id	sid	tid	token	lemma	pos
ap-1205	1	1	ap-3-10.dvi	ap-3-10.dvi	PROPN
ap-1205	1	2	acta	acta	PROPN
ap-1205	1	3	polytechnica	polytechnica	PROPN
ap-1205	1	4	vol	vol	NOUN
ap-1205	1	5	.	.	PROPN
ap-1205	2	1	50	50	NUM
ap-1205	2	2	no	no	NOUN
ap-1205	2	3	.	.	PUNCT
ap-1205	3	1	3/2010	3/2010	NUM
ap-1205	3	2	a	a	DET
ap-1205	3	3	finite	finite	ADJ
ap-1205	3	4	liouville	liouville	NOUN
ap-1205	3	5	dress	dress	NOUN
ap-1205	3	6	for	for	ADP
ap-1205	3	7	c	c	NOUN
ap-1205	3	8	<	<	X
ap-1205	3	9	1	1	NUM
ap-1205	3	10	boundary	boundary	ADJ
ap-1205	3	11	degenerate	degenerate	ADJ
ap-1205	3	12	matter	matter	NOUN
ap-1205	3	13	p.	p.	NOUN
ap-1205	3	14	furlan	furlan	PROPN
ap-1205	3	15	,	,	PUNCT
ap-1205	4	1	v.	v.	PROPN
ap-1205	4	2	b.	b.	PROPN
ap-1205	4	3	petkova	petkova	PROPN
ap-1205	4	4	,	,	PUNCT
ap-1205	5	1	m.	m.	NOUN
ap-1205	5	2	stanishkov	stanishkov	PROPN
ap-1205	5	3	abstract	abstract	NOUN
ap-1205	5	4	we	we	PRON
ap-1205	5	5	review	review	VERB
ap-1205	5	6	the	the	DET
ap-1205	5	7	derivation	derivation	NOUN
ap-1205	5	8	of	of	ADP
ap-1205	5	9	a	a	DET
ap-1205	5	10	general	general	ADJ
ap-1205	5	11	formula	formula	NOUN
ap-1205	5	12	for	for	ADP
ap-1205	5	13	the	the	DET
ap-1205	5	14	liouville	liouville	NOUN
ap-1205	5	15	dressing	dressing	NOUN
ap-1205	5	16	factor	factor	NOUN
ap-1205	5	17	in	in	ADP
ap-1205	5	18	the	the	DET
ap-1205	5	19	boundary	boundary	ADJ
ap-1205	5	20	3	3	NUM
ap-1205	5	21	-	-	PUNCT
ap-1205	5	22	point	point	NOUN
ap-1205	5	23	tachyon	tachyon	NOUN
ap-1205	5	24	correlator	correlator	NOUN
ap-1205	5	25	with	with	ADP
ap-1205	5	26	c	c	PROPN
ap-1205	5	27	<	<	X
ap-1205	5	28	1	1	NUM
ap-1205	5	29	degenerate	degenerate	ADJ
ap-1205	5	30	matter	matter	NOUN
ap-1205	5	31	.	.	PUNCT
ap-1205	6	1	keywords	keyword	NOUN
ap-1205	6	2	:	:	PUNCT
ap-1205	6	3	non	non	ADJ
ap-1205	6	4	-	-	ADJ
ap-1205	6	5	critical	critical	ADJ
ap-1205	6	6	string	string	NOUN
ap-1205	6	7	,	,	PUNCT
ap-1205	6	8	tachyon	tachyon	NOUN
ap-1205	6	9	correlators	correlator	NOUN
ap-1205	6	10	,	,	PUNCT
ap-1205	6	11	boundary	boundary	ADJ
ap-1205	6	12	conditions	condition	NOUN
ap-1205	6	13	.	.	PUNCT
ap-1205	7	1	1	1	NUM
ap-1205	7	2	introduction	introduction	NOUN
ap-1205	7	3	the	the	DET
ap-1205	7	4	simplest	simple	ADJ
ap-1205	7	5	example	example	NOUN
ap-1205	7	6	of	of	ADP
ap-1205	7	7	a	a	DET
ap-1205	7	8	non	non	ADJ
ap-1205	7	9	-	-	ADJ
ap-1205	7	10	critical	critical	ADJ
ap-1205	7	11	string	string	NOUN
ap-1205	7	12	theory	theory	NOUN
ap-1205	7	13	is	be	AUX
ap-1205	7	14	2d	2d	NUM
ap-1205	7	15	liouville	liouville	NOUN
ap-1205	7	16	gravity	gravity	NOUN
ap-1205	7	17	induced	induce	VERB
ap-1205	7	18	by	by	ADP
ap-1205	7	19	cm	cm	PROPN
ap-1205	7	20	<	<	X
ap-1205	7	21	1	1	NUM
ap-1205	7	22	matter	matter	NOUN
ap-1205	7	23	[	[	X
ap-1205	7	24	1	1	NUM
ap-1205	7	25	]	]	PUNCT
ap-1205	7	26	.	.	PUNCT
ap-1205	8	1	it	it	PRON
ap-1205	8	2	combines	combine	VERB
ap-1205	8	3	two	two	NUM
ap-1205	8	4	virasoro	virasoro	NOUN
ap-1205	8	5	theories	theory	NOUN
ap-1205	8	6	with	with	ADP
ap-1205	8	7	central	central	ADJ
ap-1205	8	8	charges	charge	NOUN
ap-1205	8	9	parametrised	parametrise	VERB
ap-1205	8	10	by	by	ADP
ap-1205	8	11	a	a	DET
ap-1205	8	12	generically	generically	ADV
ap-1205	8	13	real	real	ADJ
ap-1205	8	14	number	number	NOUN
ap-1205	8	15	b	b	NOUN
ap-1205	8	16	,	,	PUNCT
ap-1205	8	17	cm	cm	NOUN
ap-1205	8	18	=	=	SYM
ap-1205	8	19	13−6(b2	13−6(b2	NUM
ap-1205	8	20	+	+	ADJ
ap-1205	8	21	1	1	NUM
ap-1205	8	22	/	/	SYM
ap-1205	8	23	b2	b2	NOUN
ap-1205	8	24	)	)	PUNCT
ap-1205	8	25	<	<	X
ap-1205	8	26	1	1	NUM
ap-1205	8	27	and	and	CCONJ
ap-1205	8	28	cl	cl	NOUN
ap-1205	8	29	=	=	SYM
ap-1205	9	1	26	26	NUM
ap-1205	9	2	−	−	NUM
ap-1205	9	3	cm	cm	NOUN
ap-1205	9	4	>	>	X
ap-1205	9	5	25	25	NUM
ap-1205	9	6	,	,	PUNCT
ap-1205	9	7	so	so	SCONJ
ap-1205	9	8	that	that	SCONJ
ap-1205	9	9	when	when	SCONJ
ap-1205	9	10	we	we	PRON
ap-1205	9	11	add	add	VERB
ap-1205	9	12	a	a	DET
ap-1205	9	13	pair	pair	NOUN
ap-1205	9	14	of	of	ADP
ap-1205	9	15	reparametrisation	reparametrisation	NOUN
ap-1205	9	16	ghosts	ghost	NOUN
ap-1205	9	17	of	of	ADP
ap-1205	9	18	central	central	ADJ
ap-1205	9	19	charge	charge	NOUN
ap-1205	9	20	−26	−26	DET
ap-1205	9	21	the	the	DET
ap-1205	9	22	total	total	ADJ
ap-1205	9	23	conformal	conformal	NOUN
ap-1205	9	24	anomaly	anomaly	NOUN
ap-1205	9	25	vanishes	vanish	VERB
ap-1205	9	26	.	.	PUNCT
ap-1205	10	1	the	the	DET
ap-1205	10	2	d	d	ADJ
ap-1205	10	3	-	-	PUNCT
ap-1205	10	4	brane	brane	ADJ
ap-1205	10	5	dynamics	dynamic	NOUN
ap-1205	10	6	in	in	ADP
ap-1205	10	7	an	an	DET
ap-1205	10	8	open	open	ADJ
ap-1205	10	9	non	non	ADJ
ap-1205	10	10	-	-	ADJ
ap-1205	10	11	critical	critical	ADJ
ap-1205	10	12	string	string	NOUN
ap-1205	10	13	is	be	AUX
ap-1205	10	14	determined	determine	VERB
ap-1205	10	15	by	by	ADP
ap-1205	10	16	the	the	DET
ap-1205	10	17	boundary	boundary	ADJ
ap-1205	10	18	correlation	correlation	NOUN
ap-1205	10	19	functions	function	NOUN
ap-1205	10	20	(	(	PUNCT
ap-1205	10	21	numbers	number	NOUN
ap-1205	10	22	)	)	PUNCT
ap-1205	10	23	of	of	ADP
ap-1205	10	24	the	the	DET
ap-1205	10	25	physical	physical	ADJ
ap-1205	10	26	fields	field	NOUN
ap-1205	10	27	of	of	ADP
ap-1205	10	28	ghost	ghost	NOUN
ap-1205	10	29	number	number	NOUN
ap-1205	10	30	one	one	NUM
ap-1205	10	31	,	,	PUNCT
ap-1205	10	32	“	"	PUNCT
ap-1205	10	33	massless	massless	ADJ
ap-1205	10	34	tachyons	tachyon	NOUN
ap-1205	10	35	”	"	PUNCT
ap-1205	10	36	,	,	PUNCT
ap-1205	10	37	see	see	VERB
ap-1205	10	38	e.g.	e.g.	ADV
ap-1205	10	39	[	[	X
ap-1205	10	40	2	2	NUM
ap-1205	10	41	,	,	PUNCT
ap-1205	10	42	3	3	NUM
ap-1205	10	43	,	,	PUNCT
ap-1205	10	44	4	4	NUM
ap-1205	10	45	,	,	PUNCT
ap-1205	10	46	5	5	NUM
ap-1205	10	47	,	,	PUNCT
ap-1205	10	48	6	6	NUM
ap-1205	10	49	,	,	PUNCT
ap-1205	10	50	7	7	NUM
ap-1205	10	51	]	]	PUNCT
ap-1205	10	52	for	for	ADP
ap-1205	10	53	more	more	ADV
ap-1205	10	54	recent	recent	ADJ
ap-1205	10	55	discussions	discussion	NOUN
ap-1205	10	56	.	.	PUNCT
ap-1205	11	1	the	the	DET
ap-1205	11	2	full	full	ADJ
ap-1205	11	3	boundary	boundary	ADJ
ap-1205	11	4	tachyon	tachyon	NOUN
ap-1205	11	5	field	field	NOUN
ap-1205	11	6	factorises	factorise	NOUN
ap-1205	11	7	into	into	ADP
ap-1205	11	8	a	a	DET
ap-1205	11	9	matter	matter	NOUN
ap-1205	11	10	times	time	NOUN
ap-1205	11	11	a	a	DET
ap-1205	11	12	liouville	liouville	NOUN
ap-1205	11	13	“	"	PUNCT
ap-1205	11	14	dressing	dress	VERB
ap-1205	11	15	”	"	PUNCT
ap-1205	11	16	vertex	vertex	NOUN
ap-1205	11	17	operator	operator	NOUN
ap-1205	11	18	,	,	PUNCT
ap-1205	11	19	producing	produce	VERB
ap-1205	11	20	a	a	DET
ap-1205	11	21	similar	similar	ADJ
ap-1205	11	22	factorisation	factorisation	NOUN
ap-1205	11	23	of	of	ADP
ap-1205	11	24	the	the	DET
ap-1205	11	25	full	full	ADJ
ap-1205	11	26	3	3	NUM
ap-1205	11	27	-	-	PUNCT
ap-1205	11	28	point	point	NOUN
ap-1205	11	29	function	function	NOUN
ap-1205	11	30	.	.	PUNCT
ap-1205	12	1	in	in	ADP
ap-1205	12	2	this	this	DET
ap-1205	12	3	work	work	NOUN
ap-1205	12	4	we	we	PRON
ap-1205	12	5	address	address	VERB
