ap-2097	1	62	,	,	PUNCT
ap-2097	1	63	40501	40501	NUM
ap-2097	1	64	děčín	děčín	NOUN
ap-2097	1	65	,	,	PUNCT
ap-2097	1	66	czech	czech	PROPN
ap-2097	1	67	republic	republic	NOUN
ap-2097	1	68	b	b	PROPN
ap-2097	1	69	doppler	doppler	NOUN
ap-2097	1	70	institute	institute	NOUN
ap-2097	1	71	for	for	ADP
ap-2097	1	72	mathematical	mathematical	ADJ
ap-2097	1	73	physics	physics	NOUN
ap-2097	1	74	and	and	CCONJ
ap-2097	1	75	applied	apply	VERB
ap-2097	1	76	mathematics	mathematic	NOUN
ap-2097	1	77	,	,	PUNCT
ap-2097	1	78	czech	czech	PROPN
ap-2097	1	79	technical	technical	PROPN
ap-2097	1	80	university	university	PROPN
ap-2097	1	81	in	in	ADP
ap-2097	1	82	prague	prague	PROPN
ap-2097	1	83	,	,	PUNCT
ap-2097	1	84	břehová	břehová	VERB
ap-2097	1	85	7	7	NUM
ap-2097	1	86	,	,	PUNCT
ap-2097	1	87	11519	11519	NUM
ap-2097	1	88	prague	prague	NOUN
ap-2097	1	89	,	,	PUNCT
ap-2097	1	90	czech	czech	PROPN
ap-2097	1	91	republic	republic	NOUN
ap-2097	1	92	correspondence	correspondence	NOUN
ap-2097	1	93	:	:	PUNCT
ap-2097	1	94	ohyasato@fjfi.cvut.cz	ohyasato@fjfi.cvut.cz	ADJ
ap-2097	1	95	abstract	abstract	ADJ
ap-2097	1	96	.	.	PUNCT
ap-2097	2	1	we	we	PRON
ap-2097	2	2	present	present	VERB
ap-2097	2	3	a	a	DET
ap-2097	2	4	simple	simple	ADJ
ap-2097	2	5	lie	lie	NOUN
ap-2097	2	6	-	-	PUNCT
ap-2097	2	7	algebraic	algebraic	ADJ
ap-2097	2	8	approach	approach	NOUN
ap-2097	2	9	to	to	ADP
ap-2097	2	10	momentum	momentum	NOUN
ap-2097	2	11	-	-	PUNCT
ap-2097	2	12	space	space	NOUN
ap-2097	2	13	two	two	NUM
ap-2097	2	14	-	-	PUNCT
ap-2097	2	15	point	point	NOUN
ap-2097	2	16	functions	function	NOUN
ap-2097	2	17	of	of	ADP
ap-2097	2	18	two	two	NUM
ap-2097	2	19	-	-	PUNCT
ap-2097	2	20	dimensional	dimensional	ADJ
ap-2097	2	21	conformal	conformal	ADJ
ap-2097	2	22	field	field	NOUN
ap-2097	2	23	theory	theory	NOUN
ap-2097	2	24	at	at	ADP
ap-2097	2	25	finite	finite	ADJ
ap-2097	2	26	temperature	temperature	NOUN
ap-2097	2	27	dual	dual	ADJ
ap-2097	2	28	to	to	ADP
ap-2097	2	29	the	the	DET
ap-2097	2	30	btz	btz	PROPN
ap-2097	2	31	black	black	ADJ
ap-2097	2	32	hole	hole	NOUN
ap-2097	2	33	.	.	PUNCT
ap-2097	3	1	making	make	VERB
ap-2097	3	2	use	use	NOUN
ap-2097	3	3	of	of	ADP
ap-2097	3	4	the	the	DET
ap-2097	3	5	real	real	ADJ
ap-2097	3	6	-	-	PUNCT
ap-2097	3	7	time	time	NOUN
ap-2097	3	8	prescription	prescription	NOUN
ap-2097	3	9	of	of	ADP
ap-2097	3	10	ads	ad	NOUN
ap-2097	3	11	/	/	SYM
ap-2097	3	12	cft	cft	NOUN
ap-2097	3	13	correspondence	correspondence	NOUN
ap-2097	3	14	and	and	CCONJ
ap-2097	3	15	ladder	ladder	NOUN
ap-2097	3	16	equations	equation	NOUN
ap-2097	3	17	of	of	ADP
ap-2097	3	18	the	the	DET
ap-2097	3	19	lie	lie	NOUN
ap-2097	3	20	algebra	algebra	VERB
ap-2097	3	21	so(2	so(2	NOUN
ap-2097	3	22	,	,	PUNCT
ap-2097	3	23	2	2	NUM
ap-2097	3	24	)	)	PUNCT
ap-2097	3	25	∼=	∼=	PROPN
ap-2097	3	26	sl(2,r)l	sl(2,r)l	PROPN
ap-2097	3	27	⊕	⊕	PROPN
ap-2097	3	28	sl(2,r)r	sl(2,r)r	PROPN
ap-2097	3	29	,	,	PUNCT
ap-2097	3	30	we	we	PRON
ap-2097	3	31	show	show	VERB
ap-2097	3	32	that	that	SCONJ
ap-2097	3	33	the	the	DET
ap-2097	3	34	finite	finite	ADJ
ap-2097	3	35	-	-	ADJ
ap-2097	3	36	temperature	temperature	ADJ
ap-2097	3	37	two	two	NUM
ap-2097	3	38	-	-	PUNCT
ap-2097	3	39	point	point	NOUN
ap-2097	3	40	functions	function	NOUN
ap-2097	3	41	in	in	ADP
ap-2097	3	42	momentum	momentum	NOUN
ap-2097	3	43	space	space	NOUN
ap-2097	3	44	satisfy	satisfy	NOUN
ap-2097	3	45	linear	linear	PROPN
ap-2097	3	46	recurrence	recurrence	NOUN
ap-2097	3	47	relations	relation	NOUN
ap-2097	3	48	with	with	ADP
ap-2097	3	49	respect	respect	NOUN
ap-2097	3	50	to	to	ADP
ap-2097	3	51	the	the	DET
ap-2097	3	52	left	left	ADJ
ap-2097	3	53	and	and	CCONJ
ap-2097	3	54	right	right	ADJ
ap-2097	3	55	momenta	momenta	NOUN
ap-2097	3	56	.	.	PUNCT
ap-2097	4	1	these	these	DET
ap-2097	4	2	recurrence	recurrence	NOUN
ap-2097	4	3	relations	relation	NOUN
ap-2097	4	4	are	be	AUX
ap-2097	4	5	exactly	exactly	ADV
ap-2097	4	6	solvable	solvable	ADJ
ap-2097	4	7	and	and	CCONJ
ap-2097	4	8	completely	completely	ADV
ap-2097	4	9	determine	determine	VERB
ap-2097	4	10	the	the	DET
ap-2097	4	11	momentum	momentum	NOUN
ap-2097	4	12	-	-	PUNCT
ap-2097	4	13	dependence	dependence	NOUN
ap-2097	4	14	of	of	ADP
ap-2097	4	15	retarded	retarded	ADJ
ap-2097	4	16	and	and	CCONJ
ap-2097	4	17	advanced	advanced	ADJ
ap-2097	4	18	two	two	NUM
ap-2097	4	19	-	-	PUNCT
ap-2097	4	20	point	point	NOUN
ap-2097	4	21	functions	function	NOUN
ap-2097	4	22	of	of	ADP
ap-2097	4	23	finite	finite	ADJ
ap-2097	4	24	-	-	ADJ
ap-2097	4	25	temperature	temperature	ADJ
ap-2097	4	26	conformal	conformal	ADJ
ap-2097	4	27	field	field	NOUN
ap-2097	4	28	theory	theory	NOUN
ap-2097	4	29	.	.	PUNCT
ap-2097	5	1	keywords	keyword	NOUN
ap-2097	5	2	:	:	PUNCT
ap-2097	5	3	ads	ads	PROPN
ap-2097	5	4	/	/	SYM
ap-2097	5	5	cft	cft	NOUN
ap-2097	5	6	correspondence	correspondence	NOUN
ap-2097	5	7	,	,	PUNCT
ap-2097	5	8	correlation	correlation	NOUN
ap-2097	5	9	functions	function	NOUN
ap-2097	5	10	,	,	PUNCT
ap-2097	5	11	btz	btz	PROPN
ap-2097	5	12	black	black	ADJ
ap-2097	5	13	hole	hole	NOUN
ap-2097	5	14	.	.	PUNCT
ap-2097	6	1	1	1	X
ap-2097	6	2	.	.	X
ap-2097	6	3	introduction	introduction	NOUN
ap-2097	6	4	and	and	CCONJ
ap-2097	6	5	summary	summary	NOUN
ap-2097	6	6	conformal	conformal	NOUN
ap-2097	6	7	symmetry	symmetry	NOUN
ap-2097	6	8	is	be	AUX
ap-2097	6	9	powerful	powerful	ADJ
ap-2097	6	10	enough	enough	ADV
ap-2097	6	11	to	to	PART
ap-2097	6	12	constrain	constrain	VERB
ap-2097	6	13	the	the	DET
ap-2097	6	14	possible	possible	ADJ
ap-2097	6	15	forms	form	NOUN
ap-2097	6	16	of	of	ADP
ap-2097	6	17	correlation	correlation	NOUN
ap-2097	6	18	functions	function	NOUN
ap-2097	6	19	in	in	ADP
ap-2097	6	20	quantum	quantum	ADJ
ap-2097	6	21	field	field	NOUN
ap-2097	6	22	theory	theory	NOUN
ap-2097	6	23	.	.	PUNCT
ap-2097	7	1	it	it	PRON
ap-2097	7	2	has	have	AUX
ap-2097	7	3	been	be	AUX
ap-2097	7	4	long	long	ADV
ap-2097	7	5	appreciated	appreciated	ADJ
ap-2097	7	6	that	that	SCONJ
ap-2097	7	7	,	,	PUNCT
ap-2097	7	8	for	for	ADP
ap-2097	7	9	scalar	scalar	ADJ
ap-2097	7	10	(	(	PUNCT
ap-2097	7	11	quasi-)primary	quasi-)primary	ADJ
ap-2097	7	12	operators	operator	NOUN
ap-2097	7	13	,	,	PUNCT
ap-2097	7	14	for	for	ADP
ap-2097	7	15	example	example	NOUN
ap-2097	7	16	,	,	PUNCT
ap-2097	7	17	so(2	so(2	ADJ
ap-2097	7	18	,	,	PUNCT
ap-2097	7	19	d	d	NOUN
ap-2097	7	20	)	)	PUNCT
ap-2097	7	21	conformal	conformal	ADJ
ap-2097	7	22	symmetry	symmetry	NOUN
ap-2097	7	23	completely	completely	ADV
ap-2097	7	24	fixes	fix	VERB
ap-2097	7	25	the	the	DET
ap-2097	7	26	possible	possible	ADJ
ap-2097	7	27	forms	form	NOUN
ap-2097	7	28	of	of	ADP
ap-2097	7	29	twoand	twoand	NOUN
ap-2097	7	30	three	three	NUM
ap-2097	7	31	-	-	PUNCT
ap-2097	7	32	point	point	NOUN
ap-2097	7	33	functions	function	NOUN
ap-2097	7	34	up	up	ADP
ap-2097	7	35	to	to	ADP
ap-2097	7	36	an	an	DET
ap-2097	7	37	overall	overall	ADJ
ap-2097	7	38	normalization	normalization	NOUN
ap-2097	7	39	factor	factor	NOUN
ap-2097	7	40	in	in	ADP
ap-2097	7	41	any	any	DET
ap-2097	7	42	spacetime	spacetime	NOUN
ap-2097	7	43	dimension	dimension	NOUN
ap-2097	7	44	d	d	X
ap-2097	7	45	≥	≥	NUM
ap-2097	7	46	1	1	NUM
ap-2097	7	47	.	.	PUNCT
ap-2097	8	1	this	this	DET
ap-2097	8	2	symmetry	symmetry	NOUN
ap-2097	8	3	constraint	constraint	NOUN
ap-2097	8	4	works	work	VERB
ap-2097	8	5	well	well	ADV
ap-2097	8	6	in	in	ADP
ap-2097	8	7	position	position	NOUN
ap-2097	8	8	space	space	NOUN
ap-2097	8	9	,	,	PUNCT
ap-2097	8	10	however	however	ADV
ap-2097	8	11	,	,	PUNCT
ap-2097	8	12	its	its	PRON
ap-2097	8	13	direct	direct	ADJ
ap-2097	8	14	implication	implication	NOUN
ap-2097	8	15	to	to	ADP
ap-2097	8	16	momentum	momentum	NOUN
ap-2097	8	17	-	-	PUNCT
ap-2097	8	18	space	space	NOUN
ap-2097	8	19	correlators	correlator	NOUN
ap-2097	8	20	are	be	AUX
ap-2097	8	21	less	less	ADV
ap-2097	8	22	obvious	obvious	ADJ
ap-2097	8	23	before	before	ADP
ap-2097	8	24	performing	perform	VERB
ap-2097	8	25	the	the	DET
ap-2097	8	26	fourier	fourier	NOUN
ap-2097	8	27	transform	transform	NOUN
ap-2097	8	28	.	.	PUNCT
ap-2097	9	1	since	since	SCONJ
ap-2097	9	2	momentum	momentum	NOUN
ap-2097	9	3	-	-	PUNCT
ap-2097	9	4	space	space	NOUN
ap-2097	9	5	correlators	correlator	NOUN
ap-2097	9	6	are	be	AUX
ap-2097	9	7	directly	directly	ADV
ap-2097	9	8	related	relate	VERB
ap-2097	9	9	to	to	ADP
ap-2097	9	10	physical	physical	ADJ
ap-2097	9	11	observables	observable	NOUN
ap-2097	9	12	(	(	PUNCT
ap-2097	9	13	e.g.	e.g.	ADV
ap-2097	9	14	the	the	DET
ap-2097	9	15	imaginary	imaginary	ADJ
ap-2097	9	16	part	part	NOUN
ap-2097	9	17	of	of	ADP
ap-2097	9	18	a	a	DET
ap-2097	9	19	retarded	retarded	ADJ
ap-2097	9	20	two	two	NUM
ap-2097	9	21	-	-	PUNCT
ap-2097	9	22	point	point	NOUN
ap-2097	9	23	function	function	NOUN
ap-2097	9	24	in	in	ADP
ap-2097	9	25	momentum	momentum	NOUN
ap-2097	9	26	space	space	NOUN
ap-2097	9	27	gives	give	VERB
ap-2097	9	28	the	the	DET
ap-2097	9	29	spectral	spectral	ADJ
ap-2097	9	30	density	density	NOUN
ap-2097	9	31	of	of	ADP
ap-2097	9	32	many	many	ADJ
ap-2097	9	33	body	body	NOUN
ap-2097	9	34	systems	system	NOUN
ap-2097	9	35	)	)	PUNCT
ap-2097	9	36	,	,	PUNCT
ap-2097	9	37	it	it	PRON
ap-2097	9	38	is	be	AUX
ap-2097	9	39	important	important	ADJ
ap-2097	9	40	to	to	PART
ap-2097	9	41	understand	understand	VERB
ap-2097	9	42	how	how	SCONJ
ap-2097	9	43	directly	directly	ADV
ap-2097	9	44	conformal	conformal	ADJ
ap-2097	9	45	symmetry	symmetry	NOUN
ap-2097	9	46	constrains	constrain	VERB
ap-2097	9	47	the	the	DET
ap-2097	9	48	possible	possible	ADJ
ap-2097	9	49	forms	form	NOUN
ap-2097	9	50	of	of	ADP
ap-2097	9	51	momentum	momentum	NOUN
ap-2097	9	52	-	-	PUNCT
ap-2097	9	53	space	space	NOUN
ap-2097	9	54	correlators	correlator	NOUN
ap-2097	9	55	.	.	PUNCT
ap-2097	10	1	from	from	ADP
ap-2097	10	2	the	the	DET
ap-2097	10	3	practical	practical	ADJ
ap-2097	10	4	computational	computational	ADJ
ap-2097	10	5	viewpoint	viewpoint	NOUN
ap-2097	10	6	,	,	PUNCT
ap-2097	10	7	it	it	PRON
ap-2097	10	8	is	be	AUX
ap-2097	10	9	also	also	ADV
ap-2097	10	10	important	important	ADJ
ap-2097	10	11	to	to	PART
ap-2097	10	12	develop	develop	VERB
ap-2097	10	13	efficient	efficient	ADJ
ap-2097	10	14	methods	method	NOUN
ap-2097	10	15	for	for	ADP
ap-2097	10	16	computing	compute	VERB
ap-2097	10	17	momentum	momentum	NOUN
ap-2097	10	18	-	-	PUNCT
ap-2097	10	19	space	space	NOUN
ap-2097	10	20	correlators	correlator	NOUN
ap-2097	10	21	directly	directly	ADV
ap-2097	10	22	through	through	ADP
ap-2097	10	23	symmetry	symmetry	NOUN
ap-2097	10	24	considerations	consideration	NOUN
ap-2097	10	25	,	,	PUNCT
ap-2097	10	26	because	because	SCONJ
ap-2097	10	27	fourier	fourier	NOUN
ap-2097	10	28	transforms	transform	VERB
ap-2097	10	29	of	of	ADP
ap-2097	10	30	position	position	NOUN
ap-2097	10	31	-	-	PUNCT
ap-2097	10	32	space	space	NOUN
ap-2097	10	33	correlators	correlator	NOUN
ap-2097	10	34	are	be	AUX
ap-2097	10	35	hard	hard	ADJ
ap-2097	10	36	in	in	ADP
ap-2097	10	37	general	general	ADJ
ap-2097	10	38	.	.	PUNCT
ap-2097	11	1	in	in	ADP
ap-2097	11	2	this	this	DET
ap-2097	11	3	short	short	ADJ
ap-2097	11	4	paper	paper	NOUN
ap-2097	11	5	we	we	PRON
ap-2097	11	6	continue	continue	VERB
ap-2097	11	7	our	our	PRON
ap-2097	11	8	investigation	investigation	NOUN
ap-2097	11	9	[	[	X
ap-2097	11	10	1	1	X
ap-2097	11	11	]	]	PUNCT
ap-2097	11	12	and	and	CCONJ
ap-2097	11	13	present	present	VERB
ap-2097	11	14	a	a	DET
ap-2097	11	15	novel	novel	ADJ
ap-2097	11	16	lie	lie	NOUN
ap-2097	11	17	-	-	PUNCT
ap-2097	11	18	algebraic	algebraic	ADJ
ap-2097	11	19	approach	approach	NOUN
ap-2097	11	20	to	to	ADP
ap-2097	11	21	momentumspace	momentumspace	NOUN
ap-2097	11	22	two	two	NUM
ap-2097	11	23	-	-	PUNCT
ap-2097	11	24	point	point	NOUN
ap-2097	11	25	functions	function	NOUN
ap-2097	11	26	of	of	ADP
ap-2097	11	27	conformal	conformal	ADJ
ap-2097	11	28	field	field	NOUN
ap-2097	11	29	theory	theory	NOUN
ap-2097	11	30	at	at	ADP
ap-2097	11	31	finite	finite	ADJ
ap-2097	11	32	temperature	temperature	NOUN
ap-2097	11	33	by	by	ADP
ap-2097	11	34	using	use	VERB
ap-2097	11	35	the	the	DET
ap-2097	11	36	ads	ad	NOUN
ap-2097	11	37	/	/	SYM
ap-2097	11	38	cft	cft	NOUN
ap-2097	11	39	correspondence	correspondence	NOUN
ap-2097	11	40	.	.	PUNCT
ap-2097	12	1	the	the	DET
ap-2097	12	2	ads	ad	NOUN
ap-2097	12	3	/	/	SYM
ap-2097	12	4	cft	cft	PROPN
ap-2097	12	5	correspondence	correspondence	NOUN
ap-2097	12	6	relates	relate	VERB
ap-2097	12	7	stronglycoupled	stronglycouple	VERB
ap-2097	12	8	conformal	conformal	ADJ
ap-2097	12	9	field	field	NOUN
ap-2097	12	10	theory	theory	NOUN
ap-2097	12	11	to	to	ADP
ap-2097	12	12	classical	classical	ADJ
ap-2097	12	13	gravity	gravity	NOUN
ap-2097	12	14	in	in	ADP
ap-2097	12	15	a	a	DET
ap-2097	12	16	one	one	NUM
ap-2097	12	17	-	-	PUNCT
ap-2097	12	18	higher	high	ADJ
ap-2097	12	19	spatial	spatial	ADJ
ap-2097	12	20	dimension	dimension	NOUN
ap-2097	12	21	.	.	PUNCT
ap-2097	13	1	according	accord	VERB
ap-2097	13	2	to	to	ADP
ap-2097	13	3	the	the	DET
ap-2097	13	4	correspondence	correspondence	NOUN
ap-2097	13	5	,	,	PUNCT
ap-2097	13	6	finite	finite	ADJ
ap-2097	13	7	-	-	ADJ
ap-2097	13	8	temperature	temperature	ADJ
ap-2097	13	9	conformal	conformal	ADJ
ap-2097	13	10	field	field	NOUN
ap-2097	13	11	theory	theory	NOUN
ap-2097	13	12	is	be	AUX
ap-2097	13	13	dual	dual	ADJ
ap-2097	13	14	to	to	ADP
ap-2097	13	15	an	an	DET
ap-2097	13	16	asymptotically	asymptotically	ADV
ap-2097	13	17	ads	ad	NOUN
ap-2097	13	18	spacetime	spacetime	NOUN
ap-2097	13	19	that	that	PRON
ap-2097	13	20	contains	contain	VERB
ap-2097	13	21	black	black	ADJ
ap-2097	13	22	holes	hole	NOUN
ap-2097	13	23	.	.	PUNCT
ap-2097	14	1	in	in	ADP
ap-2097	14	2	this	this	DET
ap-2097	14	3	paper	paper	NOUN
ap-2097	14	4	we	we	PRON
ap-2097	14	5	focus	focus	VERB
ap-2097	14	6	on	on	ADP
ap-2097	14	7	twodimensional	twodimensional	ADJ
ap-2097	14	8	conformal	conformal	ADJ
ap-2097	14	9	field	field	NOUN
ap-2097	14	10	theory	theory	NOUN
ap-2097	14	11	(	(	PUNCT
ap-2097	14	12	cft2	cft2	PROPN
ap-2097	14	13	)	)	PUNCT
ap-2097	14	14	at	at	ADP
ap-2097	14	15	finite	finite	ADJ
ap-2097	14	16	temperature	temperature	NOUN
ap-2097	14	17	dual	dual	ADJ
ap-2097	14	18	to	to	ADP
ap-2097	14	19	the	the	DET
ap-2097	14	20	three	three	NUM
ap-2097	14	21	-	-	PUNCT
ap-2097	14	22	dimensional	dimensional	ADJ
ap-2097	14	23	anti	anti	ADJ
ap-2097	14	24	-	-	ADJ
ap-2097	14	25	de	de	ADJ
ap-2097	14	26	sitter	sitter	NOUN
ap-2097	14	27	(	(	PUNCT
ap-2097	14	28	ads3	ads3	ADJ
ap-2097	14	29	)	)	PUNCT
ap-2097	14	30	black	black	ADJ
ap-2097	14	31	hole	hole	NOUN
ap-2097	14	32	(	(	PUNCT
ap-2097	14	33	i.e.	i.e.	X
ap-2097	14	34	bañados	bañado	NOUN
ap-2097	14	35	-	-	PUNCT
ap-2097	14	36	teitelboim	teitelboim	NOUN
ap-2097	14	37	-	-	PUNCT
ap-2097	14	38	zanelli	zanelli	NOUN
ap-2097	14	39	(	(	PUNCT
ap-2097	14	40	btz	btz	PROPN
ap-2097	14	41	)	)	PUNCT
ap-2097	14	42	black	black	ADJ
ap-2097	14	43	hole	hole	NOUN
ap-2097	15	1	[	[	X
ap-2097	15	2	2	2	NUM
ap-2097	15	3	,	,	PUNCT
ap-2097	15	4	3	3	NUM
ap-2097	15	5	]	]	PUNCT
ap-2097	15	6	)	)	PUNCT
ap-2097	15	7	and	and	CCONJ
ap-2097	15	8	we	we	PRON
ap-2097	15	9	give	give	VERB
ap-2097	15	10	a	a	DET
ap-2097	15	11	simple	simple	ADJ
ap-2097	15	12	derivation	derivation	NOUN
ap-2097	15	13	of	of	ADP
ap-2097	15	14	retarded	retarded	ADJ
ap-2097	15	15	and	and	CCONJ
ap-2097	15	16	advanced	advanced	ADJ
ap-2097	15	17	two	two	NUM
ap-2097	15	18	-	-	PUNCT
ap-2097	15	19	point	point	NOUN
ap-2097	15	20	functions	function	NOUN
ap-2097	15	21	of	of	ADP
ap-2097	15	22	scalar	scalar	ADJ
ap-2097	15	23	operators	operator	NOUN
ap-2097	15	24	of	of	ADP
ap-2097	15	25	dual	dual	ADJ
ap-2097	15	26	cft2	cft2	NOUN
ap-2097	15	27	by	by	ADP
ap-2097	15	28	just	just	ADV
ap-2097	15	29	using	use	VERB
ap-2097	15	30	the	the	DET
ap-2097	15	31	real	real	ADJ
ap-2097	15	32	-	-	PUNCT
ap-2097	15	33	time	time	NOUN
ap-2097	15	34	prescription	prescription	NOUN
ap-2097	15	35	of	of	ADP
ap-2097	15	36	ads	ad	NOUN
ap-2097	15	37	/	/	SYM
ap-2097	15	38	cft	cft	NOUN
ap-2097	15	39	correspondence	correspondence	NOUN
ap-2097	15	40	à	à	X
ap-2097	15	41	la	la	PROPN
ap-2097	15	42	iqbal	iqbal	PROPN
ap-2097	15	43	and	and	CCONJ
ap-2097	15	44	liu	liu	PROPN
ap-2097	16	1	[	[	X
ap-2097	16	2	4	4	NUM
ap-2097	16	3	,	,	PUNCT
ap-2097	16	4	5	5	NUM
ap-2097	16	5	]	]	PUNCT
ap-2097	16	6	and	and	CCONJ
ap-2097	16	7	the	the	DET
ap-2097	16	8	ladder	ladder	NOUN
ap-2097	16	9	equations	equation	NOUN
ap-2097	16	10	of	of	ADP
ap-2097	16	11	the	the	DET
ap-2097	16	12	lie	lie	NOUN
ap-2097	16	13	-	-	PUNCT
ap-2097	16	14	algebra	algebra	NOUN
ap-2097	16	15	so(2	so(2	NOUN
ap-2097	16	16	,	,	PUNCT
ap-2097	16	17	2	2	NUM
ap-2097	16	18	)	)	PUNCT
ap-2097	16	19	∼=	∼=	PROPN
ap-2097	16	20	sl(2,r)l	sl(2,r)l	NOUN
ap-2097	16	21	⊕	⊕	PROPN
ap-2097	16	22	sl(2,r)r	sl(2,r)r	NOUN
ap-2097	16	23	of	of	ADP
ap-2097	16	24	the	the	DET
ap-2097	16	25	isometry	isometry	PROPN
ap-2097	16	26	group	group	NOUN
ap-2097	16	27	so(2	so(2	PROPN
ap-2097	16	28	,	,	PUNCT
ap-2097	16	29	2	2	NUM
ap-2097	16	30	)	)	PUNCT
ap-2097	16	31	∼=	∼=	PROPN
ap-2097	16	32	(	(	PUNCT
ap-2097	16	33	sl(2,r)l	sl(2,r)l	VERB
ap-2097	16	34	×	×	VERB
ap-2097	16	35	sl(2,r)r)/z2	sl(2,r)r)/z2	ADJ
ap-2097	16	36	of	of	ADP
ap-2097	16	37	ads3	ads3	PROPN
ap-2097	16	38	.	.	PUNCT
ap-2097	17	1	in	in	ADP
ap-2097	17	2	contrast	contrast	NOUN
ap-2097	17	3	to	to	ADP
ap-2097	17	4	the	the	DET
ap-2097	17	5	conventional	conventional	ADJ
ap-2097	17	6	approaches	approach	NOUN
ap-2097	17	7	to	to	ADP
ap-2097	17	8	momentumspace	momentumspace	NOUN
ap-2097	17	9	cft	cft	NOUN
ap-2097	17	10	correlators	correlator	NOUN
ap-2097	17	11	(	(	PUNCT
ap-2097	17	12	such	such	ADJ
ap-2097	17	13	as	as	ADP
ap-2097	17	14	fourier	fourier	NOUN
ap-2097	17	15	-	-	PUNCT
ap-2097	17	16	transform	transform	NOUN
ap-2097	17	17	of	of	ADP
ap-2097	17	18	position	position	NOUN
ap-2097	17	19	-	-	PUNCT
ap-2097	17	20	space	space	NOUN
ap-2097	17	21	correlators	correlator	NOUN
ap-2097	17	22	or	or	CCONJ
ap-2097	17	23	original	original	ADJ
ap-2097	17	24	real	real	ADJ
ap-2097	17	25	-	-	PUNCT
ap-2097	17	26	time	time	NOUN
ap-2097	17	27	ads	ad	NOUN
ap-2097	17	28	/	/	SYM
ap-2097	17	29	cft	cft	NOUN
ap-2097	17	30	prescription	prescription	NOUN
ap-2097	18	1	[	[	X
ap-2097	18	2	4–6	4–6	X
ap-2097	18	3	]	]	X
ap-2097	18	4	,	,	PUNCT
ap-2097	18	5	which	which	PRON
ap-2097	18	6	requires	require	VERB
ap-2097	18	7	bulk	bulk	ADJ
ap-2097	18	8	field	field	NOUN
ap-2097	18	9	equations	equation	NOUN
ap-2097	18	10	to	to	PART
ap-2097	18	11	be	be	AUX
ap-2097	18	12	solved	solve	VERB
ap-2097	18	13	explicitly	explicitly	ADV
ap-2097	18	14	)	)	PUNCT
ap-2097	18	15	,	,	PUNCT
ap-2097	18	16	our	our	PRON
ap-2097	18	17	lie	lie	NOUN
ap-2097	18	18	-	-	PUNCT
ap-2097	18	19	algebraic	algebraic	ADJ
ap-2097	18	20	method	method	NOUN
ap-2097	18	21	is	be	AUX
ap-2097	18	22	quite	quite	ADV
ap-2097	18	23	simple	simple	ADJ
ap-2097	18	24	and	and	CCONJ
ap-2097	18	25	clarifies	clarify	VERB
ap-2097	18	26	the	the	DET
ap-2097	18	27	role	role	NOUN
ap-2097	18	28	of	of	ADP
ap-2097	18	29	conformal	conformal	ADJ
ap-2097	18	30	symmetry	symmetry	NOUN
ap-2097	18	31	in	in	ADP
ap-2097	18	32	momentum	momentum	NOUN
ap-2097	18	33	-	-	PUNCT
ap-2097	18	34	space	space	NOUN
ap-2097	18	35	correlators	correlator	NOUN
ap-2097	18	36	in	in	ADP
ap-2097	18	37	a	a	DET
ap-2097	18	38	direct	direct	ADJ
ap-2097	18	39	way	way	NOUN
ap-2097	18	40	:	:	PUNCT
ap-2097	18	41	for	for	ADP
ap-2097	18	42	finite	finite	ADJ
ap-2097	18	43	-	-	ADJ
ap-2097	18	44	temperature	temperature	ADJ
ap-2097	18	45	two	two	NUM
ap-2097	18	46	-	-	PUNCT
ap-2097	18	47	point	point	NOUN
ap-2097	18	48	functions	function	NOUN
ap-2097	18	49	in	in	ADP
ap-2097	18	50	momentum	momentum	NOUN
ap-2097	18	51	space	space	NOUN
ap-2097	18	52	,	,	PUNCT
ap-2097	18	53	conformal	conformal	ADJ
ap-2097	18	54	symmetry	symmetry	NOUN
ap-2097	18	55	manifests	manifest	VERB
ap-2097	18	56	itself	itself	PRON
ap-2097	18	57	in	in	ADP
ap-2097	18	58	the	the	DET
ap-2097	18	59	form	form	NOUN
ap-2097	18	60	of	of	ADP
ap-2097	18	61	recurrence	recurrence	NOUN
ap-2097	18	62	relations	relation	NOUN
ap-2097	18	63	which	which	PRON
ap-2097	18	64	are	be	AUX
ap-2097	18	65	exactly	exactly	ADV
ap-2097	18	66	solvable	solvable	ADJ
ap-2097	18	67	and	and	CCONJ
ap-2097	18	68	,	,	PUNCT
ap-2097	18	69	up	up	ADP
ap-2097	18	70	to	to	ADP
ap-2097	18	71	an	an	DET
ap-2097	18	72	overall	overall	ADJ
ap-2097	18	73	normalization	normalization	NOUN
ap-2097	18	74	factor	factor	NOUN
ap-2097	18	75	,	,	PUNCT
ap-2097	18	76	completely	completely	ADV
ap-2097	18	77	determine	determine	VERB
ap-2097	18	78	the	the	DET
ap-2097	18	79	momentum	momentum	NOUN
ap-2097	18	80	dependence	dependence	NOUN
ap-2097	18	81	of	of	ADP
ap-2097	18	82	two	two	NUM
ap-2097	18	83	-	-	PUNCT
ap-2097	18	84	point	point	NOUN
ap-2097	18	85	functions	function	NOUN
ap-2097	18	86	.	.	PUNCT
ap-2097	19	1	the	the	DET
ap-2097	19	2	rest	rest	NOUN
ap-2097	19	3	of	of	ADP
ap-2097	19	4	the	the	DET
ap-2097	19	5	paper	paper	NOUN
ap-2097	19	6	is	be	AUX
ap-2097	19	7	organized	organize	VERB
ap-2097	19	8	as	as	SCONJ
ap-2097	19	9	follows	follow	VERB
ap-2097	19	10	.	.	PUNCT
ap-2097	20	1	in	in	ADP
ap-2097	20	2	section	section	NOUN
ap-2097	20	3	2	2	NUM
ap-2097	20	4	we	we	PRON
ap-2097	20	5	briefly	briefly	ADV
ap-2097	20	6	review	review	VERB
ap-2097	20	7	the	the	DET
ap-2097	20	8	ads3	ads3	ADJ
ap-2097	20	9	black	black	ADJ
ap-2097	20	10	hole	hole	NOUN
ap-2097	20	11	based	base	VERB
ap-2097	20	12	on	on	ADP
ap-2097	20	13	the	the	DET
ap-2097	20	14	quotient	quotient	NOUN
ap-2097	20	15	construction	construction	NOUN
ap-2097	21	1	[	[	X
ap-2097	21	2	3	3	NUM
ap-2097	21	3	,	,	PUNCT
ap-2097	21	4	7	7	NUM
ap-2097	21	5	]	]	NUM
ap-2097	21	6	:	:	PUNCT
ap-2097	21	7	the	the	DET
ap-2097	21	8	ads3	ads3	ADJ
ap-2097	21	9	black	black	ADJ
ap-2097	21	10	hole	hole	NOUN
ap-2097	21	11	is	be	AUX
ap-2097	21	12	a	a	DET
ap-2097	21	13	locally	locally	ADV
ap-2097	21	14	ads3	ads3	ADJ
ap-2097	21	15	spacetime	spacetime	NOUN
ap-2097	21	16	and	and	CCONJ
ap-2097	21	17	is	be	AUX
ap-2097	21	18	given	give	VERB
ap-2097	21	19	by	by	ADP
ap-2097	21	20	a	a	DET
ap-2097	21	21	quotient	quotient	NOUN
ap-2097	21	22	space	space	NOUN
ap-2097	21	23	of	of	ADP
ap-2097	21	24	ads3	ads3	PROPN
ap-2097	21	25	with	with	ADP
ap-2097	21	26	an	an	DET
ap-2097	21	27	identification	identification	NOUN
ap-2097	21	28	of	of	ADP
ap-2097	21	29	points	point	NOUN
ap-2097	21	30	under	under	ADP
ap-2097	21	31	the	the	DET
ap-2097	21	32	action	action	NOUN
ap-2097	21	33	of	of	ADP
ap-2097	21	34	a	a	DET
ap-2097	21	35	discrete	discrete	ADJ
ap-2097	21	36	subgroup	subgroup	NOUN
ap-2097	21	37	z	z	PROPN
ap-2097	21	38	of	of	ADP
ap-2097	21	39	the	the	DET
ap-2097	21	40	isometry	isometry	PROPN
ap-2097	21	41	group	group	NOUN
ap-2097	21	42	so(2	so(2	PROPN
ap-2097	21	43	,	,	PUNCT
ap-2097	21	44	2	2	NUM
ap-2097	21	45	)	)	PUNCT
ap-2097	21	46	of	of	ADP
ap-2097	21	47	ads3	ads3	PROPN
ap-2097	21	48	.	.	PUNCT
ap-2097	22	1	though	though	SCONJ
ap-2097	22	2	not	not	PART
ap-2097	22	3	so	so	ADV
ap-2097	22	4	widely	widely	ADV
ap-2097	22	5	appreciated	appreciate	VERB
ap-2097	22	6	,	,	PUNCT
ap-2097	22	7	the	the	DET
ap-2097	22	8	ads3	ads3	ADJ
ap-2097	22	9	black	black	ADJ
ap-2097	22	10	hole	hole	NOUN
ap-2097	22	11	is	be	AUX
ap-2097	22	12	a	a	DET
ap-2097	22	13	quotient	quotient	NOUN
ap-2097	22	14	space	space	NOUN
ap-2097	22	15	of	of	ADP
ap-2097	22	16	ads3	ads3	PROPN
ap-2097	22	17	with	with	ADP
ap-2097	22	18	a	a	DET
ap-2097	22	19	particular	particular	ADJ
ap-2097	22	20	coordinate	coordinate	NOUN
ap-2097	22	21	patch	patch	NOUN
ap-2097	22	22	in	in	ADP
ap-2097	22	23	which	which	PRON
ap-2097	22	24	both	both	CCONJ
ap-2097	22	25	the	the	DET
ap-2097	22	26	timeand	timeand	NOUN
ap-2097	22	27	angle	angle	NOUN
ap-2097	22	28	-	-	PUNCT
ap-2097	22	29	translation	translation	NOUN
ap-2097	22	30	generators	generator	NOUN
ap-2097	22	31	generate	generate	VERB
ap-2097	22	32	the	the	DET
ap-2097	22	33	one	one	NUM
ap-2097	22	34	-	-	PUNCT
ap-2097	22	35	parameter	parameter	NOUN
ap-2097	22	36	subgroup	subgroup	NOUN
ap-2097	22	37	so(1	so(1	PROPN
ap-2097	22	38	,	,	PUNCT
ap-2097	22	39	1	1	NUM
ap-2097	22	40	)	)	PUNCT
ap-2097	22	41	⊂	⊂	PROPN
ap-2097	23	1	so(2	so(2	NOUN
ap-2097	23	2	,	,	PUNCT
ap-2097	23	3	2).1	2).1	NUM
ap-2097	23	4	in	in	ADP
ap-2097	23	5	1this	1this	NUM
ap-2097	23	6	is	be	AUX
ap-2097	23	7	true	true	ADJ
ap-2097	23	8	for	for	ADP
ap-2097	23	9	a	a	DET
ap-2097	23	10	non	non	ADJ
ap-2097	23	11	-	-	ADJ
ap-2097	23	12	extremal	extremal	ADJ
ap-2097	23	13	black	black	ADJ
ap-2097	23	14	hole	hole	NOUN
ap-2097	23	15	with	with	ADP
ap-2097	23	16	positive	positive	ADJ
ap-2097	23	17	mass	mass	NOUN
ap-2097	23	18	.	.	PUNCT
ap-2097	24	1	timeand	timeand	NOUN
ap-2097	24	2	angle	angle	NOUN
ap-2097	24	3	-	-	PUNCT
ap-2097	24	4	translation	translation	NOUN
ap-2097	24	5	generators	generator	NOUN
ap-2097	24	6	generate	generate	VERB
ap-2097	24	7	other	other	ADJ
ap-2097	24	8	one	one	NUM
ap-2097	24	9	-	-	PUNCT
ap-2097	24	10	parameter	parameter	NOUN
ap-2097	24	11	subgroups	subgroup	NOUN
ap-2097	24	12	for	for	ADP
ap-2097	24	13	the	the	DET
ap-2097	24	14	zero	zero	NUM
ap-2097	24	15	-	-	PUNCT
ap-2097	24	16	mass	mass	NOUN
ap-2097	24	17	limit	limit	NOUN
ap-2097	24	18	of	of	ADP
ap-2097	24	19	a	a	DET
ap-2097	24	20	black	black	ADJ
ap-2097	24	21	hole	hole	NOUN
ap-2097	24	22	(	(	PUNCT
ap-2097	24	23	or	or	CCONJ
ap-2097	24	24	a	a	DET
ap-2097	24	25	black	black	ADJ
ap-2097	24	26	hole	hole	NOUN
ap-2097	24	27	vacuum	vacuum	NOUN
ap-2097	24	28	)	)	PUNCT
ap-2097	24	29	,	,	PUNCT
ap-2097	24	30	the	the	DET
ap-2097	24	31	extremal	extremal	ADJ
ap-2097	24	32	black	black	ADJ
ap-2097	24	33	hole	hole	NOUN
ap-2097	24	34	and	and	CCONJ
ap-2097	24	35	the	the	DET
ap-2097	24	36	negative	negative	ADJ
ap-2097	24	37	mass	mass	ADJ
ap-2097	24	38	black	black	ADJ
ap-2097	24	39	hole	hole	NOUN
ap-2097	24	40	(	(	PUNCT
ap-2097	24	41	or	or	CCONJ
ap-2097	24	42	black	black	ADJ
ap-2097	24	43	hole	hole	NOUN
ap-2097	24	44	with	with	ADP
ap-2097	24	45	naked	naked	ADJ
ap-2097	24	46	singularity	singularity	NOUN
ap-2097	24	47	)	)	PUNCT
ap-2097	24	48	.	.	PUNCT
ap-2097	25	1	for	for	ADP
ap-2097	25	2	example	example	NOUN
ap-2097	25	3	,	,	PUNCT
ap-2097	25	4	in	in	ADP
ap-2097	25	5	the	the	DET
ap-2097	25	6	case	case	NOUN
ap-2097	25	7	of	of	ADP
ap-2097	25	8	a	a	DET
ap-2097	25	9	black	black	ADJ
ap-2097	25	10	hole	hole	NOUN
ap-2097	25	11	vacuum	vacuum	NOUN
ap-2097	25	12	,	,	PUNCT
ap-2097	25	13	142	142	NUM
ap-2097	25	14	http://dx.doi.org/10.14311/ap.2014.54.0142	http://dx.doi.org/10.14311/ap.2014.54.0142	NOUN
ap-2097	25	15	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2097	25	16	vol	vol	NOUN
ap-2097	25	17	.	.	PUNCT
ap-2097	25	18	54	54	NUM
ap-2097	25	19	no	no	NOUN
ap-2097	25	20	.	.	PUNCT
ap-2097	26	1	2/2014	2/2014	NOUN
ap-2097	26	2	a	a	DET
ap-2097	26	3	simple	simple	ADJ
ap-2097	26	4	derivation	derivation	NOUN
ap-2097	26	5	of	of	ADP
ap-2097	26	6	finite	finite	ADJ
ap-2097	26	7	-	-	ADJ
ap-2097	26	8	temperature	temperature	ADJ
ap-2097	26	9	cft	cft	NOUN
ap-2097	26	10	correlators	correlator	NOUN
ap-2097	26	11	section	section	VERB
ap-2097	26	12	3	3	NUM
ap-2097	26	13	we	we	PRON
ap-2097	26	14	introduce	introduce	VERB
ap-2097	26	15	a	a	DET
ap-2097	26	16	coordinate	coordinate	NOUN
ap-2097	26	17	realization	realization	NOUN
ap-2097	26	18	of	of	ADP
ap-2097	26	19	the	the	DET
ap-2097	26	20	lie	lie	NOUN
ap-2097	26	21	algebra	algebra	VERB
ap-2097	26	22	so(2	so(2	NOUN
ap-2097	26	23	,	,	PUNCT
ap-2097	26	24	2	2	NUM
ap-2097	26	25	)	)	PUNCT
ap-2097	26	26	∼=	∼=	PROPN
ap-2097	26	27	sl(2,r)l	sl(2,r)l	NOUN
ap-2097	26	28	⊕	⊕	PROPN
ap-2097	26	29	sl(2,r)r	sl(2,r)r	PROPN
ap-2097	26	30	realized	realize	VERB
ap-2097	26	31	in	in	ADP
ap-2097	26	32	scalar	scalar	ADJ
ap-2097	26	33	field	field	NOUN
ap-2097	26	34	theory	theory	NOUN
ap-2097	26	35	on	on	ADP
ap-2097	26	36	the	the	DET
ap-2097	26	37	ads3	ads3	ADJ
ap-2097	26	38	black	black	ADJ
ap-2097	26	39	hole	hole	NOUN
ap-2097	26	40	background	background	NOUN
ap-2097	26	41	.	.	PUNCT
ap-2097	27	1	we	we	PRON
ap-2097	27	2	then	then	ADV
ap-2097	27	3	demonstrate	demonstrate	VERB
ap-2097	27	4	in	in	ADP
ap-2097	27	5	section	section	NOUN
ap-2097	27	6	4	4	NUM
ap-2097	27	7	a	a	DET
ap-2097	27	8	simple	simple	ADJ
ap-2097	27	9	lie	lie	NOUN
ap-2097	27	10	-	-	PUNCT
ap-2097	27	11	algebraic	algebraic	ADJ
ap-2097	27	12	method	method	NOUN
ap-2097	27	13	for	for	ADP
ap-2097	27	14	computing	compute	VERB
ap-2097	27	15	the	the	DET
ap-2097	27	16	retarded	retarded	ADJ
ap-2097	27	17	and	and	CCONJ
ap-2097	27	18	advanced	advanced	ADJ
ap-2097	27	19	cft2	cft2	ADJ
ap-2097	27	20	two	two	NUM
ap-2097	27	21	-	-	PUNCT
ap-2097	27	22	point	point	NOUN
ap-2097	27	23	functions	function	NOUN
ap-2097	27	24	by	by	ADP
ap-2097	27	25	just	just	ADV
ap-2097	27	26	using	use	VERB
ap-2097	27	27	the	the	DET
ap-2097	27	28	ladder	ladder	NOUN
ap-2097	27	29	equations	equation	NOUN
ap-2097	27	30	of	of	ADP
ap-2097	27	31	the	the	DET
ap-2097	27	32	lie	lie	NOUN
ap-2097	27	33	algebra	algebra	VERB
ap-2097	27	34	so(2	so(2	NOUN
ap-2097	27	35	,	,	PUNCT
ap-2097	27	36	2	2	NUM
ap-2097	27	37	)	)	PUNCT
ap-2097	27	38	∼=	∼=	NOUN
ap-2097	27	39	sl(2,r)l⊕	sl(2,r)l⊕	NOUN
ap-2097	27	40	sl(2,r)r	sl(2,r)r	NOUN
ap-2097	27	41	in	in	ADP
ap-2097	27	42	the	the	DET
ap-2097	27	43	basis	basis	NOUN
ap-2097	27	44	in	in	ADP
ap-2097	27	45	which	which	PRON
ap-2097	27	46	so(1	so(1	PROPN
ap-2097	27	47	,	,	PUNCT
ap-2097	27	48	1)×	1)×	NUM
ap-2097	27	49	so(1	so(1	PROPN
ap-2097	27	50	,	,	PUNCT
ap-2097	27	51	1	1	NUM
ap-2097	27	52	)	)	PUNCT
ap-2097	27	53	⊂	⊂	PROPN
ap-2097	28	1	so(2	so(2	NOUN
ap-2097	28	2	,	,	PUNCT
ap-2097	28	3	2	2	X
ap-2097	28	4	)	)	PUNCT
ap-2097	28	5	generators	generator	NOUN
ap-2097	28	6	become	become	VERB
ap-2097	28	7	diagonal	diagonal	ADJ
ap-2097	28	8	.	.	PUNCT
ap-2097	29	1	we	we	PRON
ap-2097	29	2	will	will	AUX
ap-2097	29	3	see	see	VERB
ap-2097	29	4	that	that	SCONJ
ap-2097	29	5	our	our	PRON
ap-2097	29	6	method	method	NOUN
ap-2097	29	7	correctly	correctly	ADV
ap-2097	29	8	reproduces	reproduce	VERB
ap-2097	29	9	the	the	DET
ap-2097	29	10	known	know	VERB
ap-2097	29	11	results	result	NOUN
ap-2097	29	12	[	[	X
ap-2097	29	13	5	5	NUM
ap-2097	29	14	,	,	PUNCT
ap-2097	29	15	8	8	NUM
ap-2097	29	16	,	,	PUNCT
ap-2097	29	17	9	9	NUM
ap-2097	29	18	]	]	PUNCT
ap-2097	29	19	.	.	PUNCT
ap-2097	30	1	2	2	X
ap-2097	30	2	.	.	X
ap-2097	30	3	ads3	ads3	PROPN
ap-2097	30	4	black	black	ADJ
ap-2097	30	5	hole	hole	NOUN
ap-2097	30	6	:	:	PUNCT
ap-2097	30	7	locally	locally	ADV
ap-2097	30	8	ads3	ads3	PROPN
ap-2097	30	9	spacetime	spacetime	NOUN
ap-2097	30	10	in	in	ADP
ap-2097	30	11	the	the	DET
ap-2097	30	12	so(1	so(1	PROPN
ap-2097	30	13	,	,	PUNCT
ap-2097	30	14	1	1	NUM
ap-2097	30	15	)	)	PUNCT
ap-2097	30	16	×so(1	×so(1	NOUN
ap-2097	30	17	,	,	PUNCT
ap-2097	30	18	1	1	X
ap-2097	30	19	)	)	PUNCT
ap-2097	30	20	diagonal	diagonal	ADJ
ap-2097	30	21	basis	basis	NOUN
ap-2097	30	22	let	let	VERB
ap-2097	30	23	us	we	PRON
ap-2097	30	24	start	start	VERB
ap-2097	30	25	with	with	ADP
ap-2097	30	26	the	the	DET
ap-2097	30	27	following	follow	VERB
ap-2097	30	28	non	non	ADJ
ap-2097	30	29	-	-	ADJ
ap-2097	30	30	rotating	rotating	ADJ
ap-2097	30	31	btz	btz	NOUN
ap-2097	30	32	black	black	ADJ
ap-2097	30	33	hole	hole	NOUN
ap-2097	30	34	described	describe	VERB
ap-2097	30	35	by	by	ADP
ap-2097	30	36	the	the	DET
ap-2097	30	37	metric	metric	ADJ
ap-2097	30	38	ds2	ds2	PROPN
ap-2097	30	39	ads3	ads3	PROPN
ap-2097	30	40	bh	bh	NOUN
ap-2097	30	41	=	=	NOUN
ap-2097	30	42	−	−	PROPN
ap-2097	30	43	(	(	PUNCT
ap-2097	30	44	ρ2	ρ2	NOUN
ap-2097	30	45	r2	r2	NOUN
ap-2097	30	46	−	−	PROPN
ap-2097	30	47	1	1	NUM
ap-2097	30	48	)	)	PUNCT
ap-2097	30	49	dτ2	dτ2	NOUN
ap-2097	30	50	+	+	CCONJ
ap-2097	30	51	dρ2	dρ2	NOUN
ap-2097	30	52	ρ2	ρ2	NOUN
ap-2097	30	53	/	/	SYM
ap-2097	30	54	r2	r2	NOUN
ap-2097	30	55	−	−	PROPN
ap-2097	30	56	1	1	NUM
ap-2097	30	57	+	+	NUM
ap-2097	30	58	ρ2dθ2	ρ2dθ2	NOUN
ap-2097	30	59	,	,	PUNCT
ap-2097	30	60	(	(	PUNCT
ap-2097	30	61	1	1	X
ap-2097	30	62	)	)	PUNCT
ap-2097	30	63	where	where	SCONJ
ap-2097	30	64	τ	τ	PROPN
ap-2097	30	65	∈	∈	PROPN
ap-2097	30	66	(	(	PUNCT
ap-2097	30	67	−∞,+∞	−∞,+∞	NUM
ap-2097	30	68	)	)	PUNCT
ap-2097	30	69	,	,	PUNCT
ap-2097	30	70	ρ	ρ	PROPN
ap-2097	30	71	∈	∈	PROPN
ap-2097	30	72	(	(	PUNCT
ap-2097	30	73	0,∞	0,∞	NOUN
ap-2097	30	74	)	)	PUNCT
ap-2097	30	75	,	,	PUNCT
ap-2097	30	76	θ	θ	PROPN
ap-2097	30	77	∈	∈	PROPN
ap-2097	31	1	[	[	X
ap-2097	31	2	0	0	NUM
ap-2097	31	3	,	,	PUNCT
ap-2097	31	4	2π	2π	NOUN
ap-2097	31	5	)	)	PUNCT
ap-2097	31	6	,	,	PUNCT
ap-2097	31	7	and	and	CCONJ
ap-2097	31	8	r	r	NOUN
ap-2097	31	9	>	>	X
ap-2097	31	10	0	0	NUM
ap-2097	31	11	is	be	AUX
ap-2097	31	12	the	the	DET
ap-2097	31	13	ads3	ads3	PROPN
ap-2097	31	14	radius	radius	NOUN
ap-2097	31	15	.	.	PUNCT
ap-2097	32	1	in	in	ADP
ap-2097	32	2	this	this	DET
ap-2097	32	3	paper	paper	NOUN
ap-2097	32	4	we	we	PRON
ap-2097	32	5	simply	simply	ADV
ap-2097	32	6	call	call	VERB
ap-2097	32	7	(	(	PUNCT
ap-2097	32	8	1	1	NUM
ap-2097	32	9	)	)	PUNCT
ap-2097	32	10	the	the	DET
ap-2097	32	11	ads3	ads3	ADJ
ap-2097	32	12	black	black	ADJ
ap-2097	32	13	hole	hole	NOUN
ap-2097	32	14	and	and	CCONJ
ap-2097	32	15	focus	focus	VERB
ap-2097	32	16	on	on	ADP
ap-2097	32	17	the	the	DET
ap-2097	32	18	region	region	NOUN
ap-2097	32	19	outside	outside	ADP
ap-2097	32	20	the	the	DET
ap-2097	32	21	horizon	horizon	NOUN
ap-2097	32	22	ρ	ρ	X
ap-2097	32	23	>	>	X
ap-2097	32	24	r.	r.	PROPN
ap-2097	32	25	for	for	ADP
ap-2097	32	26	the	the	DET
ap-2097	32	27	following	follow	VERB
ap-2097	32	28	discussions	discussion	NOUN
ap-2097	32	29	it	it	PRON
ap-2097	32	30	is	be	AUX
ap-2097	32	31	convenient	convenient	ADJ
ap-2097	32	32	to	to	PART
ap-2097	32	33	introduce	introduce	VERB
ap-2097	32	34	a	a	DET
ap-2097	32	35	new	new	ADJ
ap-2097	32	36	spatial	spatial	ADJ
ap-2097	32	37	coordinate	coordinate	NOUN
ap-2097	32	38	x	x	PUNCT
ap-2097	32	39	as	as	SCONJ
ap-2097	32	40	follows	follow	VERB
ap-2097	32	41	:	:	PUNCT
ap-2097	32	42	ρ	ρ	PROPN
ap-2097	32	43	=	=	PUNCT
ap-2097	32	44	r	r	NOUN
ap-2097	32	45	coth(x	coth(x	PROPN
ap-2097	32	46	/	/	SYM
ap-2097	32	47	r	r	NOUN
ap-2097	32	48	)	)	PUNCT
ap-2097	32	49	,	,	PUNCT
ap-2097	32	50	(	(	PUNCT
ap-2097	32	51	2	2	X
ap-2097	32	52	)	)	PUNCT
ap-2097	32	53	where	where	SCONJ
ap-2097	32	54	x	x	PRON
ap-2097	32	55	ranges	range	VERB
ap-2097	32	56	from	from	ADP
ap-2097	32	57	0	0	NUM
ap-2097	32	58	to	to	ADP
ap-2097	32	59	∞.	∞.	PROPN
ap-2097	32	60	note	note	VERB
ap-2097	32	61	that	that	SCONJ
ap-2097	32	62	the	the	DET
ap-2097	32	63	black	black	ADJ
ap-2097	32	64	hole	hole	NOUN
ap-2097	32	65	horizon	horizon	PROPN
ap-2097	32	66	ρ	ρ	NOUN
ap-2097	33	1	=	=	SYM
ap-2097	33	2	r	r	NOUN
ap-2097	33	3	corresponds	correspond	VERB
ap-2097	33	4	to	to	ADP
ap-2097	33	5	x	x	X
ap-2097	33	6	=	=	SYM
ap-2097	33	7	∞	∞	PROPN
ap-2097	33	8	,	,	PUNCT
ap-2097	33	9	while	while	SCONJ
ap-2097	33	10	the	the	DET
ap-2097	33	11	ads3	ads3	PROPN
ap-2097	33	12	boundary	boundary	ADJ
ap-2097	33	13	ρ	ρ	PROPN
ap-2097	33	14	=	=	SYM
ap-2097	33	15	∞	∞	NUM
ap-2097	33	16	corresponds	correspond	VERB
ap-2097	33	17	to	to	ADP
ap-2097	33	18	x	x	X
ap-2097	33	19	=	=	PUNCT
ap-2097	33	20	0	0	NUM
ap-2097	33	21	.	.	PUNCT
ap-2097	34	1	a	a	DET
ap-2097	34	2	straightforward	straightforward	ADJ
ap-2097	34	3	calculation	calculation	NOUN
ap-2097	34	4	shows	show	VERB
ap-2097	34	5	that	that	SCONJ
ap-2097	34	6	in	in	ADP
ap-2097	34	7	the	the	DET
ap-2097	34	8	coordinate	coordinate	NOUN
ap-2097	34	9	system	system	NOUN
ap-2097	34	10	(	(	PUNCT
ap-2097	34	11	τ	τ	X
ap-2097	34	12	,	,	PUNCT
ap-2097	34	13	x	x	NOUN
ap-2097	34	14	,	,	PUNCT
ap-2097	34	15	θ	θ	PROPN
ap-2097	34	16	)	)	PUNCT
ap-2097	34	17	the	the	DET
ap-2097	34	18	black	black	ADJ
ap-2097	34	19	hole	hole	NOUN
ap-2097	34	20	metric	metric	NOUN
ap-2097	34	21	(	(	PUNCT
ap-2097	34	22	1	1	NUM
ap-2097	34	23	)	)	PUNCT
ap-2097	34	24	takes	take	VERB
ap-2097	34	25	the	the	DET
ap-2097	34	26	following	follow	VERB
ap-2097	34	27	form	form	NOUN
ap-2097	34	28	:	:	PUNCT
ap-2097	35	1	ds2	ds2	PROPN
ap-2097	35	2	ads3	ads3	PROPN
ap-2097	35	3	bh	bh	NOUN
ap-2097	35	4	=	=	NOUN
ap-2097	35	5	−dτ	−dτ	PROPN
ap-2097	35	6	2	2	NUM
ap-2097	35	7	+	+	CCONJ
ap-2097	35	8	dx2	dx2	PROPN
ap-2097	35	9	+	+	PROPN
ap-2097	35	10	r2	r2	PROPN
ap-2097	35	11	cosh2(x	cosh2(x	NOUN
ap-2097	35	12	/	/	SYM
ap-2097	35	13	r)dθ2	r)dθ2	NOUN
ap-2097	35	14	sinh2(x	sinh2(x	PROPN
ap-2097	35	15	/	/	SYM
ap-2097	35	16	r	r	NOUN
ap-2097	35	17	)	)	PUNCT
ap-2097	35	18	.	.	PUNCT
ap-2097	36	1	(	(	PUNCT
ap-2097	36	2	3	3	X
ap-2097	36	3	)	)	PUNCT
ap-2097	36	4	for	for	ADP
ap-2097	36	5	the	the	DET
ap-2097	36	6	sake	sake	NOUN
ap-2097	36	7	of	of	ADP
ap-2097	36	8	notational	notational	ADJ
ap-2097	36	9	brevity	brevity	NOUN
ap-2097	36	10	,	,	PUNCT
ap-2097	36	11	we	we	PRON
ap-2097	36	12	will	will	AUX
ap-2097	36	13	hereafter	hereafter	VERB
ap-2097	36	14	work	work	VERB
ap-2097	36	15	in	in	ADP
ap-2097	36	16	the	the	DET
ap-2097	36	17	units	unit	NOUN
ap-2097	36	18	in	in	ADP
ap-2097	36	19	which	which	PRON
ap-2097	36	20	r	r	NOUN
ap-2097	36	21	=	=	SYM
ap-2097	36	22	1	1	NUM
ap-2097	36	23	.	.	PUNCT
ap-2097	37	1	several	several	ADJ
ap-2097	37	2	comments	comment	NOUN
ap-2097	37	3	are	be	AUX
ap-2097	37	4	in	in	ADP
ap-2097	37	5	order	order	NOUN
ap-2097	37	6	:	:	PUNCT
ap-2097	37	7	(	(	PUNCT
ap-2097	37	8	1	1	X
ap-2097	37	9	.	.	PUNCT
ap-2097	37	10	)	)	PUNCT
ap-2097	38	1	btz	btz	PROPN
ap-2097	38	2	black	black	ADJ
ap-2097	38	3	hole	hole	NOUN
ap-2097	38	4	.	.	PUNCT
ap-2097	39	1	the	the	DET
ap-2097	39	2	above	above	ADJ
ap-2097	39	3	ads3	ads3	ADJ
ap-2097	39	4	black	black	ADJ
ap-2097	39	5	hole	hole	NOUN
ap-2097	39	6	(	(	PUNCT
ap-2097	39	7	1	1	X
ap-2097	39	8	)	)	PUNCT
ap-2097	39	9	is	be	AUX
ap-2097	39	10	locally	locally	ADV
ap-2097	39	11	isometric	isometric	ADJ
ap-2097	39	12	to	to	ADP
ap-2097	39	13	the	the	DET
ap-2097	39	14	rotating	rotate	VERB
ap-2097	39	15	btz	btz	NOUN
ap-2097	39	16	black	black	ADJ
ap-2097	39	17	hole	hole	NOUN
ap-2097	39	18	[	[	X
ap-2097	39	19	2	2	NUM
ap-2097	39	20	,	,	PUNCT
ap-2097	39	21	3	3	NUM
ap-2097	39	22	]	]	PUNCT
ap-2097	39	23	and	and	CCONJ
ap-2097	39	24	obtained	obtain	VERB
ap-2097	39	25	by	by	ADP
ap-2097	39	26	suitable	suitable	ADJ
ap-2097	39	27	change	change	NOUN
ap-2097	39	28	of	of	ADP
ap-2097	39	29	spacetime	spacetime	NOUN
ap-2097	39	30	coordinates	coordinate	NOUN
ap-2097	39	31	.	.	PUNCT
ap-2097	40	1	indeed	indeed	ADV
ap-2097	40	2	,	,	PUNCT
ap-2097	40	3	it	it	PRON
ap-2097	40	4	is	be	AUX
ap-2097	40	5	easy	easy	ADJ
ap-2097	40	6	to	to	PART
ap-2097	40	7	show	show	VERB
ap-2097	40	8	that	that	SCONJ
ap-2097	40	9	the	the	DET
ap-2097	40	10	btz	btz	PROPN
ap-2097	40	11	black	black	ADJ
ap-2097	40	12	hole	hole	NOUN
ap-2097	40	13	metric	metric	ADJ
ap-2097	40	14	ds2	ds2	PROPN
ap-2097	40	15	btz	btz	NOUN
ap-2097	40	16	=	=	SYM
ap-2097	40	17	−	−	PROPN
ap-2097	40	18	(	(	PUNCT
ap-2097	40	19	r2	r2	PROPN
ap-2097	40	20	−	−	PROPN
ap-2097	40	21	r2	r2	PROPN
ap-2097	40	22	+	+	PROPN
ap-2097	40	23	)	)	PUNCT
ap-2097	40	24	(	(	PUNCT
ap-2097	40	25	r2	r2	PROPN
ap-2097	40	26	−	−	PROPN
ap-2097	40	27	r2	r2	PROPN
ap-2097	40	28	−	−	NUM
ap-2097	40	29	)	)	PUNCT
ap-2097	40	30	r2	r2	PROPN
ap-2097	40	31	dt2	dt2	PROPN
ap-2097	40	32	+	+	CCONJ
ap-2097	40	33	r2dr2	r2dr2	PROPN
ap-2097	40	34	(	(	PUNCT
ap-2097	40	35	r2	r2	PROPN
ap-2097	40	36	−	−	PROPN
ap-2097	40	37	r2	r2	PROPN
ap-2097	40	38	+	+	PROPN
ap-2097	40	39	)	)	PUNCT
ap-2097	40	40	(	(	PUNCT
ap-2097	40	41	r2	r2	PROPN
ap-2097	40	42	−	−	PROPN
ap-2097	40	43	r2	r2	PROPN
ap-2097	40	44	−	−	PROPN
ap-2097	40	45	)	)	PUNCT
ap-2097	41	1	+	+	CCONJ
ap-2097	41	2	r2	r2	PROPN
ap-2097	41	3	(	(	PUNCT
ap-2097	41	4	dφ−	dφ−	PROPN
ap-2097	41	5	r+r−	r+r−	NOUN
ap-2097	41	6	r2	r2	PROPN
ap-2097	41	7	dt	dt	PROPN
ap-2097	41	8	)	)	PUNCT
ap-2097	41	9	2	2	NUM
ap-2097	41	10	,	,	PUNCT
ap-2097	41	11	(	(	PUNCT
ap-2097	41	12	4	4	X
ap-2097	41	13	)	)	PUNCT
ap-2097	41	14	the	the	DET
ap-2097	41	15	timeand	timeand	NOUN
ap-2097	41	16	angle	angle	NOUN
ap-2097	41	17	-	-	PUNCT
ap-2097	41	18	translation	translation	NOUN
ap-2097	41	19	generators	generator	NOUN
ap-2097	41	20	generate	generate	VERB
ap-2097	41	21	the	the	DET
ap-2097	41	22	subgroup	subgroup	NOUN
ap-2097	41	23	e(1)×	e(1)×	PROPN
ap-2097	41	24	e(1	e(1	PROPN
ap-2097	41	25	)	)	PUNCT
ap-2097	41	26	⊂	⊂	PROPN
ap-2097	42	1	so(2	so(2	NOUN
ap-2097	42	2	,	,	PUNCT
ap-2097	42	3	2	2	NUM
ap-2097	42	4	)	)	PUNCT
ap-2097	42	5	∼=	∼=	PROPN
ap-2097	42	6	(	(	PUNCT
ap-2097	42	7	sl(2,r)l	sl(2,r)l	AUX
ap-2097	42	8	×	×	NOUN
ap-2097	42	9	sl(2,r)r)/z2	sl(2,r)r)/z2	ADV
ap-2097	42	10	prior	prior	ADV
ap-2097	42	11	to	to	ADP
ap-2097	42	12	making	make	VERB
ap-2097	42	13	the	the	DET
ap-2097	42	14	z	z	NOUN
ap-2097	42	15	-	-	PUNCT
ap-2097	42	16	identification	identification	NOUN
ap-2097	42	17	.	.	PUNCT
ap-2097	43	1	(	(	PUNCT
ap-2097	43	2	note	note	VERB
ap-2097	43	3	that	that	SCONJ
ap-2097	43	4	sl(2,r	sl(2,r	NOUN
ap-2097	43	5	)	)	PUNCT
ap-2097	43	6	contains	contain	VERB
ap-2097	43	7	three	three	NUM
ap-2097	43	8	distinct	distinct	ADJ
ap-2097	43	9	one	one	NUM
ap-2097	43	10	-	-	PUNCT
ap-2097	43	11	parameter	parameter	NOUN
ap-2097	43	12	subgroups	subgroup	NOUN
ap-2097	43	13	:	:	PUNCT
ap-2097	43	14	the	the	DET
ap-2097	43	15	rotation	rotation	NOUN
ap-2097	43	16	group	group	NOUN
ap-2097	43	17	so(2	so(2	PROPN
ap-2097	43	18	)	)	PUNCT
ap-2097	43	19	,	,	PUNCT
ap-2097	43	20	the	the	DET
ap-2097	43	21	lorentz	lorentz	PROPN
ap-2097	43	22	group	group	NOUN
ap-2097	43	23	so(1	so(1	PROPN
ap-2097	43	24	,	,	PUNCT
ap-2097	43	25	1	1	NUM
ap-2097	43	26	)	)	PUNCT
ap-2097	43	27	and	and	CCONJ
ap-2097	43	28	the	the	DET
ap-2097	43	29	euclidean	euclidean	ADJ
ap-2097	43	30	group	group	NOUN
ap-2097	43	31	e(1	e(1	PROPN
ap-2097	43	32	)	)	PUNCT
ap-2097	43	33	.	.	PUNCT
ap-2097	43	34	)	)	PUNCT
ap-2097	44	1	for	for	ADP
ap-2097	44	2	detailed	detailed	ADJ
ap-2097	44	3	discussions	discussion	NOUN
ap-2097	44	4	of	of	ADP
ap-2097	44	5	the	the	DET
ap-2097	44	6	quotient	quotient	NOUN
ap-2097	44	7	construction	construction	NOUN
ap-2097	44	8	,	,	PUNCT
ap-2097	44	9	we	we	PRON
ap-2097	44	10	refer	refer	VERB
ap-2097	44	11	to	to	ADP
ap-2097	44	12	the	the	DET
ap-2097	44	13	original	original	ADJ
ap-2097	44	14	paper	paper	NOUN
ap-2097	45	1	[	[	X
ap-2097	45	2	3	3	X
ap-2097	45	3	]	]	PUNCT
ap-2097	45	4	(	(	PUNCT
ap-2097	45	5	see	see	VERB
ap-2097	45	6	also	also	ADV
ap-2097	45	7	[	[	X
ap-2097	45	8	7	7	NUM
ap-2097	45	9	]	]	NUM
ap-2097	45	10	)	)	PUNCT
ap-2097	45	11	.	.	PUNCT
ap-2097	46	1	where	where	SCONJ
ap-2097	46	2	r+	r+	NOUN
ap-2097	46	3	and	and	CCONJ
ap-2097	46	4	r−	r−	PROPN
ap-2097	46	5	are	be	AUX
ap-2097	46	6	the	the	DET
ap-2097	46	7	outer	outer	ADJ
ap-2097	46	8	and	and	CCONJ
ap-2097	46	9	inner	inner	ADJ
ap-2097	46	10	horizons	horizon	NOUN
ap-2097	46	11	,	,	PUNCT
ap-2097	46	12	respectively	respectively	ADV
ap-2097	46	13	,	,	PUNCT
ap-2097	46	14	is	be	AUX
ap-2097	46	15	reduced	reduce	VERB
ap-2097	46	16	to	to	ADP
ap-2097	46	17	the	the	DET
ap-2097	46	18	ads3	ads3	ADJ
ap-2097	46	19	black	black	ADJ
ap-2097	46	20	hole	hole	NOUN
ap-2097	46	21	(	(	PUNCT
ap-2097	46	22	1	1	NUM
ap-2097	46	23	)	)	PUNCT
ap-2097	46	24	by	by	ADP
ap-2097	46	25	the	the	DET
ap-2097	46	26	following	follow	VERB
ap-2097	46	27	coordinate	coordinate	NOUN
ap-2097	46	28	change	change	NOUN
ap-2097	46	29	[	[	X
ap-2097	46	30	10	10	NUM
ap-2097	46	31	]	]	SYM
ap-2097	46	32	:	:	PUNCT
ap-2097	47	1	ρ	ρ	PROPN
ap-2097	47	2	=	=	SYM
ap-2097	47	3	√	√	PROPN
ap-2097	47	4	r2	r2	PROPN
ap-2097	47	5	−	−	PROPN
ap-2097	47	6	r2	r2	PROPN
ap-2097	47	7	−	−	PROPN
ap-2097	47	8	r2	r2	NOUN
ap-2097	47	9	+	+	CCONJ
ap-2097	47	10	−	−	PROPN
ap-2097	47	11	r2	r2	PROPN
ap-2097	47	12	−	−	PROPN
ap-2097	47	13	,	,	PUNCT
ap-2097	47	14	τ	τ	PROPN
ap-2097	47	15	=	=	PUNCT
ap-2097	47	16	r+t−	r+t−	NOUN
ap-2097	47	17	r−φ	r−φ	NOUN
ap-2097	47	18	,	,	PUNCT
ap-2097	47	19	θ	θ	X
ap-2097	47	20	=	=	SYM
ap-2097	47	21	r+φ−	r+φ−	PROPN
ap-2097	47	22	r−t	r−t	PROPN
ap-2097	47	23	.	.	PUNCT
ap-2097	48	1	(	(	PUNCT
ap-2097	48	2	5	5	X
ap-2097	48	3	)	)	PUNCT
ap-2097	48	4	note	note	NOUN
ap-2097	48	5	that	that	SCONJ
ap-2097	48	6	the	the	DET
ap-2097	48	7	light	light	ADJ
ap-2097	48	8	-	-	PUNCT
ap-2097	48	9	cone	cone	NOUN
ap-2097	48	10	coordinates	coordinate	NOUN
ap-2097	48	11	satisfy	satisfy	VERB
ap-2097	48	12	the	the	DET
ap-2097	48	13	relations	relation	NOUN
ap-2097	48	14	τ	τ	PROPN
ap-2097	48	15	±	±	NUM
ap-2097	48	16	θ	θ	NOUN
ap-2097	48	17	=	=	PUNCT
ap-2097	48	18	(	(	PUNCT
ap-2097	48	19	r+	r+	X
ap-2097	48	20	∓	∓	PROPN
ap-2097	48	21	r−)(t±	r−)(t±	PROPN
ap-2097	48	22	φ	φ	NUM
ap-2097	48	23	)	)	PUNCT
ap-2097	48	24	.	.	PUNCT
ap-2097	49	1	(	(	PUNCT
ap-2097	49	2	2	2	NUM
ap-2097	49	3	.	.	PUNCT
ap-2097	49	4	)	)	PUNCT
ap-2097	49	5	local	local	ADJ
ap-2097	49	6	coordinate	coordinate	NOUN
ap-2097	49	7	patch	patch	NOUN
ap-2097	49	8	of	of	ADP
ap-2097	49	9	ads3	ads3	PROPN
ap-2097	49	10	.	.	PUNCT
ap-2097	50	1	the	the	DET
ap-2097	50	2	ads3	ads3	PROPN
ap-2097	50	3	black	black	ADJ
ap-2097	50	4	hole	hole	NOUN
ap-2097	50	5	is	be	AUX
ap-2097	50	6	a	a	DET
ap-2097	50	7	locally	locally	ADV
ap-2097	50	8	ads3	ads3	ADJ
ap-2097	50	9	spacetime	spacetime	NOUN
ap-2097	50	10	and	and	CCONJ
ap-2097	50	11	is	be	AUX
ap-2097	50	12	obtained	obtain	VERB
ap-2097	50	13	from	from	ADP
ap-2097	50	14	the	the	DET
ap-2097	50	15	ads3	ads3	ADJ
ap-2097	50	16	spacetime	spacetime	NOUN
ap-2097	50	17	with	with	ADP
ap-2097	50	18	a	a	DET
ap-2097	50	19	suitable	suitable	ADJ
ap-2097	50	20	periodic	periodic	ADJ
ap-2097	50	21	identification	identification	NOUN
ap-2097	50	22	[	[	X
ap-2097	50	23	3	3	NUM
ap-2097	50	24	,	,	PUNCT
ap-2097	50	25	7	7	NUM
ap-2097	50	26	]	]	PUNCT
ap-2097	50	27	.	.	PUNCT
ap-2097	51	1	to	to	PART
ap-2097	51	2	see	see	VERB
ap-2097	51	3	this	this	PRON
ap-2097	51	4	,	,	PUNCT
ap-2097	51	5	let	let	VERB
ap-2097	51	6	us	we	PRON
ap-2097	51	7	first	first	ADV
ap-2097	51	8	note	note	VERB
ap-2097	51	9	that	that	SCONJ
ap-2097	51	10	the	the	DET
ap-2097	51	11	ads3	ads3	ADJ
ap-2097	51	12	spacetime	spacetime	NOUN
ap-2097	51	13	can	can	AUX
ap-2097	51	14	be	be	AUX
ap-2097	51	15	embedded	embed	VERB
ap-2097	51	16	into	into	ADP
ap-2097	51	17	the	the	DET
ap-2097	51	18	four	four	NUM
ap-2097	51	19	-	-	PUNCT
ap-2097	51	20	dimensional	dimensional	ADJ
ap-2097	51	21	ambient	ambient	ADJ
ap-2097	51	22	space	space	NOUN
ap-2097	51	23	r2,2	r2,2	PROPN
ap-2097	51	24	and	and	CCONJ
ap-2097	51	25	defined	define	VERB
ap-2097	51	26	as	as	ADP
ap-2097	51	27	the	the	DET
ap-2097	51	28	following	follow	VERB
ap-2097	51	29	hypersurface	hypersurface	NOUN
ap-2097	51	30	with	with	ADP
ap-2097	51	31	constant	constant	ADJ
ap-2097	51	32	negative	negative	ADJ
ap-2097	51	33	curvature	curvature	NOUN
ap-2097	51	34	−1	−1	NOUN
ap-2097	51	35	(=	(=	ADP
ap-2097	51	36	−1	−1	NOUN
ap-2097	51	37	/	/	SYM
ap-2097	51	38	r2	r2	NOUN
ap-2097	51	39	):	):	PUNCT
ap-2097	51	40	ads3	ads3	ADV
ap-2097	51	41	=	=	PRON
ap-2097	51	42	{	{	PUNCT
ap-2097	51	43	(	(	PUNCT
ap-2097	51	44	x−1	x−1	PROPN
ap-2097	51	45	,	,	PUNCT
ap-2097	51	46	x0	x0	PROPN
ap-2097	51	47	,	,	PUNCT
ap-2097	51	48	x1	x1	PROPN
ap-2097	51	49	,	,	PUNCT
ap-2097	51	50	x2	x2	PROPN
ap-2097	51	51	)	)	PUNCT
ap-2097	51	52	∈	∈	PROPN
ap-2097	51	53	r2,2	r2,2	PROPN
ap-2097	51	54	∣∣	∣∣	NUM
ap-2097	51	55	−	−	PROPN
ap-2097	51	56	(	(	PUNCT
ap-2097	51	57	x−1)2	x−1)2	PROPN
ap-2097	51	58	−	−	PROPN
ap-2097	52	1	(	(	PUNCT
ap-2097	52	2	x0)2	x0)2	X
ap-2097	53	1	+	+	PUNCT
ap-2097	53	2	(	(	PUNCT
ap-2097	53	3	x1)2	x1)2	PUNCT
ap-2097	53	4	+	+	PUNCT
ap-2097	53	5	(	(	PUNCT
ap-2097	53	6	x2)2	x2)2	PRON
ap-2097	53	7	=	=	SYM
ap-2097	53	8	−1	−1	NOUN
ap-2097	53	9	}	}	PUNCT
ap-2097	53	10	.	.	PUNCT
ap-2097	54	1	(	(	PUNCT
ap-2097	54	2	6	6	X
ap-2097	54	3	)	)	PUNCT
ap-2097	54	4	the	the	DET
ap-2097	54	5	ads3	ads3	ADJ
ap-2097	54	6	black	black	ADJ
ap-2097	54	7	hole	hole	NOUN
ap-2097	54	8	(	(	PUNCT
ap-2097	54	9	3	3	X
ap-2097	54	10	)	)	PUNCT
ap-2097	54	11	is	be	AUX
ap-2097	54	12	given	give	VERB
ap-2097	54	13	by	by	ADP
ap-2097	54	14	the	the	DET
ap-2097	54	15	following	follow	VERB
ap-2097	54	16	local	local	ADJ
ap-2097	54	17	coordinate	coordinate	NOUN
ap-2097	54	18	patch	patch	NOUN
ap-2097	54	19	of	of	ADP
ap-2097	54	20	the	the	DET
ap-2097	54	21	hypersurface	hypersurface	NOUN
ap-2097	54	22	:	:	PUNCT
ap-2097	54	23	(	(	PUNCT
ap-2097	54	24	x−1	x−1	PROPN
ap-2097	54	25	,	,	PUNCT
ap-2097	54	26	x0	x0	PROPN
ap-2097	54	27	,	,	PUNCT
ap-2097	54	28	x1	x1	PROPN
ap-2097	54	29	,	,	PUNCT
ap-2097	54	30	x2	x2	PROPN
ap-2097	54	31	)	)	PUNCT
ap-2097	54	32	=	=	SYM
ap-2097	54	33	(	(	PUNCT
ap-2097	54	34	coth	coth	NOUN
ap-2097	54	35	x	x	SYM
ap-2097	54	36	cosh	cosh	PROPN
ap-2097	54	37	θ	θ	PROPN
ap-2097	54	38	,	,	PUNCT
ap-2097	54	39	sinh	sinh	PROPN
ap-2097	54	40	τ	τ	PROPN
ap-2097	54	41	sinh	sinh	NOUN
ap-2097	54	42	x	x	PROPN
ap-2097	54	43	,	,	PUNCT
ap-2097	54	44	coth	coth	PROPN
ap-2097	54	45	x	x	SYM