ap-1205	12	6	our	our	PRON
ap-1205	12	7	attention	attention	NOUN
ap-1205	12	8	to	to	ADP
ap-1205	12	9	the	the	DET
ap-1205	12	10	pure	pure	ADJ
ap-1205	12	11	liouville	liouville	NOUN
ap-1205	12	12	factor	factor	NOUN
ap-1205	12	13	of	of	ADP
ap-1205	12	14	it	it	PRON
ap-1205	12	15	in	in	ADP
ap-1205	12	16	the	the	DET
ap-1205	12	17	case	case	NOUN
ap-1205	12	18	where	where	SCONJ
ap-1205	12	19	the	the	DET
ap-1205	12	20	matter	matter	NOUN
ap-1205	12	21	factor	factor	NOUN
ap-1205	12	22	corresponds	correspond	VERB
ap-1205	12	23	to	to	PART
ap-1205	12	24	degenerate	degenerate	ADJ
ap-1205	12	25	virasoro	virasoro	NOUN
ap-1205	12	26	representations	representation	NOUN
ap-1205	12	27	.	.	PUNCT
ap-1205	13	1	the	the	DET
ap-1205	13	2	matter	matter	NOUN
ap-1205	13	3	fields	field	NOUN
ap-1205	13	4	are	be	AUX
ap-1205	13	5	vertex	vertex	NOUN
ap-1205	13	6	operators	operator	NOUN
ap-1205	13	7	of	of	ADP
ap-1205	13	8	the	the	DET
ap-1205	13	9	scaling	scaling	ADJ
ap-1205	13	10	dimension	dimension	NOUN
ap-1205	13	11	δm(e	δm(e	PUNCT
ap-1205	13	12	)	)	PUNCT
ap-1205	13	13	=	=	SYM
ap-1205	13	14	e(e−1	e(e−1	PROPN
ap-1205	13	15	/	/	SYM
ap-1205	13	16	b+	b+	X
ap-1205	13	17	b	b	NOUN
ap-1205	13	18	)	)	PUNCT
ap-1205	13	19	labelled	label	VERB
ap-1205	13	20	by	by	ADP
ap-1205	13	21	degenerate	degenerate	ADJ
ap-1205	13	22	cm	cm	NOUN
ap-1205	13	23	<	<	X
ap-1205	13	24	1	1	NUM
ap-1205	13	25	virasoro	virasoro	NOUN
ap-1205	13	26	representations	representation	NOUN
ap-1205	13	27	.	.	PUNCT
ap-1205	14	1	this	this	PRON
ap-1205	14	2	implies	imply	VERB
ap-1205	14	3	that	that	SCONJ
ap-1205	14	4	the	the	DET
ap-1205	14	5	charges	charge	NOUN
ap-1205	14	6	{	{	PUNCT
ap-1205	14	7	βi	βi	PRON
ap-1205	14	8	}	}	PUNCT
ap-1205	14	9	of	of	ADP
ap-1205	14	10	the	the	DET
ap-1205	14	11	dressing	dressing	NOUN
ap-1205	14	12	liouville	liouville	NOUN
ap-1205	14	13	boundary	boundary	ADJ
ap-1205	14	14	vertex	vertex	NOUN
ap-1205	14	15	operators	operator	NOUN
ap-1205	14	16	σibσi	σibσi	VERB
ap-1205	14	17	βi	βi	PROPN
ap-1205	14	18	,	,	PUNCT
ap-1205	14	19	of	of	ADP
ap-1205	14	20	scaling	scale	VERB
ap-1205	14	21	dimensions	dimension	NOUN
ap-1205	14	22	δl(β	δl(β	PUNCT
ap-1205	14	23	)	)	PUNCT
ap-1205	14	24	=	=	SYM
ap-1205	14	25	β(q−	β(q−	NUM
ap-1205	14	26	β	β	X
ap-1205	14	27	)	)	PUNCT
ap-1205	14	28	=	=	SYM
ap-1205	15	1	1−δm	1−δm	NUM
ap-1205	15	2	(	(	PUNCT
ap-1205	15	3	e	e	NOUN
ap-1205	15	4	)	)	PUNCT
ap-1205	15	5	,	,	PUNCT
ap-1205	15	6	take	take	VERB
ap-1205	15	7	the	the	DET
ap-1205	15	8	values	value	NOUN
ap-1205	15	9	βi	βi	ADP
ap-1205	16	1	=	=	SYM
ap-1205	16	2	b	b	X
ap-1205	16	3	+	+	PROPN
ap-1205	16	4	mib−	mib−	PROPN
ap-1205	16	5	ni	ni	PROPN
ap-1205	16	6	b	b	PROPN
ap-1205	16	7	,	,	PUNCT
ap-1205	16	8	2mi	2mi	ADJ
ap-1205	16	9	,	,	PUNCT
ap-1205	16	10	2ni	2ni	ADJ
ap-1205	16	11	∈	∈	PROPN
ap-1205	16	12	z≥0	z≥0	NOUN
ap-1205	16	13	(	(	PUNCT
ap-1205	16	14	1.1	1.1	NUM
ap-1205	16	15	)	)	PUNCT
ap-1205	16	16	or	or	CCONJ
ap-1205	16	17	their	their	PRON
ap-1205	16	18	reflected	reflect	VERB
ap-1205	16	19	β	β	X
ap-1205	16	20	→	→	SYM
ap-1205	16	21	q−	q−	PROPN
ap-1205	16	22	β	β	X
ap-1205	16	23	counterparts	counterpart	NOUN
ap-1205	16	24	(	(	PUNCT
ap-1205	16	25	q	q	NOUN
ap-1205	16	26	=	=	PUNCT
ap-1205	16	27	b+	b+	NUM
ap-1205	16	28	1	1	NUM
ap-1205	16	29	/	/	SYM
ap-1205	16	30	b	b	NOUN
ap-1205	16	31	)	)	PUNCT
ap-1205	16	32	,	,	PUNCT
ap-1205	16	33	so	so	SCONJ
ap-1205	16	34	that	that	SCONJ
ap-1205	16	35	without	without	ADP
ap-1205	16	36	loss	loss	NOUN
ap-1205	16	37	of	of	ADP
ap-1205	16	38	generality	generality	NOUN
ap-1205	16	39	we	we	PRON
ap-1205	16	40	shall	shall	AUX
ap-1205	16	41	work	work	VERB
ap-1205	16	42	with	with	ADP
ap-1205	16	43	the	the	DET
ap-1205	16	44	values	value	NOUN
ap-1205	16	45	in	in	ADP
ap-1205	16	46	(	(	PUNCT
ap-1205	16	47	1.1	1.1	NUM
ap-1205	16	48	)	)	PUNCT
ap-1205	16	49	.	.	PUNCT
ap-1205	17	1	the	the	DET
ap-1205	17	2	range	range	NOUN
ap-1205	17	3	of	of	ADP
ap-1205	17	4	the	the	DET
ap-1205	17	5	boundary	boundary	ADJ
ap-1205	17	6	parameters	parameter	NOUN
ap-1205	17	7	σi	σi	PRON
ap-1205	17	8	is	be	AUX
ap-1205	17	9	generically	generically	ADV
ap-1205	17	10	parametrised	parametrise	VERB
ap-1205	17	11	by	by	ADP
ap-1205	17	12	the	the	DET
ap-1205	17	13	continuous	continuous	ADJ
ap-1205	17	14	liouville	liouville	NOUN
ap-1205	17	15	spectrum	spectrum	NOUN
ap-1205	17	16	2σ	2σ	NOUN
ap-1205	18	1	−	−	NOUN
ap-1205	18	2	q	q	NOUN
ap-1205	18	3	–	–	PUNCT
ap-1205	18	4	pure	pure	ADJ
ap-1205	18	5	imaginary	imaginary	ADJ
ap-1205	18	6	but	but	CCONJ
ap-1205	18	7	also	also	ADV
ap-1205	18	8	admits	admit	VERB
ap-1205	18	9	continuation	continuation	NOUN
ap-1205	18	10	to	to	ADP
ap-1205	18	11	real	real	ADJ
ap-1205	18	12	values	value	NOUN
ap-1205	18	13	.	.	PUNCT
ap-1205	19	1	these	these	DET
ap-1205	19	2	liouville	liouville	NOUN
ap-1205	19	3	boundary	boundary	ADJ
ap-1205	19	4	fields	field	NOUN
ap-1205	19	5	correspond	correspond	VERB
ap-1205	19	6	to	to	ADP
ap-1205	19	7	the	the	DET
ap-1205	19	8	fzz	fzz	ADJ
ap-1205	19	9	branes	brane	NOUN
ap-1205	19	10	[	[	X
ap-1205	19	11	8	8	NUM
ap-1205	19	12	]	]	PUNCT
ap-1205	19	13	.	.	PUNCT
ap-1205	20	1	the	the	DET
ap-1205	20	2	matter	matter	ADJ
ap-1205	20	3	factor	factor	NOUN
ap-1205	20	4	of	of	ADP
ap-1205	20	5	the	the	DET
ap-1205	20	6	3	3	NUM
ap-1205	20	7	-	-	PUNCT
ap-1205	20	8	point	point	NOUN
ap-1205	20	9	boundary	boundary	ADJ
ap-1205	20	10	tachyon	tachyon	NOUN
ap-1205	20	11	correlator	correlator	NOUN
ap-1205	20	12	is	be	AUX
ap-1205	20	13	a	a	DET
ap-1205	20	14	straightforward	straightforward	ADJ
ap-1205	20	15	generalisation	generalisation	NOUN
ap-1205	20	16	of	of	ADP
ap-1205	20	17	the	the	DET
ap-1205	20	18	factor	factor	NOUN
ap-1205	20	19	in	in	ADP
ap-1205	20	20	the	the	DET
ap-1205	20	21	rational	rational	ADJ
ap-1205	20	22	b2	b2	NOUN
ap-1205	20	23	-	-	PUNCT
ap-1205	20	24	case	case	NOUN
ap-1205	20	25	.	.	PUNCT
ap-1205	21	1	it	it	PRON
ap-1205	21	2	is	be	AUX
ap-1205	21	3	alternatively	alternatively	ADV
ap-1205	21	4	reproduced	reproduce	VERB
ap-1205	21	5	by	by	ADP
ap-1205	21	6	an	an	DET
ap-1205	21	7	analytic	analytic	ADJ
ap-1205	21	8	continuation	continuation	NOUN
ap-1205	21	9	of	of	ADP
ap-1205	21	10	a	a	DET
ap-1205	21	11	residuum	residuum	NOUN
ap-1205	21	12	of	of	ADP
ap-1205	21	13	the	the	DET
ap-1205	21	14	integral	integral	ADJ
ap-1205	21	15	ponsot	ponsot	NOUN
ap-1205	21	16	-	-	PUNCT
ap-1205	21	17	teschner	teschner	NOUN
ap-1205	21	18	(	(	PUNCT
ap-1205	21	19	pt	pt	NOUN
ap-1205	21	20	)	)	PUNCT
ap-1205	21	21	formula	formula	NOUN
ap-1205	21	22	[	[	X
ap-1205	21	23	9	9	NUM
ap-1205	21	24	]	]	PUNCT
ap-1205	21	25	at	at	ADP
ap-1205	21	26	points	point	NOUN
ap-1205	21	27	corresponding	correspond	VERB
ap-1205	21	28	to	to	ADP
ap-1205	21	29	c	c	PROPN
ap-1205	21	30	>	>	X
ap-1205	21	31	25	25	NUM
ap-1205	21	32	degenerate	degenerate	ADJ
ap-1205	21	33	virasoro	virasoro	NOUN
ap-1205	21	34	representations	representation	NOUN
ap-1205	21	35	.	.	PUNCT
ap-1205	22	1	the	the	DET