ap-2097	54	46	sinh	sinh	PROPN
ap-2097	54	47	θ	θ	PROPN
ap-2097	54	48	,	,	PUNCT
ap-2097	54	49	cosh	cosh	PROPN
ap-2097	54	50	τ	τ	PROPN
ap-2097	54	51	sinh	sinh	NOUN
ap-2097	54	52	x	x	PUNCT
ap-2097	54	53	)	)	PUNCT
ap-2097	54	54	,	,	PUNCT
ap-2097	54	55	(	(	PUNCT
ap-2097	54	56	7	7	X
ap-2097	54	57	)	)	PUNCT
ap-2097	54	58	with	with	ADP
ap-2097	54	59	the	the	DET
ap-2097	54	60	periodic	periodic	ADJ
ap-2097	54	61	identification	identification	NOUN
ap-2097	54	62	θ	θ	NOUN
ap-2097	54	63	∼	∼	NOUN
ap-2097	54	64	θ	θ	NOUN
ap-2097	54	65	+	+	CCONJ
ap-2097	54	66	2nπ	2nπ	NOUN
ap-2097	54	67	(	(	PUNCT
ap-2097	54	68	n	n	NOUN
ap-2097	54	69	∈	∈	PROPN
ap-2097	54	70	z	z	PROPN
ap-2097	54	71	)	)	PUNCT
ap-2097	54	72	.	.	PUNCT
ap-2097	55	1	in	in	ADP
ap-2097	55	2	fact	fact	NOUN
ap-2097	55	3	,	,	PUNCT
ap-2097	55	4	it	it	PRON
ap-2097	55	5	is	be	AUX
ap-2097	55	6	straightforward	straightforward	ADJ
ap-2097	55	7	to	to	PART
ap-2097	55	8	show	show	VERB
ap-2097	55	9	that	that	SCONJ
ap-2097	55	10	the	the	DET
ap-2097	55	11	induced	induced	ADJ
ap-2097	55	12	metric	metric	ADJ
ap-2097	55	13	ds2	ds2	PROPN
ap-2097	55	14	ads3	ads3	NOUN
ap-2097	55	15	=	=	PUNCT
ap-2097	56	1	−(dx−1)2	−(dx−1)2	ADJ
ap-2097	56	2	−	−	PUNCT
ap-2097	57	1	(	(	PUNCT
ap-2097	57	2	dx0)2	dx0)2	X
ap-2097	57	3	+	+	CCONJ
ap-2097	57	4	(	(	PUNCT
ap-2097	57	5	dx1)2	dx1)2	PROPN
ap-2097	57	6	+	+	NUM
ap-2097	57	7	(	(	PUNCT
ap-2097	57	8	dx2)2	dx2)2	X
ap-2097	57	9	∣∣	∣∣	NUM
ap-2097	57	10	(	(	PUNCT
ap-2097	57	11	x−1,x0,x1,x2)∈ads3	x−1,x0,x1,x2)∈ads3	ADV
ap-2097	57	12	on	on	ADP
ap-2097	57	13	the	the	DET
ap-2097	57	14	hypersurface	hypersurface	NOUN
ap-2097	57	15	takes	take	VERB
ap-2097	57	16	the	the	DET
ap-2097	57	17	following	follow	VERB
ap-2097	57	18	form	form	NOUN
ap-2097	57	19	:	:	PUNCT
ap-2097	58	1	ds2	ds2	PROPN
ap-2097	58	2	ads3	ads3	PROPN
ap-2097	58	3	=	=	SYM
ap-2097	58	4	−dτ	−dτ	PROPN
ap-2097	58	5	2	2	NUM
ap-2097	58	6	+	+	CCONJ
ap-2097	58	7	dx2	dx2	PROPN
ap-2097	58	8	+	+	CCONJ
ap-2097	58	9	cosh2	cosh2	PROPN
ap-2097	58	10	xdθ2	xdθ2	PROPN
ap-2097	58	11	sinh2	sinh2	PROPN
ap-2097	59	1	x	x	X
ap-2097	59	2	.	.	PUNCT
ap-2097	60	1	(	(	PUNCT
ap-2097	60	2	8)	8)	NUM
ap-2097	60	3	it	it	PRON
ap-2097	60	4	should	should	AUX
ap-2097	60	5	be	be	AUX
ap-2097	60	6	emphasized	emphasize	VERB
ap-2097	60	7	that	that	SCONJ
ap-2097	60	8	the	the	DET
ap-2097	60	9	periodic	periodic	ADJ
ap-2097	60	10	identification	identification	NOUN
ap-2097	60	11	θ	θ	NOUN
ap-2097	60	12	∼	∼	NOUN
ap-2097	60	13	θ	θ	NOUN
ap-2097	60	14	+	+	CCONJ
ap-2097	60	15	2nπ	2nπ	NOUN
ap-2097	60	16	makes	make	VERB
ap-2097	60	17	the	the	DET
ap-2097	60	18	metric	metric	ADJ
ap-2097	60	19	(	(	PUNCT
ap-2097	60	20	8)	8)	NUM
ap-2097	60	21	black	black	ADJ
ap-2097	60	22	hole	hole	NOUN
ap-2097	60	23	.	.	PUNCT
ap-2097	61	1	as	as	SCONJ
ap-2097	61	2	mentioned	mention	VERB
ap-2097	61	3	in	in	ADP
ap-2097	61	4	[	[	X
ap-2097	61	5	3	3	NUM
ap-2097	61	6	]	]	PUNCT
ap-2097	61	7	,	,	PUNCT
ap-2097	61	8	without	without	ADP
ap-2097	61	9	such	such	ADJ
ap-2097	61	10	identification	identification	NOUN
ap-2097	61	11	the	the	DET
ap-2097	61	12	metric	metric	ADJ
ap-2097	61	13	(	(	PUNCT
ap-2097	61	14	8)	8)	NUM
ap-2097	61	15	just	just	ADV
ap-2097	61	16	describes	describe	VERB
ap-2097	61	17	a	a	DET
ap-2097	61	18	portion	portion	NOUN
ap-2097	61	19	of	of	ADP
ap-2097	61	20	ads3	ads3	PROPN
ap-2097	61	21	and	and	CCONJ
ap-2097	61	22	the	the	DET
ap-2097	61	23	horizon	horizon	NOUN
ap-2097	61	24	is	be	AUX
ap-2097	61	25	just	just	ADV
ap-2097	61	26	that	that	PRON
ap-2097	61	27	of	of	ADP
ap-2097	61	28	an	an	DET
ap-2097	61	29	accelerated	accelerated	ADJ
ap-2097	61	30	observer	observer	NOUN
ap-2097	61	31	.	.	PUNCT
ap-2097	62	1	(	(	PUNCT
ap-2097	62	2	roughly	roughly	ADV
ap-2097	62	3	speaking	speak	VERB
ap-2097	62	4	,	,	PUNCT
ap-2097	62	5	(	(	PUNCT
ap-2097	62	6	7	7	X
ap-2097	62	7	)	)	PUNCT
ap-2097	62	8	is	be	AUX
ap-2097	62	9	the	the	DET
ap-2097	62	10	ads3	ads3	ADJ
ap-2097	62	11	counterpart	counterpart	NOUN
ap-2097	62	12	of	of	ADP
ap-2097	62	13	the	the	DET
ap-2097	62	14	rindler	rindler	NOUN
ap-2097	62	15	coordinate	coordinate	NOUN
ap-2097	62	16	patch	patch	NOUN
ap-2097	62	17	of	of	ADP
ap-2097	62	18	minkowski	minkowski	ADJ
ap-2097	62	19	spacetime	spacetime	NOUN
ap-2097	62	20	.	.	PUNCT
ap-2097	62	21	)	)	PUNCT
ap-2097	63	1	(	(	PUNCT
ap-2097	63	2	3	3	NUM
ap-2097	63	3	.	.	PUNCT
ap-2097	63	4	)	)	PUNCT
ap-2097	64	1	so(1	so(1	PROPN
ap-2097	64	2	,	,	PUNCT
ap-2097	64	3	1	1	NUM
ap-2097	64	4	)	)	PUNCT
ap-2097	64	5	×	×	PROPN
ap-2097	64	6	so(1	so(1	PROPN
ap-2097	64	7	,	,	PUNCT
ap-2097	64	8	1	1	NUM
ap-2097	64	9	)	)	PUNCT
ap-2097	64	10	global	global	ADJ
ap-2097	64	11	symmetry	symmetry	NOUN
ap-2097	64	12	.	.	PUNCT
ap-2097	65	1	as	as	SCONJ
ap-2097	65	2	is	be	AUX
ap-2097	65	3	well	well	ADV
ap-2097	65	4	-	-	PUNCT
ap-2097	65	5	known	know	VERB
ap-2097	65	6	,	,	PUNCT
ap-2097	65	7	the	the	DET
ap-2097	65	8	ads3	ads3	ADJ
ap-2097	65	9	spacetime	spacetime	NOUN
ap-2097	65	10	(	(	PUNCT
ap-2097	65	11	6	6	NUM
ap-2097	65	12	)	)	PUNCT
ap-2097	65	13	has	have	VERB
ap-2097	65	14	an	an	DET
ap-2097	65	15	alternative	alternative	ADJ
ap-2097	65	16	equivalent	equivalent	ADJ
ap-2097	65	17	description	description	NOUN
ap-2097	65	18	as	as	ADP
ap-2097	65	19	the	the	DET
ap-2097	65	20	sl(2,r	sl(2,r	NOUN
ap-2097	65	21	)	)	PUNCT
ap-2097	65	22	group	group	NOUN
ap-2097	65	23	manifold	manifold	NOUN
ap-2097	65	24	defined	define	VERB
ap-2097	65	25	as	as	SCONJ
ap-2097	65	26	follows	follow	VERB
ap-2097	65	27	:	:	PUNCT
ap-2097	65	28	ads3	ads3	PROPN
ap-2097	65	29	=	=	PRON
ap-2097	65	30	{	{	PUNCT
ap-2097	65	31	x	x	SYM
ap-2097	65	32	=	=	SYM
ap-2097	65	33	(	(	PUNCT
ap-2097	65	34	x−1+x2	x−1+x2	PROPN
ap-2097	65	35	x1−x0	x1−x0	PROPN
ap-2097	65	36	x1+x0	x1+x0	PROPN
ap-2097	65	37	x−1−x2	x−1−x2	PROPN
ap-2097	65	38	)	)	PUNCT
ap-2097	65	39	∣∣∣	∣∣∣	ADP
ap-2097	65	40	detx	detx	NOUN
ap-2097	65	41	=	=	NOUN
ap-2097	65	42	1	1	NUM
ap-2097	65	43	}	}	PUNCT
ap-2097	65	44	.	.	PUNCT
ap-2097	66	1	(	(	PUNCT
ap-2097	66	2	9	9	X
ap-2097	66	3	)	)	PUNCT
ap-2097	66	4	with	with	ADP
ap-2097	66	5	this	this	DET
ap-2097	66	6	definition	definition	NOUN
ap-2097	66	7	it	it	PRON
ap-2097	66	8	is	be	AUX
ap-2097	66	9	obvious	obvious	ADJ
ap-2097	66	10	that	that	SCONJ
ap-2097	66	11	the	the	DET
ap-2097	66	12	ads3	ads3	ADJ
ap-2097	66	13	spacetime	spacetime	NOUN
ap-2097	66	14	(	(	PUNCT
ap-2097	66	15	9	9	NUM
ap-2097	66	16	)	)	PUNCT
ap-2097	66	17	is	be	AUX
ap-2097	66	18	invariant	invariant	ADJ
ap-2097	66	19	under	under	ADP
ap-2097	66	20	leftand	leftand	NOUN
ap-2097	66	21	rightmultiplications	rightmultiplication	NOUN
ap-2097	66	22	of	of	ADP
ap-2097	66	23	sl(2,r	sl(2,r	NOUN
ap-2097	66	24	)	)	PUNCT
ap-2097	66	25	matrices	matrix	NOUN
ap-2097	66	26	,	,	PUNCT
ap-2097	66	27	x	x	PROPN
ap-2097	66	28	7→	7→	NUM
ap-2097	66	29	x	x	SYM
ap-2097	66	30	′	′	NUM
ap-2097	66	31	=	=	NOUN
ap-2097	66	32	glxgr	glxgr	NOUN
ap-2097	66	33	,	,	PUNCT
ap-2097	66	34	where	where	SCONJ
ap-2097	66	35	gl	gl	PROPN
ap-2097	66	36	∈	∈	PROPN
ap-2097	66	37	sl(2,r)l	sl(2,r)l	VERB
ap-2097	66	38	and	and	CCONJ
ap-2097	66	39	gr	gr	PROPN
ap-2097	66	40	∈	∈	PROPN
ap-2097	66	41	sl(2,r)r	sl(2,r)r	NOUN
ap-2097	66	42	with	with	ADP
ap-2097	66	43	the	the	DET
ap-2097	66	44	z2	z2	NOUN
ap-2097	66	45	-	-	PUNCT
ap-2097	66	46	identification	identification	NOUN
ap-2097	66	47	(	(	PUNCT
ap-2097	66	48	gl	gl	NOUN
ap-2097	66	49	,	,	PUNCT
ap-2097	66	50	gr	gr	NOUN
ap-2097	66	51	)	)	PUNCT
ap-2097	66	52	∼	∼	NOUN
ap-2097	66	53	(	(	PUNCT
ap-2097	66	54	−gl,−gr	−gl,−gr	NUM
ap-2097	66	55	)	)	PUNCT
ap-2097	66	56	.	.	PUNCT
ap-2097	67	1	143	143	NUM
ap-2097	67	2	satoshi	satoshi	PROPN
ap-2097	67	3	ohya	ohya	PROPN
ap-2097	67	4	acta	acta	PROPN
ap-2097	67	5	polytechnica	polytechnica	PROPN
ap-2097	67	6	(	(	PUNCT
ap-2097	67	7	note	note	VERB
ap-2097	67	8	that	that	SCONJ
ap-2097	67	9	(	(	PUNCT
ap-2097	67	10	gl	gl	INTJ
ap-2097	67	11	,	,	PUNCT
ap-2097	67	12	gr	gr	PROPN
ap-2097	67	13	)	)	PUNCT
ap-2097	67	14	and	and	CCONJ
ap-2097	67	15	(	(	PUNCT
ap-2097	67	16	−gl,−gr	−gl,−gr	X
ap-2097	67	17	)	)	PUNCT
ap-2097	67	18	give	give	VERB
ap-2097	67	19	the	the	DET
ap-2097	67	20	same	same	ADJ
ap-2097	67	21	x	x	NOUN
ap-2097	67	22	′.	′.	NOUN
ap-2097	67	23	)	)	PUNCT
ap-2097	67	24	in	in	ADP
ap-2097	67	25	the	the	DET
ap-2097	67	26	local	local	ADJ
ap-2097	67	27	coordinate	coordinate	NOUN
ap-2097	67	28	patch	patch	NOUN
ap-2097	67	29	(	(	PUNCT
ap-2097	67	30	7	7	NUM
ap-2097	67	31	)	)	PUNCT
ap-2097	67	32	the	the	DET
ap-2097	67	33	2×2	2×2	NUM
ap-2097	67	34	matrix	matrix	NOUN
ap-2097	67	35	x	x	PUNCT
ap-2097	67	36	=	=	PUNCT
ap-2097	67	37	(	(	PUNCT
ap-2097	67	38	x−1+x2	x−1+x2	PROPN
ap-2097	67	39	x1−x0	x1−x0	PROPN
ap-2097	67	40	x1+x0	x1+x0	PROPN
ap-2097	67	41	x−1−x2	x−1−x2	PROPN
ap-2097	67	42	)	)	PUNCT
ap-2097	67	43	takes	take	VERB
ap-2097	67	44	the	the	DET
ap-2097	67	45	following	follow	VERB
ap-2097	67	46	form	form	NOUN
ap-2097	67	47	:	:	PUNCT
ap-2097	67	48	x	x	SYM
ap-2097	67	49	=	=	SYM
ap-2097	67	50	(	(	PUNCT
ap-2097	67	51	coth	coth	NOUN
ap-2097	67	52	x	x	SYM
ap-2097	67	53	cosh	cosh	NOUN
ap-2097	67	54	θ+	θ+	PUNCT
ap-2097	67	55	cosh	cosh	PROPN
ap-2097	67	56	τ	τ	PROPN
ap-2097	67	57	sinh	sinh	NOUN
ap-2097	67	58	x	x	PUNCT
ap-2097	67	59	coth	coth	PROPN
ap-2097	67	60	x	x	PUNCT
ap-2097	67	61	sinh	sinh	NOUN
ap-2097	67	62	θ−	θ−	PROPN
ap-2097	67	63	sinh	sinh	PROPN
ap-2097	67	64	τ	τ	PROPN
ap-2097	67	65	sinh	sinh	NOUN
ap-2097	67	66	x	x	PUNCT
ap-2097	67	67	coth	coth	PROPN
ap-2097	67	68	x	x	PUNCT
ap-2097	67	69	sinh	sinh	NOUN
ap-2097	67	70	θ+	θ+	PUNCT
ap-2097	67	71	sinh	sinh	PROPN
ap-2097	67	72	τ	τ	PROPN
ap-2097	67	73	sinh	sinh	NOUN
ap-2097	67	74	x	x	PUNCT
ap-2097	67	75	coth	coth	PROPN
ap-2097	67	76	x	x	PUNCT
ap-2097	67	77	cosh	cosh	PROPN
ap-2097	67	78	θ−	θ−	PROPN
ap-2097	67	79	cosh	cosh	PROPN
ap-2097	67	80	τ	τ	PROPN
ap-2097	67	81	sinh	sinh	NOUN
ap-2097	67	82	x	x	PUNCT
ap-2097	67	83	)	)	PUNCT
ap-2097	67	84	.	.	PUNCT
ap-2097	68	1	(	(	PUNCT
ap-2097	68	2	10	10	NUM
ap-2097	68	3	)	)	PUNCT
ap-2097	68	4	now	now	ADV
ap-2097	68	5	it	it	PRON
ap-2097	68	6	is	be	AUX
ap-2097	68	7	easy	easy	ADJ
ap-2097	68	8	to	to	PART
ap-2097	68	9	see	see	VERB
ap-2097	68	10	that	that	SCONJ
ap-2097	69	1	the	the	DET
ap-2097	69	2	time	time	NOUN
ap-2097	69	3	-	-	PUNCT
ap-2097	69	4	translation	translation	NOUN
ap-2097	69	5	τ	τ	PROPN
ap-2097	69	6	7→	7→	NUM
ap-2097	69	7	τ	τ	X
ap-2097	69	8	′	′	NUM
ap-2097	69	9	=	=	PUNCT
ap-2097	69	10	τ	τ	PROPN
ap-2097	69	11	+	+	NUM
ap-2097	69	12	ε	ε	PROPN
ap-2097	69	13	is	be	AUX
ap-2097	69	14	induced	induce	VERB
ap-2097	69	15	by	by	ADP
ap-2097	69	16	the	the	DET
ap-2097	69	17	noncompact	noncompact	NOUN
ap-2097	69	18	so(1	so(1	PROPN
ap-2097	69	19	,	,	PUNCT
ap-2097	69	20	1	1	NUM
ap-2097	69	21	)	)	PUNCT
ap-2097	69	22	⊂	⊂	PROPN
ap-2097	70	1	so(2	so(2	ADJ
ap-2097	70	2	,	,	PUNCT
ap-2097	70	3	2	2	NUM
ap-2097	70	4	)	)	PUNCT
ap-2097	70	5	group	group	NOUN
ap-2097	70	6	action	action	NOUN
ap-2097	70	7	x	x	SYM
ap-2097	70	8	7→	7→	NUM
ap-2097	70	9	x	x	NOUN
ap-2097	70	10	′	′	NOUN
ap-2097	70	11	=	=	SYM
ap-2097	70	12	glxgr	glxgr	NOUN
ap-2097	70	13	given	give	VERB
ap-2097	70	14	by	by	ADP
ap-2097	70	15	the	the	DET
ap-2097	70	16	matrices	matrix	NOUN
ap-2097	70	17	gl	gl	X
ap-2097	71	1	=	=	PUNCT
ap-2097	71	2	g−1	g−1	PROPN
ap-2097	71	3	r	r	NOUN
ap-2097	71	4	=	=	PUNCT
ap-2097	71	5	(	(	PUNCT
ap-2097	71	6	cosh	cosh	NOUN
ap-2097	71	7	ε	ε	PROPN
ap-2097	71	8	2	2	NUM
ap-2097	71	9	sinh	sinh	NOUN
ap-2097	71	10	ε	ε	PROPN
ap-2097	71	11	2	2	NUM
ap-2097	71	12	sinh	sinh	NOUN
ap-2097	71	13	ε	ε	PROPN
ap-2097	71	14	2	2	NUM
ap-2097	71	15	cosh	cosh	NOUN
ap-2097	71	16	ε	ε	PROPN
ap-2097	71	17	2	2	NUM
ap-2097	71	18	)	)	PUNCT
ap-2097	71	19	∈	∈	PROPN
ap-2097	71	20	so(1	so(1	PROPN
ap-2097	71	21	,	,	PUNCT
ap-2097	71	22	1	1	NUM
ap-2097	71	23	)	)	PUNCT
ap-2097	71	24	.	.	PUNCT
ap-2097	72	1	(	(	PUNCT
ap-2097	72	2	11	11	NUM
ap-2097	72	3	)	)	PUNCT
ap-2097	72	4	likewise	likewise	ADV
ap-2097	72	5	,	,	PUNCT
ap-2097	72	6	the	the	DET
ap-2097	72	7	spatial	spatial	ADJ
ap-2097	72	8	-	-	PUNCT
ap-2097	72	9	translation	translation	NOUN
ap-2097	72	10	θ	θ	PROPN
ap-2097	72	11	7→	7→	NUM
ap-2097	72	12	θ′	θ′	NOUN
ap-2097	72	13	=	=	SYM
ap-2097	72	14	θ	θ	PROPN
ap-2097	72	15	+	+	CCONJ
ap-2097	72	16	ε	ε	PROPN
ap-2097	72	17	is	be	AUX
ap-2097	72	18	induced	induce	VERB
ap-2097	72	19	by	by	ADP
ap-2097	72	20	another	another	DET
ap-2097	72	21	so(1	so(1	PROPN
ap-2097	72	22	,	,	PUNCT
ap-2097	72	23	1	1	NUM
ap-2097	72	24	)	)	PUNCT
ap-2097	72	25	⊂	⊂	PROPN
ap-2097	73	1	so(2	so(2	ADJ
ap-2097	73	2	,	,	PUNCT
ap-2097	73	3	2	2	NUM
ap-2097	73	4	)	)	PUNCT
ap-2097	73	5	group	group	NOUN
ap-2097	73	6	action	action	NOUN
ap-2097	73	7	x	x	SYM
ap-2097	73	8	7→	7→	NUM
ap-2097	73	9	x	x	NOUN
ap-2097	73	10	′	′	NOUN
ap-2097	73	11	=	=	SYM
ap-2097	73	12	glxgr	glxgr	NOUN
ap-2097	73	13	given	give	VERB
ap-2097	73	14	by	by	ADP
ap-2097	73	15	the	the	DET
ap-2097	73	16	matrices	matrix	NOUN
ap-2097	73	17	gl	gl	NOUN
ap-2097	73	18	=	=	NOUN
ap-2097	73	19	gr	gr	PROPN
ap-2097	73	20	=	=	PUNCT
ap-2097	73	21	(	(	PUNCT
ap-2097	73	22	cosh	cosh	NOUN
ap-2097	73	23	ε	ε	PROPN
ap-2097	73	24	2	2	NUM
ap-2097	73	25	sinh	sinh	NOUN
ap-2097	73	26	ε	ε	PROPN
ap-2097	73	27	2	2	NUM
ap-2097	73	28	sinh	sinh	NOUN
ap-2097	73	29	ε	ε	PROPN
ap-2097	73	30	2	2	NUM
ap-2097	73	31	cosh	cosh	NOUN
ap-2097	73	32	ε	ε	PROPN
ap-2097	73	33	2	2	NUM
ap-2097	73	34	)	)	PUNCT
ap-2097	73	35	∈	∈	PROPN
ap-2097	73	36	so(1	so(1	PROPN
ap-2097	73	37	,	,	PUNCT
ap-2097	73	38	1	1	NUM
ap-2097	73	39	)	)	PUNCT
ap-2097	73	40	.	.	PUNCT
ap-2097	74	1	(	(	PUNCT
ap-2097	74	2	12	12	NUM
ap-2097	74	3	)	)	PUNCT
ap-2097	74	4	hence	hence	ADV
ap-2097	74	5	,	,	PUNCT
ap-2097	74	6	prior	prior	ADV
ap-2097	74	7	to	to	ADP
ap-2097	74	8	making	make	VERB
ap-2097	74	9	the	the	DET
ap-2097	74	10	periodic	periodic	ADJ
ap-2097	74	11	identification	identification	NOUN
ap-2097	74	12	θ	θ	NOUN
ap-2097	74	13	∼	∼	NOUN
ap-2097	74	14	θ	θ	NOUN
ap-2097	74	15	+	+	CCONJ
ap-2097	74	16	2nπ	2nπ	NOUN
ap-2097	74	17	,	,	PUNCT
ap-2097	74	18	the	the	DET
ap-2097	74	19	timeand	timeand	ADJ
ap-2097	74	20	spatial	spatial	ADJ
ap-2097	74	21	-	-	PUNCT
ap-2097	74	22	translation	translation	NOUN
ap-2097	74	23	generators	generator	NOUN
ap-2097	74	24	i∂τ	i∂τ	NOUN
ap-2097	74	25	and	and	CCONJ
ap-2097	74	26	−i∂θ	−i∂θ	NOUN
ap-2097	74	27	must	must	AUX
ap-2097	74	28	be	be	AUX
ap-2097	74	29	given	give	VERB
ap-2097	74	30	by	by	ADP
ap-2097	74	31	two	two	NUM
ap-2097	74	32	distinct	distinct	ADJ
ap-2097	74	33	so(1	so(1	PROPN
ap-2097	74	34	,	,	PUNCT
ap-2097	74	35	1	1	NUM
ap-2097	74	36	)	)	PUNCT
ap-2097	74	37	generators	generator	NOUN
ap-2097	74	38	of	of	ADP
ap-2097	74	39	the	the	DET
ap-2097	74	40	lie	lie	NOUN
ap-2097	74	41	group	group	NOUN
ap-2097	74	42	so(2	so(2	NOUN
ap-2097	74	43	,	,	PUNCT
ap-2097	74	44	2	2	NUM
ap-2097	74	45	)	)	PUNCT
ap-2097	74	46	∼=	∼=	PROPN
ap-2097	74	47	(	(	PUNCT
ap-2097	74	48	sl(2,r)l	sl(2,r)l	VERB
ap-2097	74	49	×	×	NOUN
ap-2097	74	50	sl(2,r)r)/z2	sl(2,r)r)/z2	NOUN
ap-2097	74	51	.	.	PUNCT
ap-2097	75	1	after	after	ADP
ap-2097	75	2	the	the	DET
ap-2097	75	3	periodic	periodic	ADJ
ap-2097	75	4	identification	identification	NOUN
ap-2097	75	5	θ	θ	NOUN
ap-2097	75	6	∼	∼	NOUN
ap-2097	75	7	θ	θ	NOUN
ap-2097	76	1	+	+	CCONJ
ap-2097	76	2	2nπ	2nπ	ADJ
ap-2097	76	3	,	,	PUNCT
ap-2097	76	4	on	on	ADP
ap-2097	76	5	the	the	DET
ap-2097	76	6	other	other	ADJ
ap-2097	76	7	hand	hand	NOUN
ap-2097	76	8	,	,	PUNCT
ap-2097	76	9	gl	gl	PROPN
ap-2097	76	10	and	and	CCONJ
ap-2097	76	11	gr	gr	NOUN
ap-2097	76	12	in	in	ADP
ap-2097	76	13	eq	eq	ADP
ap-2097	76	14	.	.	PUNCT
ap-2097	77	1	(	(	PUNCT
ap-2097	77	2	12	12	NUM
ap-2097	77	3	)	)	PUNCT
ap-2097	77	4	should	should	AUX
ap-2097	77	5	be	be	AUX
ap-2097	77	6	regarded	regard	VERB
ap-2097	77	7	as	as	ADP
ap-2097	77	8	an	an	DET
ap-2097	77	9	element	element	NOUN
ap-2097	77	10	of	of	ADP
ap-2097	77	11	the	the	DET
ap-2097	77	12	coset	coset	NOUN
ap-2097	77	13	so(1	so(1	PROPN
ap-2097	77	14	,	,	PUNCT
ap-2097	77	15	1)/z,2	1)/z,2	NUM
ap-2097	77	16	where	where	SCONJ
ap-2097	77	17	the	the	DET
ap-2097	77	18	zidentification	zidentification	NOUN
ap-2097	77	19	is	be	AUX
ap-2097	77	20	defined	define	VERB
ap-2097	77	21	by	by	ADP
ap-2097	77	22	ε	ε	PROPN
ap-2097	77	23	∼	∼	NOUN
ap-2097	77	24	ε	ε	PROPN
ap-2097	77	25	+	+	CCONJ
ap-2097	77	26	2nπ	2nπ	NOUN
ap-2097	77	27	(	(	PUNCT
ap-2097	77	28	n	n	NOUN
ap-2097	77	29	∈	∈	PROPN
ap-2097	77	30	z	z	PROPN
ap-2097	77	31	)	)	PUNCT
ap-2097	77	32	.	.	PUNCT
ap-2097	78	1	hence	hence	ADV
ap-2097	78	2	,	,	PUNCT
ap-2097	78	3	the	the	DET
ap-2097	78	4	ads3	ads3	ADJ
ap-2097	78	5	black	black	ADJ
ap-2097	78	6	hole	hole	NOUN
ap-2097	78	7	is	be	AUX
ap-2097	78	8	given	give	VERB
ap-2097	78	9	by	by	ADP
ap-2097	78	10	the	the	DET
ap-2097	78	11	quotient	quotient	NOUN
ap-2097	78	12	space	space	NOUN
ap-2097	78	13	ads3	ads3	PROPN
ap-2097	78	14	/	/	SYM
ap-2097	79	1	z	z	NOUN
ap-2097	79	2	,	,	PUNCT
ap-2097	79	3	where	where	SCONJ
ap-2097	79	4	the	the	DET
ap-2097	79	5	identification	identification	NOUN
ap-2097	79	6	subgroup	subgroup	NOUN
ap-2097	79	7	z	z	PROPN
ap-2097	79	8	=	=	PRON
ap-2097	79	9	{	{	PUNCT
ap-2097	79	10	gn	gn	INTJ
ap-2097	79	11	|	|	ADV
ap-2097	79	12	n	n	PROPN
ap-2097	79	13	=	=	SYM
ap-2097	79	14	0,±1,±2	0,±1,±2	PROPN
ap-2097	79	15	,	,	PUNCT
ap-2097	79	16	·	·	PUNCT
ap-2097	79	17	·	·	PUNCT
ap-2097	79	18	·	·	PUNCT
ap-2097	79	19	}	}	PUNCT
ap-2097	79	20	⊂	⊂	PUNCT
ap-2097	80	1	so(2	so(2	NOUN
ap-2097	80	2	,	,	PUNCT
ap-2097	80	3	2	2	NUM
ap-2097	80	4	)	)	PUNCT
ap-2097	80	5	is	be	AUX
ap-2097	80	6	generated	generate	VERB
ap-2097	80	7	by	by	ADP
ap-2097	80	8	the	the	DET
ap-2097	80	9	matrix	matrix	NOUN
ap-2097	80	10	g	g	PROPN
ap-2097	80	11	=	=	PUNCT
ap-2097	80	12	gl	gl	PROPN
ap-2097	80	13	=	=	PUNCT
ap-2097	80	14	gr	gr	PROPN
ap-2097	80	15	=	=	PUNCT
ap-2097	80	16	(	(	PUNCT
ap-2097	80	17	coshπ	coshπ	NOUN
ap-2097	80	18	sinhπ	sinhπ	PROPN
ap-2097	80	19	sinhπ	sinhπ	PROPN
ap-2097	80	20	coshπ	coshπ	PROPN
ap-2097	80	21	)	)	PUNCT
ap-2097	80	22	.	.	PUNCT
ap-2097	81	1	it	it	PRON
ap-2097	81	2	should	should	AUX
ap-2097	81	3	be	be	AUX
ap-2097	81	4	emphasized	emphasize	VERB
ap-2097	81	5	here	here	ADV
ap-2097	81	6	that	that	SCONJ
ap-2097	81	7	the	the	DET
ap-2097	81	8	fact	fact	NOUN
ap-2097	81	9	that	that	SCONJ
ap-2097	81	10	the	the	DET
ap-2097	81	11	time	time	NOUN
ap-2097	81	12	-	-	PUNCT
ap-2097	81	13	translation	translation	NOUN
ap-2097	81	14	generator	generator	NOUN
ap-2097	81	15	generates	generate	VERB
ap-2097	81	16	the	the	DET
ap-2097	81	17	noncompact	noncompact	NOUN
ap-2097	81	18	lorentz	lorentz	PROPN
ap-2097	81	19	group	group	PROPN
ap-2097	81	20	so(1	so(1	PROPN
ap-2097	81	21	,	,	PUNCT
ap-2097	81	22	1	1	NUM
ap-2097	81	23	)	)	PUNCT
ap-2097	81	24	is	be	AUX
ap-2097	81	25	a	a	DET
ap-2097	81	26	manifestation	manifestation	NOUN
ap-2097	81	27	of	of	ADP
ap-2097	81	28	thermodynamic	thermodynamic	ADJ
ap-2097	81	29	aspects	aspect	NOUN
ap-2097	81	30	of	of	ADP
ap-2097	81	31	a	a	DET
ap-2097	81	32	black	black	ADJ
ap-2097	81	33	hole	hole	NOUN
ap-2097	81	34	:	:	PUNCT
ap-2097	81	35	if	if	SCONJ
ap-2097	81	36	we	we	PRON
ap-2097	81	37	work	work	VERB
ap-2097	81	38	in	in	ADP
ap-2097	81	39	euclidean	euclidean	ADJ
ap-2097	81	40	signature	signature	NOUN
ap-2097	81	41	,	,	PUNCT
ap-2097	81	42	the	the	DET
ap-2097	81	43	noncompact	noncompact	NOUN
ap-2097	81	44	lorentz	lorentz	PROPN
ap-2097	81	45	group	group	PROPN
ap-2097	81	46	so(1	so(1	PROPN
ap-2097	81	47	,	,	PUNCT
ap-2097	81	48	1	1	NUM
ap-2097	81	49	)	)	PUNCT
ap-2097	81	50	becomes	become	VERB
ap-2097	81	51	the	the	DET
ap-2097	81	52	compact	compact	ADJ
ap-2097	81	53	rotation	rotation	NOUN
ap-2097	81	54	group	group	NOUN
ap-2097	81	55	so(2	so(2	NOUN
ap-2097	81	56	)	)	PUNCT
ap-2097	81	57	∼=	∼=	NOUN
ap-2097	81	58	s1	s1	NOUN
ap-2097	81	59	such	such	ADJ
ap-2097	81	60	that	that	SCONJ
ap-2097	81	61	the	the	DET
ap-2097	81	62	frequencies	frequency	NOUN
ap-2097	81	63	conjugate	conjugate	VERB
ap-2097	81	64	to	to	ADP
ap-2097	81	65	the	the	DET
ap-2097	81	66	imaginary	imaginary	ADJ
ap-2097	81	67	time	time	NOUN
ap-2097	81	68	are	be	AUX
ap-2097	81	69	quantized	quantize	VERB
ap-2097	81	70	and	and	CCONJ
ap-2097	81	71	hence	hence	ADV
ap-2097	81	72	give	give	VERB
ap-2097	81	73	rise	rise	NOUN
ap-2097	81	74	to	to	ADP
ap-2097	81	75	the	the	DET
ap-2097	81	76	matsubara	matsubara	NOUN
ap-2097	81	77	frequencies	frequency	NOUN
ap-2097	81	78	.	.	PUNCT
ap-2097	82	1	(	(	PUNCT
ap-2097	82	2	4	4	NUM
ap-2097	82	3	.	.	PUNCT
ap-2097	82	4	)	)	PUNCT
ap-2097	82	5	two	two	NUM
ap-2097	82	6	-	-	PUNCT
ap-2097	82	7	point	point	NOUN
ap-2097	82	8	function	function	NOUN
ap-2097	82	9	.	.	PUNCT
ap-2097	83	1	as	as	SCONJ
ap-2097	83	2	we	we	PRON
ap-2097	83	3	have	have	AUX
ap-2097	83	4	seen	see	VERB
ap-2097	83	5	,	,	PUNCT
ap-2097	83	6	the	the	DET
ap-2097	83	7	ads3	ads3	ADJ
ap-2097	83	8	black	black	ADJ
ap-2097	83	9	hole	hole	NOUN
ap-2097	83	10	(	(	PUNCT
ap-2097	83	11	1	1	X
ap-2097	83	12	)	)	PUNCT
ap-2097	83	13	is	be	AUX
ap-2097	83	14	a	a	DET
ap-2097	83	15	locally	locally	ADV
ap-2097	83	16	ads3	ads3	ADJ
ap-2097	83	17	spacetime	spacetime	NOUN
ap-2097	83	18	but	but	CCONJ
ap-2097	83	19	its	its	PRON
ap-2097	83	20	global	global	ADJ
ap-2097	83	21	structure	structure	NOUN
ap-2097	83	22	is	be	AUX
ap-2097	83	23	quite	quite	ADV
ap-2097	83	24	different	different	ADJ
ap-2097	83	25	from	from	ADP
ap-2097	83	26	ads3	ads3	PROPN
ap-2097	83	27	.	.	PUNCT
ap-2097	84	1	this	this	DET
ap-2097	84	2	global	global	ADJ
ap-2097	84	3	difference	difference	NOUN
ap-2097	84	4	of	of	ADP
ap-2097	84	5	course	course	NOUN
ap-2097	84	6	leads	lead	VERB
ap-2097	84	7	to	to	ADP
ap-2097	84	8	a	a	DET
ap-2097	84	9	big	big	ADJ
ap-2097	84	10	difference	difference	NOUN
ap-2097	84	11	between	between	ADP
ap-2097	84	12	the	the	DET
ap-2097	84	13	structure	structure	NOUN
ap-2097	84	14	of	of	ADP
ap-2097	84	15	two	two	NUM
ap-2097	84	16	-	-	PUNCT
ap-2097	84	17	point	point	NOUN
ap-2097	84	18	functions	function	NOUN
ap-2097	84	19	of	of	ADP
ap-2097	84	20	cft2	cft2	NOUN
ap-2097	84	21	living	live	VERB
ap-2097	84	22	on	on	ADP
ap-2097	84	23	the	the	DET
ap-2097	84	24	boundary	boundary	NOUN
ap-2097	84	25	of	of	ADP
ap-2097	84	26	the	the	DET
ap-2097	84	27	ads3	ads3	ADJ
ap-2097	84	28	black	black	ADJ
ap-2097	84	29	hole	hole	NOUN
ap-2097	84	30	and	and	CCONJ
ap-2097	84	31	those	those	PRON
ap-2097	84	32	living	live	VERB
ap-2097	84	33	on	on	ADP
ap-2097	84	34	the	the	DET
ap-2097	84	35	boundary	boundary	NOUN
ap-2097	84	36	of	of	ADP
ap-2097	84	37	ads3	ads3	PROPN
ap-2097	85	1	[	[	X
ap-2097	85	2	10	10	NUM
ap-2097	85	3	]	]	PUNCT
ap-2097	85	4	.	.	PUNCT
ap-2097	86	1	to	to	PART
ap-2097	86	2	see	see	VERB
ap-2097	86	3	this	this	PRON
ap-2097	86	4	,	,	PUNCT
ap-2097	86	5	let	let	VERB
ap-2097	86	6	gads3	gads3	PROPN
ap-2097	86	7	bh(τ	bh(τ	NUM
ap-2097	86	8	,	,	PUNCT
ap-2097	86	9	θ	θ	NOUN
ap-2097	86	10	)	)	PUNCT
ap-2097	86	11	be	be	AUX
ap-2097	86	12	a	a	DET
ap-2097	86	13	scalar	scalar	ADJ
ap-2097	86	14	two	two	NUM
ap-2097	86	15	-	-	PUNCT
ap-2097	86	16	point	point	NOUN
ap-2097	86	17	function	function	NOUN
ap-2097	86	18	of	of	ADP
ap-2097	86	19	cft2	cft2	NOUN
ap-2097	86	20	dual	dual	ADJ
ap-2097	86	21	to	to	ADP
ap-2097	86	22	the	the	DET
ap-2097	86	23	ads3	ads3	ADJ
ap-2097	86	24	black	black	ADJ
ap-2097	86	25	hole	hole	NOUN
ap-2097	86	26	and	and	CCONJ
ap-2097	86	27	let	let	VERB
ap-2097	86	28	gads3(τ	gads3(τ	NOUN
ap-2097	86	29	,	,	PUNCT
ap-2097	86	30	θ	θ	NOUN
ap-2097	86	31	)	)	PUNCT
ap-2097	86	32	2note	2note	NUM
ap-2097	86	33	that	that	SCONJ
ap-2097	86	34	the	the	DET
ap-2097	86	35	parameter	parameter	NOUN
ap-2097	86	36	space	space	NOUN
ap-2097	86	37	of	of	ADP
ap-2097	86	38	so(1	so(1	PROPN
ap-2097	86	39	,	,	PUNCT
ap-2097	86	40	1	1	NUM
ap-2097	86	41	)	)	PUNCT
ap-2097	86	42	(	(	PUNCT
ap-2097	86	43	more	more	ADV
ap-2097	86	44	precisely	precisely	ADV
ap-2097	86	45	,	,	PUNCT
ap-2097	86	46	so+(1	so+(1	ADJ
ap-2097	86	47	,	,	PUNCT
ap-2097	86	48	1	1	NUM
ap-2097	86	49	)	)	PUNCT
ap-2097	86	50	,	,	PUNCT
ap-2097	86	51	i.e.	i.e.	X
ap-2097	86	52	the	the	DET
ap-2097	86	53	connected	connected	ADJ
ap-2097	86	54	component	component	NOUN
ap-2097	86	55	to	to	ADP
ap-2097	86	56	the	the	DET
ap-2097	86	57	identity	identity	NOUN
ap-2097	86	58	element	element	NOUN
ap-2097	86	59	)	)	PUNCT
ap-2097	86	60	is	be	AUX
ap-2097	86	61	the	the	DET
ap-2097	86	62	whole	whole	ADJ
ap-2097	86	63	line	line	NOUN
ap-2097	86	64	r.	r.	PROPN