ap-1205	22	2	same	same	ADJ
ap-1205	22	3	analytic	analytic	ADJ
ap-1205	22	4	continuation	continuation	NOUN
ap-1205	22	5	applies	apply	VERB
ap-1205	22	6	to	to	ADP
ap-1205	22	7	fusing	fuse	VERB
ap-1205	22	8	matrices	matrix	NOUN
ap-1205	22	9	,	,	PUNCT
ap-1205	22	10	which	which	PRON
ap-1205	22	11	differ	differ	VERB
ap-1205	22	12	from	from	ADP
ap-1205	22	13	the	the	DET
ap-1205	22	14	boundary	boundary	ADJ
ap-1205	22	15	field	field	NOUN
ap-1205	22	16	crossing	crossing	NOUN
ap-1205	22	17	matrices	matrix	NOUN
ap-1205	22	18	(	(	PUNCT
ap-1205	22	19	3	3	NUM
ap-1205	22	20	-	-	PUNCT
ap-1205	22	21	point	point	NOUN
ap-1205	22	22	boundary	boundary	ADJ
ap-1205	22	23	correlators	correlator	NOUN
ap-1205	22	24	)	)	PUNCT
ap-1205	22	25	by	by	ADP
ap-1205	22	26	a	a	DET
ap-1205	22	27	renormalisation	renormalisation	NOUN
ap-1205	22	28	of	of	ADP
ap-1205	22	29	the	the	DET
ap-1205	22	30	three	three	NUM
ap-1205	22	31	boundary	boundary	ADJ
ap-1205	22	32	vertices	vertex	NOUN
ap-1205	22	33	.	.	PUNCT
ap-1205	23	1	thus	thus	ADV
ap-1205	23	2	the	the	DET
ap-1205	23	3	formulae	formulae	NOUN
ap-1205	23	4	in	in	ADP
ap-1205	23	5	[	[	X
ap-1205	23	6	9	9	NUM
ap-1205	23	7	,	,	PUNCT
ap-1205	23	8	10	10	NUM
ap-1205	23	9	]	]	PUNCT
ap-1205	23	10	for	for	ADP
ap-1205	23	11	the	the	DET
ap-1205	23	12	quantum	quantum	ADJ
ap-1205	23	13	3j	3j	NOUN
ap-1205	23	14	and	and	CCONJ
ap-1205	23	15	6j	6j	NUM
ap-1205	23	16	symbols	symbol	NOUN
ap-1205	23	17	,	,	PUNCT
ap-1205	23	18	designed	design	VERB
ap-1205	23	19	generically	generically	ADV
ap-1205	23	20	for	for	ADP
ap-1205	23	21	the	the	DET
ap-1205	23	22	continuous	continuous	ADJ
ap-1205	23	23	c	c	PROPN
ap-1205	23	24	>	>	X
ap-1205	23	25	25	25	NUM
ap-1205	23	26	spectrum	spectrum	NOUN
ap-1205	23	27	,	,	PUNCT
ap-1205	23	28	are	be	AUX
ap-1205	23	29	in	in	ADP
ap-1205	23	30	a	a	DET
ap-1205	23	31	sense	sense	NOUN
ap-1205	23	32	universal	universal	ADJ
ap-1205	23	33	,	,	PUNCT
ap-1205	23	34	since	since	SCONJ
ap-1205	23	35	we	we	PRON
ap-1205	23	36	can	can	AUX
ap-1205	23	37	reproduce	reproduce	VERB
ap-1205	23	38	from	from	ADP
ap-1205	23	39	them	they	PRON
ap-1205	23	40	the	the	DET
ap-1205	23	41	coulomb	coulomb	NOUN
ap-1205	23	42	gas	gas	NOUN
ap-1205	23	43	quantities	quantity	NOUN
ap-1205	23	44	in	in	ADP
ap-1205	23	45	both	both	CCONJ
ap-1205	23	46	c	c	PROPN
ap-1205	23	47	<	<	X
ap-1205	23	48	1	1	NUM
ap-1205	23	49	and	and	CCONJ
ap-1205	23	50	c	c	X
ap-1205	23	51	>	>	X
ap-1205	23	52	25	25	NUM
ap-1205	23	53	virasoro	virasoro	NOUN
ap-1205	23	54	regions	region	NOUN
ap-1205	23	55	.	.	PUNCT
ap-1205	24	1	however	however	ADV
ap-1205	24	2	this	this	DET
ap-1205	24	3	integral	integral	ADJ
ap-1205	24	4	formula	formula	NOUN
ap-1205	24	5	is	be	AUX
ap-1205	24	6	not	not	PART
ap-1205	24	7	very	very	ADV
ap-1205	24	8	explicit	explicit	ADJ
ap-1205	24	9	,	,	PUNCT
ap-1205	24	10	and	and	CCONJ
ap-1205	24	11	its	its	PRON
ap-1205	24	12	main	main	ADJ
ap-1205	24	13	characteristics	characteristic	NOUN
ap-1205	24	14	are	be	AUX
ap-1205	24	15	not	not	PART
ap-1205	24	16	immediately	immediately	ADV
ap-1205	24	17	visible	visible	ADJ
ap-1205	24	18	when	when	SCONJ
ap-1205	24	19	applied	apply	VERB
ap-1205	24	20	to	to	ADP
ap-1205	24	21	the	the	DET
ap-1205	24	22	spectrum	spectrum	NOUN
ap-1205	24	23	of	of	ADP
ap-1205	24	24	representations	representation	NOUN
ap-1205	24	25	(	(	PUNCT
ap-1205	24	26	1.1	1.1	NUM
ap-1205	24	27	)	)	PUNCT
ap-1205	24	28	.	.	PUNCT
ap-1205	25	1	another	another	DET
ap-1205	25	2	alternative	alternative	NOUN
ap-1205	25	3	is	be	AUX
ap-1205	25	4	to	to	PART
ap-1205	25	5	solve	solve	VERB
ap-1205	25	6	the	the	DET
ap-1205	25	7	pentagon	pentagon	PROPN
ap-1205	25	8	equations	equation	NOUN
ap-1205	25	9	recursively	recursively	ADV
ap-1205	25	10	.	.	PUNCT
ap-1205	26	1	the	the	DET
ap-1205	26	2	final	final	ADJ
ap-1205	26	3	result	result	NOUN
ap-1205	26	4	is	be	AUX
ap-1205	26	5	a	a	DET
ap-1205	26	6	meromorphic	meromorphic	ADJ
ap-1205	26	7	expression	expression	NOUN
ap-1205	26	8	in	in	ADP
ap-1205	26	9	the	the	DET
ap-1205	26	10	boundary	boundary	ADJ
ap-1205	26	11	cosmological	cosmological	ADJ
ap-1205	26	12	parameters	parameter	NOUN
ap-1205	26	13	,	,	PUNCT
ap-1205	26	14	the	the	DET
ap-1205	26	15	derivation	derivation	NOUN
ap-1205	26	16	of	of	ADP
ap-1205	26	17	which	which	PRON
ap-1205	26	18	we	we	PRON
ap-1205	26	19	review	review	VERB
ap-1205	26	20	here	here	ADV
ap-1205	26	21	,	,	PUNCT
ap-1205	26	22	see	see	VERB
ap-1205	26	23	[	[	X
ap-1205	26	24	11	11	NUM
ap-1205	26	25	]	]	PUNCT
ap-1205	26	26	for	for	ADP
ap-1205	26	27	more	more	ADJ
ap-1205	26	28	details	detail	NOUN
ap-1205	26	29	.	.	PUNCT
ap-1205	27	1	it	it	PRON
ap-1205	27	2	generalises	generalise	VERB
ap-1205	27	3	a	a	DET
ap-1205	27	4	special	special	ADJ
ap-1205	27	5	(	(	PUNCT
ap-1205	27	6	thermal	thermal	ADJ
ap-1205	27	7	)	)	PUNCT
ap-1205	27	8	case	case	NOUN
ap-1205	27	9	result	result	NOUN
ap-1205	27	10	of	of	ADP
ap-1205	27	11	[	[	X
ap-1205	27	12	6	6	NUM
ap-1205	27	13	]	]	PUNCT
ap-1205	27	14	and	and	CCONJ
ap-1205	27	15	partial	partial	ADJ
ap-1205	27	16	results	result	NOUN
ap-1205	27	17	in	in	ADP
ap-1205	27	18	the	the	DET
ap-1205	27	19	microscopic	microscopic	ADJ
ap-1205	27	20	approach	approach	NOUN
ap-1205	27	21	in	in	ADP
ap-1205	27	22	[	[	X
ap-1205	27	23	5	5	NUM
ap-1205	27	24	]	]	PUNCT
ap-1205	27	25	.	.	PUNCT
ap-1205	28	1	2	2	NUM
ap-1205	28	2	boundary	boundary	ADJ
ap-1205	28	3	3	3	NUM
ap-1205	28	4	-	-	PUNCT
ap-1205	28	5	point	point	NOUN
ap-1205	28	6	liouville	liouville	NOUN
ap-1205	28	7	constant	constant	ADJ
ap-1205	28	8	the	the	DET
ap-1205	28	9	matter	matter	NOUN
ap-1205	28	10	fusion	fusion	NOUN
ap-1205	28	11	rules	rule	NOUN
ap-1205	28	12	impose	impose	VERB
ap-1205	28	13	restrictions	restriction	NOUN
ap-1205	28	14	on	on	ADP
ap-1205	28	15	the	the	DET
ap-1205	28	16	values	value	NOUN
ap-1205	28	17	in	in	ADP
ap-1205	28	18	(	(	PUNCT
ap-1205	28	19	1.1	1.1	NUM
ap-1205	28	20	)	)	PUNCT
ap-1205	28	21	,	,	PUNCT
ap-1205	28	22	namely	namely	ADV
ap-1205	28	23	allmk	allmk	VERB
ap-1205	28	24	ij	ij	NOUN
ap-1205	28	25	:	:	PUNCT
ap-1205	28	26	=	=	SYM
ap-1205	28	27	mi+mj−mk	mi+mj−mk	X
ap-1205	28	28	,	,	PUNCT
ap-1205	28	29	n	n	CCONJ
ap-1205	28	30	k	k	PROPN
ap-1205	28	31	ij	ij	NOUN
ap-1205	28	32	=	=	NOUN
ap-1205	28	33	ni+nj−nk	ni+nj−nk	NOUN
ap-1205	28	34	are	be	AUX
ap-1205	28	35	non	non	ADJ
ap-1205	28	36	-	-	ADJ
ap-1205	28	37	negative	negative	ADJ
ap-1205	28	38	integers	integer	NOUN
ap-1205	28	39	,	,	PUNCT
ap-1205	29	1	so	so	SCONJ
ap-1205	29	2	that	that	SCONJ
ap-1205	29	3	2m123	2m123	NUM
ap-1205	29	4	=	=	SYM
ap-1205	29	5	3∑	3∑	NUM
ap-1205	29	6	i=1	i=1	X
ap-1205	30	1	2mi	2mi	NOUN
ap-1205	30	2	=	=	SYM
ap-1205	30	3	0	0	NUM
ap-1205	30	4	mod	mod	NOUN
ap-1205	30	5	2	2	NUM
ap-1205	30	6	.	.	X
ap-1205	30	7	84	84	NUM
ap-1205	30	8	acta	acta	PROPN
ap-1205	30	9	polytechnica	polytechnica	PROPN
ap-1205	30	10	vol	vol	NOUN
ap-1205	30	11	.	.	PROPN
ap-1205	31	1	50	50	NUM
ap-1205	31	2	no	no	NOUN
ap-1205	31	3	.	.	PUNCT
ap-1205	32	1	3/2010	3/2010	NUM
ap-1205	32	2	the	the	DET
ap-1205	32	3	3	3	NUM
ap-1205	32	4	-	-	PUNCT
ap-1205	32	5	point	point	NOUN
ap-1205	32	6	boundary	boundary	ADJ
ap-1205	32	7	liouville	liouville	NOUN
ap-1205	32	8	functions	function	NOUN
ap-1205	32	9	that	that	PRON
ap-1205	32	10	we	we	PRON
ap-1205	32	11	are	be	AUX
ap-1205	32	12	interested	interested	ADJ
ap-1205	32	13	in	in	ADP
ap-1205	32	14	are	be	AUX
ap-1205	32	15	related	relate	VERB
ap-1205	32	16	to	to	ADP
ap-1205	32	17	the	the	DET
ap-1205	32	18	boundary	boundary	ADJ
ap-1205	32	19	field	field	NOUN
ap-1205	32	20	crossing	crossing	NOUN
ap-1205	32	21	matrices	matrix	NOUN
ap-1205	32	22	cσ2,q−β3	cσ2,q−β3	PROPN
ap-1205	32	23	[	[	PUNCT
ap-1205	32	24	β2	β2	NOUN
ap-1205	32	25	β1	β1	PROPN
ap-1205	32	26	σ3	σ3	PROPN
ap-1205	32	27	σ1	σ1	PROPN
ap-1205	32	28	]	]	PUNCT
ap-1205	33	1	=	=	PUNCT
ap-1205	33	2	〈	〈	VERB
ap-1205	33	3	σ1bβ3	σ1bβ3	NOUN
ap-1205	33	4	σ3bβ2	σ3bβ2	NOUN
ap-1205	33	5	σ2bβ1	σ2bβ1	NOUN
ap-1205	33	6	σ1	σ1	PROPN
ap-1205	33	7	〉	〉	NUM
ap-1205	33	8	=	=	SYM
ap-1205	33	9	cσ3,σ2,σ1	cσ3,σ2,σ1	ADV
ap-1205	33	10	β3,β2,β1	β3,β2,β1	NOUN
ap-1205	33	11	=	=	SYM
ap-1205	33	12	s(σ1	s(σ1	ADV
ap-1205	33	13	,	,	PUNCT
ap-1205	33	14	β3	β3	VERB
ap-1205	33	15	,	,	PUNCT
ap-1205	33	16	σ3)cσ3,σ2,σ1	σ3)cσ3,σ2,σ1	NUM
ap-1205	33	17	q−β3,β2,β1	q−β3,β2,β1	PROPN
ap-1205	33	18	,	,	PUNCT
ap-1205	33	19	(	(	PUNCT
ap-1205	33	20	2.1	2.1	NUM
ap-1205	33	21	)	)	PUNCT
ap-1205	33	22	where	where	SCONJ
ap-1205	33	23	s(σ1	s(σ1	NOUN
ap-1205	33	24	,	,	PUNCT
ap-1205	33	25	β3	β3	VERB
ap-1205	33	26	,	,	PUNCT
ap-1205	33	27	σ3	σ3	PROPN
ap-1205	33	28	)	)	PUNCT
ap-1205	33	29	is	be	AUX
ap-1205	33	30	the	the	DET
ap-1205	33	31	reflection	reflection	NOUN
ap-1205	33	32	amplitude	amplitude	NOUN
ap-1205	33	33	[	[	X
ap-1205	33	34	8	8	NUM
ap-1205	33	35	]	]	PUNCT
ap-1205	33	36	.	.	PUNCT
ap-1205	34	1	the	the	DET
ap-1205	34	2	associativity	associativity	NOUN
ap-1205	34	3	condition	condition	NOUN
ap-1205	34	4	for	for	ADP
ap-1205	34	5	ope	ope	NOUN
ap-1205	34	6	of	of	ADP
ap-1205	34	7	boundary	boundary	ADJ
ap-1205	34	8	fields	field	NOUN
ap-1205	34	9	,	,	PUNCT
ap-1205	34	10	together	together	ADV
ap-1205	34	11	with	with	ADP
ap-1205	34	12	the	the	DET
ap-1205	34	13	fusion	fusion	NOUN
ap-1205	34	14	transformation	transformation	NOUN
ap-1205	34	15	relating	relate	VERB
ap-1205	34	16	the	the	DET
ap-1205	34	17	s	s	NOUN
ap-1205	34	18	and	and	CCONJ
ap-1205	34	19	t	t	NOUN
ap-1205	34	20	channels	channel	NOUN
ap-1205	34	21	,	,	PUNCT
ap-1205	34	22	lead	lead	VERB
ap-1205	34	23	to	to	ADP
ap-1205	34	24	an	an	DET
ap-1205	34	25	integral	integral	ADJ
ap-1205	34	26	pentagon	pentagon	NOUN
ap-1205	34	27	-	-	PUNCT
ap-1205	34	28	like	like	ADJ
ap-1205	34	29	equation	equation	NOUN
ap-1205	34	30	for	for	ADP
ap-1205	34	31	the	the	DET
ap-1205	34	32	boundary	boundary	ADJ
ap-1205	34	33	field	field	NOUN
ap-1205	34	34	3	3	NUM
ap-1205	34	35	-	-	PUNCT
ap-1205	34	36	point	point	NOUN
ap-1205	34	37	functions∫	functions∫	ADV
ap-1205	34	38	dβscσ4,σ3,σ1	dβscσ4,σ3,σ1	VERB
ap-1205	34	39	q−β3,β2,βs	q−β3,β2,βs	NOUN
ap-1205	34	40	cσ3,σ2,σ1	cσ3,σ2,σ1	PROPN
ap-1205	34	41	q−βs	q−βs	NOUN
ap-1205	34	42	,	,	PUNCT
ap-1205	34	43	β	β	X
ap-1205	34	44	,	,	PUNCT
ap-1205	34	45	β1	β1	NOUN
ap-1205	34	46	fβs	fβs	NOUN
ap-1205	34	47	,	,	PUNCT
ap-1205	34	48	βt	βt	PRON
ap-1205	34	49	[	[	PUNCT
ap-1205	34	50	β2	β2	NOUN
ap-1205	34	51	β	β	NOUN
ap-1205	34	52	β3	β3	VERB
ap-1205	34	53	β1	β1	PROPN
ap-1205	34	54	]	]	PUNCT
ap-1205	35	1	=	=	SYM
ap-1205	35	2	cσ4,σ2,σ1	cσ4,σ2,σ1	PROPN
ap-1205	35	3	q−β3,βt	q−β3,βt	PROPN
ap-1205	35	4	,	,	PUNCT
ap-1205	35	5	β1	β1	NOUN
ap-1205	35	6	cσ4,σ3,σ2	cσ4,σ3,σ2	ADJ
ap-1205	35	7	q−βt	q−βt	NOUN
ap-1205	35	8	,	,	PUNCT
ap-1205	35	9	β2,β	β2,β	PROPN
ap-1205	35	10	,	,	PUNCT
ap-1205	35	11	(	(	PUNCT
ap-1205	35	12	2.2	2.2	NUM
ap-1205	35	13	)	)	PUNCT
ap-1205	35	14	where	where	SCONJ
ap-1205	35	15	fβs	fβs	NOUN
ap-1205	35	16	,	,	PUNCT
ap-1205	35	17	βt	βt	NOUN
ap-1205	35	18	is	be	AUX
ap-1205	35	19	the	the	DET
ap-1205	35	20	fusing	fuse	VERB
ap-1205	35	21	matrix	matrix	NOUN
ap-1205	35	22	computed	compute	VERB
ap-1205	35	23	in	in	ADP
ap-1205	35	24	[	[	X
ap-1205	35	25	10	10	NUM
ap-1205	35	26	]	]	PUNCT
ap-1205	35	27	.	.	PUNCT
ap-1205	36	1	the	the	DET
ap-1205	36	2	boundary	boundary	ADJ
ap-1205	36	3	3	3	NUM
ap-1205	36	4	-	-	PUNCT
ap-1205	36	5	point	point	NOUN
ap-1205	36	6	functions	function	NOUN
ap-1205	36	7	c	c	NOUN
ap-1205	36	8	σ3,σ2,σ1	σ3,σ2,σ1	ADV
ap-1205	36	9	β3,β2,β1	β3,β2,β1	VERB
ap-1205	36	10	are	be	AUX
ap-1205	36	11	meromorphic	meromorphic	ADJ
ap-1205	36	12	with	with	ADP
ap-1205	36	13	respect	respect	NOUN
ap-1205	36	14	to	to	ADP
ap-1205	36	15	the	the	DET
ap-1205	36	16	variables	variable	NOUN
ap-1205	36	17	β1	β1	PROPN
ap-1205	36	18	,	,	PUNCT
ap-1205	36	19	β2	β2	VERB
ap-1205	36	20	,	,	PUNCT
ap-1205	36	21	β3	β3	VERB
ap-1205	36	22	[	[	PUNCT
ap-1205	36	23	9	9	NUM
ap-1205	36	24	]	]	PUNCT
ap-1205	36	25	,	,	PUNCT
ap-1205	36	26	while	while	SCONJ
ap-1205	36	27	the	the	DET
ap-1205	36	28	fusion	fusion	NOUN
ap-1205	36	29	coeficients	coeficient	NOUN
ap-1205	36	30	fβs	fβs	NOUN
ap-1205	36	31	,	,	PUNCT
ap-1205	36	32	βt	βt	PRON
ap-1205	36	33	[	[	PUNCT
ap-1205	36	34	β2	β2	NOUN
ap-1205	36	35	β	β	NOUN
ap-1205	36	36	β3	β3	VERB
ap-1205	36	37	β1	β1	PROPN
ap-1205	36	38	]	]	PUNCT
ap-1205	36	39	are	be	AUX
ap-1205	36	40	meromorphic	meromorphic	ADJ
ap-1205	36	41	in	in	ADP
ap-1205	36	42	all	all	DET
ap-1205	36	43	six	six	NUM
ap-1205	36	44	variables	variable	NOUN
ap-1205	36	45	and	and	CCONJ
ap-1205	36	46	invariant	invariant	ADJ
ap-1205	36	47	under	under	ADP
ap-1205	36	48	the	the	DET
ap-1205	36	49	reflections	reflection	NOUN
ap-1205	36	50	βi	βi	NUM
ap-1205	36	51	→	→	SYM
ap-1205	36	52	q−	q−	PROPN
ap-1205	36	53	βi	βi	PRON
ap-1205	36	54	.	.	PUNCT
ap-1205	37	1	when	when	SCONJ
ap-1205	37	2	one	one	NUM
ap-1205	37	3	of	of	ADP
ap-1205	37	4	the	the	DET
ap-1205	37	5	operators	operator	NOUN
ap-1205	37	6	corresponds	correspond	VERB
ap-1205	37	7	to	to	ADP
ap-1205	37	8	a	a	DET
ap-1205	37	9	degenerate	degenerate	ADJ
ap-1205	37	10	representation	representation	NOUN
ap-1205	37	11	,	,	PUNCT
ap-1205	37	12	the	the	DET
ap-1205	37	13	fβs	fβs	NOUN
ap-1205	37	14	,	,	PUNCT
ap-1205	37	15	βt	βt	NOUN
ap-1205	37	16	and	and	CCONJ
ap-1205	37	17	c	c	AUX
ap-1205	37	18	σ3,σ2,σ1	σ3,σ2,σ1	ADV
ap-1205	37	19	β3,β2,β1	β3,β2,β1	AUX
ap-1205	37	20	coeficients	coeficient	NOUN
ap-1205	37	21	develop	develop	VERB
ap-1205	37	22	singularities	singularity	NOUN
ap-1205	37	23	such	such	ADJ
ap-1205	37	24	that	that	SCONJ
ap-1205	37	25	the	the	DET
ap-1205	37	26	integral	integral	ADJ
ap-1205	37	27	in	in	ADP
ap-1205	37	28	(	(	PUNCT
ap-1205	37	29	2.2	2.2	NUM
ap-1205	37	30	)	)	PUNCT
ap-1205	37	31	gives	give	VERB
ap-1205	37	32	rise	rise	NOUN
ap-1205	37	33	to	to	ADP
ap-1205	37	34	a	a	DET
ap-1205	37	35	finite	finite	ADJ
ap-1205	37	36	sum	sum	NOUN
ap-1205	37	37	over	over	ADP
ap-1205	37	38	representations	representation	NOUN