ap-2097	86	65	hence	hence	ADV
ap-2097	86	66	the	the	DET
ap-2097	86	67	parameter	parameter	NOUN
ap-2097	86	68	space	space	NOUN
ap-2097	86	69	of	of	ADP
ap-2097	86	70	so(1	so(1	PROPN
ap-2097	86	71	,	,	PUNCT
ap-2097	86	72	1)/z	1)/z	NUM
ap-2097	86	73	is	be	AUX
ap-2097	86	74	r	r	NOUN
ap-2097	86	75	/	/	SYM
ap-2097	86	76	z	z	NOUN
ap-2097	86	77	,	,	PUNCT
ap-2097	86	78	which	which	PRON
ap-2097	86	79	is	be	AUX
ap-2097	86	80	isomorphic	isomorphic	ADJ
ap-2097	86	81	to	to	ADP
ap-2097	86	82	a	a	DET
ap-2097	86	83	circle	circle	NOUN
ap-2097	86	84	s1	s1	NOUN
ap-2097	86	85	.	.	PUNCT
ap-2097	87	1	be	be	AUX
ap-2097	87	2	a	a	DET
ap-2097	87	3	scalar	scalar	ADJ
ap-2097	87	4	two	two	NUM
ap-2097	87	5	-	-	PUNCT
ap-2097	87	6	point	point	NOUN
ap-2097	87	7	function	function	NOUN
ap-2097	87	8	of	of	ADP
ap-2097	87	9	cft2	cft2	PROPN
ap-2097	87	10	living	live	VERB
ap-2097	87	11	on	on	ADP
ap-2097	87	12	the	the	DET
ap-2097	87	13	ads3	ads3	PROPN
ap-2097	87	14	boundary	boundary	NOUN
ap-2097	87	15	without	without	ADP
ap-2097	87	16	periodic	periodic	ADJ
ap-2097	87	17	identification	identification	NOUN
ap-2097	87	18	.	.	PUNCT
ap-2097	88	1	then	then	ADV
ap-2097	88	2	,	,	PUNCT
ap-2097	88	3	once	once	SCONJ
ap-2097	88	4	we	we	PRON
ap-2097	88	5	get	get	VERB
ap-2097	88	6	gads3(τ	gads3(τ	NOUN
ap-2097	88	7	,	,	PUNCT
ap-2097	88	8	θ	θ	PROPN
ap-2097	88	9	)	)	PUNCT
ap-2097	88	10	,	,	PUNCT
ap-2097	88	11	the	the	DET
ap-2097	88	12	scalar	scalar	ADJ
ap-2097	88	13	two	two	NUM
ap-2097	88	14	-	-	PUNCT
ap-2097	88	15	point	point	NOUN
ap-2097	88	16	function	function	NOUN
ap-2097	88	17	of	of	ADP
ap-2097	88	18	cft2	cft2	NOUN
ap-2097	88	19	dual	dual	ADJ
ap-2097	88	20	to	to	ADP
ap-2097	88	21	the	the	DET
ap-2097	88	22	ads3	ads3	ADJ
ap-2097	88	23	black	black	ADJ
ap-2097	88	24	hole	hole	NOUN
ap-2097	88	25	is	be	AUX
ap-2097	88	26	given	give	VERB
ap-2097	88	27	by	by	ADP
ap-2097	88	28	the	the	DET
ap-2097	88	29	coset	coset	NOUN
ap-2097	88	30	construction	construction	NOUN
ap-2097	88	31	(	(	PUNCT
ap-2097	88	32	or	or	CCONJ
ap-2097	88	33	the	the	DET
ap-2097	88	34	method	method	NOUN
ap-2097	88	35	of	of	ADP
ap-2097	88	36	images	image	NOUN
ap-2097	88	37	[	[	X
ap-2097	88	38	10	10	NUM
ap-2097	88	39	]	]	SYM
ap-2097	88	40	):	):	PUNCT
ap-2097	88	41	gads3	gads3	PROPN
ap-2097	88	42	bh(τ	bh(τ	PROPN
ap-2097	88	43	,	,	PUNCT
ap-2097	88	44	θ	θ	NOUN
ap-2097	88	45	)	)	PUNCT
ap-2097	88	46	=	=	SYM
ap-2097	89	1	∑	∑	PROPN
ap-2097	89	2	n∈z	n∈z	DET
ap-2097	89	3	ρ(n)gads3(τ	ρ(n)gads3(τ	NOUN
ap-2097	89	4	,	,	PUNCT
ap-2097	90	1	θ	θ	PROPN
ap-2097	90	2	+	+	CCONJ
ap-2097	90	3	2nπ	2nπ	NOUN
ap-2097	90	4	)	)	PUNCT
ap-2097	90	5	,	,	PUNCT
ap-2097	90	6	(	(	PUNCT
ap-2097	90	7	13	13	NUM
ap-2097	90	8	)	)	PUNCT
ap-2097	90	9	where	where	SCONJ
ap-2097	90	10	ρ	ρ	NOUN
ap-2097	90	11	:	:	PUNCT
ap-2097	90	12	z→	z→	PROPN
ap-2097	90	13	u(1	u(1	PROPN
ap-2097	90	14	)	)	PUNCT
ap-2097	90	15	is	be	AUX
ap-2097	90	16	a	a	DET
ap-2097	90	17	scalar	scalar	ADJ
ap-2097	90	18	(	(	PUNCT
ap-2097	90	19	i.e.	i.e.	X
ap-2097	90	20	one	one	NUM
ap-2097	90	21	-	-	PUNCT
ap-2097	90	22	dimensional	dimensional	ADJ
ap-2097	90	23	)	)	PUNCT
ap-2097	90	24	unitary	unitary	ADJ
ap-2097	90	25	representation	representation	NOUN
ap-2097	90	26	of	of	ADP
ap-2097	90	27	the	the	DET
ap-2097	90	28	identification	identification	NOUN
ap-2097	90	29	subgroup	subgroup	NOUN
ap-2097	90	30	z	z	PROPN
ap-2097	90	31	and	and	CCONJ
ap-2097	90	32	given	give	VERB
ap-2097	90	33	by	by	ADP
ap-2097	90	34	ρ(n	ρ(n	PROPN
ap-2097	90	35	)	)	PUNCT
ap-2097	91	1	=	=	VERB
ap-2097	91	2	einα	einα	NOUN
ap-2097	91	3	.	.	PUNCT
ap-2097	92	1	here	here	ADV
ap-2097	92	2	α	α	PROPN
ap-2097	92	3	is	be	AUX
ap-2097	92	4	a	a	DET
ap-2097	92	5	real	real	ADJ
ap-2097	92	6	parameter	parameter	NOUN
ap-2097	92	7	and	and	CCONJ
ap-2097	92	8	its	its	PRON
ap-2097	92	9	value	value	NOUN
ap-2097	92	10	depends	depend	VERB
ap-2097	92	11	on	on	ADP
ap-2097	92	12	the	the	DET
ap-2097	92	13	model	model	NOUN
ap-2097	92	14	.	.	PUNCT
ap-2097	93	1	for	for	ADP
ap-2097	93	2	example	example	NOUN
ap-2097	93	3	,	,	PUNCT
ap-2097	93	4	for	for	ADP
ap-2097	93	5	scalar	scalar	ADJ
ap-2097	93	6	operator	operator	NOUN
ap-2097	93	7	o(τ	o(τ	PROPN
ap-2097	93	8	,	,	PUNCT
ap-2097	93	9	θ	θ	PROPN
ap-2097	93	10	)	)	PUNCT
ap-2097	93	11	that	that	PRON
ap-2097	93	12	satisfies	satisfy	VERB
ap-2097	93	13	the	the	DET
ap-2097	93	14	periodic	periodic	ADJ
ap-2097	93	15	boundary	boundary	ADJ
ap-2097	93	16	condition	condition	NOUN
ap-2097	93	17	o(τ	o(τ	PROPN
ap-2097	93	18	,	,	PUNCT
ap-2097	93	19	θ	θ	PROPN
ap-2097	93	20	+	+	PUNCT
ap-2097	93	21	2π	2π	NOUN
ap-2097	93	22	)	)	PUNCT
ap-2097	94	1	=	=	SYM
ap-2097	94	2	o(τ	o(τ	PROPN
ap-2097	94	3	,	,	PUNCT
ap-2097	94	4	θ	θ	PROPN
ap-2097	94	5	)	)	PUNCT
ap-2097	94	6	,	,	PUNCT
ap-2097	94	7	α	α	PROPN
ap-2097	94	8	is	be	AUX
ap-2097	94	9	zero	zero	NUM
ap-2097	94	10	(	(	PUNCT
ap-2097	94	11	i.e.	i.e.	X
ap-2097	94	12	ρ	ρ	PROPN
ap-2097	94	13	is	be	AUX
ap-2097	94	14	the	the	DET
ap-2097	94	15	trivial	trivial	ADJ
ap-2097	94	16	representation	representation	NOUN
ap-2097	94	17	)	)	PUNCT
ap-2097	94	18	.	.	PUNCT
ap-2097	95	1	(	(	PUNCT
ap-2097	95	2	basically	basically	ADV
ap-2097	95	3	,	,	PUNCT
ap-2097	95	4	α	α	PROPN
ap-2097	95	5	is	be	AUX
ap-2097	95	6	a	a	DET
ap-2097	95	7	boundary	boundary	ADJ
ap-2097	95	8	condition	condition	NOUN
ap-2097	95	9	parameter	parameter	NOUN
ap-2097	95	10	for	for	ADP
ap-2097	95	11	o(τ	o(τ	PROPN
ap-2097	95	12	,	,	PUNCT
ap-2097	95	13	θ	θ	PROPN
ap-2097	95	14	)	)	PUNCT
ap-2097	95	15	with	with	ADP
ap-2097	95	16	respect	respect	NOUN
ap-2097	95	17	to	to	ADP
ap-2097	95	18	angle	angle	NOUN
ap-2097	95	19	θ	θ	PROPN
ap-2097	95	20	.	.	PUNCT
ap-2097	95	21	)	)	PUNCT
ap-2097	96	1	we	we	PRON
ap-2097	96	2	emphasize	emphasize	VERB
ap-2097	96	3	that	that	SCONJ
ap-2097	96	4	,	,	PUNCT
ap-2097	96	5	regardless	regardless	ADV
ap-2097	96	6	of	of	ADP
ap-2097	96	7	the	the	DET
ap-2097	96	8	value	value	NOUN
ap-2097	96	9	of	of	ADP
ap-2097	96	10	α	α	NOUN
ap-2097	96	11	,	,	PUNCT
ap-2097	96	12	thus	thus	ADV
ap-2097	96	13	constructed	construct	VERB
ap-2097	96	14	two	two	NUM
ap-2097	96	15	-	-	PUNCT
ap-2097	96	16	point	point	NOUN
ap-2097	96	17	function	function	NOUN
ap-2097	96	18	(	(	PUNCT
ap-2097	96	19	13	13	NUM
ap-2097	96	20	)	)	PUNCT
ap-2097	96	21	indeed	indeed	ADV
ap-2097	96	22	satisfies	satisfy	VERB
ap-2097	96	23	the	the	DET
ap-2097	96	24	periodic	periodic	ADJ
ap-2097	96	25	boundary	boundary	ADJ
ap-2097	96	26	condition	condition	NOUN
ap-2097	96	27	gads3	gads3	PROPN
ap-2097	96	28	bh(τ	bh(τ	PROPN
ap-2097	96	29	,	,	PUNCT
ap-2097	96	30	θ	θ	PROPN
ap-2097	96	31	+	+	PUNCT
ap-2097	96	32	2π	2π	NOUN
ap-2097	96	33	)	)	PUNCT
ap-2097	97	1	=	=	SYM
ap-2097	97	2	gads3	gads3	PROPN
ap-2097	97	3	bh(τ	bh(τ	PROPN
ap-2097	97	4	,	,	PUNCT
ap-2097	97	5	θ	θ	PROPN
ap-2097	97	6	)	)	PUNCT
ap-2097	97	7	.	.	PUNCT
ap-2097	98	1	for	for	ADP
ap-2097	98	2	simplicity	simplicity	NOUN
ap-2097	98	3	throughout	throughout	ADP
ap-2097	98	4	this	this	DET
ap-2097	98	5	paper	paper	NOUN
ap-2097	98	6	we	we	PRON
ap-2097	98	7	will	will	AUX
ap-2097	98	8	focus	focus	VERB
ap-2097	98	9	on	on	ADP
ap-2097	98	10	gads3	gads3	PROPN
ap-2097	98	11	(	(	PUNCT
ap-2097	98	12	i.e.	i.e.	X
ap-2097	98	13	the	the	DET
ap-2097	98	14	zero	zero	NUM
ap-2097	98	15	-	-	PUNCT
ap-2097	98	16	winding	wind	VERB
ap-2097	98	17	sector	sector	NOUN
ap-2097	98	18	of	of	ADP
ap-2097	98	19	gads3	gads3	PROPN
ap-2097	98	20	bh	bh	PROPN
ap-2097	98	21	)	)	PUNCT
ap-2097	98	22	,	,	PUNCT
ap-2097	98	23	because	because	SCONJ
ap-2097	98	24	gads3	gads3	NOUN
ap-2097	98	25	bh	bh	PROPN
ap-2097	98	26	can	can	AUX
ap-2097	98	27	be	be	AUX
ap-2097	98	28	constructed	construct	VERB
ap-2097	98	29	from	from	ADP
ap-2097	98	30	the	the	DET
ap-2097	98	31	knowledge	knowledge	NOUN
ap-2097	98	32	of	of	ADP
ap-2097	98	33	gads3	gads3	NOUN
ap-2097	98	34	.	.	PUNCT
ap-2097	99	1	hence	hence	ADV
ap-2097	99	2	in	in	ADP
ap-2097	99	3	what	what	PRON
ap-2097	99	4	follows	follow	VERB
ap-2097	99	5	we	we	PRON
ap-2097	99	6	do	do	AUX
ap-2097	99	7	not	not	PART
ap-2097	99	8	need	need	VERB
ap-2097	99	9	to	to	PART
ap-2097	99	10	worry	worry	VERB
ap-2097	99	11	about	about	ADP
ap-2097	99	12	the	the	DET
ap-2097	99	13	subtleties	subtlety	NOUN
ap-2097	99	14	of	of	ADP
ap-2097	99	15	periodic	periodic	ADJ
ap-2097	99	16	identification	identification	NOUN
ap-2097	99	17	and	and	CCONJ
ap-2097	99	18	global	global	ADJ
ap-2097	99	19	difference	difference	NOUN
ap-2097	99	20	between	between	ADP
ap-2097	99	21	the	the	DET
ap-2097	99	22	ads3	ads3	ADJ
ap-2097	99	23	black	black	ADJ
ap-2097	99	24	hole	hole	NOUN
ap-2097	99	25	and	and	CCONJ
ap-2097	99	26	the	the	DET
ap-2097	99	27	ads3	ads3	NOUN
ap-2097	99	28	spacetime.3	spacetime.3	AUX
ap-2097	99	29	let	let	VERB
ap-2097	99	30	us	we	PRON
ap-2097	99	31	next	next	ADV
ap-2097	99	32	consider	consider	VERB
ap-2097	99	33	a	a	DET
ap-2097	99	34	massive	massive	ADJ
ap-2097	99	35	scalar	scalar	ADJ
ap-2097	99	36	field	field	NOUN
ap-2097	99	37	φ	φ	PROPN
ap-2097	99	38	of	of	ADP
ap-2097	99	39	mass	mass	PROPN
ap-2097	99	40	m	m	PROPN
ap-2097	99	41	on	on	ADP
ap-2097	99	42	the	the	DET
ap-2097	99	43	background	background	NOUN
ap-2097	99	44	spacetime	spacetime	NOUN
ap-2097	99	45	(	(	PUNCT
ap-2097	99	46	8)	8)	NUM
ap-2097	99	47	(	(	PUNCT
ap-2097	99	48	without	without	ADP
ap-2097	99	49	periodic	periodic	ADJ
ap-2097	99	50	identification	identification	NOUN
ap-2097	99	51	)	)	PUNCT
ap-2097	99	52	that	that	PRON
ap-2097	99	53	satisfies	satisfy	VERB
ap-2097	99	54	the	the	DET
ap-2097	99	55	klein	klein	PROPN
ap-2097	99	56	-	-	PUNCT
ap-2097	99	57	gordon	gordon	PROPN
ap-2097	99	58	equation	equation	NOUN
ap-2097	99	59	(	(	PUNCT
ap-2097	99	60	�	�	NOUN
ap-2097	99	61	ads3−m2)φ	ads3−m2)φ	NOUN
ap-2097	99	62	=	=	SYM
ap-2097	99	63	0	0	NUM
ap-2097	99	64	,	,	PUNCT
ap-2097	99	65	where	where	SCONJ
ap-2097	99	66	the	the	DET
ap-2097	99	67	d’alembertian	d’alembertian	NOUN
ap-2097	99	68	is	be	AUX
ap-2097	99	69	given	give	VERB
ap-2097	99	70	by	by	ADP
ap-2097	99	71	�	�	NOUN
ap-2097	99	72	ads3	ads3	PROPN
ap-2097	99	73	=	=	PUNCT
ap-2097	99	74	sinh2	sinh2	NOUN
ap-2097	100	1	x	x	PUNCT
ap-2097	100	2	[	[	PUNCT
ap-2097	100	3	−∂2	−∂2	PROPN
ap-2097	100	4	τ	τ	PROPN
ap-2097	100	5	+	+	CCONJ
ap-2097	100	6	∂2	∂2	NUM
ap-2097	100	7	x	x	SYM
ap-2097	100	8	−	−	PROPN
ap-2097	100	9	1	1	NUM
ap-2097	100	10	sinh	sinh	NOUN
ap-2097	100	11	x	x	PROPN
ap-2097	100	12	cosh	cosh	PROPN
ap-2097	100	13	x∂x	x∂x	X
ap-2097	101	1	−	−	PROPN
ap-2097	101	2	−∂2	−∂2	PROPN
ap-2097	101	3	θ	θ	PROPN
ap-2097	101	4	cosh2	cosh2	VERB
ap-2097	101	5	x	x	X
ap-2097	101	6	]	]	PUNCT
ap-2097	101	7	.	.	PUNCT
ap-2097	102	1	in	in	ADP
ap-2097	102	2	order	order	NOUN
ap-2097	102	3	to	to	PART
ap-2097	102	4	get	get	VERB
ap-2097	102	5	cft	cft	PROPN
ap-2097	102	6	two	two	NUM
ap-2097	102	7	-	-	PUNCT
ap-2097	102	8	point	point	NOUN
ap-2097	102	9	functions	function	NOUN
ap-2097	102	10	via	via	ADP
ap-2097	102	11	real	real	ADJ
ap-2097	102	12	-	-	PUNCT
ap-2097	102	13	time	time	NOUN
ap-2097	102	14	ads	ad	NOUN
ap-2097	102	15	/	/	SYM
ap-2097	102	16	cft	cft	NOUN
ap-2097	102	17	prescription	prescription	NOUN
ap-2097	102	18	,	,	PUNCT
ap-2097	102	19	we	we	PRON
ap-2097	102	20	need	need	VERB
ap-2097	102	21	to	to	PART
ap-2097	102	22	find	find	VERB
ap-2097	102	23	a	a	DET
ap-2097	102	24	solution	solution	NOUN
ap-2097	102	25	to	to	ADP
ap-2097	102	26	the	the	DET
ap-2097	102	27	klein	klein	PROPN
ap-2097	102	28	-	-	PUNCT
ap-2097	102	29	gordon	gordon	PROPN
ap-2097	102	30	equation	equation	NOUN
ap-2097	102	31	whose	whose	DET
ap-2097	102	32	τ	τ	PROPN
ap-2097	102	33	and	and	CCONJ
ap-2097	102	34	θ	θ	NOUN
ap-2097	102	35	-	-	NOUN
ap-2097	102	36	dependences	dependence	NOUN
ap-2097	102	37	are	be	AUX
ap-2097	102	38	given	give	VERB
ap-2097	102	39	by	by	ADP
ap-2097	102	40	the	the	DET
ap-2097	102	41	plane	plane	NOUN
ap-2097	102	42	waves	wave	NOUN
ap-2097	102	43	,	,	PUNCT
ap-2097	102	44	φ(τ	φ(τ	NOUN
ap-2097	102	45	,	,	PUNCT
ap-2097	102	46	x	x	X
ap-2097	102	47	,	,	PUNCT
ap-2097	102	48	θ	θ	NOUN
ap-2097	102	49	)	)	PUNCT
ap-2097	102	50	=	=	SYM
ap-2097	102	51	φω	φω	PROPN
ap-2097	102	52	,	,	PUNCT
ap-2097	102	53	k(x)e−iωτ+ikθ	k(x)e−iωτ+ikθ	NOUN
ap-2097	102	54	;	;	PUNCT
ap-2097	102	55	that	that	PRON
ap-2097	102	56	is	is	ADV
ap-2097	102	57	,	,	PUNCT
ap-2097	102	58	we	we	PRON
ap-2097	102	59	need	need	VERB
ap-2097	102	60	to	to	PART
ap-2097	102	61	know	know	VERB
ap-2097	102	62	a	a	DET
ap-2097	102	63	simultaneous	simultaneous	ADJ
ap-2097	102	64	eigenfunction	eigenfunction	NOUN
ap-2097	102	65	of	of	ADP
ap-2097	102	66	the	the	DET
ap-2097	102	67	d’alembertian	d’alembertian	PROPN
ap-2097	102	68	�	�	PROPN
ap-2097	102	69	ads3	ads3	PROPN
ap-2097	102	70	,	,	PUNCT
ap-2097	102	71	the	the	DET
ap-2097	102	72	time	time	NOUN
ap-2097	102	73	-	-	PUNCT
ap-2097	102	74	translation	translation	NOUN
ap-2097	102	75	generator	generator	NOUN
ap-2097	102	76	i∂τ	i∂τ	NOUN
ap-2097	102	77	and	and	CCONJ
ap-2097	102	78	the	the	DET
ap-2097	102	79	spatial	spatial	ADJ
ap-2097	102	80	-	-	PUNCT
ap-2097	102	81	translation	translation	NOUN
ap-2097	102	82	generator	generator	NOUN
ap-2097	102	83	−i∂θ	−i∂θ	PROPN
ap-2097	102	84	.	.	PUNCT
ap-2097	103	1	for	for	ADP
ap-2097	103	2	such	such	DET
ap-2097	103	3	a	a	DET
ap-2097	103	4	simultaneous	simultaneous	ADJ
ap-2097	103	5	eigenfunction	eigenfunction	NOUN
ap-2097	103	6	the	the	DET
ap-2097	103	7	klein	klein	PROPN
ap-2097	103	8	-	-	PUNCT
ap-2097	103	9	gordon	gordon	PROPN
ap-2097	103	10	equation	equation	NOUN
ap-2097	103	11	reduces	reduce	VERB
ap-2097	103	12	to	to	ADP
ap-2097	103	13	the	the	DET
ap-2097	103	14	following	follow	VERB
ap-2097	103	15	differential	differential	NOUN
ap-2097	103	16	equation:4	equation:4	VERB
ap-2097	103	17	(	(	PUNCT
ap-2097	103	18	−∂2	−∂2	NOUN
ap-2097	103	19	x	x	SYM
ap-2097	103	20	+	+	NUM
ap-2097	103	21	1	1	NUM
ap-2097	103	22	sinh	sinh	NOUN
ap-2097	103	23	x	x	PROPN
ap-2097	103	24	cosh	cosh	NOUN
ap-2097	103	25	x∂x	x∂x	PUNCT
ap-2097	104	1	+	+	CCONJ
ap-2097	104	2	∆(∆−	∆(∆−	PROPN
ap-2097	104	3	2	2	NUM
ap-2097	104	4	)	)	PUNCT
ap-2097	104	5	sinh2	sinh2	NOUN
ap-2097	104	6	x	x	PUNCT
ap-2097	105	1	+	+	CCONJ
ap-2097	105	2	k2	k2	ADJ
ap-2097	105	3	cosh2	cosh2	PROPN
ap-2097	105	4	x	x	X
ap-2097	105	5	)	)	PUNCT
ap-2097	105	6	φω	φω	ADP
ap-2097	105	7	,	,	PUNCT
ap-2097	105	8	k	k	PROPN
ap-2097	105	9	=	=	SYM
ap-2097	105	10	ω2φω	ω2φω	PROPN
ap-2097	105	11	,	,	PUNCT
ap-2097	105	12	k	k	NOUN
ap-2097	105	13	,	,	PUNCT
ap-2097	105	14	(	(	PUNCT
ap-2097	105	15	14	14	NUM
ap-2097	105	16	)	)	PUNCT
ap-2097	106	1	where	where	SCONJ
ap-2097	106	2	∆	∆	VERB
ap-2097	106	3	=	=	SYM
ap-2097	106	4	1	1	NUM
ap-2097	106	5	+	+	CCONJ
ap-2097	106	6	√	√	PROPN
ap-2097	106	7	m2	m2	PROPN
ap-2097	106	8	+	+	CCONJ
ap-2097	106	9	1	1	NUM
ap-2097	106	10	is	be	AUX
ap-2097	106	11	one	one	NUM
ap-2097	106	12	of	of	ADP
ap-2097	106	13	the	the	DET
ap-2097	106	14	solutions	solution	NOUN
ap-2097	106	15	to	to	ADP
ap-2097	106	16	the	the	DET
ap-2097	106	17	quadratic	quadratic	ADJ
ap-2097	106	18	equation	equation	NOUN
ap-2097	106	19	∆(∆−	∆(∆−	ADJ
ap-2097	106	20	2	2	NUM
ap-2097	106	21	)	)	PUNCT
ap-2097	106	22	=	=	SYM
ap-2097	106	23	m2	m2	PROPN
ap-2097	106	24	.	.	PROPN
ap-2097	106	25	note	note	VERB
ap-2097	106	26	that	that	SCONJ
ap-2097	106	27	near	near	ADP
ap-2097	106	28	the	the	DET
ap-2097	106	29	3actually	3actually	NUM
ap-2097	106	30	,	,	PUNCT
ap-2097	106	31	the	the	DET
ap-2097	106	32	momentum	momentum	NOUN
ap-2097	106	33	-	-	PUNCT
ap-2097	106	34	space	space	NOUN
ap-2097	106	35	two	two	NUM
ap-2097	106	36	-	-	PUNCT
ap-2097	106	37	point	point	NOUN
ap-2097	106	38	functions	function	NOUN
ap-2097	106	39	computed	compute	VERB
ap-2097	106	40	in	in	ADP
ap-2097	106	41	refs	ref	NOUN
ap-2097	106	42	.	.	PUNCT
ap-2097	107	1	[	[	X
ap-2097	107	2	5	5	NUM
ap-2097	107	3	,	,	PUNCT
ap-2097	107	4	8	8	NUM
ap-2097	107	5	,	,	PUNCT
ap-2097	107	6	9	9	NUM
ap-2097	107	7	]	]	PUNCT
ap-2097	107	8	are	be	AUX
ap-2097	107	9	nothing	nothing	PRON
ap-2097	107	10	but	but	SCONJ
ap-2097	107	11	the	the	DET
ap-2097	107	12	momentum	momentum	NOUN
ap-2097	107	13	-	-	PUNCT
ap-2097	107	14	space	space	NOUN
ap-2097	107	15	representation	representation	NOUN
ap-2097	107	16	of	of	ADP
ap-2097	107	17	gads3	gads3	PROPN
ap-2097	107	18	rather	rather	ADV
ap-2097	107	19	than	than	ADP
ap-2097	107	20	gads3	gads3	NOUN
ap-2097	107	21	bh	bh	NOUN
ap-2097	107	22	(	(	PUNCT
ap-2097	107	23	or	or	CCONJ
ap-2097	107	24	gbtz	gbtz	NOUN
ap-2097	107	25	)	)	PUNCT
ap-2097	107	26	.	.	PUNCT
ap-2097	108	1	4redefining	4redefine	VERB
ap-2097	108	2	the	the	DET
ap-2097	108	3	field	field	NOUN
ap-2097	108	4	as	as	ADP
ap-2097	108	5	φ	φ	PROPN
ap-2097	108	6	7→	7→	PROPN
ap-2097	108	7	φ̃	φ̃	PROPN
ap-2097	108	8	=	=	SYM
ap-2097	108	9	(	(	PUNCT
ap-2097	108	10	cothx)−1/2φ	cothx)−1/2φ	PROPN
ap-2097	108	11	,	,	PUNCT
ap-2097	108	12	one	one	NUM
ap-2097	108	13	sees	see	VERB
ap-2097	108	14	that	that	SCONJ
ap-2097	108	15	the	the	DET
ap-2097	108	16	differential	differential	ADJ
ap-2097	108	17	equation	equation	NOUN
ap-2097	108	18	(	(	PUNCT
ap-2097	108	19	14	14	NUM
ap-2097	108	20	)	)	PUNCT
ap-2097	108	21	reduces	reduce	VERB
ap-2097	108	22	to	to	ADP
ap-2097	108	23	the	the	DET
ap-2097	108	24	schrödinger	schrödinger	ADJ
ap-2097	108	25	equation	equation	NOUN
ap-2097	108	26	with	with	ADP
ap-2097	108	27	hyperbolic	hyperbolic	ADJ
ap-2097	108	28	pöschl	pöschl	NOUN
ap-2097	108	29	-	-	PUNCT
ap-2097	108	30	teller	teller	NOUN
ap-2097	108	31	potential	potential	NOUN
ap-2097	108	32	(	(	PUNCT
ap-2097	108	33	−∂2	−∂2	NOUN
ap-2097	108	34	x	x	SYM
ap-2097	108	35	+	+	CCONJ
ap-2097	108	36	(	(	PUNCT
ap-2097	108	37	∆−	∆−	NOUN
ap-2097	108	38	1)2	1)2	NUM
ap-2097	108	39	−	−	PROPN
ap-2097	108	40	1/4	1/4	NUM
ap-2097	108	41	sinh2	sinh2	NOUN
ap-2097	108	42	x	x	PUNCT
ap-2097	109	1	+	+	CCONJ
ap-2097	109	2	k2	k2	ADJ
ap-2097	109	3	+	+	PROPN
ap-2097	109	4	1/4	1/4	NUM
ap-2097	109	5	cosh2	cosh2	NOUN
ap-2097	109	6	x	x	SYM
ap-2097	109	7	)	)	PUNCT
ap-2097	109	8	φ̃ω	φ̃ω	NOUN
ap-2097	109	9	,	,	PUNCT
ap-2097	109	10	k	k	NOUN
ap-2097	109	11	=	=	SYM
ap-2097	109	12	ω2φ̃ω	ω2φ̃ω	PROPN
ap-2097	109	13	,	,	PUNCT
ap-2097	109	14	k.	k.	NOUN
ap-2097	109	15	144	144	NUM
ap-2097	109	16	vol	vol	NOUN
ap-2097	109	17	.	.	PUNCT
ap-2097	110	1	54	54	NUM
ap-2097	110	2	no	no	NOUN
ap-2097	110	3	.	.	PUNCT
ap-2097	111	1	2/2014	2/2014	NOUN
ap-2097	111	2	a	a	DET
ap-2097	111	3	simple	simple	ADJ
ap-2097	111	4	derivation	derivation	NOUN
ap-2097	111	5	of	of	ADP
ap-2097	111	6	finite	finite	ADJ
ap-2097	111	7	-	-	ADJ
ap-2097	111	8	temperature	temperature	ADJ
ap-2097	111	9	cft	cft	NOUN
ap-2097	111	10	correlators	correlator	NOUN
ap-2097	111	11	ads3	ads3	ADV
ap-2097	111	12	boundary	boundary	ADJ
ap-2097	111	13	x	x	X
ap-2097	112	1	=	=	SYM
ap-2097	112	2	0	0	NUM
ap-2097	112	3	the	the	DET
ap-2097	112	4	differential	differential	ADJ
ap-2097	112	5	operator	operator	NOUN
ap-2097	112	6	in	in	ADP
ap-2097	112	7	the	the	DET
ap-2097	112	8	lefthand	lefthand	PROPN
ap-2097	112	9	side	side	NOUN
ap-2097	112	10	of	of	ADP
ap-2097	112	11	(	(	PUNCT
ap-2097	112	12	13	13	NUM
ap-2097	112	13	)	)	PUNCT
ap-2097	112	14	behaves	behave	VERB
ap-2097	112	15	as	as	SCONJ
ap-2097	112	16	−∂2	−∂2	PROPN
ap-2097	112	17	x+	x+	ADJ
ap-2097	112	18	1	1	NUM
ap-2097	112	19	x∂x+	x∂x+	PROPN
ap-2097	112	20	∆(∆−2	∆(∆−2	VERB
ap-2097	112	21	)	)	PUNCT
ap-2097	112	22	x2	x2	PROPN
ap-2097	113	1	+	+	NOUN
ap-2097	113	2	o(1	o(1	NOUN
ap-2097	113	3	)	)	PUNCT
ap-2097	113	4	.	.	PUNCT
ap-2097	114	1	hence	hence	ADV
ap-2097	114	2	the	the	DET
ap-2097	114	3	general	general	ADJ
ap-2097	114	4	solution	solution	NOUN
ap-2097	114	5	has	have	VERB
ap-2097	114	6	the	the	DET
ap-2097	114	7	following	follow	VERB
ap-2097	114	8	asymptotic	asymptotic	ADJ
ap-2097	114	9	near	near	ADJ
ap-2097	114	10	-	-	PUNCT
ap-2097	114	11	boundary	boundary	NOUN
ap-2097	114	12	behavior	behavior	NOUN
ap-2097	114	13	:	:	PUNCT
ap-2097	114	14	φ(τ	φ(τ	NOUN
ap-2097	114	15	,	,	PUNCT
ap-2097	114	16	x	x	X
ap-2097	114	17	,	,	PUNCT
ap-2097	114	18	θ	θ	NOUN
ap-2097	114	19	)	)	PUNCT
ap-2097	114	20	∼	∼	NOUN
ap-2097	114	21	a∆(ω	a∆(ω	ADP
ap-2097	114	22	,	,	PUNCT
ap-2097	114	23	k)x∆e−iωτ+ikθ	k)x∆e−iωτ+ikθ	PROPN
ap-2097	114	24	+	+	NOUN
ap-2097	114	25	b∆(ω	b∆(ω	NOUN
ap-2097	114	26	,	,	PUNCT
ap-2097	114	27	k)x2−∆e−iωτ+ikθ	k)x2−∆e−iωτ+ikθ	NOUN
ap-2097	114	28	as	as	ADP
ap-2097	114	29	x→	x→	PROPN
ap-2097	114	30	0	0	NUM
ap-2097	114	31	,	,	PUNCT
ap-2097	114	32	(	(	PUNCT
ap-2097	114	33	15	15	NUM
ap-2097	114	34	)	)	PUNCT
ap-2097	114	35	where	where	SCONJ
ap-2097	114	36	a∆(ω	a∆(ω	ADP
ap-2097	114	37	,	,	PUNCT
ap-2097	114	38	k	k	NOUN
ap-2097	114	39	)	)	PUNCT
ap-2097	114	40	and	and	CCONJ
ap-2097	114	41	b∆(ω	b∆(ω	ADP
ap-2097	114	42	,	,	PUNCT
ap-2097	114	43	k	k	NOUN
ap-2097	114	44	)	)	PUNCT
ap-2097	114	45	are	be	AUX
ap-2097	114	46	integration	integration	NOUN
ap-2097	114	47	constants	constant	NOUN
ap-2097	114	48	which	which	PRON
ap-2097	114	49	may	may	AUX
ap-2097	114	50	depend	depend	VERB
ap-2097	114	51	on	on	ADP
ap-2097	114	52	∆	∆	PROPN
ap-2097	114	53	,	,	PUNCT
ap-2097	114	54	ω	ω	PROPN
ap-2097	114	55	and	and	CCONJ
ap-2097	114	56	k.	k.	NOUN
ap-2097	114	57	the	the	DET
ap-2097	114	58	real	real	ADJ
ap-2097	114	59	-	-	PUNCT
ap-2097	114	60	time	time	NOUN
ap-2097	114	61	prescription	prescription	NOUN
ap-2097	114	62	of	of	ADP
ap-2097	114	63	ads	ad	NOUN
ap-2097	114	64	/	/	SYM
ap-2097	114	65	cft	cft	NOUN
ap-2097	114	66	correspondence	correspondence	NOUN
ap-2097	114	67	tells	tell	VERB
ap-2097	114	68	us	we	PRON
ap-2097	114	69	that	that	SCONJ
ap-2097	114	70	the	the	DET
ap-2097	114	71	retarded	retarded	ADJ
ap-2097	114	72	and	and	CCONJ
ap-2097	114	73	advanced	advanced	ADJ
ap-2097	114	74	two	two	NUM
ap-2097	114	75	-	-	PUNCT
ap-2097	114	76	point	point	NOUN
ap-2097	114	77	functions	function	NOUN
ap-2097	114	78	are	be	AUX
ap-2097	114	79	given	give	VERB
ap-2097	114	80	by	by	ADP
ap-2097	114	81	the	the	DET
ap-2097	114	82	ratio	ratio	NOUN
ap-2097	114	83	[	[	X
ap-2097	114	84	4	4	NUM
ap-2097	114	85	,	,	PUNCT
ap-2097	114	86	5	5	NUM
ap-2097	114	87	]	]	PUNCT
ap-2097	114	88	g	g	NOUN
ap-2097	114	89	r	r	PROPN
ap-2097	114	90	/	/	SYM
ap-2097	114	91	a	a	DET
ap-2097	114	92	∆	∆	PROPN
ap-2097	114	93	(	(	PUNCT
ap-2097	114	94	ω	ω	PROPN
ap-2097	114	95	,	,	PUNCT
ap-2097	114	96	k	k	NOUN
ap-2097	114	97	)	)	PUNCT
ap-2097	114	98	=	=	SYM
ap-2097	114	99	(	(	PUNCT
ap-2097	114	100	2∆−	2∆−	NUM
ap-2097	114	101	2)a∆(ω	2)a∆(ω	NUM
ap-2097	114	102	,	,	PUNCT
ap-2097	114	103	k	k	NOUN
ap-2097	114	104	)	)	PUNCT
ap-2097	114	105	b∆(ω	b∆(ω	NOUN
ap-2097	114	106	,	,	PUNCT
ap-2097	114	107	k	k	NOUN
ap-2097	114	108	)	)	PUNCT
ap-2097	114	109	,	,	PUNCT
ap-2097	114	110	(	(	PUNCT
ap-2097	114	111	16	16	NUM
ap-2097	114	112	)	)	PUNCT
ap-2097	114	113	where	where	SCONJ
ap-2097	114	114	the	the	DET
ap-2097	114	115	retarded	retarded	ADJ
ap-2097	114	116	two	two	NUM
ap-2097	114	117	-	-	PUNCT
ap-2097	114	118	point	point	NOUN
ap-2097	114	119	function	function	NOUN
ap-2097	114	120	gr∆	gr∆	PROPN
ap-2097	114	121	is	be	AUX
ap-2097	114	122	obtained	obtain	VERB
ap-2097	114	123	by	by	ADP
ap-2097	114	124	the	the	DET
ap-2097	114	125	solution	solution	NOUN
ap-2097	114	126	that	that	PRON
ap-2097	114	127	satisfies	satisfy	VERB
ap-2097	114	128	the	the	DET
ap-2097	114	129	in	in	ADV
ap-2097	114	130	-	-	PUNCT
ap-2097	114	131	falling	fall	VERB
ap-2097	114	132	boundary	boundary	ADJ
ap-2097	114	133	conditions	condition	NOUN
ap-2097	114	134	at	at	ADP
ap-2097	114	135	the	the	DET
ap-2097	114	136	horizon	horizon	NOUN
ap-2097	114	137	,	,	PUNCT
ap-2097	114	138	whereas	whereas	SCONJ
ap-2097	114	139	the	the	DET
ap-2097	114	140	advanced	advanced	ADJ
ap-2097	114	141	twopoint	twopoint	NOUN
ap-2097	114	142	function	function	NOUN
ap-2097	114	143	ga∆	ga∆	PROPN
ap-2097	114	144	is	be	AUX
ap-2097	114	145	obtained	obtain	VERB
ap-2097	114	146	by	by	ADP
ap-2097	114	147	the	the	DET
ap-2097	114	148	solution	solution	NOUN
ap-2097	114	149	that	that	PRON
ap-2097	114	150	satisfies	satisfy	VERB
ap-2097	114	151	the	the	DET
ap-2097	114	152	out	out	ADV
ap-2097	114	153	-	-	PUNCT
ap-2097	114	154	going	go	VERB
ap-2097	114	155	boundary	boundary	ADJ
ap-2097	114	156	conditions	condition	NOUN
ap-2097	114	157	at	at	ADP
ap-2097	114	158	the	the	DET
ap-2097	114	159	horizon	horizon	NOUN
ap-2097	115	1	[	[	X
ap-2097	115	2	6	6	NUM
ap-2097	115	3	]	]	PUNCT
ap-2097	115	4	.	.	PUNCT
ap-2097	116	1	the	the	DET
ap-2097	116	2	goal	goal	NOUN