ap-1205	37	39	in	in	ADP
ap-1205	37	40	accordance	accordance	NOUN
ap-1205	37	41	with	with	ADP
ap-1205	37	42	the	the	DET
ap-1205	37	43	fusion	fusion	NOUN
ap-1205	37	44	rules	rule	NOUN
ap-1205	37	45	[	[	X
ap-1205	37	46	9	9	NUM
ap-1205	37	47	]	]	PUNCT
ap-1205	37	48	.	.	PUNCT
ap-1205	38	1	in	in	ADP
ap-1205	38	2	particular	particular	ADJ
ap-1205	38	3	,	,	PUNCT
ap-1205	38	4	for	for	ADP
ap-1205	38	5	β	β	X
ap-1205	38	6	=	=	SYM
ap-1205	38	7	−b/2	−b/2	NOUN
ap-1205	38	8	,	,	PUNCT
ap-1205	38	9	equation	equation	NOUN
ap-1205	38	10	(	(	PUNCT
ap-1205	38	11	2.2	2.2	NUM
ap-1205	38	12	)	)	PUNCT
ap-1205	38	13	becomes	become	VERB
ap-1205	38	14	(	(	PUNCT
ap-1205	38	15	see	see	VERB
ap-1205	38	16	e.g.	e.g.	ADV
ap-1205	38	17	[	[	X
ap-1205	38	18	5	5	NUM
ap-1205	38	19	]	]	PUNCT
ap-1205	38	20	):	):	PUNCT
ap-1205	38	21	cσ3,β2−t	cσ3,β2−t	PROPN
ap-1205	38	22	b	b	PROPN
ap-1205	38	23	2	2	NUM
ap-1205	38	24	⎡⎣	⎡⎣	ADJ
ap-1205	38	25	β2	β2	NOUN
ap-1205	38	26	−	−	PROPN
ap-1205	38	27	b	b	SYM
ap-1205	38	28	2	2	NUM
ap-1205	38	29	σ4	σ4	NOUN
ap-1205	38	30	σ2	σ2	PROPN
ap-1205	38	31	⎤⎦	⎤⎦	PROPN
ap-1205	38	32	cσ2	cσ2	PROPN
ap-1205	39	1	=	=	NOUN
ap-1205	39	2	σ3±	σ3±	PROPN
ap-1205	39	3	b	b	PROPN
ap-1205	39	4	2	2	NUM
ap-1205	39	5	,	,	PUNCT
ap-1205	39	6	β3	β3	VERB
ap-1205	39	7	⎡⎣	⎡⎣	VERB
ap-1205	39	8	β2	β2	PROPN
ap-1205	39	9	−	−	PROPN
ap-1205	39	10	t	t	PROPN
ap-1205	39	11	b	b	SYM
ap-1205	39	12	2	2	NUM
ap-1205	39	13	β1	β1	PROPN
ap-1205	39	14	σ4	σ4	NOUN
ap-1205	39	15	σ1	σ1	PROPN
ap-1205	39	16	⎤⎦	⎤⎦	PROPN
ap-1205	40	1	=	=	PUNCT
ap-1205	40	2	f+t	f+t	PROPN
ap-1205	40	3	⎡⎣	⎡⎣	PROPN
ap-1205	40	4	β2	β2	NOUN
ap-1205	40	5	−	−	PROPN
ap-1205	40	6	b	b	SYM
ap-1205	40	7	2	2	NUM
ap-1205	40	8	β3	β3	NOUN
ap-1205	40	9	β1	β1	VERB
ap-1205	40	10	⎤⎦cσ3±	⎤⎦cσ3±	PROPN
ap-1205	40	11	b	b	PROPN
ap-1205	40	12	2β1−	2β1−	NUM
ap-1205	40	13	b	b	SYM
ap-1205	40	14	2	2	NUM
ap-1205	40	15	⎡⎣	⎡⎣	VERB
ap-1205	40	16	−	−	PROPN
ap-1205	40	17	b	b	SYM
ap-1205	40	18	2	2	NUM
ap-1205	40	19	β1	β1	PROPN
ap-1205	40	20	σ3	σ3	PROPN
ap-1205	40	21	σ1	σ1	PROPN
ap-1205	40	22	⎤⎦	⎤⎦	PROPN
ap-1205	40	23	cσ3,β3	cσ3,β3	PROPN
ap-1205	41	1	⎡⎣	⎡⎣	AUX
ap-1205	41	2	β2	β2	PROPN
ap-1205	41	3	β1	β1	PROPN
ap-1205	41	4	−	−	PROPN
ap-1205	41	5	b	b	SYM
ap-1205	41	6	2	2	NUM
ap-1205	41	7	σ4	σ4	NOUN
ap-1205	41	8	σ1	σ1	PROPN
ap-1205	41	9	⎤⎦+	⎤⎦+	PROPN
ap-1205	41	10	(	(	PUNCT
ap-1205	41	11	2.3	2.3	NUM
ap-1205	41	12	)	)	PUNCT
ap-1205	41	13	f−t	f−t	NOUN
ap-1205	41	14	⎡⎣	⎡⎣	VERB
ap-1205	41	15	β2	β2	NOUN
ap-1205	41	16	−	−	PROPN
ap-1205	41	17	b	b	SYM
ap-1205	41	18	2	2	NUM
ap-1205	41	19	β3	β3	NOUN
ap-1205	41	20	β1	β1	VERB
ap-1205	41	21	⎤⎦cσ3±	⎤⎦cσ3±	PROPN
ap-1205	41	22	b	b	PROPN
ap-1205	42	1	2β1	2β1	NUM
ap-1205	42	2	+	+	SYM
ap-1205	42	3	b	b	SYM
ap-1205	42	4	2	2	NUM
ap-1205	42	5	⎡⎣	⎡⎣	VERB
ap-1205	42	6	−	−	PROPN
ap-1205	42	7	b	b	SYM
ap-1205	42	8	2	2	NUM
ap-1205	42	9	β1	β1	PROPN
ap-1205	42	10	σ3	σ3	PROPN
ap-1205	42	11	σ1	σ1	PROPN
ap-1205	42	12	⎤⎦	⎤⎦	PROPN
ap-1205	42	13	cσ3,β3	cσ3,β3	PROPN
ap-1205	43	1	⎡⎣	⎡⎣	AUX
ap-1205	43	2	β2	β2	VERB
ap-1205	43	3	β1	β1	PROPN
ap-1205	44	1	+	+	CCONJ
ap-1205	44	2	b	b	SYM
ap-1205	44	3	2	2	NUM
ap-1205	44	4	σ4	σ4	NOUN
ap-1205	44	5	σ1	σ1	PROPN
ap-1205	44	6	⎤⎦	⎤⎦	PROPN
ap-1205	44	7	,	,	PUNCT
ap-1205	44	8	t	t	PROPN
ap-1205	44	9	=	=	PUNCT
ap-1205	44	10	±1	±1	VERB
ap-1205	44	11	where	where	SCONJ
ap-1205	44	12	c	c	PROPN
ap-1205	44	13	and	and	CCONJ
ap-1205	44	14	f	f	PROPN
ap-1205	44	15	are	be	AUX
ap-1205	44	16	the	the	DET
ap-1205	44	17	appropriate	appropriate	ADJ
ap-1205	44	18	residues	residue	NOUN
ap-1205	44	19	of	of	ADP
ap-1205	44	20	c	c	PROPN
ap-1205	44	21	and	and	CCONJ
ap-1205	44	22	f	f	PROPN
ap-1205	44	23	.	.	PUNCT
ap-1205	45	1	for	for	ADP
ap-1205	45	2	t	t	NOUN
ap-1205	45	3	=	=	SYM
ap-1205	45	4	1	1	NUM
ap-1205	45	5	it	it	PRON
ap-1205	45	6	becomes	become	VERB
ap-1205	45	7	cσ3,σ2±	cσ3,σ2±	ADP
ap-1205	45	8	b	b	NOUN
ap-1205	45	9	2	2	NUM
ap-1205	45	10	,	,	PUNCT
ap-1205	45	11	σ1	σ1	NOUN
ap-1205	45	12	β3,β2,β1	β3,β2,β1	NOUN
ap-1205	45	13	=	=	SYM
ap-1205	45	14	γ(1−	γ(1−	PROPN
ap-1205	45	15	2β2b)γ((2β1	2β2b)γ((2β1	NUM
ap-1205	45	16	−	−	PROPN
ap-1205	45	17	b)b	b)b	ADJ
ap-1205	45	18	)	)	PUNCT
ap-1205	45	19	γ(1−	γ(1−	PROPN
ap-1205	45	20	b(β2	b(β2	NOUN
ap-1205	46	1	+	+	CCONJ
ap-1205	46	2	β3	β3	ADJ
ap-1205	46	3	−	−	NOUN
ap-1205	46	4	β1))γ(b(β1	β1))γ(b(β1	NOUN
ap-1205	46	5	+	+	CCONJ
ap-1205	46	6	β3	β3	ADP
ap-1205	46	7	−	−	PROPN
ap-1205	46	8	β2	β2	NOUN
ap-1205	46	9	−	−	PROPN
ap-1205	46	10	b	b	NOUN
ap-1205	46	11	)	)	PUNCT
ap-1205	46	12	)	)	PUNCT
ap-1205	46	13	·	·	PUNCT
ap-1205	47	1	cσ3,σ2,σ1	cσ3,σ2,σ1	ADP
ap-1205	47	2	β3,β2	β3,β2	PROPN
ap-1205	47	3	+	+	CCONJ
ap-1205	47	4	b	b	SYM
ap-1205	47	5	2	2	NUM
ap-1205	47	6	,	,	PUNCT
ap-1205	47	7	β1−	β1−	PROPN
ap-1205	47	8	b	b	PROPN
ap-1205	47	9	2	2	NUM
ap-1205	47	10	+	+	CCONJ
ap-1205	47	11	(	(	PUNCT
ap-1205	47	12	2.4	2.4	NUM
ap-1205	47	13	)	)	PUNCT
ap-1205	47	14	b2	b2	NOUN
ap-1205	47	15	√	√	NOUN
ap-1205	47	16	λlγ(1−	λlγ(1−	PROPN
ap-1205	47	17	2β2b)γ(1−	2β2b)γ(1−	NOUN
ap-1205	47	18	2β1b)g	2β1b)g	NUM
ap-1205	47	19	∓	∓	PROPN
ap-1205	47	20	(	(	PUNCT
ap-1205	47	21	σ2	σ2	NOUN
ap-1205	47	22	,	,	PUNCT
ap-1205	47	23	β1	β1	PROPN
ap-1205	47	24	,	,	PUNCT
ap-1205	47	25	σ1	σ1	PROPN
ap-1205	47	26	)	)	PUNCT
ap-1205	47	27	2	2	NUM
ap-1205	47	28	sinπb(2β1	sinπb(2β1	PROPN
ap-1205	47	29	−q)γ(1−	−q)γ(1−	NOUN
ap-1205	47	30	b(β1	b(β1	NOUN
ap-1205	47	31	+	+	CCONJ
ap-1205	47	32	β2	β2	NOUN
ap-1205	47	33	+	+	CCONJ
ap-1205	47	34	β3	β3	ADJ
ap-1205	47	35	−q))γ(1−	−q))γ(1−	NUM
ap-1205	47	36	b(β1	b(β1	NOUN
ap-1205	47	37	+	+	CCONJ
ap-1205	47	38	β2	β2	NOUN
ap-1205	47	39	−	−	PROPN
ap-1205	47	40	β3	β3	ADJ
ap-1205	47	41	)	)	PUNCT
ap-1205	47	42	)	)	PUNCT
ap-1205	47	43	·	·	PUNCT
ap-1205	48	1	cσ3,σ2,σ1	cσ3,σ2,σ1	VERB
ap-1205	48	2	β3,β2	β3,β2	PROPN
ap-1205	48	3	+	+	CCONJ
ap-1205	48	4	b	b	SYM
ap-1205	48	5	2	2	NUM
ap-1205	48	6	,	,	PUNCT
ap-1205	48	7	β1	β1	PROPN
ap-1205	48	8	+	+	CCONJ
ap-1205	48	9	b	b	NOUN
ap-1205	48	10	2	2	NUM
ap-1205	48	11	,	,	PUNCT
ap-1205	48	12	where	where	SCONJ
ap-1205	48	13	λl	λl	VERB
ap-1205	48	14	=	=	SYM
ap-1205	48	15	πμγ(b2	πμγ(b2	NOUN
ap-1205	48	16	)	)	PUNCT
ap-1205	48	17	is	be	AUX
ap-1205	48	18	the	the	DET
ap-1205	48	19	(	(	PUNCT
ap-1205	48	20	normalised	normalise	VERB
ap-1205	48	21	)	)	PUNCT
ap-1205	48	22	cosmological	cosmological	ADJ
ap-1205	48	23	constant	constant	ADJ
ap-1205	48	24	and	and	CCONJ
ap-1205	48	25	g−(σ2	g−(σ2	ADJ
ap-1205	48	26	,	,	PUNCT
ap-1205	48	27	β1	β1	PROPN
ap-1205	48	28	,	,	PUNCT
ap-1205	48	29	σ1	σ1	PROPN
ap-1205	48	30	)	)	PUNCT
ap-1205	48	31	=	=	PUNCT
ap-1205	49	1	g+(σ2	g+(σ2	PROPN
ap-1205	49	2	,	,	PUNCT
ap-1205	49	3	q−	q−	PROPN
ap-1205	49	4	β1	β1	PROPN
ap-1205	49	5	,	,	PUNCT
ap-1205	49	6	σ1	σ1	PROPN
ap-1205	49	7	)	)	PUNCT
ap-1205	49	8	=	=	PUNCT
ap-1205	50	1	−	−	PROPN
ap-1205	50	2	4	4	NUM
ap-1205	50	3	sinπb	sinπb	NOUN
ap-1205	50	4	(	(	PUNCT
ap-1205	50	5	β1	β1	PROPN
ap-1205	50	6	−	−	PROPN
ap-1205	50	7	σ1	σ1	PROPN
ap-1205	50	8	−	−	PROPN
ap-1205	50	9	σ2	σ2	PROPN
ap-1205	50	10	+	+	CCONJ
ap-1205	50	11	b	b	PROPN
ap-1205	50	12	2	2	X
ap-1205	50	13	)	)	PUNCT
ap-1205	50	14	sinπb	sinπb	NOUN
ap-1205	50	15	(	(	PUNCT
ap-1205	50	16	β1	β1	PROPN
ap-1205	50	17	−	−	PROPN
ap-1205	50	18	σ2	σ2	PROPN
ap-1205	50	19	+	+	PROPN
ap-1205	50	20	σ1	σ1	PROPN
ap-1205	50	21	−	−	PROPN
ap-1205	50	22	b	b	PROPN
ap-1205	50	23	2	2	NUM
ap-1205	50	24	)	)	PUNCT
ap-1205	50	25	.	.	PUNCT
ap-1205	51	1	(	(	PUNCT
ap-1205	51	2	2.5	2.5	NUM
ap-1205	51	3	)	)	PUNCT
ap-1205	51	4	there	there	PRON
ap-1205	51	5	is	be	VERB
ap-1205	51	6	a	a	DET
ap-1205	51	7	second	second	ADJ
ap-1205	51	8	equation	equation	NOUN
ap-1205	51	9	with	with	ADP
ap-1205	51	10	a	a	DET
ap-1205	51	11	shift	shift	NOUN
ap-1205	51	12	β2	β2	NOUN
ap-1205	51	13	−	−	PROPN
ap-1205	51	14	b/2	b/2	NOUN
ap-1205	51	15	on	on	ADP
ap-1205	51	16	the	the	DET
ap-1205	51	17	r.h.s	r.h.s	NOUN
ap-1205	51	18	.	.	PUNCT
ap-1205	52	1	as	as	ADV
ap-1205	52	2	well	well	ADV
ap-1205	52	3	as	as	ADP
ap-1205	53	1	two	two	NUM
ap-1205	53	2	dual	dual	ADJ
ap-1205	53	3	equations	equation	NOUN
ap-1205	53	4	for	for	ADP
ap-1205	53	5	1	1	NUM
ap-1205	53	6	/	/	SYM
ap-1205	53	7	b→	b→	PROPN
ap-1205	53	8	b/2	b/2	NOUN
ap-1205	53	9	.	.	PUNCT
ap-1205	54	1	the	the	DET
ap-1205	54	2	derivation	derivation	NOUN
ap-1205	54	3	of	of	ADP
ap-1205	54	4	(	(	PUNCT
ap-1205	54	5	2.4	2.4	NUM
ap-1205	54	6	)	)	PUNCT
ap-1205	54	7	is	be	AUX
ap-1205	54	8	standard	standard	ADJ
ap-1205	54	9	and	and	CCONJ
ap-1205	54	10	the	the	DET
ap-1205	54	11	coeficients	coeficient	NOUN
ap-1205	54	12	in	in	ADP
ap-1205	54	13	front	front	NOUN
ap-1205	54	14	of	of	ADP
ap-1205	54	15	the	the	DET
ap-1205	54	16	correlators	correlator	NOUN
ap-1205	54	17	are	be	AUX
ap-1205	54	18	given	give	VERB
ap-1205	54	19	by	by	ADP
ap-1205	54	20	the	the	DET
ap-1205	54	21	products	product	NOUN
ap-1205	54	22	of	of	ADP
ap-1205	54	23	fusing	fuse	VERB
ap-1205	54	24	matrix	matrix	NOUN
ap-1205	54	25	elements	element	NOUN
ap-1205	54	26	and	and	CCONJ
ap-1205	54	27	3	3	NUM
ap-1205	54	28	-	-	PUNCT
ap-1205	54	29	point	point	NOUN
ap-1205	54	30	boundary	boundary	ADJ
ap-1205	54	31	functions	function	NOUN
ap-1205	54	32	containing	contain	VERB
ap-1205	54	33	a	a	DET
ap-1205	54	34	fundamental	fundamental	ADJ
ap-1205	54	35	field	field	NOUN
ap-1205	54	36	.	.	PUNCT
ap-1205	55	1	the	the	DET
ap-1205	55	2	latter	latter	ADJ
ap-1205	55	3	are	be	AUX
ap-1205	55	4	computed	compute	VERB
ap-1205	55	5	by	by	ADP
ap-1205	55	6	free	free	ADJ
ap-1205	55	7	field	field	NOUN
ap-1205	55	8	coulomb	coulomb	NOUN
ap-1205	55	9	gas	gas	NOUN
ap-1205	55	10	methods	method	NOUN
ap-1205	55	11	[	[	X
ap-1205	55	12	8	8	NUM
ap-1205	55	13	]	]	PUNCT
ap-1205	55	14	,	,	PUNCT
ap-1205	55	15	assuming	assume	VERB
ap-1205	55	16	that	that	SCONJ
ap-1205	55	17	for	for	ADP
ap-1205	55	18	degenerate	degenerate	ADJ
ap-1205	55	19	representations	representation	NOUN
ap-1205	55	20	the	the	DET
ap-1205	55	21	cardy	cardy	PROPN
ap-1205	55	22	multiplicity	multiplicity	NOUN
ap-1205	55	23	coincides	coincide	VERB
ap-1205	55	24	with	with	ADP
ap-1205	55	25	the	the	DET
ap-1205	55	26	verlinde	verlinde	NOUN
ap-1205	55	27	multiplicity	multiplicity	NOUN
ap-1205	55	28	.	.	PUNCT
ap-1205	56	1	in	in	ADP
ap-1205	56	2	the	the	DET
ap-1205	56	3	case	case	NOUN
ap-1205	56	4	above	above	ADV
ap-1205	56	5	,	,	PUNCT
ap-1205	56	6	this	this	PRON
ap-1205	56	7	means	mean	VERB
ap-1205	56	8	that	that	SCONJ
ap-1205	56	9	the	the	DET
ap-1205	56	10	two	two	NUM
ap-1205	56	11	boundaries	boundary	NOUN
ap-1205	56	12	of	of	ADP
ap-1205	56	13	the	the	DET
ap-1205	56	14	field	field	NOUN
ap-1205	56	15	σ2bσ1	σ2bσ1	NOUN
ap-1205	56	16	−	−	PROPN
ap-1205	56	17	b	b	SYM
ap-1205	56	18	2	2	NUM
ap-1205	56	19	satisfy	satisfy	NOUN
ap-1205	56	20	σ2	σ2	PROPN
ap-1205	56	21	=	=	SYM
ap-1205	56	22	σ1	σ1	PROPN
ap-1205	56	23	±	±	NUM
ap-1205	56	24	b/2	b/2	PROPN
ap-1205	56	25	.	.	PUNCT
ap-1205	57	1	2.1	2.1	NUM
ap-1205	57	2	the	the	DET
ap-1205	57	3	simplest	simple	ADJ
ap-1205	57	4	correlator	correlator	NOUN
ap-1205	57	5	we	we	PRON
ap-1205	57	6	start	start	VERB
ap-1205	57	7	with	with	ADP
ap-1205	57	8	the	the	DET
ap-1205	57	9	derivation	derivation	NOUN
ap-1205	57	10	of	of	ADP
ap-1205	57	11	the	the	DET
ap-1205	57	12	simplest	simple	ADJ
ap-1205	57	13	correlator	correlator	NOUN
ap-1205	57	14	with	with	ADP
ap-1205	57	15	three	three	NUM
ap-1205	57	16	identical	identical	ADJ
ap-1205	57	17	charges	charge	NOUN
ap-1205	57	18	equal	equal	ADJ
ap-1205	57	19	to	to	ADP
ap-1205	57	20	b	b	NUM
ap-1205	57	21	,	,	PUNCT
ap-1205	57	22	i.e.	i.e.	X
ap-1205	57	23	,	,	PUNCT
ap-1205	57	24	the	the	DET
ap-1205	57	25	correlator	correlator	NOUN
ap-1205	57	26	of	of	ADP
ap-1205	57	27	three	three	NUM
ap-1205	57	28	cosmological	cosmological	ADJ
ap-1205	57	29	operators	operator	NOUN
ap-1205	57	30	,	,	PUNCT
ap-1205	57	31	or	or	CCONJ
ap-1205	57	32	boundary	boundary	ADJ
ap-1205	57	33	liouville	liouville	NOUN
ap-1205	57	34	screening	screen	VERB
ap-1205	57	35	charges	charge	NOUN
ap-1205	57	36	.	.	PUNCT
ap-1205	58	1	it	it	PRON
ap-1205	58	2	is	be	AUX
ap-1205	58	3	reproduced	reproduce	VERB
ap-1205	58	4	by	by	ADP
ap-1205	58	5	the	the	DET
ap-1205	58	6	second	second	ADJ
ap-1205	58	7	term	term	NOUN
ap-1205	58	8	on	on	ADP
ap-1205	58	9	the	the	DET
ap-1205	58	10	r.h.s	r.h.s	NOUN
ap-1205	58	11	.	.	PUNCT
ap-1205	58	12	of	of	ADP
ap-1205	58	13	the	the	DET
ap-1205	58	14	equality	equality	NOUN
ap-1205	58	15	(	(	PUNCT
ap-1205	58	16	2.4	2.4	NUM
ap-1205	58	17	)	)	PUNCT
ap-1205	58	18	choosing	choose	VERB
ap-1205	58	19	β1	β1	PROPN
ap-1205	58	20	=	=	SYM
ap-1205	58	21	b	b	PROPN
ap-1205	58	22	2	2	NUM
ap-1205	58	23	=	=	SYM
ap-1205	58	24	β2	β2	VERB
ap-1205	58	25	,	,	PUNCT
ap-1205	58	26	β3	β3	PROPN
ap-1205	58	27	=	=	SYM
ap-1205	58	28	b.	b.	PROPN
ap-1205	58	29	for	for	ADP
ap-1205	58	30	this	this	DET
ap-1205	58	31	choice	choice	NOUN
ap-1205	58	32	the	the	DET
ap-1205	58	33	equation	equation	NOUN
ap-1205	58	34	needs	need	VERB
ap-1205	58	35	regularisation	regularisation	NOUN
ap-1205	58	36	since	since	SCONJ
ap-1205	58	37	the	the	DET
ap-1205	58	38	coeficient	coeficient	NOUN
ap-1205	58	39	in	in	ADP
ap-1205	58	40	front	front	NOUN
ap-1205	58	41	of	of	ADP
ap-1205	58	42	the	the	DET
ap-1205	58	43	correlator	correlator	NOUN
ap-1205	58	44	becomes	become	VERB
ap-1205	58	45	divergent	divergent	ADJ
ap-1205	58	46	.	.	PUNCT
ap-1205	59	1	the	the	DET
ap-1205	59	2	remaining	remain	VERB
ap-1205	59	3	two	two	NUM
ap-1205	59	4	correlators	correlator	NOUN
ap-1205	59	5	are	be	AUX
ap-1205	59	6	represented	represent	VERB
ap-1205	59	7	85	85	NUM
ap-1205	59	8	acta	acta	PROPN
ap-1205	59	9	polytechnica	polytechnica	PROPN
ap-1205	59	10	vol	vol	NOUN
ap-1205	59	11	.	.	PROPN
ap-1205	60	1	50	50	NUM
ap-1205	60	2	no	no	NOUN
ap-1205	60	3	.	.	PUNCT
ap-1205	61	1	3/2010	3/2010	NUM
ap-1205	61	2	as	as	ADP
ap-1205	61	3	reflections	reflection	NOUN
ap-1205	61	4	(	(	PUNCT
ap-1205	61	5	2.1	2.1	NUM
ap-1205	61	6	)	)	PUNCT
ap-1205	61	7	with	with	ADP