ap-2097	116	3	of	of	ADP
ap-2097	116	4	this	this	DET
ap-2097	116	5	paper	paper	NOUN
ap-2097	116	6	is	be	AUX
ap-2097	116	7	to	to	PART
ap-2097	116	8	compute	compute	VERB
ap-2097	116	9	the	the	DET
ap-2097	116	10	ratio	ratio	NOUN
ap-2097	116	11	(	(	PUNCT
ap-2097	116	12	15	15	NUM
ap-2097	116	13	)	)	PUNCT
ap-2097	116	14	in	in	ADP
ap-2097	116	15	a	a	DET
ap-2097	116	16	lie	lie	NOUN
ap-2097	116	17	-	-	PUNCT
ap-2097	116	18	algebraic	algebraic	ADJ
ap-2097	116	19	fashion	fashion	NOUN
ap-2097	116	20	without	without	ADP
ap-2097	116	21	solving	solve	VERB
ap-2097	116	22	the	the	DET
ap-2097	116	23	klein	klein	PROPN
ap-2097	116	24	-	-	PUNCT
ap-2097	116	25	gordon	gordon	PROPN
ap-2097	116	26	equation	equation	NOUN
ap-2097	116	27	explicitly	explicitly	ADV
ap-2097	116	28	.	.	PUNCT
ap-2097	117	1	3	3	X
ap-2097	117	2	.	.	X
ap-2097	117	3	lie	lie	NOUN
ap-2097	117	4	algebra	algebra	NOUN
ap-2097	117	5	sl(2,r)l	sl(2,r)l	PROPN
ap-2097	117	6	⊕	⊕	PROPN
ap-2097	117	7	sl(2,r)r	sl(2,r)r	PROPN
ap-2097	117	8	in	in	ADP
ap-2097	117	9	the	the	DET
ap-2097	117	10	so(1	so(1	PROPN
ap-2097	117	11	,	,	PUNCT
ap-2097	117	12	1)×	1)×	NUM
ap-2097	117	13	so(1	so(1	PROPN
ap-2097	117	14	,	,	PUNCT
ap-2097	117	15	1	1	NUM
ap-2097	117	16	)	)	PUNCT
ap-2097	117	17	diagonal	diagonal	ADJ
ap-2097	117	18	basis	basis	NOUN
ap-2097	117	19	in	in	ADP
ap-2097	117	20	order	order	NOUN
ap-2097	117	21	to	to	PART
ap-2097	117	22	get	get	VERB
ap-2097	117	23	the	the	DET
ap-2097	117	24	momentum	momentum	NOUN
ap-2097	117	25	-	-	PUNCT
ap-2097	117	26	space	space	NOUN
ap-2097	117	27	two	two	NUM
ap-2097	117	28	-	-	PUNCT
ap-2097	117	29	point	point	NOUN
ap-2097	117	30	functions	function	NOUN
ap-2097	117	31	,	,	PUNCT
ap-2097	117	32	we	we	PRON
ap-2097	117	33	need	need	VERB
ap-2097	117	34	to	to	PART
ap-2097	117	35	find	find	VERB
ap-2097	117	36	a	a	DET
ap-2097	117	37	simultaneous	simultaneous	ADJ
ap-2097	117	38	eigenfunction	eigenfunction	NOUN
ap-2097	117	39	of	of	ADP
ap-2097	117	40	the	the	DET
ap-2097	117	41	d’alembertian	d’alembertian	PROPN
ap-2097	117	42	�	�	PROPN
ap-2097	117	43	ads3	ads3	PROPN
ap-2097	117	44	,	,	PUNCT
ap-2097	117	45	the	the	DET
ap-2097	117	46	time	time	NOUN
ap-2097	117	47	-	-	PUNCT
ap-2097	117	48	translation	translation	NOUN
ap-2097	117	49	generator	generator	NOUN
ap-2097	117	50	i∂τ	i∂τ	NOUN
ap-2097	117	51	and	and	CCONJ
ap-2097	117	52	the	the	DET
ap-2097	117	53	spatial	spatial	ADJ
ap-2097	117	54	-	-	PUNCT
ap-2097	117	55	translation	translation	NOUN
ap-2097	117	56	generator	generator	NOUN
ap-2097	117	57	−i∂θ	−i∂θ	PROPN
ap-2097	117	58	.	.	PUNCT
ap-2097	118	1	as	as	SCONJ
ap-2097	118	2	we	we	PRON
ap-2097	118	3	will	will	AUX
ap-2097	118	4	see	see	VERB
ap-2097	118	5	below	below	ADV
ap-2097	118	6	,	,	PUNCT
ap-2097	118	7	the	the	DET
ap-2097	118	8	d’alembertian	d’alembertian	NOUN
ap-2097	118	9	is	be	AUX
ap-2097	118	10	given	give	VERB
ap-2097	118	11	by	by	ADP
ap-2097	118	12	the	the	DET
ap-2097	118	13	quadratic	quadratic	ADJ
ap-2097	118	14	casimir	casimir	NOUN
ap-2097	118	15	of	of	ADP
ap-2097	118	16	the	the	DET
ap-2097	118	17	lie	lie	NOUN
ap-2097	118	18	algebra	algebra	VERB
ap-2097	118	19	so(2	so(2	NOUN
ap-2097	118	20	,	,	PUNCT
ap-2097	118	21	2	2	NUM
ap-2097	118	22	)	)	PUNCT
ap-2097	118	23	∼=	∼=	PROPN
ap-2097	118	24	sl(2,r)l	sl(2,r)l	NOUN
ap-2097	118	25	⊕	⊕	PROPN
ap-2097	118	26	sl(2,r)r	sl(2,r)r	PROPN
ap-2097	118	27	.	.	PUNCT
ap-2097	119	1	on	on	ADP
ap-2097	119	2	the	the	DET
ap-2097	119	3	other	other	ADJ
ap-2097	119	4	hand	hand	NOUN
ap-2097	119	5	,	,	PUNCT
ap-2097	119	6	as	as	SCONJ
ap-2097	119	7	we	we	PRON
ap-2097	119	8	have	have	AUX
ap-2097	119	9	seen	see	VERB
ap-2097	119	10	in	in	ADP
ap-2097	119	11	the	the	DET
ap-2097	119	12	previous	previous	ADJ
ap-2097	119	13	section	section	NOUN
ap-2097	119	14	,	,	PUNCT
ap-2097	119	15	the	the	DET
ap-2097	119	16	timeand	timeand	NOUN
ap-2097	119	17	spatialtranslations	spatialtranslation	NOUN
ap-2097	119	18	are	be	AUX
ap-2097	119	19	induced	induce	VERB
ap-2097	119	20	by	by	ADP
ap-2097	119	21	two	two	NUM
ap-2097	119	22	distinct	distinct	ADJ
ap-2097	119	23	noncompact	noncompact	NOUN
ap-2097	119	24	so(1	so(1	PROPN
ap-2097	119	25	,	,	PUNCT
ap-2097	119	26	1	1	NUM
ap-2097	119	27	)	)	PUNCT
ap-2097	119	28	group	group	NOUN
ap-2097	119	29	actions	action	NOUN
ap-2097	119	30	such	such	ADJ
ap-2097	119	31	that	that	DET
ap-2097	119	32	i∂τ	i∂τ	NOUN
ap-2097	119	33	and	and	CCONJ
ap-2097	119	34	−i∂θ	−i∂θ	NOUN
ap-2097	119	35	must	must	AUX
ap-2097	119	36	be	be	AUX
ap-2097	119	37	given	give	VERB
ap-2097	119	38	by	by	ADP
ap-2097	119	39	so(1	so(1	PROPN
ap-2097	119	40	,	,	PUNCT
ap-2097	119	41	1	1	NUM
ap-2097	119	42	)	)	PUNCT
ap-2097	119	43	generators	generator	NOUN
ap-2097	119	44	of	of	ADP
ap-2097	119	45	the	the	DET
ap-2097	119	46	lie	lie	NOUN
ap-2097	120	1	algebra	algebra	VERB
ap-2097	120	2	so(2	so(2	NOUN
ap-2097	120	3	,	,	PUNCT
ap-2097	120	4	2	2	NUM
ap-2097	120	5	)	)	PUNCT
ap-2097	120	6	∼=	∼=	PROPN
ap-2097	120	7	sl(2,r)l	sl(2,r)l	NOUN
ap-2097	120	8	⊕	⊕	PROPN
ap-2097	120	9	sl(2,r)r	sl(2,r)r	PROPN
ap-2097	120	10	.	.	PUNCT
ap-2097	121	1	hence	hence	ADV
ap-2097	121	2	we	we	PRON
ap-2097	121	3	need	need	VERB
ap-2097	121	4	to	to	PART
ap-2097	121	5	work	work	VERB
ap-2097	121	6	in	in	ADP
ap-2097	121	7	the	the	DET
ap-2097	121	8	basis	basis	NOUN
ap-2097	121	9	in	in	ADP
ap-2097	121	10	which	which	PRON
ap-2097	121	11	the	the	DET
ap-2097	121	12	noncompact	noncompact	NOUN
ap-2097	121	13	so(1	so(1	PROPN
ap-2097	121	14	,	,	PUNCT
ap-2097	121	15	1	1	NUM
ap-2097	121	16	)	)	PUNCT
ap-2097	121	17	generators	generator	NOUN
ap-2097	121	18	become	become	VERB
ap-2097	121	19	diagonal	diagonal	ADJ
ap-2097	121	20	.	.	PUNCT
ap-2097	122	1	we	we	PRON
ap-2097	122	2	note	note	VERB
ap-2097	122	3	that	that	SCONJ
ap-2097	122	4	unitary	unitary	ADJ
ap-2097	122	5	representations	representation	NOUN
ap-2097	122	6	of	of	ADP
ap-2097	122	7	the	the	DET
ap-2097	122	8	lie	lie	NOUN
ap-2097	122	9	algebra	algebra	NOUN
ap-2097	122	10	sl(2,r	sl(2,r	NOUN
ap-2097	122	11	)	)	PUNCT
ap-2097	122	12	in	in	ADP
ap-2097	122	13	the	the	DET
ap-2097	122	14	noncompact	noncompact	NOUN
ap-2097	122	15	so(1	so(1	PROPN
ap-2097	122	16	,	,	PUNCT
ap-2097	122	17	1	1	NUM
ap-2097	122	18	)	)	PUNCT
ap-2097	122	19	basis	basis	NOUN
ap-2097	122	20	have	have	AUX
ap-2097	122	21	been	be	AUX
ap-2097	122	22	studied	study	VERB
ap-2097	122	23	in	in	ADP
ap-2097	122	24	the	the	DET
ap-2097	122	25	mathematical	mathematical	ADJ
ap-2097	122	26	literature	literature	NOUN
ap-2097	123	1	[	[	X
ap-2097	123	2	11	11	NUM
ap-2097	123	3	,	,	PUNCT
ap-2097	123	4	12	12	NUM
ap-2097	123	5	]	]	PUNCT
ap-2097	123	6	,	,	PUNCT
ap-2097	123	7	and	and	CCONJ
ap-2097	123	8	are	be	AUX
ap-2097	123	9	known	know	VERB
ap-2097	123	10	to	to	PART
ap-2097	123	11	be	be	AUX
ap-2097	123	12	a	a	DET
ap-2097	123	13	bit	bit	NOUN
ap-2097	123	14	complicated	complicated	ADJ
ap-2097	123	15	.	.	PUNCT
ap-2097	124	1	in	in	ADP
ap-2097	124	2	this	this	DET
ap-2097	124	3	paper	paper	NOUN
ap-2097	124	4	we	we	PRON
ap-2097	124	5	will	will	AUX
ap-2097	124	6	not	not	PART
ap-2097	124	7	touch	touch	VERB
ap-2097	124	8	upon	upon	SCONJ
ap-2097	124	9	these	these	DET
ap-2097	124	10	mathematical	mathematical	ADJ
ap-2097	124	11	subtleties	subtlety	NOUN
ap-2097	124	12	and	and	CCONJ
ap-2097	124	13	will	will	AUX
ap-2097	124	14	not	not	PART
ap-2097	124	15	discuss	discuss	VERB
ap-2097	124	16	which	which	PRON
ap-2097	124	17	of	of	ADP
ap-2097	124	18	the	the	DET
ap-2097	124	19	unitary	unitary	ADJ
ap-2097	124	20	representations	representation	NOUN
ap-2097	124	21	are	be	AUX
ap-2097	124	22	realized	realize	VERB
ap-2097	124	23	in	in	ADP
ap-2097	124	24	the	the	DET
ap-2097	124	25	scalar	scalar	ADJ
ap-2097	124	26	field	field	NOUN
ap-2097	124	27	theory	theory	NOUN
ap-2097	124	28	on	on	ADP
ap-2097	124	29	the	the	DET
ap-2097	124	30	background	background	NOUN
ap-2097	124	31	(	(	PUNCT
ap-2097	124	32	8)	8)	NUM
ap-2097	124	33	(	(	PUNCT
ap-2097	124	34	without	without	ADP
ap-2097	124	35	periodic	periodic	ADJ
ap-2097	124	36	identification).5	identification).5	NOUN
ap-2097	124	37	instead	instead	ADV
ap-2097	124	38	,	,	PUNCT
ap-2097	124	39	we	we	PRON
ap-2097	124	40	will	will	AUX
ap-2097	124	41	present	present	VERB
ap-2097	124	42	a	a	DET
ap-2097	124	43	rather	rather	ADV
ap-2097	124	44	heuristic	heuristic	ADJ
ap-2097	124	45	argument	argument	NOUN
ap-2097	124	46	that	that	PRON
ap-2097	124	47	reproduces	reproduce	VERB
ap-2097	124	48	the	the	DET
ap-2097	124	49	known	know	VERB
ap-2097	124	50	results	result	NOUN
ap-2097	124	51	by	by	ADP
ap-2097	124	52	just	just	ADV
ap-2097	124	53	5one	5one	NUM
ap-2097	124	54	way	way	NOUN
ap-2097	124	55	to	to	PART
ap-2097	124	56	avoid	avoid	VERB
ap-2097	124	57	these	these	DET
ap-2097	124	58	subtleties	subtlety	NOUN
ap-2097	124	59	is	be	AUX
ap-2097	124	60	to	to	PART
ap-2097	124	61	wick	wick	VERB
ap-2097	124	62	-	-	PUNCT
ap-2097	124	63	rotate	rotate	VERB
ap-2097	124	64	both	both	DET
ap-2097	124	65	the	the	DET
ap-2097	124	66	time	time	NOUN
ap-2097	124	67	τ	τ	PROPN
ap-2097	124	68	and	and	CCONJ
ap-2097	124	69	angle	angle	PROPN
ap-2097	124	70	θ	θ	PROPN
ap-2097	124	71	.	.	PUNCT
ap-2097	125	1	in	in	ADP
ap-2097	125	2	such	such	ADJ
ap-2097	125	3	euclidean	euclidean	ADJ
ap-2097	125	4	-	-	PUNCT
ap-2097	125	5	like	like	ADJ
ap-2097	125	6	signature	signature	NOUN
ap-2097	125	7	,	,	PUNCT
ap-2097	125	8	the	the	DET
ap-2097	125	9	noncompact	noncompact	NOUN
ap-2097	125	10	so(1	so(1	PROPN
ap-2097	125	11	,	,	PUNCT
ap-2097	125	12	1)×	1)×	NUM
ap-2097	125	13	so(1	so(1	PROPN
ap-2097	125	14	,	,	PUNCT
ap-2097	125	15	1	1	NUM
ap-2097	125	16	)	)	PUNCT
ap-2097	125	17	symmetry	symmetry	NOUN
ap-2097	125	18	becomes	become	VERB
ap-2097	125	19	the	the	DET
ap-2097	125	20	compact	compact	ADJ
ap-2097	125	21	so(2)×	so(2)×	NOUN
ap-2097	125	22	so(2	so(2	NOUN
ap-2097	125	23	)	)	PUNCT
ap-2097	125	24	symmetry	symmetry	NOUN
ap-2097	125	25	such	such	ADJ
ap-2097	125	26	that	that	SCONJ
ap-2097	125	27	we	we	PRON
ap-2097	125	28	can	can	AUX
ap-2097	125	29	use	use	VERB
ap-2097	125	30	standard	standard	ADJ
ap-2097	125	31	unitary	unitary	ADJ
ap-2097	125	32	representations	representation	NOUN
ap-2097	125	33	of	of	ADP
ap-2097	125	34	the	the	DET
ap-2097	125	35	lie	lie	NOUN
ap-2097	125	36	-	-	PUNCT
ap-2097	125	37	algebra	algebra	NOUN
ap-2097	125	38	so(2	so(2	NOUN
ap-2097	125	39	,	,	PUNCT
ap-2097	125	40	2	2	NUM
ap-2097	125	41	)	)	PUNCT
ap-2097	125	42	∼=	∼=	NOUN
ap-2097	125	43	sl(2,r)l⊕sl(2,r)r	sl(2,r)l⊕sl(2,r)r	NOUN
ap-2097	125	44	in	in	ADP
ap-2097	125	45	the	the	DET
ap-2097	125	46	so(2)×so(2	so(2)×so(2	NOUN
ap-2097	125	47	)	)	PUNCT
ap-2097	125	48	diagonal	diagonal	ADJ
ap-2097	125	49	basis	basis	NOUN
ap-2097	125	50	.	.	PUNCT
ap-2097	126	1	in	in	ADP
ap-2097	126	2	this	this	DET
ap-2097	126	3	approach	approach	NOUN
ap-2097	126	4	,	,	PUNCT
ap-2097	126	5	computations	computation	NOUN
ap-2097	126	6	of	of	ADP
ap-2097	126	7	momentum	momentum	NOUN
ap-2097	126	8	-	-	PUNCT
ap-2097	126	9	space	space	NOUN
ap-2097	126	10	two	two	NUM
ap-2097	126	11	-	-	PUNCT
ap-2097	126	12	point	point	NOUN
ap-2097	126	13	functions	function	NOUN
ap-2097	126	14	are	be	AUX
ap-2097	126	15	essentially	essentially	ADV
ap-2097	126	16	reduced	reduce	VERB
ap-2097	126	17	to	to	ADP
ap-2097	126	18	those	those	PRON
ap-2097	126	19	presented	present	VERB
ap-2097	126	20	in	in	ADP
ap-2097	126	21	ref	ref	NOUN
ap-2097	126	22	.	.	PUNCT
ap-2097	127	1	[	[	X
ap-2097	127	2	1	1	NUM
ap-2097	127	3	]	]	PUNCT
ap-2097	127	4	.	.	PUNCT
ap-2097	128	1	using	use	VERB
ap-2097	128	2	the	the	DET
ap-2097	128	3	ladder	ladder	NOUN
ap-2097	128	4	equations	equation	NOUN
ap-2097	128	5	of	of	ADP
ap-2097	128	6	the	the	DET
ap-2097	128	7	lie	lie	NOUN
ap-2097	128	8	algebra	algebra	VERB
ap-2097	128	9	so(2	so(2	NOUN
ap-2097	128	10	,	,	PUNCT
ap-2097	128	11	2	2	NUM
ap-2097	128	12	)	)	PUNCT
ap-2097	128	13	in	in	ADP
ap-2097	128	14	the	the	DET
ap-2097	128	15	so(1	so(1	PROPN
ap-2097	128	16	,	,	PUNCT
ap-2097	128	17	1)×	1)×	NUM
ap-2097	128	18	so(1	so(1	PROPN
ap-2097	128	19	,	,	PUNCT
ap-2097	128	20	1	1	NUM
ap-2097	128	21	)	)	PUNCT
ap-2097	128	22	diagonal	diagonal	ADJ
ap-2097	128	23	basis	basis	NOUN
ap-2097	128	24	.	.	PUNCT
ap-2097	129	1	to	to	PART
ap-2097	129	2	begin	begin	VERB
ap-2097	129	3	with	with	ADP
ap-2097	129	4	,	,	PUNCT
ap-2097	129	5	let	let	VERB
ap-2097	129	6	us	we	PRON
ap-2097	129	7	first	first	ADV
ap-2097	129	8	recall	recall	VERB
ap-2097	129	9	the	the	DET
ap-2097	129	10	lie	lie	NOUN
ap-2097	129	11	algebra	algebra	VERB
ap-2097	129	12	so(2	so(2	NOUN
ap-2097	129	13	,	,	PUNCT
ap-2097	129	14	2	2	NUM
ap-2097	129	15	)	)	PUNCT
ap-2097	129	16	∼=	∼=	PROPN
ap-2097	129	17	sl(2,r)l	sl(2,r)l	NOUN
ap-2097	129	18	⊕	⊕	PROPN
ap-2097	129	19	sl(2,r)r	sl(2,r)r	PROPN
ap-2097	129	20	,	,	PUNCT
ap-2097	129	21	which	which	PRON
ap-2097	129	22	is	be	AUX
ap-2097	129	23	spanned	span	VERB
ap-2097	129	24	by	by	ADP
ap-2097	129	25	six	six	NUM
ap-2097	129	26	self	self	NOUN
ap-2097	129	27	-	-	PUNCT
ap-2097	129	28	adjoint	adjoint	NOUN
ap-2097	129	29	generators	generator	NOUN
ap-2097	129	30	{	{	PUNCT
ap-2097	129	31	a0	a0	PROPN
ap-2097	129	32	,	,	PUNCT
ap-2097	129	33	a1	a1	PROPN
ap-2097	129	34	,	,	PUNCT
ap-2097	129	35	a2	a2	PROPN
ap-2097	129	36	,	,	PUNCT
ap-2097	129	37	b0	b0	NOUN
ap-2097	129	38	,	,	PUNCT
ap-2097	129	39	b1	b1	NOUN
ap-2097	129	40	,	,	PUNCT
ap-2097	129	41	b2	b2	NOUN
ap-2097	129	42	}	}	PUNCT
ap-2097	129	43	that	that	PRON
ap-2097	129	44	satisfy	satisfy	VERB
ap-2097	129	45	the	the	DET
ap-2097	129	46	following	follow	VERB
ap-2097	129	47	commutation	commutation	NOUN
ap-2097	129	48	relations	relation	NOUN
ap-2097	129	49	:	:	PUNCT
ap-2097	130	1	[	[	X
ap-2097	130	2	a0	a0	NOUN
ap-2097	130	3	,	,	PUNCT
ap-2097	130	4	a1	a1	PROPN
ap-2097	130	5	]	]	X
ap-2097	130	6	=	=	SYM
ap-2097	130	7	ia2	ia2	PROPN
ap-2097	130	8	,	,	PUNCT
ap-2097	130	9	[	[	X
ap-2097	130	10	a1	a1	NOUN
ap-2097	130	11	,	,	PUNCT
ap-2097	130	12	a2	a2	PROPN
ap-2097	130	13	]	]	X
ap-2097	130	14	=	=	PUNCT
ap-2097	130	15	−ia0	−ia0	ADP
ap-2097	130	16	,	,	PUNCT
ap-2097	130	17	[	[	X
ap-2097	130	18	a2	a2	PROPN
ap-2097	130	19	,	,	PUNCT
ap-2097	130	20	a0	a0	NOUN
ap-2097	130	21	]	]	X
ap-2097	130	22	=	=	SYM
ap-2097	130	23	ia1	ia1	PROPN
ap-2097	130	24	,	,	PUNCT
ap-2097	130	25	(	(	PUNCT
ap-2097	130	26	17a	17a	X
ap-2097	130	27	)	)	PUNCT
ap-2097	131	1	[	[	X
ap-2097	131	2	b0	b0	NOUN
ap-2097	131	3	,	,	PUNCT
ap-2097	131	4	b1	b1	NOUN
ap-2097	131	5	]	]	PUNCT
ap-2097	131	6	=	=	SYM
ap-2097	131	7	ib2	ib2	NOUN
ap-2097	131	8	,	,	PUNCT
ap-2097	131	9	[	[	X
ap-2097	131	10	b1	b1	NOUN
ap-2097	131	11	,	,	PUNCT
ap-2097	131	12	b2	b2	NOUN
ap-2097	131	13	]	]	X
ap-2097	131	14	=	=	SYM
ap-2097	131	15	−ib0	−ib0	NUM
ap-2097	131	16	,	,	PUNCT
ap-2097	131	17	[	[	X
ap-2097	131	18	b2	b2	NOUN
ap-2097	131	19	,	,	PUNCT
ap-2097	131	20	b0	b0	NOUN
ap-2097	131	21	]	]	PUNCT
ap-2097	131	22	=	=	PUNCT
ap-2097	131	23	ib1	ib1	PROPN
ap-2097	131	24	,	,	PUNCT
ap-2097	131	25	(	(	PUNCT
ap-2097	131	26	17b	17b	NUM
ap-2097	131	27	)	)	PUNCT
ap-2097	131	28	with	with	ADP
ap-2097	131	29	other	other	ADJ
ap-2097	131	30	commutators	commutator	NOUN
ap-2097	131	31	vanishing	vanish	VERB
ap-2097	131	32	,	,	PUNCT
ap-2097	131	33	[	[	X
ap-2097	131	34	aa	aa	INTJ
ap-2097	131	35	,	,	PUNCT
ap-2097	131	36	bb	bb	NOUN
ap-2097	131	37	]	]	X
ap-2097	131	38	=	=	SYM
ap-2097	131	39	0	0	PUNCT
ap-2097	131	40	(	(	PUNCT
ap-2097	131	41	a	a	PRON
ap-2097	131	42	,	,	PUNCT
ap-2097	131	43	b	b	NOUN
ap-2097	131	44	=	=	SYM
ap-2097	131	45	0	0	NUM
ap-2097	131	46	,	,	PUNCT
ap-2097	131	47	1	1	NUM
ap-2097	131	48	,	,	PUNCT
ap-2097	131	49	2	2	NUM
ap-2097	131	50	)	)	PUNCT
ap-2097	131	51	.	.	PUNCT
ap-2097	132	1	we	we	PRON
ap-2097	132	2	note	note	VERB
ap-2097	132	3	that	that	SCONJ
ap-2097	132	4	a0	a0	PROPN
ap-2097	132	5	and	and	CCONJ
ap-2097	132	6	b0	b0	NOUN
ap-2097	132	7	are	be	AUX
ap-2097	132	8	compact	compact	ADJ
ap-2097	132	9	so(2	so(2	NOUN
ap-2097	132	10	)	)	PUNCT
ap-2097	132	11	generators	generator	NOUN
ap-2097	132	12	,	,	PUNCT
ap-2097	132	13	whereas	whereas	SCONJ
ap-2097	132	14	a1	a1	PROPN
ap-2097	132	15	,	,	PUNCT
ap-2097	132	16	a2	a2	PROPN
ap-2097	132	17	,	,	PUNCT
ap-2097	132	18	b1	b1	NOUN
ap-2097	132	19	,	,	PUNCT
ap-2097	132	20	b2	b2	NOUN
ap-2097	132	21	are	be	AUX
ap-2097	132	22	noncompact	noncompact	ADJ
ap-2097	132	23	so(1	so(1	PROPN
ap-2097	132	24	,	,	PUNCT
ap-2097	132	25	1	1	NUM
ap-2097	132	26	)	)	PUNCT
ap-2097	132	27	generators	generator	NOUN
ap-2097	132	28	.	.	PUNCT
ap-2097	133	1	note	note	VERB
ap-2097	133	2	also	also	ADV
ap-2097	133	3	that	that	SCONJ
ap-2097	133	4	the	the	DET
ap-2097	133	5	standard	standard	ADJ
ap-2097	133	6	classification	classification	NOUN
ap-2097	133	7	of	of	ADP
ap-2097	133	8	unitary	unitary	ADJ
ap-2097	133	9	representations	representation	NOUN
ap-2097	133	10	of	of	ADP
ap-2097	133	11	the	the	DET
ap-2097	133	12	lie	lie	NOUN
ap-2097	133	13	algebra	algebra	VERB
ap-2097	133	14	so(2	so(2	NOUN
ap-2097	133	15	,	,	PUNCT
ap-2097	133	16	2	2	NUM
ap-2097	133	17	)	)	PUNCT
ap-2097	133	18	is	be	AUX
ap-2097	133	19	based	base	VERB
ap-2097	133	20	on	on	ADP
ap-2097	133	21	the	the	DET
ap-2097	133	22	cartan	cartan	ADJ
ap-2097	133	23	-	-	PUNCT
ap-2097	133	24	weyl	weyl	VERB
ap-2097	133	25	basis	basis	NOUN
ap-2097	133	26	{	{	PUNCT
ap-2097	133	27	a0	a0	NOUN
ap-2097	133	28	,	,	PUNCT
ap-2097	133	29	a1	a1	PROPN
ap-2097	133	30	±	±	NUM
ap-2097	133	31	ia2	ia2	PROPN
ap-2097	133	32	,	,	PUNCT
ap-2097	133	33	b0	b0	NOUN
ap-2097	133	34	,	,	PUNCT
ap-2097	133	35	b1	b1	NOUN
ap-2097	133	36	±	±	NUM
ap-2097	133	37	ib2	ib2	NOUN
ap-2097	133	38	}	}	PUNCT
ap-2097	133	39	,	,	PUNCT
ap-2097	133	40	where	where	SCONJ
ap-2097	133	41	a1	a1	PROPN
ap-2097	133	42	±	±	PROPN
ap-2097	133	43	ia2	ia2	NOUN
ap-2097	133	44	and	and	CCONJ
ap-2097	133	45	b1±	b1±	NOUN
ap-2097	133	46	ib2	ib2	NOUN
ap-2097	133	47	play	play	VERB
ap-2097	133	48	the	the	DET
ap-2097	133	49	role	role	NOUN
ap-2097	133	50	of	of	ADP
ap-2097	133	51	ladder	ladder	NOUN
ap-2097	133	52	operators	operator	NOUN
ap-2097	133	53	that	that	PRON
ap-2097	133	54	raise	raise	VERB
ap-2097	133	55	and	and	CCONJ
ap-2097	133	56	lower	lower	VERB
ap-2097	133	57	the	the	DET
ap-2097	133	58	eigenvalues	eigenvalue	NOUN
ap-2097	133	59	of	of	ADP
ap-2097	133	60	a0	a0	NOUN
ap-2097	133	61	and	and	CCONJ
ap-2097	133	62	b0	b0	NOUN
ap-2097	133	63	by	by	ADP
ap-2097	133	64	±1	±1	NOUN
ap-2097	133	65	.	.	PUNCT
ap-2097	134	1	for	for	ADP
ap-2097	134	2	the	the	DET
ap-2097	134	3	following	follow	VERB
ap-2097	134	4	discussions	discussion	NOUN
ap-2097	134	5	,	,	PUNCT
ap-2097	134	6	however	however	ADV
ap-2097	134	7	,	,	PUNCT
ap-2097	134	8	it	it	PRON
ap-2097	134	9	is	be	AUX
ap-2097	134	10	convenient	convenient	ADJ
ap-2097	134	11	to	to	PART
ap-2097	134	12	introduce	introduce	VERB
ap-2097	134	13	the	the	DET
ap-2097	134	14	hermitian	hermitian	ADJ
ap-2097	134	15	linear	linear	PROPN
ap-2097	134	16	combinations	combination	NOUN
ap-2097	134	17	a±	a±	PROPN
ap-2097	134	18	=	=	SYM
ap-2097	134	19	a2	a2	PROPN
ap-2097	134	20	∓a0	∓a0	PROPN
ap-2097	134	21	and	and	CCONJ
ap-2097	134	22	b±	b±	PROPN
ap-2097	134	23	=	=	SYM
ap-2097	134	24	b2	b2	NOUN
ap-2097	134	25	∓b0	∓b0	PROPN
ap-2097	134	26	,	,	PUNCT
ap-2097	134	27	which	which	PRON
ap-2097	134	28	also	also	ADV
ap-2097	134	29	play	play	VERB
ap-2097	134	30	the	the	DET
ap-2097	134	31	role	role	NOUN
ap-2097	134	32	of	of	ADP
ap-2097	134	33	“	"	PUNCT
ap-2097	134	34	ladder	ladder	NOUN
ap-2097	134	35	”	"	PUNCT
ap-2097	134	36	operators	operator	NOUN
ap-2097	134	37	;	;	PUNCT
ap-2097	134	38	see	see	VERB
ap-2097	134	39	next	next	ADJ
ap-2097	134	40	section	section	NOUN
ap-2097	134	41	.	.	PUNCT
ap-2097	135	1	in	in	ADP
ap-2097	135	2	the	the	DET
ap-2097	135	3	basis	basis	NOUN
ap-2097	135	4	{	{	PUNCT
ap-2097	135	5	a1	a1	NOUN
ap-2097	135	6	,	,	PUNCT
ap-2097	135	7	a±	a±	PROPN
ap-2097	135	8	,	,	PUNCT
ap-2097	135	9	b1	b1	NOUN
ap-2097	135	10	,	,	PUNCT
ap-2097	135	11	b±	b±	VERB
ap-2097	135	12	}	}	PUNCT
ap-2097	135	13	the	the	DET
ap-2097	135	14	commutation	commutation	NOUN
ap-2097	135	15	relations	relation	NOUN
ap-2097	135	16	(	(	PUNCT
ap-2097	135	17	17a	17a	NOUN
ap-2097	135	18	)	)	PUNCT
ap-2097	135	19	and	and	CCONJ
ap-2097	135	20	(	(	PUNCT
ap-2097	135	21	17b	17b	NUM
ap-2097	135	22	)	)	PUNCT
ap-2097	135	23	are	be	AUX
ap-2097	135	24	cast	cast	VERB
ap-2097	135	25	into	into	ADP
ap-2097	135	26	the	the	DET
ap-2097	135	27	following	follow	VERB
ap-2097	135	28	forms	form	NOUN
ap-2097	135	29	:	:	PUNCT
ap-2097	136	1	[	[	X
ap-2097	136	2	a1	a1	NOUN
ap-2097	136	3	,	,	PUNCT
ap-2097	136	4	a±	a±	PROPN
ap-2097	136	5	]	]	X
ap-2097	136	6	=	=	SYM
ap-2097	136	7	±ia±	±ia±	NOUN
ap-2097	136	8	,	,	PUNCT
ap-2097	136	9	[	[	X
ap-2097	136	10	a+	a+	X
ap-2097	136	11	,	,	PUNCT
ap-2097	136	12	a−	a−	ADJ
ap-2097	136	13	]	]	PUNCT
ap-2097	136	14	=	=	SYM
ap-2097	136	15	2ia1	2ia1	NOUN
ap-2097	136	16	,	,	PUNCT
ap-2097	136	17	(	(	PUNCT
ap-2097	136	18	18a	18a	NOUN
ap-2097	136	19	)	)	PUNCT
ap-2097	137	1	[	[	X
ap-2097	137	2	b1	b1	NOUN
ap-2097	137	3	,	,	PUNCT
ap-2097	137	4	b±	b±	NOUN
ap-2097	137	5	]	]	X
ap-2097	137	6	=	=	PUNCT
ap-2097	137	7	±ib±	±ib±	PROPN
ap-2097	137	8	,	,	PUNCT
ap-2097	137	9	[	[	X
ap-2097	137	10	b+	b+	X
ap-2097	137	11	,	,	PUNCT
ap-2097	137	12	b−	b−	NOUN
ap-2097	137	13	]	]	X
ap-2097	137	14	=	=	SYM
ap-2097	137	15	2ib1	2ib1	NUM
ap-2097	137	16	.	.	PUNCT
ap-2097	137	17	(	(	PUNCT
ap-2097	137	18	18b	18b	NUM
ap-2097	137	19	)	)	PUNCT
ap-2097	137	20	in	in	ADP
ap-2097	137	21	the	the	DET
ap-2097	137	22	problem	problem	NOUN
ap-2097	137	23	of	of	ADP
ap-2097	137	24	scalar	scalar	ADJ
ap-2097	137	25	field	field	NOUN
ap-2097	137	26	theory	theory	NOUN
ap-2097	137	27	on	on	ADP
ap-2097	137	28	the	the	DET
ap-2097	137	29	background	background	NOUN
ap-2097	137	30	(	(	PUNCT
ap-2097	137	31	8)	8)	NUM
ap-2097	137	32	(	(	PUNCT
ap-2097	137	33	without	without	ADP
ap-2097	137	34	periodic	periodic	ADJ
ap-2097	137	35	identification	identification	NOUN
ap-2097	137	36	)	)	PUNCT
ap-2097	137	37	,	,	PUNCT
ap-2097	137	38	these	these	DET
ap-2097	137	39	symmetry	symmetry	NOUN
ap-2097	137	40	generators	generator	NOUN
ap-2097	137	41	turn	turn	VERB
ap-2097	137	42	out	out	ADP
ap-2097	137	43	to	to	PART
ap-2097	137	44	be	be	AUX
ap-2097	137	45	given	give	VERB
ap-2097	137	46	by	by	ADP
ap-2097	137	47	the	the	DET
ap-2097	137	48	following	follow	VERB
ap-2097	137	49	firstorder	firstorder	NOUN
ap-2097	137	50	differential	differential	PROPN
ap-2097	137	51	operators	operator	NOUN
ap-2097	137	52	:	:	PUNCT
ap-2097	138	1	a1	a1	NOUN
ap-2097	138	2	=	=	NOUN
ap-2097	139	1	i	i	PRON
ap-2097	139	2	2(∂τ	2(∂τ	AUX
ap-2097	139	3	+	+	CCONJ
ap-2097	139	4	∂θ	∂θ	NOUN
ap-2097	139	5	)	)	PUNCT
ap-2097	139	6	,	,	PUNCT
ap-2097	139	7	(	(	PUNCT
ap-2097	139	8	19a	19a	NUM
ap-2097	139	9	)	)	PUNCT
ap-2097	139	10	a±	a±	PROPN
ap-2097	139	11	=	=	SYM
ap-2097	139	12	−	−	PROPN
ap-2097	139	13	i2e±(τ+θ	i2e±(τ+θ	NUM
ap-2097	139	14	)	)	PUNCT
ap-2097	139	15	[	[	PUNCT
ap-2097	139	16	sinh	sinh	NOUN
ap-2097	139	17	x	x	SYM
ap-2097	139	18	∂x	∂x	PROPN
ap-2097	139	19	±	±	NUM
ap-2097	139	20	(	(	PUNCT
ap-2097	139	21	cosh	cosh	NOUN
ap-2097	139	22	x	x	PART
ap-2097	139	23	∂τ	∂τ	PROPN
ap-2097	139	24	+	+	CCONJ
ap-2097	139	25	1	1	NUM
ap-2097	139	26	cosh	cosh	NOUN
ap-2097	139	27	x∂θ	x∂θ	NUM
ap-2097	139	28	)	)	PUNCT
ap-2097	139	29	]	]	PUNCT
ap-2097	139	30	,	,	PUNCT
ap-2097	139	31	(	(	PUNCT
ap-2097	139	32	19b	19b	NOUN
ap-2097	139	33	)	)	PUNCT
ap-2097	139	34	b1	b1	NOUN
ap-2097	139	35	=	=	NOUN
ap-2097	140	1	i	i	PRON
ap-2097	140	2	2(∂τ	2(∂τ	AUX
ap-2097	140	3	−	−	PROPN
ap-2097	141	1	∂θ	∂θ	PROPN
ap-2097	141	2	)	)	PUNCT
ap-2097	141	3	,	,	PUNCT
ap-2097	141	4	(	(	PUNCT
ap-2097	141	5	19c	19c	X
ap-2097	141	6	)	)	PUNCT
ap-2097	141	7	b±	b±	PROPN
ap-2097	141	8	=	=	PUNCT
ap-2097	142	1	+	+	CCONJ
ap-2097	142	2	i	i	NOUN
ap-2097	142	3	2e±(τ−θ	2e±(τ−θ	NUM
ap-2097	142	4	)	)	PUNCT
ap-2097	142	5	[	[	PUNCT
ap-2097	142	6	sinh	sinh	NOUN
ap-2097	142	7	x	x	SYM
ap-2097	142	8	∂x	∂x	PROPN
ap-2097	142	9	±	±	NUM
ap-2097	142	10	(	(	PUNCT
ap-2097	142	11	cosh	cosh	NOUN
ap-2097	142	12	x	x	SYM
ap-2097	143	1	∂τ	∂τ	NOUN
ap-2097	143	2	−	−	NOUN
ap-2097	143	3	1	1	NUM
ap-2097	143	4	cosh	cosh	NOUN
ap-2097	143	5	x∂θ	x∂θ	NUM
ap-2097	143	6	)	)	PUNCT
ap-2097	143	7	]	]	PUNCT
ap-2097	143	8	,	,	PUNCT
ap-2097	143	9	(	(	PUNCT
ap-2097	143	10	19d	19d	NOUN
ap-2097	143	11	)	)	PUNCT
ap-2097	143	12	which	which	PRON