ap-1205	61	8	respect	respect	NOUN
ap-1205	61	9	to	to	ADP
ap-1205	61	10	β3	β3	PROPN
ap-1205	61	11	(	(	PUNCT
ap-1205	61	12	the	the	DET
ap-1205	61	13	l.h.s	l.h.s	NOUN
ap-1205	61	14	.	.	PUNCT
ap-1205	61	15	)	)	PUNCT
ap-1205	62	1	and	and	CCONJ
ap-1205	62	2	β2	β2	NOUN
ap-1205	62	3	(	(	PUNCT
ap-1205	62	4	the	the	DET
ap-1205	62	5	first	first	ADJ
ap-1205	62	6	term	term	NOUN
ap-1205	62	7	on	on	ADP
ap-1205	62	8	the	the	DET
ap-1205	62	9	r.h.s	r.h.s	NOUN
ap-1205	62	10	.	.	PUNCT
ap-1205	62	11	)	)	PUNCT
ap-1205	62	12	of	of	ADP
ap-1205	62	13	correlators	correlator	NOUN
ap-1205	62	14	which	which	PRON
ap-1205	62	15	also	also	ADV
ap-1205	62	16	diverge	diverge	VERB
ap-1205	62	17	,	,	PUNCT
ap-1205	62	18	if	if	SCONJ
ap-1205	62	19	we	we	PRON
ap-1205	62	20	assume	assume	VERB
ap-1205	62	21	that	that	SCONJ
ap-1205	62	22	they	they	PRON
ap-1205	62	23	are	be	AUX
ap-1205	62	24	given	give	VERB
ap-1205	62	25	by	by	ADP
ap-1205	62	26	the	the	DET
ap-1205	62	27	integral	integral	ADJ
ap-1205	62	28	pt	pt	NOUN
ap-1205	62	29	formula	formula	NOUN
ap-1205	62	30	.	.	PUNCT
ap-1205	63	1	indeed	indeed	ADV
ap-1205	63	2	they	they	PRON
ap-1205	63	3	satisfy	satisfy	VERB
ap-1205	63	4	the	the	DET
ap-1205	63	5	charge	charge	NOUN
ap-1205	63	6	conservation	conservation	NOUN
ap-1205	63	7	conditions	condition	NOUN
ap-1205	63	8	(	(	PUNCT
ap-1205	63	9	q−	q−	PROPN
ap-1205	63	10	β3	β3	PROPN
ap-1205	63	11	)	)	PUNCT
ap-1205	63	12	+	+	CCONJ
ap-1205	63	13	β2	β2	NOUN
ap-1205	63	14	+	+	CCONJ
ap-1205	63	15	β1	β1	PROPN
ap-1205	63	16	=	=	PUNCT
ap-1205	63	17	q	q	NOUN
ap-1205	63	18	and	and	CCONJ
ap-1205	63	19	β3	β3	VERB
ap-1205	63	20	+	+	CCONJ
ap-1205	63	21	(	(	PUNCT
ap-1205	63	22	q−	q−	PROPN
ap-1205	63	23	β2	β2	NOUN
ap-1205	63	24	−	−	PROPN
ap-1205	63	25	b/2	b/2	NOUN
ap-1205	63	26	)	)	PUNCT
ap-1205	64	1	+	+	CCONJ
ap-1205	64	2	(	(	PUNCT
ap-1205	64	3	β1	β1	PROPN
ap-1205	64	4	−	−	PROPN
ap-1205	64	5	b/2	b/2	NOUN
ap-1205	64	6	)	)	PUNCT
ap-1205	65	1	=	=	SYM
ap-1205	65	2	q	q	NOUN
ap-1205	65	3	,	,	PUNCT
ap-1205	65	4	respectively	respectively	ADV
ap-1205	65	5	,	,	PUNCT
ap-1205	65	6	and	and	CCONJ
ap-1205	65	7	their	their	PRON
ap-1205	65	8	residua	residuum	NOUN
ap-1205	65	9	equal	equal	VERB
ap-1205	65	10	1/2π	1/2π	NUM
ap-1205	65	11	(	(	PUNCT
ap-1205	65	12	to	to	PART
ap-1205	65	13	agree	agree	VERB
ap-1205	65	14	with	with	ADP
ap-1205	65	15	the	the	DET
ap-1205	65	16	normalisation	normalisation	NOUN
ap-1205	65	17	in	in	ADP
ap-1205	65	18	[	[	X
ap-1205	65	19	9	9	NUM
ap-1205	65	20	]	]	NUM
ap-1205	65	21	)	)	PUNCT
ap-1205	65	22	.	.	PUNCT
ap-1205	66	1	thus	thus	ADV
ap-1205	66	2	,	,	PUNCT
ap-1205	66	3	in	in	ADP
ap-1205	66	4	a	a	DET
ap-1205	66	5	proper	proper	ADJ
ap-1205	66	6	regularisation	regularisation	NOUN
ap-1205	66	7	of	of	ADP
ap-1205	66	8	(	(	PUNCT
ap-1205	66	9	2.4	2.4	NUM
ap-1205	66	10	)	)	PUNCT
ap-1205	66	11	,	,	PUNCT
ap-1205	66	12	these	these	DET
ap-1205	66	13	two	two	NUM
ap-1205	66	14	correlators	correlator	NOUN
ap-1205	66	15	are	be	AUX
ap-1205	66	16	replaced	replace	VERB
ap-1205	66	17	by	by	ADP
ap-1205	66	18	the	the	DET
ap-1205	66	19	corresponding	corresponding	ADJ
ap-1205	66	20	reflection	reflection	NOUN
ap-1205	66	21	amplitudes	amplitude	NOUN
ap-1205	66	22	,	,	PUNCT
ap-1205	66	23	which	which	PRON
ap-1205	66	24	appear	appear	VERB
ap-1205	66	25	as	as	ADP
ap-1205	66	26	the	the	DET
ap-1205	66	27	initial	initial	ADJ
ap-1205	66	28	data	datum	NOUN
ap-1205	66	29	in	in	ADP
ap-1205	66	30	the	the	DET
ap-1205	66	31	equation	equation	NOUN
ap-1205	66	32	.	.	PUNCT
ap-1205	67	1	we	we	PRON
ap-1205	67	2	recall	recall	VERB
ap-1205	67	3	their	their	PRON
ap-1205	67	4	general	general	ADJ
ap-1205	67	5	expression	expression	NOUN
ap-1205	67	6	computed	compute	VERB
ap-1205	67	7	in	in	ADP
ap-1205	67	8	[	[	X
ap-1205	67	9	8	8	NUM
ap-1205	67	10	]	]	PUNCT
ap-1205	67	11	,	,	PUNCT
ap-1205	67	12	s(σ2	s(σ2	PROPN
ap-1205	67	13	,	,	PUNCT
ap-1205	67	14	β	β	X
ap-1205	67	15	,	,	PUNCT
ap-1205	67	16	σ1	σ1	PROPN
ap-1205	67	17	)	)	PUNCT
ap-1205	67	18	=	=	PUNCT
ap-1205	68	1	2π	2π	PROPN
ap-1205	69	1	bγ(1	bγ(1	PROPN
ap-1205	69	2	+	+	CCONJ
ap-1205	69	3	1b	1b	NUM
ap-1205	69	4	(	(	PUNCT
ap-1205	69	5	q−	q−	PROPN
ap-1205	69	6	2β))γ(b(q−	2β))γ(b(q−	NUM
ap-1205	69	7	2β	2β	NOUN
ap-1205	69	8	)	)	PUNCT
ap-1205	69	9	)	)	PUNCT
ap-1205	70	1	g2(σ2	g2(σ2	NUM
ap-1205	70	2	,	,	PUNCT
ap-1205	70	3	β	β	X
ap-1205	70	4	,	,	PUNCT
ap-1205	70	5	σ1	σ1	PROPN
ap-1205	70	6	)	)	PUNCT
ap-1205	70	7	,	,	PUNCT
ap-1205	70	8	(	(	PUNCT
ap-1205	70	9	2.6	2.6	NUM
ap-1205	70	10	)	)	PUNCT
ap-1205	70	11	g2(σ2	g2(σ2	PROPN
ap-1205	70	12	,	,	PUNCT
ap-1205	70	13	β	β	X
ap-1205	70	14	,	,	PUNCT
ap-1205	70	15	σ1	σ1	NOUN
ap-1205	70	16	)	)	PUNCT
ap-1205	70	17	=	=	PUNCT
ap-1205	71	1	λ	λ	X
ap-1205	71	2	1	1	NUM
ap-1205	71	3	2b	2b	NUM
ap-1205	71	4	(	(	PUNCT
ap-1205	71	5	q−2β	q−2β	NOUN
ap-1205	71	6	)	)	PUNCT
ap-1205	71	7	l	l	NOUN
ap-1205	71	8	sb(2β	sb(2β	AUX
ap-1205	71	9	−q)∏	−q)∏	PUNCT
ap-1205	71	10	s=±	s=±	NOUN
ap-1205	71	11	sb(β	sb(β	VERB
ap-1205	71	12	+	+	CCONJ
ap-1205	71	13	s(σ2	s(σ2	NOUN
ap-1205	71	14	+	+	CCONJ
ap-1205	71	15	σ1	σ1	PROPN
ap-1205	71	16	−q))sb(β	−q))sb(β	X
ap-1205	71	17	+	+	CCONJ
ap-1205	71	18	s(σ2	s(σ2	ADJ
ap-1205	71	19	−	−	PROPN
ap-1205	71	20	σ1	σ1	PROPN
ap-1205	71	21	)	)	PUNCT
ap-1205	71	22	)	)	PUNCT
ap-1205	71	23	,	,	PUNCT
ap-1205	71	24	where	where	SCONJ
ap-1205	71	25	sb(α	sb(α	PUNCT
ap-1205	71	26	)	)	PUNCT
ap-1205	71	27	=	=	PUNCT
ap-1205	72	1	γb(α)/γb(q−	γb(α)/γb(q−	PROPN
ap-1205	72	2	α	α	X
ap-1205	72	3	)	)	PUNCT
ap-1205	72	4	=	=	SYM
ap-1205	72	5	2	2	NUM
ap-1205	72	6	sinπb(α−	sinπb(α−	NOUN
ap-1205	72	7	b)sb(α−	b)sb(α−	NOUN
ap-1205	72	8	b	b	X
ap-1205	72	9	)	)	PUNCT
ap-1205	72	10	and	and	CCONJ
ap-1205	72	11	γb(x	γb(x	NUM
ap-1205	72	12	)	)	PUNCT
ap-1205	72	13	is	be	AUX
ap-1205	72	14	the	the	DET
ap-1205	72	15	double	double	ADJ
ap-1205	72	16	gamma	gamma	NOUN
ap-1205	72	17	function	function	NOUN
ap-1205	72	18	;	;	PUNCT
ap-1205	72	19	sb(b	sb(b	NOUN
ap-1205	72	20	)	)	PUNCT
ap-1205	72	21	=	=	SYM
ap-1205	72	22	b.	b.	PROPN
ap-1205	72	23	in	in	ADP
ap-1205	72	24	the	the	DET
ap-1205	72	25	case	case	NOUN
ap-1205	72	26	under	under	ADP
ap-1205	72	27	consideration	consideration	NOUN
ap-1205	72	28	here	here	ADV
ap-1205	72	29	β	β	X
ap-1205	72	30	=	=	SYM
ap-1205	72	31	b	b	PROPN
ap-1205	72	32	and	and	CCONJ
ap-1205	72	33	inserting	insert	VERB
ap-1205	72	34	in	in	ADP
ap-1205	72	35	(	(	PUNCT
ap-1205	72	36	2.4	2.4	NUM
ap-1205	72	37	)	)	PUNCT
ap-1205	72	38	we	we	PRON
ap-1205	72	39	reproduce	reproduce	VERB
ap-1205	72	40	the	the	DET
ap-1205	72	41	cyclically	cyclically	ADV
ap-1205	72	42	symmetric	symmetric	ADJ
ap-1205	72	43	expression	expression	NOUN
ap-1205	72	44	proposed	propose	VERB
ap-1205	72	45	in	in	ADP
ap-1205	72	46	the	the	DET
ap-1205	72	47	microscopic	microscopic	ADJ
ap-1205	72	48	approach	approach	NOUN
ap-1205	72	49	[	[	X
ap-1205	72	50	5	5	NUM
ap-1205	72	51	]	]	PUNCT
ap-1205	72	52	,	,	PUNCT
ap-1205	72	53	cσ3,σ2,σ1	cσ3,σ2,σ1	PROPN