ap-2097	143	13	indeed	indeed	ADV
ap-2097	143	14	satisfy	satisfy	VERB
ap-2097	143	15	the	the	DET
ap-2097	143	16	commutation	commutation	NOUN
ap-2097	143	17	relations	relation	NOUN
ap-2097	143	18	(	(	PUNCT
ap-2097	143	19	18a	18a	NOUN
ap-2097	143	20	)	)	PUNCT
ap-2097	143	21	and	and	CCONJ
ap-2097	143	22	(	(	PUNCT
ap-2097	143	23	18b	18b	NUM
ap-2097	143	24	)	)	PUNCT
ap-2097	143	25	.	.	PUNCT
ap-2097	144	1	the	the	DET
ap-2097	144	2	quadratic	quadratic	ADJ
ap-2097	144	3	casimir	casimir	NOUN
ap-2097	144	4	of	of	ADP
ap-2097	144	5	the	the	DET
ap-2097	144	6	lie	lie	NOUN
ap-2097	144	7	algebra	algebra	VERB
ap-2097	144	8	so(2	so(2	NOUN
ap-2097	144	9	,	,	PUNCT
ap-2097	144	10	2	2	NUM
ap-2097	144	11	)	)	PUNCT
ap-2097	144	12	∼=	∼=	PROPN
ap-2097	144	13	sl(2,r)l⊕sl(2,r)r	sl(2,r)l⊕sl(2,r)r	NOUN
ap-2097	144	14	yields	yield	VERB
ap-2097	144	15	the	the	DET
ap-2097	144	16	d’alembertian	d’alembertian	PROPN
ap-2097	144	17	on	on	ADP
ap-2097	144	18	the	the	DET
ap-2097	144	19	ads3	ads3	ADJ
ap-2097	144	20	black	black	ADJ
ap-2097	144	21	hole	hole	NOUN
ap-2097	144	22	c2(so(2	c2(so(2	PROPN
ap-2097	144	23	,	,	PUNCT
ap-2097	144	24	2	2	NUM
ap-2097	144	25	)	)	PUNCT
ap-2097	144	26	)	)	PUNCT
ap-2097	145	1	=	=	SYM
ap-2097	145	2	2c2(sl(2,r)l	2c2(sl(2,r)l	NOUN
ap-2097	145	3	)	)	PUNCT
ap-2097	145	4	+	+	CCONJ
ap-2097	145	5	2c2(sl(2,r)r	2c2(sl(2,r)r	NUM
ap-2097	145	6	)	)	PUNCT
ap-2097	145	7	=	=	PUNCT
ap-2097	146	1	sinh2	sinh2	NOUN
ap-2097	146	2	x	x	X
ap-2097	146	3	(	(	PUNCT
ap-2097	146	4	−∂2	−∂2	PROPN
ap-2097	146	5	τ	τ	PROPN
ap-2097	147	1	+	+	CCONJ
ap-2097	147	2	∂2	∂2	NUM
ap-2097	147	3	x	x	SYM
ap-2097	147	4	−	−	PROPN
ap-2097	147	5	1	1	NUM
ap-2097	147	6	sinh	sinh	NOUN
ap-2097	147	7	x	x	PROPN
ap-2097	147	8	cosh	cosh	PROPN
ap-2097	147	9	x∂x	x∂x	X
ap-2097	148	1	−	−	PROPN
ap-2097	148	2	−∂2	−∂2	PROPN
ap-2097	148	3	θ	θ	PROPN
ap-2097	148	4	cosh2	cosh2	VERB
ap-2097	148	5	x	x	X
ap-2097	148	6	)	)	PUNCT
ap-2097	148	7	,	,	PUNCT
ap-2097	148	8	(	(	PUNCT
ap-2097	148	9	20	20	NUM
ap-2097	148	10	)	)	PUNCT
ap-2097	148	11	where	where	SCONJ
ap-2097	148	12	the	the	DET
ap-2097	148	13	quadratic	quadratic	ADJ
ap-2097	148	14	casimir	casimir	NOUN
ap-2097	148	15	of	of	ADP
ap-2097	148	16	each	each	DET
ap-2097	148	17	sl(2,r	sl(2,r	NOUN
ap-2097	148	18	)	)	PUNCT
ap-2097	148	19	is	be	AUX
ap-2097	148	20	given	give	VERB
ap-2097	148	21	by	by	ADP
ap-2097	148	22	c2(sl(2,r)l	c2(sl(2,r)l	NOUN
ap-2097	148	23	)	)	PUNCT
ap-2097	148	24	=	=	PUNCT
ap-2097	148	25	(	(	PUNCT
ap-2097	148	26	a0)2−(a1)2−(a2)2	a0)2−(a1)2−(a2)2	NOUN
ap-2097	148	27	=	=	PUNCT
ap-2097	148	28	−a1(a1±i)−	−a1(a1±i)−	NOUN
ap-2097	148	29	145	145	NUM
ap-2097	148	30	satoshi	satoshi	PROPN
ap-2097	148	31	ohya	ohya	PROPN
ap-2097	148	32	acta	acta	PROPN
ap-2097	148	33	polytechnica	polytechnica	PROPN
ap-2097	148	34	a∓a±	a∓a±	PUNCT
ap-2097	148	35	and	and	CCONJ
ap-2097	148	36	c2(sl(2,r)r	c2(sl(2,r)r	NOUN
ap-2097	148	37	)	)	PUNCT
ap-2097	148	38	=	=	PUNCT
ap-2097	149	1	(	(	PUNCT
ap-2097	149	2	b0)2	b0)2	NUM
ap-2097	149	3	−	−	PROPN
ap-2097	149	4	(	(	PUNCT
ap-2097	149	5	b1)2	b1)2	NUM
ap-2097	149	6	−	−	PROPN
ap-2097	149	7	(	(	PUNCT
ap-2097	149	8	b2)2	b2)2	PUNCT
ap-2097	149	9	=	=	SYM
ap-2097	149	10	−b1(b1	−b1(b1	NUM
ap-2097	149	11	±	±	NUM
ap-2097	149	12	i)−b∓b±.	i)−b∓b±.	PROPN
ap-2097	149	13	a	a	DET
ap-2097	149	14	straightforward	straightforward	ADJ
ap-2097	149	15	calculation	calculation	NOUN
ap-2097	149	16	shows	show	VERB
ap-2097	149	17	that	that	SCONJ
ap-2097	149	18	c2(sl(2,r)l	c2(sl(2,r)l	VERB
ap-2097	149	19	)	)	PUNCT
ap-2097	149	20	and	and	CCONJ
ap-2097	149	21	c2(sl(2,r)r	c2(sl(2,r)r	NOUN
ap-2097	149	22	)	)	PUNCT
ap-2097	149	23	coincide	coincide	NOUN
ap-2097	149	24	and	and	CCONJ
ap-2097	149	25	are	be	AUX
ap-2097	149	26	given	give	VERB
ap-2097	149	27	by	by	ADP
ap-2097	149	28	c2(sl(2,r)l	c2(sl(2,r)l	NOUN
ap-2097	149	29	)	)	PUNCT
ap-2097	149	30	=	=	NOUN
ap-2097	149	31	c2(sl(2,r)r	c2(sl(2,r)r	NOUN
ap-2097	149	32	)	)	PUNCT
ap-2097	149	33	=	=	SYM
ap-2097	149	34	1	1	NUM
ap-2097	149	35	4c2(so(2	4c2(so(2	NUM
ap-2097	149	36	,	,	PUNCT
ap-2097	149	37	2	2	NUM
ap-2097	149	38	)	)	PUNCT
ap-2097	149	39	)	)	PUNCT
ap-2097	149	40	.	.	PUNCT
ap-2097	150	1	(	(	PUNCT
ap-2097	150	2	21	21	NUM
ap-2097	150	3	)	)	PUNCT
ap-2097	150	4	asymptotic	asymptotic	ADJ
ap-2097	150	5	near	near	ADJ
ap-2097	150	6	-	-	PUNCT
ap-2097	150	7	boundary	boundary	NOUN
ap-2097	150	8	algebra	algebra	NOUN
ap-2097	150	9	.	.	PUNCT
ap-2097	151	1	we	we	PRON
ap-2097	151	2	are	be	AUX
ap-2097	151	3	interested	interested	ADJ
ap-2097	151	4	in	in	ADP
ap-2097	151	5	the	the	DET
ap-2097	151	6	asymptotic	asymptotic	ADJ
ap-2097	151	7	near	near	ADJ
ap-2097	151	8	-	-	PUNCT
ap-2097	151	9	boundary	boundary	NOUN
ap-2097	151	10	behavior	behavior	NOUN
ap-2097	151	11	of	of	ADP
ap-2097	151	12	the	the	DET
ap-2097	151	13	solution	solution	NOUN
ap-2097	151	14	to	to	ADP
ap-2097	151	15	the	the	DET
ap-2097	151	16	klein	klein	PROPN
ap-2097	151	17	-	-	PUNCT
ap-2097	151	18	gordon	gordon	PROPN
ap-2097	151	19	equation	equation	NOUN
ap-2097	151	20	(	(	PUNCT
ap-2097	151	21	14	14	NUM
ap-2097	151	22	)	)	PUNCT
ap-2097	151	23	.	.	PUNCT
ap-2097	152	1	to	to	PART
ap-2097	152	2	analyze	analyze	VERB
ap-2097	152	3	this	this	PRON
ap-2097	152	4	,	,	PUNCT
ap-2097	152	5	let	let	VERB
ap-2097	152	6	us	we	PRON
ap-2097	152	7	introduce	introduce	VERB
ap-2097	152	8	the	the	DET
ap-2097	152	9	boundary	boundary	ADJ
ap-2097	152	10	symmetry	symmetry	NOUN
ap-2097	152	11	generators	generator	NOUN
ap-2097	152	12	defined	define	VERB
ap-2097	152	13	as	as	ADP
ap-2097	152	14	the	the	DET
ap-2097	152	15	limit	limit	NOUN
ap-2097	152	16	x→	x→	X
ap-2097	152	17	0	0	NUM
ap-2097	152	18	of	of	ADP
ap-2097	152	19	(	(	PUNCT
ap-2097	152	20	19a)–(19d	19a)–(19d	NUM
ap-2097	152	21	):	):	PUNCT
ap-2097	152	22	a0	a0	NOUN
ap-2097	152	23	1	1	NUM
ap-2097	152	24	:	:	PUNCT
ap-2097	153	1	=	=	SYM
ap-2097	153	2	lim	lim	PROPN
ap-2097	153	3	x→0	x→0	PROPN
ap-2097	153	4	a1	a1	PROPN
ap-2097	154	1	=	=	NOUN
ap-2097	155	1	i	i	PRON
ap-2097	155	2	2(∂τ	2(∂τ	NUM
ap-2097	155	3	+	+	CCONJ
ap-2097	155	4	∂θ	∂θ	NOUN
ap-2097	155	5	)	)	PUNCT
ap-2097	155	6	,	,	PUNCT
ap-2097	155	7	(	(	PUNCT
ap-2097	155	8	22a	22a	NOUN
ap-2097	155	9	)	)	PUNCT
ap-2097	155	10	a0	a0	NOUN
ap-2097	155	11	±	±	NUM
ap-2097	155	12	:	:	PUNCT
ap-2097	155	13	=	=	PROPN
ap-2097	155	14	lim	lim	PROPN
ap-2097	155	15	x→0	x→0	PUNCT
ap-2097	155	16	a±	a±	PROPN
ap-2097	155	17	=	=	PUNCT
ap-2097	156	1	−	−	PROPN
ap-2097	156	2	i2e±(τ+θ)[x∂x	i2e±(τ+θ)[x∂x	PROPN
ap-2097	156	3	±	±	PROPN
ap-2097	156	4	(	(	PUNCT
ap-2097	156	5	∂τ	∂τ	PROPN
ap-2097	156	6	+	+	CCONJ
ap-2097	156	7	∂θ	∂θ	PROPN
ap-2097	156	8	)	)	PUNCT
ap-2097	156	9	]	]	PUNCT
ap-2097	156	10	,	,	PUNCT
ap-2097	156	11	(	(	PUNCT
ap-2097	156	12	22b	22b	NOUN
ap-2097	156	13	)	)	PUNCT
ap-2097	156	14	b0	b0	NOUN
ap-2097	156	15	1	1	NUM
ap-2097	156	16	:	:	PUNCT
ap-2097	156	17	=	=	PROPN
ap-2097	156	18	lim	lim	PROPN
ap-2097	156	19	x→0	x→0	PROPN
ap-2097	156	20	b1	b1	PROPN
ap-2097	156	21	=	=	NOUN
ap-2097	157	1	i	i	PRON
ap-2097	157	2	2(∂τ	2(∂τ	AUX
ap-2097	157	3	−	−	PROPN
ap-2097	158	1	∂θ	∂θ	PROPN
ap-2097	158	2	)	)	PUNCT
ap-2097	158	3	,	,	PUNCT
ap-2097	158	4	(	(	PUNCT
ap-2097	158	5	22c	22c	NOUN
ap-2097	158	6	)	)	PUNCT
ap-2097	158	7	b0	b0	NOUN
ap-2097	158	8	±	±	NUM
ap-2097	158	9	:	:	PUNCT
ap-2097	158	10	=	=	PROPN
ap-2097	158	11	lim	lim	PROPN
ap-2097	158	12	x→0	x→0	PROPN
ap-2097	158	13	b±	b±	PROPN
ap-2097	158	14	=	=	PUNCT
ap-2097	159	1	+	+	CCONJ
ap-2097	160	1	i	i	PRON
ap-2097	160	2	2e±(τ−θ)[x∂x	2e±(τ−θ)[x∂x	NUM
ap-2097	160	3	±	±	INTJ
ap-2097	160	4	(	(	PUNCT
ap-2097	160	5	∂τ	∂τ	PROPN
ap-2097	160	6	−	−	PROPN
ap-2097	160	7	∂θ	∂θ	PROPN
ap-2097	160	8	)	)	PUNCT
ap-2097	160	9	]	]	PUNCT
ap-2097	160	10	,	,	PUNCT
ap-2097	160	11	(	(	PUNCT
ap-2097	160	12	22d	22d	NOUN
ap-2097	160	13	)	)	PUNCT
ap-2097	160	14	which	which	PRON
ap-2097	160	15	still	still	ADV
ap-2097	160	16	satisfy	satisfy	VERB
ap-2097	160	17	the	the	DET
ap-2097	160	18	commutation	commutation	NOUN
ap-2097	160	19	relations	relation	NOUN
ap-2097	160	20	of	of	ADP
ap-2097	160	21	the	the	DET
ap-2097	160	22	lie	lie	NOUN
ap-2097	160	23	algebra	algebra	VERB
ap-2097	160	24	so(2	so(2	NOUN
ap-2097	160	25	,	,	PUNCT
ap-2097	160	26	2	2	NUM
ap-2097	160	27	)	)	PUNCT
ap-2097	160	28	∼=	∼=	PROPN
ap-2097	160	29	sl(2,r)l	sl(2,r)l	NOUN
ap-2097	160	30	⊕	⊕	PROPN
ap-2097	160	31	sl(2,r)r	sl(2,r)r	PUNCT
ap-2097	161	1	[	[	X
ap-2097	161	2	a0	a0	PROPN
ap-2097	161	3	1	1	NUM
ap-2097	161	4	,	,	PUNCT
ap-2097	161	5	a	a	DET
ap-2097	161	6	0	0	NUM
ap-2097	161	7	±	±	NUM
ap-2097	161	8	]	]	PUNCT
ap-2097	161	9	=	=	PUNCT
ap-2097	161	10	±ia0	±ia0	VERB
ap-2097	161	11	±	±	NOUN
ap-2097	161	12	,	,	PUNCT
ap-2097	161	13	[	[	X
ap-2097	161	14	a0	a0	NOUN
ap-2097	161	15	+	+	PROPN
ap-2097	161	16	,	,	PUNCT
ap-2097	161	17	a	a	DET
ap-2097	161	18	0	0	NUM
ap-2097	161	19	−	−	NOUN
ap-2097	161	20	]	]	X
ap-2097	161	21	=	=	SYM
ap-2097	161	22	2ia0	2ia0	NUM
ap-2097	161	23	1	1	NUM
ap-2097	161	24	,	,	PUNCT
ap-2097	161	25	(	(	PUNCT
ap-2097	161	26	23a	23a	NUM
ap-2097	161	27	)	)	PUNCT
ap-2097	162	1	[	[	X
ap-2097	162	2	b0	b0	ADP
ap-2097	162	3	1	1	NUM
ap-2097	162	4	,	,	PUNCT
ap-2097	162	5	b	b	PROPN
ap-2097	162	6	0	0	NUM
ap-2097	162	7	±	±	NUM
ap-2097	162	8	]	]	PUNCT
ap-2097	162	9	=	=	SYM
ap-2097	162	10	±ib0	±ib0	NOUN
ap-2097	162	11	±	±	NUM
ap-2097	162	12	,	,	PUNCT
ap-2097	162	13	[	[	X
ap-2097	162	14	b0	b0	ADP
ap-2097	162	15	+	+	PROPN
ap-2097	162	16	,	,	PUNCT
ap-2097	162	17	b	b	NOUN
ap-2097	162	18	0	0	NUM
ap-2097	162	19	−	−	NOUN
ap-2097	162	20	]	]	X
ap-2097	162	21	=	=	SYM
ap-2097	162	22	2ib0	2ib0	NUM
ap-2097	162	23	1	1	NUM
ap-2097	162	24	.	.	PUNCT
ap-2097	163	1	(	(	PUNCT
ap-2097	163	2	23b	23b	NOUN
ap-2097	163	3	)	)	PUNCT
ap-2097	163	4	the	the	DET
ap-2097	163	5	quadratic	quadratic	ADJ
ap-2097	163	6	casimir	casimir	NOUN
ap-2097	163	7	of	of	ADP
ap-2097	163	8	this	this	DET
ap-2097	163	9	asymptotic	asymptotic	ADJ
ap-2097	163	10	near	near	ADJ
ap-2097	163	11	-	-	PUNCT
ap-2097	163	12	boundary	boundary	NOUN
ap-2097	163	13	algebra	algebra	NOUN
ap-2097	163	14	,	,	PUNCT
ap-2097	163	15	which	which	PRON
ap-2097	163	16	we	we	PRON
ap-2097	163	17	denote	denote	VERB
ap-2097	163	18	by	by	ADP
ap-2097	163	19	so(2	so(2	PROPN
ap-2097	163	20	,	,	PUNCT
ap-2097	163	21	2)0	2)0	PROPN
ap-2097	163	22	∼=	∼=	PROPN
ap-2097	163	23	sl(2,r)0	sl(2,r)0	NOUN
ap-2097	163	24	l	l	PROPN
ap-2097	163	25	⊕	⊕	PROPN
ap-2097	163	26	sl(2,r)0	sl(2,r)0	NOUN
ap-2097	163	27	r	r	NOUN
ap-2097	163	28	,	,	PUNCT
ap-2097	163	29	takes	take	VERB
ap-2097	163	30	the	the	DET
ap-2097	163	31	following	follow	VERB
ap-2097	163	32	simple	simple	ADJ
ap-2097	163	33	form	form	NOUN
ap-2097	163	34	:	:	PUNCT
ap-2097	163	35	c2(so(2	c2(so(2	PROPN
ap-2097	163	36	,	,	PUNCT
ap-2097	163	37	2)0	2)0	NUM
ap-2097	163	38	)	)	PUNCT
ap-2097	163	39	=	=	SYM
ap-2097	164	1	4c2(sl(2,r)0	4c2(sl(2,r)0	NUM
ap-2097	164	2	l	l	NOUN
ap-2097	164	3	)	)	PUNCT
ap-2097	165	1	=	=	PUNCT
ap-2097	166	1	4c2(sl(2,r)0	4c2(sl(2,r)0	NUM
ap-2097	166	2	r	r	NOUN
ap-2097	166	3	)	)	PUNCT
ap-2097	166	4	=	=	PUNCT
ap-2097	167	1	x2∂2	x2∂2	NOUN
ap-2097	167	2	x	x	PUNCT
ap-2097	168	1	−	−	NOUN
ap-2097	168	2	x∂x	x∂x	X
ap-2097	169	1	=	=	NOUN
ap-2097	169	2	:	:	PUNCT
ap-2097	169	3	c0	c0	PROPN
ap-2097	169	4	2	2	NUM
ap-2097	169	5	.	.	PUNCT
ap-2097	170	1	(	(	PUNCT
ap-2097	170	2	24	24	NUM
ap-2097	170	3	)	)	PUNCT
ap-2097	170	4	as	as	SCONJ
ap-2097	170	5	we	we	PRON
ap-2097	170	6	have	have	AUX
ap-2097	170	7	repeatedly	repeatedly	ADV
ap-2097	170	8	emphasized	emphasize	VERB
ap-2097	170	9	,	,	PUNCT
ap-2097	170	10	we	we	PRON
ap-2097	170	11	are	be	AUX
ap-2097	170	12	interested	interested	ADJ
ap-2097	170	13	in	in	ADP
ap-2097	170	14	simultaneous	simultaneous	ADJ
ap-2097	170	15	eigenstates	eigenstate	NOUN
ap-2097	170	16	of	of	ADP
ap-2097	170	17	the	the	DET
ap-2097	170	18	d’alembertian	d’alembertian	PROPN
ap-2097	170	19	�	�	PROPN
ap-2097	170	20	ads3	ads3	PROPN
ap-2097	170	21	x→0→	x→0→	PROPN
ap-2097	171	1	c0	c0	PROPN
ap-2097	171	2	2	2	NUM
ap-2097	171	3	,	,	PUNCT
ap-2097	171	4	the	the	DET
ap-2097	171	5	time	time	NOUN
ap-2097	171	6	-	-	PUNCT
ap-2097	171	7	translation	translation	NOUN
ap-2097	171	8	generator	generator	NOUN
ap-2097	171	9	i∂τ	i∂τ	NOUN
ap-2097	171	10	=	=	PUNCT
ap-2097	171	11	b0	b0	NOUN
ap-2097	171	12	1	1	NUM
ap-2097	171	13	+	+	NOUN
ap-2097	171	14	a0	a0	PROPN
ap-2097	171	15	1	1	NUM
ap-2097	171	16	and	and	CCONJ
ap-2097	171	17	the	the	DET
ap-2097	171	18	spatial	spatial	ADJ
ap-2097	171	19	-	-	PUNCT
ap-2097	171	20	translation	translation	NOUN
ap-2097	171	21	generator	generator	NOUN
ap-2097	171	22	−i∂θ	−i∂θ	PROPN
ap-2097	171	23	=	=	SYM
ap-2097	171	24	b0	b0	VERB
ap-2097	171	25	1	1	NUM
ap-2097	171	26	−a0	−a0	PROPN
ap-2097	171	27	1	1	NUM
ap-2097	171	28	.	.	PUNCT
ap-2097	172	1	let	let	VERB
ap-2097	172	2	|∆	|∆	NOUN
ap-2097	172	3	,	,	PUNCT
ap-2097	172	4	kl	kl	PROPN
ap-2097	172	5	,	,	PUNCT
ap-2097	172	6	kr〉0	kr〉0	PROPN
ap-2097	172	7	be	be	VERB
ap-2097	172	8	a	a	DET
ap-2097	172	9	simultaneous	simultaneous	ADJ
ap-2097	172	10	eigenstate	eigenstate	NOUN
ap-2097	172	11	of	of	ADP
ap-2097	172	12	c0	c0	PROPN
ap-2097	172	13	2	2	NUM
ap-2097	172	14	,	,	PUNCT
ap-2097	172	15	a0	a0	PROPN
ap-2097	172	16	1	1	NUM
ap-2097	172	17	and	and	CCONJ
ap-2097	172	18	b0	b0	NOUN
ap-2097	172	19	1	1	NUM
ap-2097	172	20	that	that	PRON
ap-2097	172	21	satisfies	satisfy	VERB
ap-2097	172	22	the	the	DET
ap-2097	172	23	following	follow	VERB
ap-2097	172	24	eigenvalue	eigenvalue	PROPN
ap-2097	172	25	equations	equation	NOUN
ap-2097	172	26	:	:	PUNCT
ap-2097	172	27	c0	c0	NOUN
ap-2097	172	28	2	2	NUM
ap-2097	172	29	|∆	|∆	NOUN
ap-2097	172	30	,	,	PUNCT
ap-2097	172	31	kl	kl	PROPN
ap-2097	172	32	,	,	PUNCT
ap-2097	172	33	kr〉0	kr〉0	PROPN
ap-2097	172	34	=	=	SYM
ap-2097	172	35	∆(∆−	∆(∆−	PROPN
ap-2097	172	36	2)|∆	2)|∆	NUM
ap-2097	172	37	,	,	PUNCT
ap-2097	172	38	kl	kl	PROPN
ap-2097	172	39	,	,	PUNCT
ap-2097	172	40	kr〉0	kr〉0	PROPN
ap-2097	172	41	,	,	PUNCT
ap-2097	172	42	(	(	PUNCT
ap-2097	172	43	25a	25a	NOUN
ap-2097	172	44	)	)	PUNCT
ap-2097	172	45	a0	a0	PROPN
ap-2097	172	46	1|∆	1|∆	PROPN
ap-2097	172	47	,	,	PUNCT
ap-2097	172	48	kl	kl	PROPN
ap-2097	172	49	,	,	PUNCT
ap-2097	172	50	kr〉0	kr〉0	PROPN
ap-2097	172	51	=	=	SYM
ap-2097	172	52	kl|∆	kl|∆	PROPN
ap-2097	172	53	,	,	PUNCT
ap-2097	172	54	kl	kl	PROPN
ap-2097	172	55	,	,	PUNCT
ap-2097	172	56	kr〉0	kr〉0	PROPN
ap-2097	172	57	,	,	PUNCT
ap-2097	172	58	(	(	PUNCT
ap-2097	172	59	25b	25b	NOUN
ap-2097	172	60	)	)	PUNCT
ap-2097	172	61	b0	b0	NOUN
ap-2097	172	62	1	1	NUM
ap-2097	172	63	|∆	|∆	NOUN
ap-2097	172	64	,	,	PUNCT
ap-2097	172	65	kl	kl	PROPN
ap-2097	172	66	,	,	PUNCT
ap-2097	172	67	kr〉0	kr〉0	PROPN
ap-2097	172	68	=	=	SYM
ap-2097	172	69	kr|∆	kr|∆	PROPN
ap-2097	172	70	,	,	PUNCT
ap-2097	172	71	kl	kl	PROPN
ap-2097	172	72	,	,	PUNCT
ap-2097	172	73	kr〉0	kr〉0	PROPN
ap-2097	172	74	.	.	PROPN
ap-2097	172	75	(	(	PUNCT
ap-2097	172	76	25c	25c	NOUN
ap-2097	172	77	)	)	PUNCT
ap-2097	172	78	in	in	ADP
ap-2097	172	79	the	the	DET
ap-2097	172	80	coordinate	coordinate	NOUN
ap-2097	172	81	realization	realization	NOUN
ap-2097	172	82	these	these	DET
ap-2097	172	83	eigenvalue	eigenvalue	PROPN
ap-2097	172	84	equations	equation	NOUN
ap-2097	172	85	become	become	VERB
ap-2097	172	86	the	the	DET
ap-2097	172	87	following	following	ADJ
ap-2097	172	88	differential	differential	ADJ
ap-2097	172	89	equations	equation	NOUN
ap-2097	172	90	:(	:(	PUNCT
ap-2097	173	1	−∂2	−∂2	PROPN
ap-2097	173	2	x	x	SYM
ap-2097	173	3	+	+	PUNCT
ap-2097	173	4	1	1	NUM
ap-2097	173	5	x	x	NOUN
ap-2097	173	6	∂x	∂x	PROPN
ap-2097	173	7	+	+	CCONJ
ap-2097	173	8	∆(∆−	∆(∆−	PROPN
ap-2097	173	9	2	2	NUM
ap-2097	173	10	)	)	PUNCT
ap-2097	173	11	x2	x2	NOUN
ap-2097	173	12	)	)	PUNCT
ap-2097	174	1	φ0	φ0	ADJ
ap-2097	174	2	∆,kl	∆,kl	NOUN
ap-2097	174	3	,	,	PUNCT
ap-2097	174	4	kr	kr	PROPN
ap-2097	174	5	=	=	SYM
ap-2097	174	6	0	0	NUM
ap-2097	174	7	,	,	PUNCT
ap-2097	174	8	(	(	PUNCT
ap-2097	174	9	26a	26a	NOUN
ap-2097	174	10	)	)	PUNCT
ap-2097	174	11	(	(	PUNCT
ap-2097	174	12	i∂xl	i∂xl	NOUN
ap-2097	174	13	−	−	NOUN
ap-2097	174	14	kl)φ0	kl)φ0	PROPN
ap-2097	174	15	∆,kl	∆,kl	NOUN
ap-2097	174	16	,	,	PUNCT
ap-2097	174	17	kr	kr	PROPN
ap-2097	174	18	=	=	SYM
ap-2097	174	19	0	0	NUM
ap-2097	174	20	,	,	PUNCT
ap-2097	174	21	(	(	PUNCT
ap-2097	174	22	26b	26b	NOUN
ap-2097	174	23	)	)	PUNCT
ap-2097	174	24	(	(	PUNCT
ap-2097	174	25	i∂xr	i∂xr	PROPN
ap-2097	174	26	−	−	PROPN
ap-2097	174	27	kr)φ0	kr)φ0	PROPN
ap-2097	174	28	∆,kl	∆,kl	NOUN
ap-2097	174	29	,	,	PUNCT
ap-2097	174	30	kr	kr	PROPN
ap-2097	174	31	=	=	SYM
ap-2097	174	32	0	0	NUM
ap-2097	174	33	,	,	PUNCT
ap-2097	174	34	(	(	PUNCT
ap-2097	174	35	26c	26c	NOUN
ap-2097	174	36	)	)	PUNCT
ap-2097	174	37	where	where	SCONJ
ap-2097	174	38	xl	xl	PROPN
ap-2097	174	39	and	and	CCONJ
ap-2097	174	40	xr	xr	PROPN
ap-2097	174	41	are	be	AUX
ap-2097	174	42	light	light	ADJ
ap-2097	174	43	-	-	PUNCT
ap-2097	174	44	cone	cone	NOUN
ap-2097	174	45	coordinates	coordinate	NOUN
ap-2097	174	46	given	give	VERB
ap-2097	174	47	by	by	ADP
ap-2097	174	48	xl	xl	PROPN
ap-2097	174	49	=	=	PROPN
ap-2097	174	50	τ	τ	PROPN
ap-2097	174	51	+	+	NUM
ap-2097	174	52	θ	θ	PROPN
ap-2097	174	53	and	and	CCONJ
ap-2097	174	54	xr	xr	PROPN
ap-2097	174	55	=	=	PROPN
ap-2097	174	56	τ	τ	PROPN
ap-2097	174	57	−	−	PROPN
ap-2097	174	58	θ	θ	PROPN
ap-2097	174	59	,	,	PUNCT
ap-2097	174	60	and	and	CCONJ
ap-2097	174	61	(	(	PUNCT
ap-2097	174	62	kl	kl	PROPN
ap-2097	174	63	,	,	PUNCT
ap-2097	174	64	kr	kr	PROPN
ap-2097	174	65	)	)	PUNCT
ap-2097	174	66	and	and	CCONJ
ap-2097	174	67	(	(	PUNCT
ap-2097	174	68	ω	ω	PROPN
ap-2097	174	69	,	,	PUNCT
ap-2097	174	70	k	k	NOUN
ap-2097	174	71	)	)	PUNCT
ap-2097	174	72	are	be	AUX
ap-2097	174	73	related	relate	VERB
ap-2097	174	74	by	by	ADP
ap-2097	174	75	kl	kl	NOUN
ap-2097	174	76	=	=	SYM
ap-2097	174	77	(	(	PUNCT
ap-2097	174	78	ω	ω	NOUN
ap-2097	174	79	−	−	PROPN
ap-2097	174	80	k)/2	k)/2	PROPN
ap-2097	174	81	and	and	CCONJ
ap-2097	174	82	kr	kr	PROPN
ap-2097	174	83	=	=	SYM
ap-2097	174	84	(	(	PUNCT
ap-2097	174	85	ω	ω	PROPN
ap-2097	174	86	+	+	CCONJ
ap-2097	175	1	k)/2	k)/2	PROPN
ap-2097	175	2	.	.	PUNCT
ap-2097	176	1	these	these	DET
ap-2097	176	2	differential	differential	ADJ
ap-2097	176	3	equations	equation	NOUN
ap-2097	176	4	are	be	AUX
ap-2097	176	5	easily	easily	ADV
ap-2097	176	6	solved	solve	VERB
ap-2097	176	7	with	with	ADP
ap-2097	176	8	the	the	DET
ap-2097	176	9	result	result	NOUN
ap-2097	176	10	φ0	φ0	ADJ
ap-2097	176	11	∆,kl	∆,kl	NOUN
ap-2097	176	12	,	,	PUNCT
ap-2097	176	13	kr(τ	kr(τ	NOUN
ap-2097	176	14	,	,	PUNCT
ap-2097	176	15	x	x	NOUN
ap-2097	176	16	,	,	PUNCT
ap-2097	176	17	θ	θ	NOUN
ap-2097	176	18	)	)	PUNCT
ap-2097	176	19	=	=	NOUN
ap-2097	176	20	a∆(kl	a∆(kl	NOUN
ap-2097	176	21	,	,	PUNCT
ap-2097	176	22	kr)x∆e−iklxle−ikrxr	kr)x∆e−iklxle−ikrxr	VERB
ap-2097	176	23	+	+	ADV
ap-2097	176	24	b∆(kl	b∆(kl	ADJ
ap-2097	176	25	,	,	PUNCT
ap-2097	176	26	kr)x2−∆e−iklxle−ikrxr	kr)x2−∆e−iklxle−ikrxr	X
ap-2097	176	27	,	,	PUNCT
ap-2097	176	28	(	(	PUNCT
ap-2097	176	29	27	27	NUM
ap-2097	176	30	)	)	PUNCT
ap-2097	176	31	which	which	PRON
ap-2097	176	32	precisely	precisely	ADV
ap-2097	176	33	coincides	coincide	VERB
ap-2097	176	34	with	with	ADP
ap-2097	176	35	the	the	DET
ap-2097	176	36	asymptotic	asymptotic	ADJ
ap-2097	176	37	nearboundary	nearboundary	ADJ
ap-2097	176	38	behavior	behavior	NOUN
ap-2097	176	39	of	of	ADP
ap-2097	176	40	the	the	DET
ap-2097	176	41	solution	solution	NOUN
ap-2097	176	42	(	(	PUNCT
ap-2097	176	43	15	15	NUM
ap-2097	176	44	)	)	PUNCT
ap-2097	176	45	.	.	PUNCT
ap-2097	177	1	4	4	X
ap-2097	177	2	.	.	X
ap-2097	177	3	recurrence	recurrence	NOUN
ap-2097	177	4	relations	relation	NOUN
ap-2097	177	5	for	for	ADP
ap-2097	177	6	finite	finite	ADJ
ap-2097	177	7	-	-	ADJ
ap-2097	177	8	temperature	temperature	ADJ
ap-2097	177	9	cft2	cft2	ADJ
ap-2097	177	10	two	two	NUM
ap-2097	177	11	-	-	PUNCT
ap-2097	177	12	point	point	NOUN
ap-2097	177	13	functions	function	NOUN
ap-2097	177	14	as	as	SCONJ
ap-2097	177	15	mentioned	mention	VERB
ap-2097	177	16	in	in	ADP
ap-2097	177	17	the	the	DET
ap-2097	177	18	previous	previous	ADJ
ap-2097	177	19	section	section	NOUN
ap-2097	177	20	,	,	PUNCT
ap-2097	177	21	a±	a±	PROPN
ap-2097	177	22	and	and	CCONJ
ap-2097	177	23	b±	b±	PROPN
ap-2097	177	24	(	(	PUNCT
ap-2097	177	25	and	and	CCONJ
ap-2097	177	26	also	also	ADV
ap-2097	177	27	a0	a0	PROPN
ap-2097	177	28	±	±	PROPN
ap-2097	177	29	and	and	CCONJ
ap-2097	177	30	b0	b0	PROPN
ap-2097	177	31	±	±	PROPN
ap-2097	177	32	)	)	PUNCT
ap-2097	177	33	play	play	VERB
ap-2097	177	34	the	the	DET
ap-2097	177	35	role	role	NOUN
ap-2097	177	36	of	of	ADP
ap-2097	177	37	“	"	PUNCT
ap-2097	177	38	ladder	ladder	NOUN
ap-2097	177	39	”	"	PUNCT
ap-2097	177	40	operators	operator	NOUN
ap-2097	177	41	.	.	PUNCT
ap-2097	178	1	to	to	PART
ap-2097	178	2	see	see	VERB
ap-2097	178	3	this	this	PRON
ap-2097	178	4	,	,	PUNCT
ap-2097	178	5	let	let	VERB
ap-2097	178	6	us	we	PRON
ap-2097	178	7	consider	consider	VERB
ap-2097	178	8	states	state	NOUN
ap-2097	178	9	a0	a0	PROPN
ap-2097	178	10	±|∆	±|∆	PROPN
ap-2097	178	11	,	,	PUNCT
ap-2097	178	12	kl	kl	PROPN
ap-2097	178	13	,	,	PUNCT
ap-2097	178	14	kr〉0	kr〉0	PROPN
ap-2097	178	15	and	and	CCONJ
ap-2097	178	16	b0	b0	PROPN
ap-2097	178	17	±|∆	±|∆	PROPN
ap-2097	178	18	,	,	PUNCT
ap-2097	178	19	kl	kl	PROPN
ap-2097	178	20	,	,	PUNCT
ap-2097	178	21	kr〉0	kr〉0	PROPN
ap-2097	178	22	.	.	PUNCT
ap-2097	179	1	the	the	DET
ap-2097	179	2	commutation	commutation	NOUN
ap-2097	179	3	relations	relation	NOUN
ap-2097	179	4	[	[	X
ap-2097	179	5	a0	a0	NOUN
ap-2097	179	6	1	1	NUM
ap-2097	179	7	,	,	PUNCT
ap-2097	179	8	a	a	DET
ap-2097	179	9	0	0	NUM
ap-2097	179	10	±	±	NUM
ap-2097	179	11	]	]	PUNCT
ap-2097	179	12	=	=	PUNCT
ap-2097	179	13	±ia0	±ia0	VERB
ap-2097	179	14	±	±	NOUN
ap-2097	179	15	and	and	CCONJ
ap-2097	179	16	[	[	X
ap-2097	179	17	b0	b0	PROPN
ap-2097	179	18	1	1	NUM
ap-2097	179	19	,	,	PUNCT
ap-2097	179	20	b	b	PROPN
ap-2097	179	21	0	0	NUM
ap-2097	179	22	±	±	NUM
ap-2097	179	23	]	]	PUNCT
ap-2097	179	24	=	=	SYM
ap-2097	179	25	±ib0	±ib0	NOUN
ap-2097	179	26	±	±	NOUN
ap-2097	179	27	give	give	VERB
ap-2097	179	28	a0	a0	PROPN
ap-2097	179	29	1a	1a	PROPN
ap-2097	179	30	0	0	PUNCT
ap-2097	180	1	±|∆	±|∆	PROPN
ap-2097	180	2	,	,	PUNCT
ap-2097	180	3	kl	kl	PROPN
ap-2097	180	4	,	,	PUNCT
ap-2097	180	5	kr〉0	kr〉0	PROPN
ap-2097	180	6	=	=	SYM
ap-2097	180	7	(	(	PUNCT
ap-2097	180	8	kl±i)a0	kl±i)a0	PROPN
ap-2097	180	9	±|∆	±|∆	PROPN
ap-2097	180	10	,	,	PUNCT
ap-2097	180	11	kl	kl	PROPN
ap-2097	180	12	,	,	PUNCT
ap-2097	180	13	kr〉0	kr〉0	PROPN
ap-2097	180	14	and	and	CCONJ
ap-2097	180	15	b0	b0	VERB
ap-2097	180	16	1b	1b	NUM
ap-2097	180	17	0	0	PUNCT
ap-2097	181	1	±|∆	±|∆	PROPN
ap-2097	181	2	,	,	PUNCT
ap-2097	181	3	kl	kl	PROPN
ap-2097	181	4	,	,	PUNCT
ap-2097	181	5	kr〉0	kr〉0	PROPN
ap-2097	181	6	=	=	SYM
ap-2097	181	7	(	(	PUNCT
ap-2097	181	8	kr±	kr±	PROPN
ap-2097	181	9	i)b0	i)b0	PROPN
ap-2097	181	10	±|∆	±|∆	PROPN
ap-2097	181	11	,	,	PUNCT
ap-2097	181	12	kr	kr	PROPN
ap-2097	181	13	,	,	PUNCT
ap-2097	181	14	kl〉0	kl〉0	PROPN
ap-2097	181	15	,	,	PUNCT
ap-2097	181	16	which	which	PRON
ap-2097	181	17	imply	imply	VERB
ap-2097	181	18	that	that	SCONJ
ap-2097	181	19	a0	a0	PROPN
ap-2097	181	20	±	±	PROPN
ap-2097	181	21	and	and	CCONJ
ap-2097	181	22	b0	b0	NOUN
ap-2097	181	23	±	±	NOUN
ap-2097	181	24	raise	raise	NOUN
ap-2097	181	25	and	and	CCONJ
ap-2097	181	26	lower	lower	VERB
ap-2097	181	27	the	the	DET
ap-2097	181	28	eigenvalues	eigenvalue	NOUN
ap-2097	181	29	kl	kl	PROPN
ap-2097	181	30	and	and	CCONJ
ap-2097	181	31	kr	kr	PROPN
ap-2097	181	32	by	by	ADP
ap-2097	181	33	±i:6	±i:6	PROPN
ap-2097	181	34	a0	a0	PROPN
ap-2097	181	35	±|∆	±|∆	PROPN
ap-2097	181	36	,	,	PUNCT
ap-2097	181	37	kl	kl	PROPN
ap-2097	181	38	,	,	PUNCT
ap-2097	181	39	kr〉0	kr〉0	PROPN
ap-2097	181	40	∝	∝	PROPN
ap-2097	181	41	|∆	|∆	NOUN
ap-2097	181	42	,	,	PUNCT
ap-2097	181	43	kl	kl	PROPN
ap-2097	181	44	±	±	PROPN
ap-2097	181	45	i	i	PROPN
ap-2097	181	46	,	,	PUNCT
ap-2097	181	47	kr〉0	kr〉0	PROPN
ap-2097	181	48	,	,	PUNCT
ap-2097	181	49	(	(	PUNCT
ap-2097	181	50	28a	28a	NOUN
ap-2097	181	51	)	)	PUNCT
ap-2097	181	52	b0	b0	PROPN
ap-2097	181	53	±|∆	±|∆	PROPN
ap-2097	181	54	,	,	PUNCT
ap-2097	181	55	kl	kl	PROPN
ap-2097	181	56	,	,	PUNCT
ap-2097	181	57	kr〉0	kr〉0	PROPN
ap-2097	181	58	∝	∝	PROPN
ap-2097	181	59	|∆	|∆	NOUN
ap-2097	181	60	,	,	PUNCT
ap-2097	181	61	kl	kl	PROPN
ap-2097	181	62	,	,	PUNCT
ap-2097	181	63	kr	kr	PROPN
ap-2097	181	64	±	±	NUM
ap-2097	181	65	i〉0	i〉0	PROPN
ap-2097	181	66	.	.	PUNCT
ap-2097	182	1	(	(	PUNCT
ap-2097	182	2	28b	28b	NOUN
ap-2097	182	3	)	)	PUNCT
ap-2097	182	4	in	in	ADP
ap-2097	182	5	the	the	DET
ap-2097	182	6	coordinate	coordinate	NOUN
ap-2097	182	7	realization	realization	NOUN
ap-2097	182	8	(	(	PUNCT
ap-2097	182	9	22a	22a	NOUN
ap-2097	182	10	)	)	PUNCT
ap-2097	182	11	and	and	CCONJ
ap-2097	182	12	(	(	PUNCT
ap-2097	182	13	22c	22c	NOUN
ap-2097	182	14	)	)	PUNCT
ap-2097	182	15	with	with	ADP
ap-2097	182	16	the	the	DET
ap-2097	182	17	solution	solution	NOUN
ap-2097	182	18	(	(	PUNCT
ap-2097	182	19	27	27	NUM
ap-2097	182	20	)	)	PUNCT
ap-2097	182	21	,	,	PUNCT
ap-2097	182	22	the	the	DET
ap-2097	182	23	left	left	ADJ
ap-2097	182	24	-	-	PUNCT
ap-2097	182	25	hand	hand	NOUN
ap-2097	182	26	sides	side	NOUN
ap-2097	182	27	become	become	VERB
ap-2097	182	28	a0	a0	NOUN
ap-2097	182	29	±φ	±φ	X
ap-2097	182	30	0	0	NUM
ap-2097	182	31	∆,kl	∆,kl	NOUN
ap-2097	182	32	,	,	PUNCT
ap-2097	183	1	kr	kr	PROPN
ap-2097	183	2	=	=	PUNCT
ap-2097	183	3	i	i	PROPN
ap-2097	183	4	(	(	PUNCT
ap-2097	183	5	−∆	−∆	PROPN
ap-2097	183	6	2	2	NUM
ap-2097	183	7	±	±	NUM
ap-2097	183	8	ikl	ikl	PROPN
ap-2097	183	9	)	)	PUNCT
ap-2097	183	10	a∆(kl	a∆(kl	PROPN
ap-2097	183	11	,	,	PUNCT
ap-2097	183	12	kr	kr	PROPN
ap-2097	183	13	)	)	PUNCT
ap-2097	183	14	×	×	NOUN
ap-2097	183	15	x∆e−i(kl±i)xle−ikrxr	x∆e−i(kl±i)xle−ikrxr	PROPN
ap-2097	184	1	+	+	CCONJ
ap-2097	185	1	i	i	PRON
ap-2097	185	2	(	(	PUNCT
ap-2097	185	3	∆	∆	PROPN
ap-2097	185	4	2	2	NUM
ap-2097	185	5	−	−	PROPN
ap-2097	185	6	1±	1±	NUM
ap-2097	185	7	ikl	ikl	NOUN
ap-2097	185	8	)	)	PUNCT
ap-2097	185	9	b∆(kl	b∆(kl	PROPN
ap-2097	185	10	,	,	PUNCT
ap-2097	185	11	kr	kr	PROPN
ap-2097	185	12	)	)	PUNCT
ap-2097	185	13	×	×	NOUN
ap-2097	185	14	x2−∆e−i(kl±i)xle−ikrxr	x2−∆e−i(kl±i)xle−ikrxr	PROPN
ap-2097	185	15	,	,	PUNCT
ap-2097	185	16	(	(	PUNCT
ap-2097	185	17	29a	29a	NOUN
ap-2097	185	18	)	)	PUNCT
ap-2097	185	19	b0	b0	NOUN
ap-2097	185	20	±φ	±φ	NUM
ap-2097	185	21	0	0	NUM
ap-2097	185	22	∆,kl	∆,kl	NOUN
ap-2097	185	23	,	,	PUNCT
ap-2097	185	24	kr	kr	PROPN
ap-2097	185	25	=	=	SYM
ap-2097	185	26	−i	−i	PROPN
ap-2097	185	27	(	(	PUNCT
ap-2097	185	28	−∆	−∆	PROPN
ap-2097	185	29	2	2	NUM
ap-2097	185	30	±	±	NUM
ap-2097	185	31	ikr	ikr	NOUN
ap-2097	185	32	)	)	PUNCT
ap-2097	185	33	a∆(kl	a∆(kl	PROPN
ap-2097	185	34	,	,	PUNCT
ap-2097	185	35	kr	kr	PROPN
ap-2097	185	36	)	)	PUNCT
ap-2097	185	37	×	×	PROPN
ap-2097	185	38	x∆e−iklxle−i(kr±i)xr	x∆e−iklxle−i(kr±i)xr	PROPN
ap-2097	185	39	−	−	NOUN
ap-2097	186	1	i	i	PRON
ap-2097	186	2	(	(	PUNCT
ap-2097	186	3	∆	∆	PROPN
ap-2097	186	4	2	2	NUM
ap-2097	186	5	−	−	PROPN
ap-2097	186	6	1±	1±	NUM
ap-2097	186	7	ikr	ikr	NOUN
ap-2097	186	8	)	)	PUNCT
ap-2097	186	9	b∆(kl	b∆(kl	PROPN
ap-2097	186	10	,	,	PUNCT
ap-2097	186	11	kr	kr	PROPN
ap-2097	186	12	)	)	PUNCT
ap-2097	186	13	×	×	NOUN
ap-2097	186	14	x2−∆e−iklxle−i(kr±i)xr	x2−∆e−iklxle−i(kr±i)xr	PROPN
ap-2097	186	15	,	,	PUNCT
ap-2097	186	16	(	(	PUNCT
ap-2097	186	17	29b	29b	NUM
ap-2097	186	18	)	)	PUNCT
ap-2097	186	19	which	which	PRON
ap-2097	186	20	should	should	AUX
ap-2097	186	21	be	be	AUX
ap-2097	186	22	proportional	proportional	ADJ
ap-2097	186	23	to	to	ADP
ap-2097	186	24	φ0	φ0	PROPN
ap-2097	186	25	∆,kl±i	∆,kl±i	PROPN
ap-2097	186	26	,	,	PUNCT
ap-2097	186	27	kr	kr	PROPN
ap-2097	186	28	and	and	CCONJ
ap-2097	186	29	φ0	φ0	PROPN
ap-2097	186	30	∆,kl	∆,kl	NOUN
ap-2097	186	31	,	,	PUNCT
ap-2097	186	32	kr±i	kr±i	PROPN
ap-2097	186	33	,	,	PUNCT
ap-2097	186	34	respectively	respectively	ADV
ap-2097	186	35	.	.	PUNCT
ap-2097	187	1	in	in	ADP
ap-2097	187	2	other	other	ADJ
ap-2097	187	3	words	word	NOUN
ap-2097	187	4	,	,	PUNCT
ap-2097	187	5	the	the	DET
ap-2097	187	6	integration	integration	NOUN
ap-2097	187	7	constants	constant	NOUN
ap-2097	187	8	should	should	AUX
ap-2097	187	9	satisfy	satisfy	VERB
ap-2097	187	10	the	the	DET
ap-2097	187	11	recurrence	recurrence	NOUN
ap-2097	187	12	relations	relation	NOUN
ap-2097	187	13	(	(	PUNCT
ap-2097	187	14	−∆	−∆	NOUN
ap-2097	187	15	2	2	NUM
ap-2097	187	16	±	±	NUM
ap-2097	187	17	ikl)a∆(kl	ikl)a∆(kl	NOUN
ap-2097	187	18	,	,	PUNCT
ap-2097	187	19	kr	kr	PROPN
ap-2097	187	20	)	)	PUNCT
ap-2097	187	21	∝	∝	PROPN
ap-2097	187	22	a∆(kl	a∆(kl	VERB
ap-2097	187	23	±	±	NUM
ap-2097	187	24	i	i	PROPN
ap-2097	187	25	,	,	PUNCT
ap-2097	187	26	kr	kr	PROPN
ap-2097	187	27	)	)	PUNCT
ap-2097	187	28	and	and	CCONJ
ap-2097	187	29	(	(	PUNCT
ap-2097	187	30	∆	∆	PROPN
ap-2097	187	31	2	2	NUM
ap-2097	187	32	−	−	PROPN
ap-2097	187	33	1±	1±	NUM
ap-2097	187	34	ikl)b∆(kl	ikl)b∆(kl	NOUN
ap-2097	187	35	,	,	PUNCT
ap-2097	187	36	kr	kr	PROPN
ap-2097	187	37	)	)	PUNCT
ap-2097	187	38	∝	∝	PROPN
ap-2097	187	39	b∆(kl	b∆(kl	VERB
ap-2097	187	40	±	±	NUM
ap-2097	188	1	i	i	PROPN
ap-2097	188	2	,	,	PUNCT
ap-2097	188	3	kr	kr	PROPN
ap-2097	188	4	)	)	PUNCT
ap-2097	188	5	,	,	PUNCT
ap-2097	188	6	and	and	CCONJ
ap-2097	188	7	similar	similar	ADJ
ap-2097	188	8	expressions	expression	NOUN
ap-2097	188	9	for	for	ADP
ap-2097	188	10	kr	kr	PROPN
ap-2097	188	11	.	.	PROPN
ap-2097	189	1	hence	hence	ADV
ap-2097	189	2	the	the	DET
ap-2097	189	3	two	two	NUM
ap-2097	189	4	-	-	PUNCT
ap-2097	189	5	point	point	NOUN
ap-2097	189	6	function	function	NOUN
ap-2097	189	7	g∆(kl	g∆(kl	NOUN
ap-2097	189	8	,	,	PUNCT
ap-2097	189	9	kr	kr	PROPN
ap-2097	189	10	)	)	PUNCT
ap-2097	189	11	,	,	PUNCT
ap-2097	189	12	which	which	PRON
ap-2097	189	13	is	be	AUX
ap-2097	189	14	given	give	VERB
ap-2097	189	15	by	by	ADP
ap-2097	189	16	the	the	DET
ap-2097	189	17	ratio	ratio	NOUN
ap-2097	189	18	g∆(kl	g∆(kl	NOUN
ap-2097	189	19	,	,	PUNCT
ap-2097	189	20	kr	kr	PROPN
ap-2097	189	21	)	)	PUNCT
ap-2097	190	1	=	=	PUNCT
ap-2097	191	1	6one	6one	NOUN
ap-2097	191	2	may	may	AUX
ap-2097	191	3	wonder	wonder	VERB
ap-2097	191	4	why	why	SCONJ
ap-2097	191	5	the	the	DET
ap-2097	191	6	eigenvalues	eigenvalue	NOUN
ap-2097	191	7	of	of	ADP
ap-2097	191	8	the	the	DET
ap-2097	191	9	self	self	NOUN
ap-2097	191	10	-	-	PUNCT
ap-2097	191	11	adjoint	adjoint	NOUN
ap-2097	191	12	operators	operator	NOUN
ap-2097	191	13	a0	a0	PROPN
ap-2097	191	14	1	1	NUM
ap-2097	191	15	and	and	CCONJ
ap-2097	191	16	b0	b0	NOUN
ap-2097	191	17	1	1	NUM
ap-2097	191	18	take	take	VERB
ap-2097	191	19	the	the	DET
ap-2097	191	20	complex	complex	ADJ
ap-2097	191	21	values	value	NOUN
ap-2097	191	22	kl	kl	INTJ
ap-2097	191	23	±	±	NOUN
ap-2097	192	1	i	i	PROPN
ap-2097	192	2	and	and	CCONJ
ap-2097	192	3	kr	kr	PROPN
ap-2097	192	4	±	±	PROPN
ap-2097	192	5	i.	i.	NOUN
ap-2097	192	6	the	the	DET
ap-2097	192	7	reason	reason	NOUN
ap-2097	192	8	is	be	AUX
ap-2097	192	9	that	that	SCONJ
ap-2097	192	10	,	,	PUNCT
ap-2097	192	11	even	even	ADV
ap-2097	192	12	if	if	SCONJ
ap-2097	192	13	the	the	DET
ap-2097	192	14	state	state	NOUN
ap-2097	192	15	|∆	|∆	NOUN
ap-2097	192	16	,	,	PUNCT
ap-2097	192	17	kl	kl	PROPN
ap-2097	192	18	,	,	PUNCT
ap-2097	192	19	kr〉0	kr〉0	PROPN
ap-2097	192	20	lies	lie	VERB
ap-2097	192	21	inside	inside	ADP
ap-2097	192	22	the	the	DET
ap-2097	192	23	domain	domain	NOUN
ap-2097	192	24	in	in	ADP
ap-2097	192	25	which	which	PRON
ap-2097	192	26	the	the	DET
ap-2097	192	27	operators	operator	NOUN
ap-2097	192	28	a0	a0	PROPN
ap-2097	192	29	1	1	NUM
ap-2097	192	30	and	and	CCONJ
ap-2097	192	31	b0	b0	NOUN
ap-2097	192	32	1	1	NUM
ap-2097	192	33	become	become	VERB
ap-2097	192	34	self	self	NOUN
ap-2097	192	35	-	-	PUNCT
ap-2097	192	36	adjoint	adjoint	NOUN
ap-2097	192	37	,	,	PUNCT
ap-2097	192	38	the	the	DET
ap-2097	192	39	states	states	PROPN
ap-2097	192	40	a0	a0	PROPN
ap-2097	192	41	±|∆	±|∆	PROPN
ap-2097	192	42	,	,	PUNCT
ap-2097	192	43	kl	kl	PROPN
ap-2097	192	44	,	,	PUNCT
ap-2097	192	45	kr〉0	kr〉0	PROPN
ap-2097	192	46	and	and	CCONJ
ap-2097	192	47	b0	b0	PROPN
ap-2097	192	48	±|∆	±|∆	PROPN
ap-2097	192	49	,	,	PUNCT
ap-2097	192	50	kl	kl	PROPN
ap-2097	192	51	,	,	PUNCT
ap-2097	192	52	kr〉0	kr〉0	PROPN
ap-2097	192	53	turn	turn	VERB
ap-2097	192	54	out	out	ADP
ap-2097	192	55	to	to	PART
ap-2097	192	56	lie	lie	VERB
ap-2097	192	57	outside	outside	ADP
ap-2097	192	58	the	the	DET
ap-2097	192	59	self	self	NOUN
ap-2097	192	60	-	-	PUNCT
ap-2097	192	61	adjoint	adjoint	NOUN
ap-2097	192	62	domain	domain	NOUN
ap-2097	192	63	of	of	ADP
ap-2097	192	64	a0	a0	PROPN
ap-2097	192	65	1	1	NUM
ap-2097	192	66	and	and	CCONJ
ap-2097	192	67	b0	b0	NOUN
ap-2097	192	68	1	1	NUM
ap-2097	192	69	.	.	PUNCT
ap-2097	193	1	(	(	PUNCT
ap-2097	193	2	for	for	ADP
ap-2097	193	3	rigorous	rigorous	ADJ
ap-2097	193	4	mathematical	mathematical	ADJ
ap-2097	193	5	discussions	discussion	NOUN
ap-2097	193	6	we	we	PRON
ap-2097	193	7	refer	refer	VERB
ap-2097	193	8	to	to	ADP
ap-2097	193	9	the	the	DET
ap-2097	193	10	literature	literature	NOUN
ap-2097	193	11	[	[	X
ap-2097	193	12	11	11	NUM
ap-2097	193	13	,	,	PUNCT
ap-2097	193	14	12	12	NUM
ap-2097	193	15	]	]	PUNCT
ap-2097	193	16	.	.	PUNCT
ap-2097	193	17	)	)	PUNCT
ap-2097	194	1	as	as	SCONJ
ap-2097	194	2	we	we	PRON
ap-2097	194	3	will	will	AUX
ap-2097	194	4	see	see	VERB
ap-2097	194	5	below	below	ADV
ap-2097	194	6	,	,	PUNCT
ap-2097	194	7	however	however	ADV
ap-2097	194	8	,	,	PUNCT
ap-2097	194	9	a	a	DET
ap-2097	194	10	naive	naive	ADJ
ap-2097	194	11	use	use	NOUN
ap-2097	194	12	of	of	ADP
ap-2097	194	13	the	the	DET
ap-2097	194	14	“	"	PUNCT
ap-2097	194	15	ladder	ladder	NOUN
ap-2097	194	16	”	"	PUNCT
ap-2097	194	17	equations	equation	NOUN
ap-2097	194	18	(	(	PUNCT
ap-2097	194	19	28a	28a	NUM
ap-2097	194	20	)	)	PUNCT
ap-2097	194	21	and	and	CCONJ
ap-2097	194	22	(	(	PUNCT
ap-2097	194	23	28b	28b	NOUN
ap-2097	194	24	)	)	PUNCT
ap-2097	194	25	correctly	correctly	ADV
ap-2097	194	26	yields	yield	VERB
ap-2097	194	27	the	the	DET
ap-2097	194	28	retarded	retarded	ADJ
ap-2097	194	29	and	and	CCONJ
ap-2097	194	30	advanced	advanced	ADJ
ap-2097	194	31	two	two	NUM
ap-2097	194	32	-	-	PUNCT
ap-2097	194	33	point	point	NOUN
ap-2097	194	34	functions	function	NOUN
ap-2097	194	35	.	.	PUNCT
ap-2097	195	1	146	146	NUM
ap-2097	195	2	vol	vol	NOUN
ap-2097	195	3	.	.	PUNCT
ap-2097	196	1	54	54	NUM
ap-2097	196	2	no	no	NOUN
ap-2097	196	3	.	.	PUNCT
ap-2097	197	1	2/2014	2/2014	NOUN
ap-2097	197	2	a	a	DET
ap-2097	197	3	simple	simple	ADJ
ap-2097	197	4	derivation	derivation	NOUN
ap-2097	197	5	of	of	ADP
ap-2097	197	6	finite	finite	ADJ
ap-2097	197	7	-	-	ADJ
ap-2097	197	8	temperature	temperature	ADJ
ap-2097	197	9	cft	cft	NOUN
ap-2097	197	10	correlators	correlator	NOUN
ap-2097	197	11	(	(	PUNCT
ap-2097	197	12	2∆	2∆	NUM
ap-2097	197	13	−	−	NOUN
ap-2097	197	14	2)a∆(kl	2)a∆(kl	NUM
ap-2097	197	15	,	,	PUNCT
ap-2097	197	16	kr)/b∆(kl	kr)/b∆(kl	PROPN
ap-2097	197	17	,	,	PUNCT
ap-2097	197	18	kr	kr	PROPN
ap-2097	197	19	)	)	PUNCT
ap-2097	197	20	,	,	PUNCT
ap-2097	197	21	should	should	AUX
ap-2097	197	22	satisfy	satisfy	VERB
ap-2097	197	23	the	the	DET
ap-2097	197	24	following	follow	VERB
ap-2097	197	25	recurrence	recurrence	NOUN
ap-2097	197	26	relations	relation	NOUN
ap-2097	197	27	:	:	PUNCT
ap-2097	197	28	g∆(kl	g∆(kl	PROPN
ap-2097	197	29	,	,	PUNCT
ap-2097	197	30	kr	kr	PROPN
ap-2097	197	31	)	)	PUNCT
ap-2097	197	32	=	=	PUNCT
ap-2097	198	1	∆	∆	X
ap-2097	198	2	2	2	NUM
ap-2097	198	3	−	−	NUM
ap-2097	198	4	1±	1±	NUM
ap-2097	198	5	ikl	ikl	PROPN
ap-2097	198	6	−∆	−∆	PROPN
ap-2097	198	7	2	2	NUM
ap-2097	198	8	±	±	NUM
ap-2097	198	9	ikl	ikl	PROPN
ap-2097	198	10	g∆(kl	g∆(kl	NOUN
ap-2097	198	11	±	±	PROPN
ap-2097	198	12	i	i	PROPN
ap-2097	198	13	,	,	PUNCT
ap-2097	198	14	kr	kr	PROPN
ap-2097	198	15	)	)	PUNCT
ap-2097	198	16	,	,	PUNCT
ap-2097	198	17	(	(	PUNCT
ap-2097	198	18	30a	30a	NOUN
ap-2097	198	19	)	)	PUNCT
ap-2097	198	20	g∆(kl	g∆(kl	NOUN
ap-2097	198	21	,	,	PUNCT
ap-2097	198	22	kr	kr	PROPN
ap-2097	198	23	)	)	PUNCT
ap-2097	198	24	=	=	PUNCT
ap-2097	199	1	∆	∆	X
ap-2097	199	2	2	2	NUM
ap-2097	199	3	−	−	PROPN
ap-2097	199	4	1±	1±	NUM
ap-2097	199	5	ikr	ikr	NOUN
ap-2097	199	6	−∆	−∆	PROPN
ap-2097	199	7	2	2	NUM
ap-2097	199	8	±	±	NUM
ap-2097	199	9	ikr	ikr	NOUN
ap-2097	199	10	g∆(kl	g∆(kl	PROPN
ap-2097	199	11	,	,	PUNCT
ap-2097	199	12	kr	kr	PROPN
ap-2097	199	13	±	±	PROPN
ap-2097	199	14	i	i	PROPN
ap-2097	199	15	)	)	PUNCT
ap-2097	199	16	.	.	PUNCT
ap-2097	200	1	(	(	PUNCT
ap-2097	200	2	30b	30b	NOUN
ap-2097	200	3	)	)	PUNCT
ap-2097	200	4	these	these	DET
ap-2097	200	5	recurrence	recurrence	NOUN
ap-2097	200	6	relations	relation	NOUN
ap-2097	200	7	are	be	AUX
ap-2097	200	8	linear	linear	ADJ
ap-2097	200	9	such	such	ADJ
ap-2097	200	10	that	that	SCONJ
ap-2097	200	11	they	they	PRON
ap-2097	200	12	are	be	AUX
ap-2097	200	13	easily	easily	ADV
ap-2097	200	14	solved	solve	VERB
ap-2097	200	15	by	by	ADP
ap-2097	200	16	iteration	iteration	NOUN
ap-2097	200	17	.	.	PUNCT
ap-2097	201	1	but	but	CCONJ
ap-2097	201	2	how	how	SCONJ
ap-2097	201	3	should	should	AUX
ap-2097	201	4	we	we	PRON
ap-2097	201	5	identify	identify	VERB
ap-2097	201	6	the	the	DET
ap-2097	201	7	solutions	solution	NOUN
ap-2097	201	8	to	to	ADP
ap-2097	201	9	these	these	DET
ap-2097	201	10	recurrence	recurrence	NOUN
ap-2097	201	11	relations	relation	NOUN
ap-2097	201	12	with	with	ADP
ap-2097	201	13	the	the	DET
ap-2097	201	14	retarded	retarded	ADJ
ap-2097	201	15	and	and	CCONJ
ap-2097	201	16	advanced	advanced	ADJ
ap-2097	201	17	two	two	NUM
ap-2097	201	18	-	-	PUNCT
ap-2097	201	19	point	point	NOUN
ap-2097	201	20	functions	function	NOUN
ap-2097	201	21	?	?	PUNCT
ap-2097	202	1	a	a	DET
ap-2097	202	2	standard	standard	ADJ
ap-2097	202	3	prescription	prescription	NOUN
ap-2097	202	4	to	to	PART
ap-2097	202	5	get	get	VERB
ap-2097	202	6	the	the	DET
ap-2097	202	7	retarded	retarded	ADJ
ap-2097	202	8	(	(	PUNCT
ap-2097	202	9	advanced	advanced	ADJ
ap-2097	202	10	)	)	PUNCT
ap-2097	202	11	two	two	NUM
ap-2097	202	12	-	-	PUNCT
ap-2097	202	13	point	point	NOUN
ap-2097	202	14	functions	function	NOUN
ap-2097	202	15	via	via	ADP
ap-2097	202	16	ads	ad	NOUN
ap-2097	202	17	/	/	SYM
ap-2097	202	18	cft	cft	NOUN
ap-2097	202	19	is	be	AUX
ap-2097	202	20	to	to	PART
ap-2097	202	21	use	use	VERB
ap-2097	202	22	the	the	DET
ap-2097	202	23	solution	solution	NOUN
ap-2097	202	24	to	to	ADP
ap-2097	202	25	the	the	DET
ap-2097	202	26	klein	klein	PROPN
ap-2097	202	27	-	-	PUNCT
ap-2097	202	28	gordon	gordon	PROPN
ap-2097	202	29	equation	equation	NOUN
ap-2097	202	30	that	that	PRON
ap-2097	202	31	satisfies	satisfy	VERB
ap-2097	202	32	the	the	DET
ap-2097	202	33	in	in	ADV
ap-2097	202	34	-	-	PUNCT
ap-2097	202	35	falling	fall	VERB
ap-2097	202	36	(	(	PUNCT
ap-2097	202	37	out	out	ADV
ap-2097	202	38	-	-	PUNCT
ap-2097	202	39	going	go	VERB
ap-2097	202	40	)	)	PUNCT
ap-2097	202	41	boundary	boundary	ADJ
ap-2097	202	42	conditions	condition	NOUN
ap-2097	202	43	at	at	ADP
ap-2097	202	44	the	the	DET
ap-2097	202	45	horizon	horizon	NOUN
ap-2097	202	46	x	x	PUNCT
ap-2097	203	1	=	=	SYM
ap-2097	203	2	∞	∞	NUM
ap-2097	204	1	[	[	X
ap-2097	204	2	6	6	NUM
ap-2097	204	3	]	]	PUNCT
ap-2097	204	4	.	.	PUNCT
ap-2097	205	1	here	here	ADV
ap-2097	205	2	we	we	PRON
ap-2097	205	3	present	present	VERB
ap-2097	205	4	an	an	DET
ap-2097	205	5	alternative	alternative	ADJ
ap-2097	205	6	approach	approach	NOUN
ap-2097	205	7	to	to	PART
ap-2097	205	8	get	get	VERB
ap-2097	205	9	the	the	DET
ap-2097	205	10	retarded	retarded	ADJ
ap-2097	205	11	and	and	CCONJ
ap-2097	205	12	advanced	advanced	ADJ
ap-2097	205	13	twopoint	twopoint	NOUN
ap-2097	205	14	functions	function	NOUN
ap-2097	205	15	without	without	ADP
ap-2097	205	16	knowing	know	VERB
ap-2097	205	17	the	the	DET
ap-2097	205	18	boundary	boundary	ADJ
ap-2097	205	19	conditions	condition	NOUN
ap-2097	205	20	at	at	ADP
ap-2097	205	21	the	the	DET
ap-2097	205	22	horizon	horizon	NOUN
ap-2097	205	23	x	x	PUNCT
ap-2097	206	1	=	=	SYM
ap-2097	206	2	∞.	∞.	PROPN
ap-2097	206	3	a	a	DET
ap-2097	206	4	key	key	NOUN
ap-2097	206	5	is	be	AUX
ap-2097	206	6	the	the	DET
ap-2097	206	7	generic	generic	ADJ
ap-2097	206	8	causal	causal	ADJ
ap-2097	206	9	properties	property	NOUN
ap-2097	206	10	of	of	ADP
ap-2097	206	11	two	two	NUM
ap-2097	206	12	-	-	PUNCT
ap-2097	206	13	point	point	NOUN
ap-2097	206	14	functions	function	NOUN
ap-2097	206	15	:	:	PUNCT
ap-2097	206	16	the	the	DET
ap-2097	206	17	retarded	retarded	ADJ
ap-2097	206	18	two	two	NUM
ap-2097	206	19	-	-	PUNCT
ap-2097	206	20	point	point	NOUN
ap-2097	206	21	function	function	NOUN
ap-2097	206	22	has	have	AUX
ap-2097	206	23	support	support	NOUN
ap-2097	206	24	only	only	ADV
ap-2097	206	25	on	on	ADP
ap-2097	206	26	the	the	DET
ap-2097	206	27	future	future	ADJ
ap-2097	206	28	light	light	ADJ
ap-2097	206	29	-	-	PUNCT
ap-2097	206	30	cone	cone	NOUN
ap-2097	206	31	,	,	PUNCT
ap-2097	206	32	whereas	whereas	SCONJ
ap-2097	206	33	the	the	DET
ap-2097	206	34	advanced	advanced	ADJ
ap-2097	206	35	two	two	NUM
ap-2097	206	36	-	-	PUNCT
ap-2097	206	37	point	point	NOUN
ap-2097	206	38	function	function	NOUN
ap-2097	206	39	has	have	AUX
ap-2097	206	40	support	support	NOUN
ap-2097	206	41	only	only	ADV
ap-2097	206	42	on	on	ADP
ap-2097	206	43	the	the	DET
ap-2097	206	44	past	past	ADJ
ap-2097	206	45	light	light	NOUN
ap-2097	206	46	-	-	PUNCT
ap-2097	206	47	cone	cone	NOUN
ap-2097	206	48	.	.	PUNCT
ap-2097	207	1	let	let	VERB
ap-2097	207	2	us	we	PRON
ap-2097	207	3	first	first	ADJ
ap-2097	207	4	focus	focus	VERB
ap-2097	207	5	on	on	ADP
ap-2097	207	6	the	the	DET
ap-2097	207	7	case	case	NOUN
ap-2097	207	8	where	where	SCONJ
ap-2097	207	9	the	the	DET
ap-2097	207	10	point	point	NOUN
ap-2097	207	11	(	(	PUNCT
ap-2097	207	12	τ	τ	PROPN
ap-2097	207	13	,	,	PUNCT
ap-2097	207	14	θ	θ	PROPN
ap-2097	207	15	)	)	PUNCT
ap-2097	207	16	on	on	ADP
ap-2097	207	17	the	the	DET
ap-2097	207	18	ads3	ads3	ADJ
ap-2097	207	19	boundary	boundary	NOUN
ap-2097	207	20	(	(	PUNCT
ap-2097	207	21	∂ads3	∂ads3	NOUN
ap-2097	207	22	)	)	PUNCT
ap-2097	207	23	lies	lie	VERB
ap-2097	207	24	inside	inside	ADP
ap-2097	207	25	the	the	DET
ap-2097	207	26	future	future	ADJ
ap-2097	207	27	light	light	NOUN
ap-2097	207	28	-	-	PUNCT
ap-2097	207	29	cone	cone	NOUN
ap-2097	207	30	xl	xl	PROPN
ap-2097	208	1	=	=	PUNCT
ap-2097	208	2	τ	τ	PROPN
ap-2097	209	1	+	+	NUM
ap-2097	209	2	θ	θ	PROPN
ap-2097	209	3	>	>	PUNCT
ap-2097	209	4	0	0	PUNCT
ap-2097	210	1	and	and	CCONJ
ap-2097	210	2	xr	xr	PROPN
ap-2097	210	3	=	=	SYM
ap-2097	211	1	τ	τ	PROPN
ap-2097	211	2	−	−	PROPN
ap-2097	211	3	θ	θ	X
ap-2097	211	4	>	>	X
ap-2097	211	5	0	0	X
ap-2097	211	6	.	.	PUNCT
ap-2097	212	1	in	in	ADP
ap-2097	212	2	this	this	DET
ap-2097	212	3	case	case	NOUN
ap-2097	212	4	the	the	DET
ap-2097	212	5	state	state	NOUN
ap-2097	212	6	(	(	PUNCT
ap-2097	212	7	a0	a0	PROPN
ap-2097	212	8	−)n(b0	−)n(b0	NUM
ap-2097	212	9	−)mφ0	−)mφ0	NOUN
ap-2097	212	10	∆,kl	∆,kl	NOUN
ap-2097	212	11	,	,	PUNCT
ap-2097	212	12	kr	kr	PROPN
ap-2097	212	13	∝	∝	PROPN
ap-2097	212	14	e−i(kl−in)xle−i(kr−im)xr	e−i(kl−in)xle−i(kr−im)xr	PROPN
ap-2097	212	15	converges	converge	VERB
ap-2097	212	16	as	as	ADP
ap-2097	212	17	n	n	NOUN
ap-2097	212	18	,	,	PUNCT
ap-2097	212	19	m	m	VERB
ap-2097	212	20	→	→	SYM
ap-2097	212	21	∞	∞	NUM
ap-2097	212	22	such	such	ADJ
ap-2097	212	23	that	that	SCONJ
ap-2097	212	24	(	(	PUNCT
ap-2097	212	25	a0	a0	PROPN
ap-2097	212	26	−)n(b0	−)n(b0	NUM
ap-2097	212	27	−)mφ0	−)mφ0	NOUN
ap-2097	212	28	∆,kl	∆,kl	NOUN
ap-2097	212	29	,	,	PUNCT
ap-2097	212	30	kr	kr	PROPN
ap-2097	212	31	would	would	AUX
ap-2097	212	32	be	be	AUX
ap-2097	212	33	well	well	ADV
ap-2097	212	34	-	-	PUNCT
ap-2097	212	35	defined	define	VERB
ap-2097	212	36	.	.	PUNCT
ap-2097	213	1	hence	hence	ADV
ap-2097	213	2	it	it	PRON
ap-2097	213	3	would	would	AUX
ap-2097	213	4	be	be	AUX
ap-2097	213	5	natural	natural	ADJ
ap-2097	213	6	to	to	PART
ap-2097	213	7	expect	expect	VERB
ap-2097	213	8	that	that	SCONJ
ap-2097	213	9	the	the	DET
ap-2097	213	10	ladder	ladder	NOUN
ap-2097	213	11	equations	equation	NOUN
ap-2097	213	12	a0	a0	PROPN
ap-2097	213	13	−φ	−φ	NOUN
ap-2097	213	14	0	0	NUM
ap-2097	213	15	∆,kl	∆,kl	NOUN
ap-2097	213	16	,	,	PUNCT
ap-2097	213	17	kr	kr	PROPN
ap-2097	213	18	∝	∝	PROPN
ap-2097	213	19	φ0	φ0	PROPN
ap-2097	213	20	∆,kl−i	∆,kl−i	NOUN
ap-2097	213	21	,	,	PUNCT
ap-2097	213	22	kr	kr	PROPN
ap-2097	213	23	and	and	CCONJ
ap-2097	213	24	b0	b0	VERB
ap-2097	213	25	−φ	−φ	NOUN
ap-2097	213	26	0	0	NUM
ap-2097	213	27	∆,kl	∆,kl	NOUN
ap-2097	213	28	,	,	PUNCT
ap-2097	213	29	kr	kr	PROPN
ap-2097	213	30	∝	∝	PROPN
ap-2097	213	31	φ	φ	X
ap-2097	213	32	0	0	NUM
ap-2097	213	33	∆,kl	∆,kl	NOUN
ap-2097	213	34	,	,	PUNCT
ap-2097	213	35	kr−i	kr−i	PROPN
ap-2097	213	36	would	would	AUX
ap-2097	213	37	lead	lead	VERB
ap-2097	213	38	to	to	ADP
ap-2097	213	39	the	the	DET
ap-2097	213	40	retarded	retarded	ADJ
ap-2097	213	41	two	two	NUM
ap-2097	213	42	-	-	PUNCT
ap-2097	213	43	point	point	NOUN
ap-2097	213	44	function	function	NOUN
ap-2097	213	45	.	.	PUNCT
ap-2097	214	1	indeed	indeed	ADV
ap-2097	214	2	,	,	PUNCT
ap-2097	214	3	iterative	iterative	NOUN
ap-2097	214	4	use	use	NOUN
ap-2097	214	5	of	of	ADP
ap-2097	214	6	the	the	DET
ap-2097	214	7	relations	relation	NOUN
ap-2097	214	8	g∆(kl	g∆(kl	VERB
ap-2097	214	9	,	,	PUNCT
ap-2097	214	10	kr	kr	PROPN
ap-2097	214	11	)	)	PUNCT
ap-2097	214	12	=	=	PUNCT
ap-2097	215	1	∆	∆	X
ap-2097	215	2	2	2	NUM
ap-2097	216	1	−1−ikl	−1−ikl	PROPN
ap-2097	216	2	−∆	−∆	NOUN
ap-2097	216	3	2	2	NUM
ap-2097	216	4	−ikl	−ikl	NOUN
ap-2097	216	5	g∆(kl	g∆(kl	VERB
ap-2097	216	6	−	−	PROPN
ap-2097	217	1	i	i	PROPN
ap-2097	217	2	,	,	PUNCT
ap-2097	217	3	kr	kr	PROPN
ap-2097	217	4	)	)	PUNCT
ap-2097	217	5	and	and	CCONJ
ap-2097	217	6	g∆(kl	g∆(kl	NOUN
ap-2097	217	7	,	,	PUNCT
ap-2097	217	8	kr	kr	PROPN
ap-2097	217	9	)	)	PUNCT
ap-2097	217	10	=	=	PUNCT
ap-2097	218	1	∆	∆	X
ap-2097	218	2	2	2	NUM
ap-2097	218	3	−1−ikr	−1−ikr	PROPN
ap-2097	218	4	−∆	−∆	ADP
ap-2097	218	5	2	2	NUM
ap-2097	218	6	−ikr	−ikr	NOUN
ap-2097	218	7	g∆(kl	g∆(kl	VERB
ap-2097	218	8	,	,	PUNCT
ap-2097	218	9	kr	kr	PROPN
ap-2097	218	10	−	−	PROPN
ap-2097	218	11	i	i	PROPN
ap-2097	218	12	)	)	PUNCT
ap-2097	218	13	gives	give	VERB
ap-2097	218	14	gr∆(kl	gr∆(kl	PROPN
ap-2097	218	15	,	,	PUNCT
ap-2097	218	16	kr	kr	PROPN
ap-2097	218	17	)	)	PUNCT
ap-2097	218	18	=	=	SYM
ap-2097	219	1	γ(∆	γ(∆	NUM
ap-2097	219	2	2	2	NUM
ap-2097	219	3	−	−	NUM
ap-2097	219	4	ikl	ikl	PROPN
ap-2097	219	5	)	)	PUNCT
ap-2097	219	6	γ(1−	γ(1−	NOUN
ap-2097	220	1	∆	∆	PROPN
ap-2097	220	2	2	2	NUM
ap-2097	220	3	−	−	NUM
ap-2097	220	4	ikl	ikl	PROPN
ap-2097	220	5	)	)	PUNCT
ap-2097	220	6	×	×	NOUN
ap-2097	220	7	γ(∆	γ(∆	NUM
ap-2097	220	8	2	2	NUM
ap-2097	220	9	−	−	PROPN
ap-2097	220	10	ikr	ikr	PROPN
ap-2097	220	11	)	)	PUNCT
ap-2097	220	12	γ(1−	γ(1−	PROPN
ap-2097	221	1	∆	∆	PROPN
ap-2097	221	2	2	2	NUM
ap-2097	221	3	−	−	PROPN
ap-2097	221	4	ikr	ikr	PROPN
ap-2097	221	5	)	)	PUNCT
ap-2097	221	6	gr(∆	gr(∆	NOUN
ap-2097	221	7	)	)	PUNCT
ap-2097	221	8	,	,	PUNCT
ap-2097	221	9	(	(	PUNCT
ap-2097	221	10	31	31	NUM
ap-2097	221	11	)	)	PUNCT
ap-2097	221	12	where	where	SCONJ
ap-2097	221	13	gr(∆	gr(∆	NOUN
ap-2097	221	14	)	)	PUNCT
ap-2097	221	15	is	be	AUX
ap-2097	221	16	a	a	DET
ap-2097	221	17	normalization	normalization	NOUN
ap-2097	221	18	factor	factor	NOUN
ap-2097	221	19	given	give	VERB
ap-2097	221	20	by	by	ADP
ap-2097	221	21	gr(∆	gr(∆	NOUN
ap-2097	221	22	)	)	PUNCT
ap-2097	221	23	=	=	SYM
ap-2097	221	24	limn	limn	NOUN
ap-2097	221	25	,	,	PUNCT
ap-2097	221	26	m→∞gr∆(kl	m→∞gr∆(kl	PROPN
ap-2097	221	27	−	−	PROPN
ap-2097	221	28	in	in	ADV
ap-2097	221	29	,	,	PUNCT
ap-2097	221	30	kr	kr	PROPN
ap-2097	221	31	−	−	PROPN
ap-2097	221	32	i	i	PRON
ap-2097	221	33	m	m	PROPN
ap-2097	221	34	)	)	PUNCT
ap-2097	221	35	.	.	PUNCT
ap-2097	222	1	this	this	PRON
ap-2097	222	2	is	be	AUX
ap-2097	222	3	the	the	DET
ap-2097	222	4	retarded	retarded	ADJ
ap-2097	222	5	two	two	NUM
ap-2097	222	6	-	-	PUNCT
ap-2097	222	7	point	point	NOUN
ap-2097	222	8	function	function	NOUN
ap-2097	222	9	with	with	ADP
ap-2097	222	10	the	the	DET
ap-2097	222	11	desired	desire	VERB
ap-2097	222	12	analytic	analytic	ADJ
ap-2097	222	13	structure	structure	NOUN
ap-2097	222	14	:	:	PUNCT
ap-2097	222	15	gr∆(kl	gr∆(kl	PROPN
ap-2097	222	16	,	,	PUNCT
ap-2097	222	17	kr	kr	PROPN
ap-2097	222	18	)	)	PUNCT
ap-2097	222	19	is	be	AUX
ap-2097	222	20	analytic	analytic	ADJ
ap-2097	222	21	in	in	ADP
ap-2097	222	22	the	the	DET
ap-2097	222	23	upper	upper	ADJ
ap-2097	222	24	-	-	PUNCT
ap-2097	222	25	half	half	NOUN
ap-2097	222	26	complex	complex	ADJ
ap-2097	222	27	kland	kland	NOUN
ap-2097	222	28	kr	kr	NOUN
ap-2097	222	29	-	-	PUNCT
ap-2097	222	30	planes	plane	NOUN
ap-2097	222	31	and	and	CCONJ
ap-2097	222	32	has	have	VERB
ap-2097	222	33	simple	simple	ADJ
ap-2097	222	34	poles	pole	NOUN
ap-2097	222	35	at	at	ADP
ap-2097	222	36	kl	kl	PROPN
ap-2097	223	1	=	=	SYM
ap-2097	223	2	−i2πt	−i2πt	NUM
ap-2097	223	3	(	(	PUNCT
ap-2097	223	4	∆	∆	X
ap-2097	223	5	2	2	NUM
ap-2097	223	6	+	+	NUM
ap-2097	223	7	n	n	CCONJ
ap-2097	223	8	)	)	PUNCT
ap-2097	223	9	and	and	CCONJ
ap-2097	223	10	kr	kr	PROPN
ap-2097	223	11	=	=	SYM
ap-2097	223	12	−i2πt	−i2πt	NUM
ap-2097	223	13	(	(	PUNCT
ap-2097	223	14	∆	∆	PROPN
ap-2097	223	15	2	2	NUM
ap-2097	223	16	+	+	NOUN
ap-2097	223	17	m	m	X
ap-2097	223	18	)	)	PUNCT
ap-2097	223	19	(	(	PUNCT
ap-2097	223	20	n	n	X
ap-2097	223	21	,	,	PUNCT
ap-2097	223	22	m	m	NOUN
ap-2097	223	23	∈	∈	NOUN
ap-2097	223	24	z≥0	z≥0	NOUN
ap-2097	223	25	)	)	PUNCT
ap-2097	223	26	on	on	ADP
ap-2097	223	27	the	the	DET
ap-2097	223	28	lowerhalf	lowerhalf	PROPN
ap-2097	223	29	complex	complex	PROPN
ap-2097	223	30	kland	kland	PROPN
ap-2097	223	31	kr	kr	PROPN
ap-2097	223	32	-	-	PUNCT
ap-2097	223	33	planes	plane	NOUN
ap-2097	223	34	,	,	PUNCT
ap-2097	223	35	where	where	SCONJ
ap-2097	223	36	t	t	NOUN
ap-2097	223	37	=	=	SYM
ap-2097	223	38	1	1	NUM
ap-2097	223	39	2π	2π	NOUN
ap-2097	223	40	(=	(=	NOUN
ap-2097	223	41	1	1	NUM
ap-2097	223	42	2πr	2πr	NOUN
ap-2097	223	43	)	)	PUNCT
ap-2097	223	44	is	be	AUX
ap-2097	223	45	the	the	DET
ap-2097	223	46	hawking	hawk	VERB
ap-2097	223	47	temperature	temperature	NOUN
ap-2097	223	48	with	with	ADP
ap-2097	223	49	respect	respect	NOUN
ap-2097	223	50	to	to	ADP
ap-2097	223	51	time	time	NOUN
ap-2097	223	52	τ	τ	PROPN
ap-2097	223	53	.	.	PUNCT
ap-2097	224	1	let	let	VERB
ap-2097	224	2	us	we	PRON
ap-2097	224	3	next	next	ADV
ap-2097	224	4	derive	derive	VERB
ap-2097	224	5	the	the	DET
ap-2097	224	6	retarded	retarded	ADJ
ap-2097	224	7	two	two	NUM
ap-2097	224	8	-	-	PUNCT
ap-2097	224	9	point	point	NOUN
ap-2097	224	10	function	function	NOUN
ap-2097	224	11	of	of	ADP
ap-2097	224	12	cft2	cft2	NOUN
ap-2097	224	13	dual	dual	ADJ
ap-2097	224	14	to	to	ADP
ap-2097	224	15	the	the	DET
ap-2097	224	16	rotating	rotate	VERB
ap-2097	224	17	btz	btz	NOUN
ap-2097	224	18	black	black	ADJ
ap-2097	224	19	hole	hole	NOUN
ap-2097	224	20	(	(	PUNCT
ap-2097	224	21	4	4	NUM
ap-2097	224	22	)	)	PUNCT
ap-2097	224	23	.	.	PUNCT
ap-2097	225	1	to	to	ADP
ap-2097	225	2	this	this	DET
ap-2097	225	3	end	end	NOUN
ap-2097	225	4	,	,	PUNCT
ap-2097	225	5	let	let	VERB
ap-2097	225	6	pl	pl	NOUN
ap-2097	225	7	and	and	CCONJ
ap-2097	225	8	pr	pr	NOUN
ap-2097	225	9	be	be	AUX
ap-2097	225	10	momenta	momenta	ADJ
ap-2097	225	11	conjugate	conjugate	ADJ
ap-2097	225	12	to	to	ADP
ap-2097	225	13	the	the	DET
ap-2097	225	14	btz	btz	NOUN
ap-2097	225	15	light	light	ADJ
ap-2097	225	16	-	-	PUNCT
ap-2097	225	17	cone	cone	NOUN
ap-2097	225	18	coordinates	coordinate	NOUN
ap-2097	225	19	t±	t±	ADP
ap-2097	225	20	φ	φ	PROPN
ap-2097	225	21	.	.	PUNCT
ap-2097	226	1	since	since	SCONJ
ap-2097	226	2	τ	τ	PROPN
ap-2097	226	3	±	±	NUM
ap-2097	226	4	θ	θ	NOUN
ap-2097	226	5	and	and	CCONJ
ap-2097	226	6	t±	t±	PROPN
ap-2097	226	7	φ	φ	NUM
ap-2097	226	8	are	be	AUX
ap-2097	226	9	related	relate	VERB
ap-2097	226	10	as	as	ADP
ap-2097	226	11	τ	τ	PROPN
ap-2097	226	12	±	±	NUM
ap-2097	226	13	θ	θ	NOUN
ap-2097	226	14	=	=	PUNCT
ap-2097	226	15	(	(	PUNCT
ap-2097	226	16	r+	r+	X
ap-2097	226	17	∓	∓	PROPN
ap-2097	226	18	r−)(t±	r−)(t±	PROPN
ap-2097	226	19	φ	φ	NUM
ap-2097	226	20	)	)	PUNCT
ap-2097	226	21	,	,	PUNCT
ap-2097	226	22	we	we	PRON
ap-2097	226	23	have	have	VERB
ap-2097	226	24	kl	kl	NOUN
ap-2097	226	25	=	=	NOUN
ap-2097	226	26	1	1	NUM
ap-2097	226	27	r+−r−	r+−r−	X
ap-2097	226	28	pl	pl	PROPN
ap-2097	226	29	and	and	CCONJ
ap-2097	226	30	kr	kr	PROPN
ap-2097	226	31	=	=	SYM
ap-2097	226	32	1	1	NUM
ap-2097	226	33	r++r−	r++r−	NUM
ap-2097	226	34	pr	pr	NOUN
ap-2097	226	35	,	,	PUNCT
ap-2097	226	36	from	from	ADP
ap-2097	226	37	which	which	PRON
ap-2097	226	38	we	we	PRON
ap-2097	226	39	get	get	VERB
ap-2097	226	40	gr∆(pl	gr∆(pl	NOUN
ap-2097	226	41	,	,	PUNCT
ap-2097	226	42	pr	pr	NOUN
ap-2097	226	43	)	)	PUNCT
ap-2097	226	44	=	=	SYM
ap-2097	226	45	γ(hl	γ(hl	NOUN
ap-2097	226	46	−	−	PROPN
ap-2097	226	47	ipl	ipl	PROPN
ap-2097	226	48	2πtl	2πtl	PROPN
ap-2097	226	49	)	)	PUNCT
ap-2097	226	50	γ(h̄l	γ(h̄l	X
ap-2097	227	1	−	−	PROPN
ap-2097	227	2	ipl	ipl	PROPN
ap-2097	227	3	2πtl	2πtl	NUM
ap-2097	227	4	)	)	PUNCT
ap-2097	227	5	γ(hr	γ(hr	PROPN
ap-2097	227	6	−	−	PROPN
ap-2097	227	7	ipr	ipr	PROPN
ap-2097	227	8	2πtr	2πtr	PROPN
ap-2097	227	9	)	)	PUNCT
ap-2097	228	1	γ(h̄r	γ(h̄r	NOUN
ap-2097	228	2	−	−	PROPN
ap-2097	228	3	ipr	ipr	PROPN
ap-2097	228	4	2πtr	2πtr	PROPN
ap-2097	228	5	)	)	PUNCT
ap-2097	228	6	gr(∆	gr(∆	NOUN
ap-2097	228	7	)	)	PUNCT
ap-2097	228	8	,	,	PUNCT
ap-2097	228	9	(	(	PUNCT
ap-2097	228	10	32	32	NUM
ap-2097	228	11	)	)	PUNCT
ap-2097	228	12	where	where	SCONJ
ap-2097	228	13	tl	tl	PROPN
ap-2097	228	14	and	and	CCONJ
ap-2097	228	15	tr	tr	PRON
ap-2097	228	16	are	be	AUX
ap-2097	228	17	the	the	DET
ap-2097	228	18	hawking	hawk	VERB
ap-2097	228	19	temperature	temperature	NOUN
ap-2097	228	20	for	for	ADP
ap-2097	228	21	leftand	leftand	NOUN
ap-2097	228	22	right	right	ADV
ap-2097	228	23	-	-	PUNCT
ap-2097	228	24	moving	move	VERB
ap-2097	228	25	sectors	sector	NOUN
ap-2097	228	26	with	with	ADP
ap-2097	228	27	respect	respect	NOUN
ap-2097	228	28	to	to	ADP
ap-2097	228	29	the	the	DET
ap-2097	228	30	btz	btz	PROPN
ap-2097	228	31	time	time	PROPN
ap-2097	228	32	t	t	PROPN
ap-2097	228	33	and	and	CCONJ
ap-2097	228	34	given	give	VERB
ap-2097	228	35	by	by	ADP
ap-2097	228	36	tl	tl	PROPN
ap-2097	228	37	=	=	PUNCT
ap-2097	228	38	r+	r+	PUNCT
ap-2097	228	39	−	−	PROPN
ap-2097	228	40	r−	r−	VERB
ap-2097	228	41	2π	2π	NOUN
ap-2097	228	42	and	and	CCONJ
ap-2097	228	43	tr	tr	VERB
ap-2097	228	44	=	=	X
ap-2097	228	45	r+	r+	NOUN
ap-2097	228	46	+	+	CCONJ
ap-2097	228	47	r−	r−	NOUN
ap-2097	228	48	2π	2π	NOUN
ap-2097	228	49	.	.	PUNCT
ap-2097	229	1	(	(	PUNCT
ap-2097	229	2	33	33	NUM
ap-2097	229	3	)	)	PUNCT
ap-2097	229	4	hl	hl	NOUN
ap-2097	229	5	and	and	CCONJ
ap-2097	229	6	hr	hr	NOUN
ap-2097	229	7	are	be	AUX
ap-2097	229	8	conformal	conformal	ADJ
ap-2097	229	9	weights	weight	NOUN
ap-2097	229	10	for	for	ADP
ap-2097	229	11	a	a	DET
ap-2097	229	12	scalar	scalar	ADJ
ap-2097	229	13	operator	operator	NOUN
ap-2097	229	14	of	of	ADP
ap-2097	229	15	dual	dual	ADJ
ap-2097	229	16	cft2	cft2	NOUN
ap-2097	229	17	given	give	VERB
ap-2097	229	18	by	by	ADP
ap-2097	229	19	hl	hl	NOUN
ap-2097	229	20	=	=	NOUN
ap-2097	229	21	hr	hr	NOUN
ap-2097	229	22	=	=	PUNCT
ap-2097	229	23	∆	∆	X
ap-2097	229	24	2	2	NUM
ap-2097	229	25	with	with	ADP
ap-2097	229	26	h̄l	h̄l	NOUN
ap-2097	229	27	=	=	SYM
ap-2097	229	28	h̄r	h̄r	PROPN
ap-2097	229	29	=	=	SYM
ap-2097	229	30	1−	1−	NUM
ap-2097	229	31	∆	∆	X
ap-2097	229	32	2	2	NUM
ap-2097	229	33	.	.	PUNCT
ap-2097	230	1	(	(	PUNCT
ap-2097	230	2	34	34	NUM
ap-2097	230	3	)	)	PUNCT
ap-2097	230	4	note	note	VERB
ap-2097	230	5	that	that	SCONJ
ap-2097	230	6	eq	eq	ADP
ap-2097	230	7	.	.	PUNCT
ap-2097	231	1	(	(	PUNCT
ap-2097	231	2	32	32	NUM
ap-2097	231	3	)	)	PUNCT
ap-2097	231	4	precisely	precisely	ADV
ap-2097	231	5	coincides	coincide	VERB
ap-2097	231	6	with	with	ADP
ap-2097	231	7	the	the	DET
ap-2097	231	8	known	know	VERB
ap-2097	231	9	results	result	NOUN
ap-2097	231	10	[	[	X
ap-2097	231	11	8	8	NUM
ap-2097	231	12	]	]	PUNCT
ap-2097	231	13	(	(	PUNCT
ap-2097	231	14	see	see	VERB
ap-2097	231	15	also	also	ADV
ap-2097	231	16	[	[	X
ap-2097	231	17	5	5	NUM
ap-2097	231	18	,	,	PUNCT
ap-2097	231	19	9	9	NUM
ap-2097	231	20	]	]	PUNCT
ap-2097	231	21	for	for	ADP
ap-2097	231	22	the	the	DET
ap-2097	231	23	case	case	NOUN
ap-2097	231	24	of	of	ADP
ap-2097	231	25	fermionic	fermionic	NOUN
ap-2097	231	26	operators	operator	NOUN
ap-2097	231	27	.	.	PUNCT
ap-2097	231	28	)	)	PUNCT
ap-2097	232	1	let	let	VERB
ap-2097	232	2	us	we	PRON
ap-2097	232	3	next	next	ADJ
ap-2097	232	4	move	move	NOUN
ap-2097	232	5	on	on	ADP
ap-2097	232	6	to	to	ADP
ap-2097	232	7	the	the	DET
ap-2097	232	8	case	case	NOUN
ap-2097	232	9	where	where	SCONJ
ap-2097	232	10	the	the	DET
ap-2097	232	11	point	point	NOUN
ap-2097	232	12	(	(	PUNCT
ap-2097	232	13	τ	τ	PROPN
ap-2097	232	14	,	,	PUNCT
ap-2097	232	15	θ	θ	NOUN
ap-2097	232	16	)	)	PUNCT
ap-2097	232	17	∈	∈	PROPN
ap-2097	232	18	∂ads3	∂ads3	PROPN
ap-2097	232	19	lies	lie	VERB
ap-2097	232	20	inside	inside	ADP
ap-2097	232	21	the	the	DET
ap-2097	232	22	past	past	ADJ
ap-2097	233	1	lightcone	lightcone	PROPN
ap-2097	233	2	xl	xl	PROPN
ap-2097	233	3	=	=	SYM
ap-2097	233	4	τ	τ	PROPN
ap-2097	234	1	+	+	NUM
ap-2097	234	2	θ	θ	X
ap-2097	234	3	<	<	X
ap-2097	234	4	0	0	NUM
ap-2097	234	5	and	and	CCONJ
ap-2097	234	6	xr	xr	PROPN
ap-2097	235	1	=	=	SYM
ap-2097	235	2	τ	τ	PROPN
ap-2097	235	3	−	−	PROPN
ap-2097	235	4	θ	θ	X
ap-2097	235	5	<	<	X
ap-2097	235	6	0	0	NUM
ap-2097	235	7	.	.	PUNCT
ap-2097	236	1	in	in	ADP
ap-2097	236	2	this	this	DET
ap-2097	236	3	case	case	NOUN
ap-2097	236	4	the	the	DET
ap-2097	236	5	state	state	NOUN
ap-2097	236	6	(	(	PUNCT
ap-2097	236	7	a0	a0	NOUN
ap-2097	236	8	+	+	NOUN
ap-2097	236	9	)	)	PUNCT
ap-2097	236	10	n(b0	n(b0	ADJ
ap-2097	236	11	+	+	X
ap-2097	236	12	)	)	PUNCT
ap-2097	236	13	mφ0	mφ0	NOUN
ap-2097	236	14	∆,kl	∆,kl	NOUN
ap-2097	236	15	,	,	PUNCT
ap-2097	236	16	kr	kr	PROPN
ap-2097	236	17	∝	∝	PROPN
ap-2097	236	18	e−i(kl+in)xle−i(kr+im)xr	e−i(kl+in)xle−i(kr+im)xr	PROPN
ap-2097	236	19	converges	converge	VERB
ap-2097	236	20	as	as	ADP
ap-2097	236	21	n	n	NUM
ap-2097	236	22	,	,	PUNCT
ap-2097	236	23	m→∞	m→∞	NOUN
ap-2097	236	24	such	such	ADJ
ap-2097	236	25	that	that	SCONJ
ap-2097	236	26	(	(	PUNCT
ap-2097	236	27	a0	a0	NOUN
ap-2097	236	28	+	+	NOUN
ap-2097	236	29	)	)	PUNCT
ap-2097	236	30	n(b0	n(b0	ADJ
ap-2097	236	31	+	+	X
ap-2097	236	32	)	)	PUNCT
ap-2097	236	33	mφ0	mφ0	NOUN
ap-2097	236	34	∆,kl	∆,kl	NOUN
ap-2097	236	35	,	,	PUNCT
ap-2097	236	36	kr	kr	PROPN
ap-2097	236	37	would	would	AUX
ap-2097	236	38	be	be	AUX
ap-2097	236	39	well	well	ADV
ap-2097	236	40	-	-	PUNCT
ap-2097	236	41	defined	define	VERB
ap-2097	236	42	.	.	PUNCT
ap-2097	237	1	iterative	iterative	NOUN
ap-2097	237	2	use	use	NOUN
ap-2097	237	3	of	of	ADP
ap-2097	237	4	the	the	DET
ap-2097	237	5	relations	relation	NOUN
ap-2097	237	6	g∆(kl	g∆(kl	VERB
ap-2097	237	7	,	,	PUNCT
ap-2097	237	8	kr	kr	PROPN
ap-2097	237	9	)	)	PUNCT
ap-2097	237	10	=	=	PUNCT
ap-2097	238	1	∆	∆	X
ap-2097	238	2	2	2	NUM
ap-2097	238	3	−	−	NOUN
ap-2097	238	4	1	1	NUM
ap-2097	238	5	+	+	CCONJ
ap-2097	238	6	ikl	ikl	PROPN
ap-2097	238	7	−∆	−∆	NOUN
ap-2097	238	8	2	2	NUM
ap-2097	238	9	+	+	CCONJ
ap-2097	238	10	ikl	ikl	X
ap-2097	238	11	g∆(kl	g∆(kl	NOUN
ap-2097	238	12	+	+	CCONJ
ap-2097	238	13	i	i	PROPN
ap-2097	238	14	,	,	PUNCT
ap-2097	238	15	kr	kr	PROPN
ap-2097	238	16	)	)	PUNCT
ap-2097	238	17	,	,	PUNCT
ap-2097	238	18	(	(	PUNCT
ap-2097	238	19	35a	35a	NOUN
ap-2097	238	20	)	)	PUNCT
ap-2097	238	21	g∆(kl	g∆(kl	NOUN
ap-2097	238	22	,	,	PUNCT
ap-2097	238	23	kr	kr	PROPN
ap-2097	238	24	)	)	PUNCT
ap-2097	238	25	=	=	PUNCT
ap-2097	239	1	∆	∆	X
ap-2097	239	2	2	2	NUM
ap-2097	239	3	−	−	NOUN
ap-2097	239	4	1	1	NUM
ap-2097	239	5	+	+	NUM
ap-2097	239	6	ikr	ikr	INTJ
ap-2097	239	7	−∆	−∆	NOUN
ap-2097	239	8	2	2	NUM
ap-2097	239	9	+	+	CCONJ
ap-2097	239	10	ikr	ikr	INTJ
ap-2097	239	11	g∆(kl	g∆(kl	NOUN
ap-2097	239	12	,	,	PUNCT
ap-2097	239	13	kr	kr	PROPN
ap-2097	239	14	+	+	PROPN
ap-2097	239	15	i	i	PROPN
ap-2097	239	16	)	)	PUNCT
ap-2097	239	17	,	,	PUNCT
ap-2097	239	18	(	(	PUNCT
ap-2097	239	19	35b	35b	NOUN
ap-2097	239	20	)	)	PUNCT
ap-2097	239	21	then	then	ADV
ap-2097	239	22	gives	give	VERB
ap-2097	239	23	the	the	DET
ap-2097	239	24	advanced	advanced	ADJ
ap-2097	239	25	two	two	NUM
ap-2097	239	26	-	-	PUNCT
ap-2097	239	27	point	point	NOUN
ap-2097	239	28	function	function	NOUN
ap-2097	239	29	ga∆(pl	ga∆(pl	NOUN
ap-2097	239	30	,	,	PUNCT
ap-2097	239	31	pr	pr	NOUN
ap-2097	239	32	)	)	PUNCT
ap-2097	239	33	=	=	SYM
ap-2097	239	34	γ(hl	γ(hl	NOUN
ap-2097	239	35	+	+	NUM
ap-2097	239	36	ipl	ipl	PROPN
ap-2097	239	37	2πtl	2πtl	NUM
ap-2097	239	38	)	)	PUNCT
ap-2097	239	39	γ(h̄l	γ(h̄l	PROPN
ap-2097	240	1	+	+	NUM
ap-2097	240	2	ipl	ipl	PROPN
ap-2097	240	3	2πtl	2πtl	NUM
ap-2097	240	4	)	)	PUNCT
ap-2097	240	5	γ(hr	γ(hr	PROPN
ap-2097	240	6	+	+	CCONJ
ap-2097	240	7	ipr	ipr	PROPN
ap-2097	240	8	2πtr	2πtr	PROPN
ap-2097	240	9	)	)	PUNCT
ap-2097	240	10	γ(h̄r	γ(h̄r	NOUN
ap-2097	241	1	+	+	CCONJ
ap-2097	241	2	ipr	ipr	PROPN
ap-2097	241	3	2πtr	2πtr	PROPN
ap-2097	241	4	)	)	PUNCT
ap-2097	241	5	ga(∆	ga(∆	PROPN
ap-2097	241	6	)	)	PUNCT
ap-2097	241	7	,	,	PUNCT
ap-2097	241	8	(	(	PUNCT
ap-2097	241	9	36	36	NUM
ap-2097	241	10	)	)	PUNCT
ap-2097	241	11	where	where	SCONJ
ap-2097	241	12	ga(∆	ga(∆	NOUN
ap-2097	241	13	)	)	PUNCT
ap-2097	241	14	=	=	SYM
ap-2097	241	15	limn	limn	NOUN
ap-2097	241	16	,	,	PUNCT
ap-2097	241	17	m→∞ga∆(pl	m→∞ga∆(pl	PROPN
ap-2097	241	18	+	+	CCONJ
ap-2097	241	19	in	in	ADV
ap-2097	241	20	,	,	PUNCT
ap-2097	241	21	pr	pr	X
ap-2097	241	22	+	+	CCONJ
ap-2097	241	23	i	i	NOUN
ap-2097	241	24	m	m	PROPN
ap-2097	241	25	)	)	PUNCT
ap-2097	241	26	.	.	PUNCT
ap-2097	242	1	we	we	PRON
ap-2097	242	2	note	note	VERB
ap-2097	242	3	that	that	SCONJ
ap-2097	242	4	,	,	PUNCT
ap-2097	242	5	since	since	SCONJ
ap-2097	242	6	in	in	ADP
ap-2097	242	7	general	general	ADJ
ap-2097	242	8	the	the	DET
ap-2097	242	9	retarded	retarded	ADJ
ap-2097	242	10	and	and	CCONJ
ap-2097	242	11	advanced	advanced	ADJ
ap-2097	242	12	two	two	NUM
ap-2097	242	13	-	-	PUNCT
ap-2097	242	14	point	point	NOUN
ap-2097	242	15	functions	function	NOUN
ap-2097	242	16	are	be	AUX
ap-2097	242	17	related	relate	VERB
ap-2097	242	18	by	by	ADP
ap-2097	242	19	complex	complex	ADJ
ap-2097	242	20	conjugate	conjugate	ADJ
ap-2097	242	21	ga∆(pl	ga∆(pl	NOUN
ap-2097	242	22	,	,	PUNCT
ap-2097	242	23	pr	pr	NOUN
ap-2097	242	24	)	)	PUNCT
ap-2097	242	25	=	=	PUNCT
ap-2097	243	1	[	[	X
ap-2097	243	2	gr∆(pl	gr∆(pl	NOUN
ap-2097	243	3	,	,	PUNCT
ap-2097	243	4	pr)]∗	pr)]∗	PROPN
ap-2097	243	5	,	,	PUNCT
ap-2097	243	6	the	the	DET
ap-2097	243	7	normalization	normalization	NOUN
ap-2097	243	8	constants	constant	NOUN
ap-2097	243	9	must	must	AUX
ap-2097	243	10	be	be	AUX
ap-2097	243	11	related	relate	VERB
ap-2097	243	12	by	by	ADP
ap-2097	243	13	ga(∆	ga(∆	NOUN
ap-2097	243	14	)	)	PUNCT
ap-2097	243	15	=	=	PUNCT
ap-2097	244	1	[	[	X
ap-2097	244	2	gr(∆)]∗.	gr(∆)]∗.	NOUN
ap-2097	244	3	acknowledgements	acknowledgement	VERB
ap-2097	244	4	the	the	DET
ap-2097	244	5	author	author	NOUN
ap-2097	244	6	is	be	AUX
ap-2097	244	7	supported	support	VERB
ap-2097	244	8	in	in	ADP
ap-2097	244	9	part	part	NOUN
ap-2097	244	10	by	by	ADP
ap-2097	244	11	esf	esf	PROPN
ap-2097	244	12	grant	grant	PROPN
ap-2097	244	13	cz.1.07/2.3.00/30.0034	cz.1.07/2.3.00/30.0034	PROPN
ap-2097	244	14	references	reference	NOUN
ap-2097	244	15	[	[	X
ap-2097	244	16	1	1	NUM
ap-2097	244	17	]	]	PUNCT
ap-2097	244	18	s.	s.	PROPN
ap-2097	244	19	ohya	ohya	PROPN
ap-2097	244	20	,	,	PUNCT
ap-2097	244	21	“	"	PUNCT
ap-2097	244	22	recurrence	recurrence	NOUN
ap-2097	244	23	relations	relation	NOUN
ap-2097	244	24	for	for	ADP
ap-2097	244	25	finite	finite	ADJ
ap-2097	244	26	-	-	ADJ
ap-2097	244	27	temperature	temperature	ADJ
ap-2097	244	28	correlators	correlator	NOUN
ap-2097	244	29	via	via	ADP
ap-2097	244	30	ads2	ads2	ADJ
ap-2097	244	31	/	/	SYM
ap-2097	244	32	cft1	cft1	NOUN
ap-2097	244	33	,	,	PUNCT
ap-2097	244	34	”	"	PUNCT
ap-2097	244	35	jhep	jhep	ADJ
ap-2097	244	36	12	12	NUM
ap-2097	244	37	(	(	PUNCT
ap-2097	244	38	2013	2013	NUM
ap-2097	244	39	)	)	PUNCT
ap-2097	244	40	011	011	NUM
ap-2097	244	41	,	,	PUNCT
ap-2097	244	42	arxiv:1309.2939	arxiv:1309.2939	NOUN
ap-2097	245	1	[	[	X
ap-2097	245	2	hep	hep	NOUN
ap-2097	245	3	-	-	PUNCT
ap-2097	245	4	th	th	X
ap-2097	245	5	]	]	PUNCT
ap-2097	245	6	.	.	PUNCT
ap-2097	246	1	doi	doi	NOUN
ap-2097	246	2	:	:	PUNCT
ap-2097	246	3	10.1007	10.1007	NUM
ap-2097	246	4	/	/	SYM
ap-2097	246	5	jhep12(2013)011	jhep12(2013)011	PROPN
ap-2097	246	6	[	[	X
ap-2097	246	7	2	2	NUM
ap-2097	246	8	]	]	PUNCT
ap-2097	246	9	m.	m.	NOUN
ap-2097	246	10	bañados	bañado	NOUN
ap-2097	246	11	,	,	PUNCT
ap-2097	246	12	c.	c.	PROPN
ap-2097	246	13	teitelboim	teitelboim	PROPN
ap-2097	246	14	,	,	PUNCT
ap-2097	246	15	and	and	CCONJ
ap-2097	246	16	j.	j.	PROPN
ap-2097	246	17	zanelli	zanelli	PROPN
ap-2097	246	18	,	,	PUNCT
ap-2097	246	19	“	"	PUNCT
ap-2097	246	20	black	black	ADJ
ap-2097	246	21	hole	hole	NOUN
ap-2097	246	22	in	in	ADP
ap-2097	246	23	three	three	NUM
ap-2097	246	24	-	-	PUNCT
ap-2097	246	25	dimensional	dimensional	ADJ
ap-2097	246	26	spacetime	spacetime	NOUN
ap-2097	246	27	,	,	PUNCT
ap-2097	246	28	”	"	PUNCT
ap-2097	246	29	phys	phy	NOUN
ap-2097	246	30	.	.	PUNCT
ap-2097	247	1	rev	rev	PROPN
ap-2097	247	2	.	.	PROPN
ap-2097	247	3	lett	lett	PROPN
ap-2097	247	4	.	.	PUNCT
ap-2097	248	1	69	69	NUM
ap-2097	248	2	(	(	PUNCT
ap-2097	248	3	1992	1992	NUM
ap-2097	248	4	)	)	PUNCT
ap-2097	248	5	1849–1851	1849–1851	NUM
ap-2097	248	6	,	,	PUNCT
ap-2097	248	7	arxiv	arxiv	NOUN
ap-2097	248	8	:	:	PUNCT
ap-2097	248	9	hep	hep	NOUN
ap-2097	248	10	-	-	PROPN
ap-2097	248	11	th/9204099	th/9204099	X
ap-2097	248	12	[	[	PUNCT
ap-2097	248	13	hep	hep	NOUN
ap-2097	248	14	-	-	PUNCT
ap-2097	248	15	th	th	X
ap-2097	248	16	]	]	PUNCT
ap-2097	248	17	.	.	PUNCT
ap-2097	249	1	doi	doi	NOUN
ap-2097	249	2	:	:	PUNCT
ap-2097	249	3	10.1103	10.1103	NUM
ap-2097	249	4	/	/	SYM
ap-2097	249	5	physrevlett.69.1849	physrevlett.69.1849	NOUN
ap-2097	249	6	147	147	NUM
ap-2097	249	7	http://dx.doi.org/10.1007/jhep12(2013)011	http://dx.doi.org/10.1007/jhep12(2013)011	NUM
ap-2097	249	8	http://arxiv.org/abs/1309.2939	http://arxiv.org/abs/1309.2939	NOUN
ap-2097	250	1	http://dx.doi.org/10.1007/jhep12(2013)011	http://dx.doi.org/10.1007/jhep12(2013)011	ADV
ap-2097	250	2	http://dx.doi.org/10.1103/physrevlett.69.1849	http://dx.doi.org/10.1103/physrevlett.69.1849	ADV
ap-2097	250	3	http://dx.doi.org/10.1103/physrevlett.69.1849	http://dx.doi.org/10.1103/physrevlett.69.1849	VERB
ap-2097	250	4	http://arxiv.org/abs/hep-th/9204099	http://arxiv.org/abs/hep-th/9204099	ADJ
ap-2097	250	5	http://dx.doi.org/10.1103/physrevlett.69.1849	http://dx.doi.org/10.1103/physrevlett.69.1849	NOUN
ap-2097	250	6	satoshi	satoshi	NOUN
ap-2097	250	7	ohya	ohya	PROPN
ap-2097	250	8	acta	acta	PROPN
ap-2097	250	9	polytechnica	polytechnica	PROPN
ap-2097	250	10	[	[	X
ap-2097	250	11	3	3	NUM
ap-2097	250	12	]	]	PUNCT
ap-2097	250	13	m.	m.	NOUN
ap-2097	250	14	bañados	bañado	NOUN
ap-2097	250	15	,	,	PUNCT
ap-2097	250	16	m.	m.	NOUN
ap-2097	250	17	henneaux	henneaux	PROPN
ap-2097	250	18	,	,	PUNCT
ap-2097	250	19	c.	c.	PROPN
ap-2097	250	20	teitelboim	teitelboim	PROPN
ap-2097	250	21	,	,	PUNCT
ap-2097	250	22	and	and	CCONJ
ap-2097	250	23	j.	j.	PROPN
ap-2097	250	24	zanelli	zanelli	PROPN
ap-2097	250	25	,	,	PUNCT
ap-2097	250	26	“	"	PUNCT
ap-2097	250	27	geometry	geometry	NOUN
ap-2097	250	28	of	of	ADP
ap-2097	250	29	the	the	DET
ap-2097	250	30	2	2	NUM
ap-2097	250	31	+	+	SYM
ap-2097	250	32	1	1	NUM
ap-2097	250	33	black	black	ADJ
ap-2097	250	34	hole	hole	NOUN
ap-2097	250	35	,	,	PUNCT
ap-2097	250	36	”	"	PUNCT
ap-2097	250	37	phys	phy	NOUN
ap-2097	250	38	.	.	PUNCT
ap-2097	251	1	rev	rev	PROPN
ap-2097	251	2	.	.	PROPN
ap-2097	251	3	d48	d48	PROPN
ap-2097	251	4	(	(	PUNCT
ap-2097	251	5	1993	1993	NUM
ap-2097	251	6	)	)	PUNCT
ap-2097	251	7	1506–1525	1506–1525	NUM
ap-2097	251	8	,	,	PUNCT
ap-2097	251	9	arxiv	arxiv	NOUN
ap-2097	251	10	:	:	PUNCT
ap-2097	251	11	gr	gr	PROPN
ap-2097	251	12	-	-	PUNCT
ap-2097	251	13	qc/9302012	qc/9302012	NOUN
ap-2097	251	14	[	[	PUNCT
ap-2097	251	15	gr	gr	NOUN
ap-2097	251	16	-	-	PUNCT
ap-2097	251	17	qc	qc	NOUN
ap-2097	251	18	]	]	X
ap-2097	251	19	.	.	PUNCT
ap-2097	252	1	doi	doi	NOUN
ap-2097	252	2	:	:	PUNCT
ap-2097	252	3	10.1103	10.1103	NUM
ap-2097	252	4	/	/	SYM
ap-2097	252	5	physrevd.48.1506	physrevd.48.1506	NOUN
ap-2097	252	6	[	[	X
ap-2097	252	7	4	4	NUM
ap-2097	252	8	]	]	X
ap-2097	252	9	n.	n.	PROPN
ap-2097	252	10	iqbal	iqbal	PROPN
ap-2097	252	11	and	and	CCONJ
ap-2097	252	12	h.	h.	PROPN
ap-2097	252	13	liu	liu	PROPN
ap-2097	252	14	,	,	PUNCT
ap-2097	252	15	“	"	PUNCT
ap-2097	252	16	universality	universality	NOUN
ap-2097	252	17	of	of	ADP
ap-2097	252	18	the	the	DET
ap-2097	252	19	hydrodynamic	hydrodynamic	ADJ
ap-2097	252	20	limit	limit	NOUN
ap-2097	252	21	in	in	ADP
ap-2097	252	22	ads	ad	NOUN
ap-2097	252	23	/	/	SYM
ap-2097	252	24	cft	cft	PROPN
ap-2097	252	25	and	and	CCONJ
ap-2097	252	26	the	the	DET
ap-2097	252	27	membrane	membrane	NOUN
ap-2097	252	28	paradigm	paradigm	NOUN
ap-2097	252	29	,	,	PUNCT
ap-2097	252	30	”	"	PUNCT
ap-2097	252	31	phys	phy	NOUN
ap-2097	252	32	.	.	PUNCT
ap-2097	253	1	rev	rev	PROPN
ap-2097	253	2	.	.	PROPN
ap-2097	253	3	d79	d79	PROPN
ap-2097	253	4	(	(	PUNCT
ap-2097	253	5	2009	2009	NUM
ap-2097	253	6	)	)	PUNCT
ap-2097	253	7	025023	025023	NUM
ap-2097	253	8	,	,	PUNCT
ap-2097	253	9	arxiv:0809.3808	arxiv:0809.3808	X
ap-2097	254	1	[	[	X
ap-2097	254	2	hep	hep	NOUN
ap-2097	254	3	-	-	PUNCT
ap-2097	254	4	th	th	X
ap-2097	254	5	]	]	PUNCT
ap-2097	254	6	.	.	PUNCT
ap-2097	255	1	doi	doi	NOUN
ap-2097	255	2	:	:	PUNCT
ap-2097	255	3	10.1103	10.1103	NUM
ap-2097	255	4	/	/	SYM
ap-2097	255	5	physrevd.79.025023	physrevd.79.025023	NOUN
ap-2097	256	1	[	[	X
ap-2097	256	2	5	5	NUM
ap-2097	256	3	]	]	X
ap-2097	256	4	n.	n.	PROPN
ap-2097	256	5	iqbal	iqbal	PROPN
ap-2097	256	6	and	and	CCONJ
ap-2097	256	7	h.	h.	PROPN
ap-2097	256	8	liu	liu	PROPN
ap-2097	256	9	,	,	PUNCT
ap-2097	256	10	“	"	PUNCT
ap-2097	256	11	real	real	ADJ
ap-2097	256	12	-	-	PUNCT
ap-2097	256	13	time	time	NOUN
ap-2097	256	14	response	response	NOUN
ap-2097	256	15	in	in	ADP
ap-2097	256	16	ads	ad	NOUN
ap-2097	256	17	/	/	SYM
ap-2097	256	18	cft	cft	NOUN
ap-2097	256	19	with	with	ADP
ap-2097	256	20	application	application	NOUN
ap-2097	256	21	to	to	ADP
ap-2097	256	22	spinors	spinor	NOUN
ap-2097	256	23	,	,	PUNCT
ap-2097	256	24	”	"	PUNCT
ap-2097	256	25	fortsch	fortsch	NOUN
ap-2097	256	26	.	.	PUNCT
ap-2097	257	1	phys	phy	NOUN
ap-2097	257	2	.	.	PUNCT
ap-2097	258	1	57	57	NUM
ap-2097	258	2	(	(	PUNCT
ap-2097	258	3	2009	2009	NUM
ap-2097	258	4	)	)	PUNCT
ap-2097	259	1	367–384	367–384	NUM
ap-2097	259	2	,	,	PUNCT
ap-2097	259	3	arxiv:0903.2596	arxiv:0903.2596	NUM
ap-2097	259	4	[	[	X
ap-2097	259	5	hep	hep	NOUN
ap-2097	259	6	-	-	PUNCT
ap-2097	259	7	th	th	X
ap-2097	259	8	]	]	PUNCT
ap-2097	259	9	.	.	PUNCT
ap-2097	260	1	doi	doi	NOUN
ap-2097	260	2	:	:	PUNCT
ap-2097	260	3	10.1002	10.1002	NUM
ap-2097	260	4	/	/	SYM
ap-2097	260	5	prop.200900057	prop.200900057	NOUN
ap-2097	261	1	[	[	X
ap-2097	261	2	6	6	NUM
ap-2097	261	3	]	]	PUNCT
ap-2097	261	4	d.	d.	PROPN
ap-2097	261	5	t.	t.	PROPN
ap-2097	261	6	son	son	PROPN
ap-2097	261	7	and	and	CCONJ
ap-2097	261	8	a.	a.	NOUN
ap-2097	261	9	o.	o.	PROPN
ap-2097	261	10	starinets	starinet	NOUN
ap-2097	261	11	,	,	PUNCT
ap-2097	261	12	“	"	PUNCT
ap-2097	261	13	minkowski	minkowski	ADJ
ap-2097	261	14	-	-	PUNCT
ap-2097	261	15	space	space	NOUN
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ap-2097	261	32	)	)	PUNCT
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ap-2097	263	8	,	,	PUNCT
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ap-2097	264	9	.	.	PUNCT
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ap-2097	271	4	)	)	PUNCT
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ap-2097	276	10	-	-	SYM
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ap-2097	282	6	)	)	PUNCT
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ap-2097	282	8	.	.	PUNCT
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ap-2097	284	59	basis	basis	NOUN
ap-2097	284	60	3	3	NUM
ap-2097	284	61	lie	lie	NOUN
ap-2097	284	62	algebra	algebra	NOUN
ap-2097	284	63	sl(2,r)l	sl(2,r)l	VERB
ap-2097	284	64	+	+	CCONJ
ap-2097	284	65	sl(2,r)r	sl(2,r)r	NOUN
ap-2097	284	66	in	in	ADP
ap-2097	284	67	the	the	DET
ap-2097	284	68	so(1,1	so(1,1	ADJ
ap-2097	284	69	)	)	PUNCT
ap-2097	284	70	x	x	PUNCT
ap-2097	284	71	so(1,1	so(1,1	ADJ
ap-2097	284	72	)	)	PUNCT
ap-2097	284	73	diagonal	diagonal	ADJ
ap-2097	284	74	basis	basis	NOUN
ap-2097	284	75	4	4	NUM
ap-2097	284	76	recurrence	recurrence	NOUN
ap-2097	284	77	relations	relation	NOUN
ap-2097	284	78	for	for	ADP
ap-2097	284	79	finite	finite	ADJ
ap-2097	284	80	-	-	ADJ
ap-2097	284	81	temperature	temperature	ADJ
ap-2097	284	82	cft2	cft2	ADJ
ap-2097	284	83	two	two	NUM
ap-2097	284	84	-	-	PUNCT
ap-2097	284	85	point	point	NOUN
ap-2097	284	86	functions	function	NOUN
ap-2097	284	87	acknowledgements	acknowledgement	NOUN
ap-2097	284	88	references	reference	NOUN