ap-1205	72	54	b	b	PROPN
ap-1205	72	55	,	,	PUNCT
ap-1205	72	56	b	b	PROPN
ap-1205	72	57	,	,	PUNCT
ap-1205	72	58	b	b	X
ap-1205	72	59	=	=	SYM
ap-1205	72	60	2π	2π	NOUN
ap-1205	72	61	√	√	VERB
ap-1205	72	62	λl	λl	NUM
ap-1205	72	63	−1	−1	NOUN
ap-1205	72	64	(	(	PUNCT
ap-1205	72	65	γ(1	γ(1	PROPN
ap-1205	72	66	−	−	PROPN
ap-1205	72	67	b2))2γ	b2))2γ	PROPN
ap-1205	72	68	(	(	PUNCT
ap-1205	72	69	1b2	1b2	NUM
ap-1205	72	70	−	−	NOUN
ap-1205	72	71	1	1	NUM
ap-1205	72	72	)	)	PUNCT
ap-1205	72	73	·	·	PUNCT
ap-1205	73	1	g2(σ3	g2(σ3	NOUN
ap-1205	73	2	,	,	PUNCT
ap-1205	73	3	b	b	NOUN
ap-1205	73	4	,	,	PUNCT
ap-1205	73	5	σ1)−g2(σ3	σ1)−g2(σ3	PROPN
ap-1205	73	6	,	,	PUNCT
ap-1205	73	7	b	b	NOUN
ap-1205	73	8	,	,	PUNCT
ap-1205	73	9	σ2	σ2	NOUN
ap-1205	73	10	)	)	PUNCT
ap-1205	73	11	g−(σ1	g−(σ1	NOUN
ap-1205	73	12	,	,	PUNCT
ap-1205	73	13	b	b	PROPN
ap-1205	73	14	2	2	NUM
ap-1205	73	15	,	,	PUNCT
ap-1205	73	16	σ2	σ2	NOUN
ap-1205	73	17	)	)	PUNCT
ap-1205	73	18	=	=	PUNCT
ap-1205	73	19	(	(	PUNCT
ap-1205	73	20	2.7	2.7	NUM
ap-1205	73	21	)	)	PUNCT
ap-1205	73	22	2πλ	2πλ	NOUN
ap-1205	74	1	q−3b	q−3b	ADV
ap-1205	74	2	2b	2b	NUM
ap-1205	74	3	l	l	NOUN
ap-1205	74	4	sb(2b	sb(2b	NUM
ap-1205	74	5	)	)	PUNCT
ap-1205	74	6	(	(	PUNCT
ap-1205	74	7	γ(1	γ(1	PROPN
ap-1205	74	8	−	−	PROPN
ap-1205	74	9	b2))2γ	b2))2γ	PROPN
ap-1205	74	10	(	(	PUNCT
ap-1205	74	11	1b2	1b2	NUM
ap-1205	74	12	−	−	NOUN
ap-1205	74	13	1	1	NUM
ap-1205	74	14	)	)	PUNCT
ap-1205	74	15	·	·	PUNCT
ap-1205	74	16	(	(	PUNCT
ap-1205	74	17	c̃1(c2	c̃1(c2	PROPN
ap-1205	74	18	−	−	PROPN
ap-1205	74	19	c3	c3	PROPN
ap-1205	74	20	)	)	PUNCT
ap-1205	74	21	+	+	NUM
ap-1205	74	22	c̃2(c3	c̃2(c3	PROPN
ap-1205	74	23	−	−	PROPN
ap-1205	74	24	c1	c1	NOUN
ap-1205	74	25	)	)	PUNCT
ap-1205	75	1	+	+	SYM
ap-1205	75	2	c̃3(c1	c̃3(c1	NOUN
ap-1205	75	3	−	−	PROPN
ap-1205	75	4	c2	c2	PROPN
ap-1205	75	5	)	)	PUNCT
ap-1205	75	6	(	(	PUNCT
ap-1205	75	7	c2	c2	PROPN
ap-1205	75	8	−	−	PROPN
ap-1205	75	9	c1)(c1	c1)(c1	PROPN
ap-1205	75	10	−	−	PROPN
ap-1205	75	11	c3)(c3	c3)(c3	NOUN
ap-1205	75	12	−	−	PROPN
ap-1205	75	13	c2	c2	PROPN
ap-1205	75	14	)	)	PUNCT
ap-1205	75	15	where	where	SCONJ
ap-1205	75	16	the	the	DET
ap-1205	75	17	boundary	boundary	ADJ
ap-1205	75	18	cosmological	cosmological	ADJ
ap-1205	75	19	constants	constant	NOUN
ap-1205	75	20	∼	∼	NOUN
ap-1205	75	21	ci	ci	NOUN
ap-1205	75	22	and	and	CCONJ
ap-1205	75	23	their	their	PRON
ap-1205	75	24	dual	dual	ADJ
ap-1205	75	25	appear	appear	NOUN
ap-1205	75	26	,	,	PUNCT
ap-1205	75	27	ci	ci	NOUN
ap-1205	75	28	=	=	SYM
ap-1205	75	29	2	2	NUM
ap-1205	75	30	cosπb(b−	cosπb(b−	NOUN
ap-1205	75	31	2σi	2σi	NOUN
ap-1205	75	32	)	)	PUNCT
ap-1205	75	33	,	,	PUNCT
ap-1205	75	34	c̃i	c̃i	NOUN
ap-1205	75	35	=	=	SYM
ap-1205	75	36	2	2	NUM
ap-1205	75	37	cosπ	cosπ	NOUN
ap-1205	75	38	1	1	NUM
ap-1205	75	39	b	b	PROPN
ap-1205	75	40	(	(	PUNCT
ap-1205	75	41	1	1	NUM
ap-1205	75	42	b	b	NOUN
ap-1205	75	43	−	−	NOUN
ap-1205	75	44	2σi	2σi	NOUN
ap-1205	75	45	)	)	PUNCT
ap-1205	75	46	.	.	PUNCT
ap-1205	76	1	(	(	PUNCT
ap-1205	76	2	2.8	2.8	NUM
ap-1205	76	3	)	)	PUNCT
ap-1205	76	4	similar	similar	ADJ
ap-1205	76	5	regularised	regularise	VERB
ap-1205	76	6	versions	version	NOUN
ap-1205	76	7	of	of	ADP
ap-1205	76	8	(	(	PUNCT
ap-1205	76	9	2.4	2.4	NUM
ap-1205	76	10	)	)	PUNCT
ap-1205	76	11	arise	arise	NOUN
ap-1205	76	12	for	for	ADP
ap-1205	76	13	other	other	ADJ
ap-1205	76	14	values	value	NOUN
ap-1205	76	15	of	of	ADP
ap-1205	76	16	the	the	DET
ap-1205	76	17	charges	charge	NOUN
ap-1205	76	18	corresponding	correspond	VERB
ap-1205	76	19	to	to	ADP
ap-1205	76	20	reflections	reflection	NOUN
ap-1205	76	21	of	of	ADP
ap-1205	76	22	coulomb	coulomb	NOUN
ap-1205	76	23	gas	gas	NOUN
ap-1205	76	24	correlators	correlator	NOUN
ap-1205	76	25	.	.	PUNCT
ap-1205	77	1	2.2	2.2	NUM
ap-1205	77	2	one	one	NUM
ap-1205	77	3	parameter	parameter	NOUN
ap-1205	77	4	correlators	correlator	NOUN
ap-1205	77	5	,	,	PUNCT
ap-1205	77	6	cyclic	cyclic	ADJ
ap-1205	77	7	symmetry	symmetry	NOUN
ap-1205	77	8	we	we	PRON
ap-1205	77	9	shall	shall	AUX
ap-1205	77	10	use	use	VERB
ap-1205	77	11	eq	eq	ADP
ap-1205	77	12	.	.	PUNCT
ap-1205	77	13	(	(	PUNCT
ap-1205	77	14	2.4	2.4	NUM
ap-1205	77	15	)	)	PUNCT
ap-1205	77	16	as	as	ADP
ap-1205	77	17	a	a	DET
ap-1205	77	18	recursion	recursion	NOUN
ap-1205	77	19	relation	relation	NOUN
ap-1205	77	20	,	,	PUNCT
ap-1205	77	21	starting	start	VERB
ap-1205	77	22	from	from	ADP
ap-1205	77	23	the	the	DET
ap-1205	77	24	explicit	explicit	ADJ
ap-1205	77	25	expression	expression	NOUN
ap-1205	77	26	(	(	PUNCT
ap-1205	77	27	2.7	2.7	NUM
ap-1205	77	28	)	)	PUNCT
ap-1205	77	29	.	.	PUNCT
ap-1205	78	1	let	let	VERB
ap-1205	78	2	us	we	PRON
ap-1205	78	3	first	first	ADV
ap-1205	78	4	introduce	introduce	VERB
ap-1205	78	5	some	some	DET
ap-1205	78	6	general	general	ADJ
ap-1205	78	7	notation	notation	NOUN
ap-1205	78	8	:	:	PUNCT
ap-1205	78	9	g(−)(σ2	g(−)(σ2	ADJ
ap-1205	78	10	,	,	PUNCT
ap-1205	78	11	β	β	X
ap-1205	78	12	,	,	PUNCT
ap-1205	78	13	σ1	σ1	PROPN
ap-1205	78	14	)	)	PUNCT
ap-1205	78	15	:	:	PUNCT
ap-1205	79	1	=	=	PUNCT
ap-1205	79	2	sb(−β	sb(−β	PROPN
ap-1205	79	3	+	+	CCONJ
ap-1205	79	4	σ2	σ2	NOUN
ap-1205	79	5	+	+	CCONJ
ap-1205	79	6	σ1)sb(q−	σ1)sb(q−	PROPN
ap-1205	79	7	β	β	X
ap-1205	79	8	+	+	PROPN
ap-1205	79	9	σ2	σ2	PROPN
ap-1205	79	10	−	−	PROPN
ap-1205	79	11	σ1	σ1	PROPN
ap-1205	79	12	)	)	PUNCT
ap-1205	79	13	=	=	PUNCT
ap-1205	80	1	g−	g−	PROPN
ap-1205	80	2	(	(	PUNCT
ap-1205	80	3	σ2	σ2	NOUN
ap-1205	80	4	,	,	PUNCT
ap-1205	80	5	β	β	X
ap-1205	80	6	+	+	CCONJ
ap-1205	80	7	b	b	SYM
ap-1205	80	8	2	2	NUM
ap-1205	80	9	,	,	PUNCT
ap-1205	80	10	σ1	σ1	NOUN
ap-1205	80	11	)	)	PUNCT
ap-1205	80	12	g(−)(σ2	g(−)(σ2	PROPN
ap-1205	80	13	,	,	PUNCT
ap-1205	80	14	β	β	X
ap-1205	80	15	+	+	SYM
ap-1205	80	16	b	b	PROPN
ap-1205	80	17	,	,	PUNCT
ap-1205	80	18	σ1	σ1	PROPN
ap-1205	80	19	)	)	PUNCT
ap-1205	80	20	.	.	PUNCT
ap-1205	81	1	(	(	PUNCT
ap-1205	81	2	2.9	2.9	NUM
ap-1205	81	3	)	)	PUNCT
ap-1205	81	4	for	for	ADP
ap-1205	81	5	a	a	DET
ap-1205	81	6	non	non	ADJ
ap-1205	81	7	-	-	ADJ
ap-1205	81	8	negative	negative	ADJ
ap-1205	81	9	integer	integer	NOUN
ap-1205	81	10	k	k	PROPN
ap-1205	81	11	and	and	CCONJ
ap-1205	81	12	an	an	DET
ap-1205	81	13	integer	integer	NOUN
ap-1205	81	14	n	n	PROPN
ap-1205	81	15	of	of	ADP
ap-1205	81	16	parity	parity	NOUN
ap-1205	81	17	p(n	p(n	NOUN
ap-1205	81	18	)	)	PUNCT
ap-1205	81	19	denote	denote	NOUN
ap-1205	81	20	b(σ2	b(σ2	ADJ
ap-1205	81	21	,	,	PUNCT
ap-1205	81	22	σ1	σ1	PROPN
ap-1205	81	23	)	)	PUNCT
ap-1205	81	24	(	(	PUNCT
ap-1205	81	25	k;p(n	k;p(n	PROPN
ap-1205	81	26	)	)	PUNCT
ap-1205	81	27	)	)	PUNCT
ap-1205	82	1	:	:	PUNCT
ap-1205	82	2	=	=	NOUN
ap-1205	82	3	g(−)(σ2,−kb	g(−)(σ2,−kb	VERB
ap-1205	82	4	2	2	NUM
ap-1205	82	5	−	−	NOUN
ap-1205	82	6	n	n	PRON
ap-1205	82	7	2b	2b	NUM
ap-1205	82	8	,	,	PUNCT
ap-1205	82	9	σ1	σ1	NOUN
ap-1205	82	10	)	)	PUNCT
ap-1205	82	11	g(−)(σ2	g(−)(σ2	VERB
ap-1205	82	12	,	,	PUNCT
ap-1205	82	13	b+	b+	VERB
ap-1205	82	14	kb	kb	PROPN
ap-1205	82	15	2	2	NUM
ap-1205	82	16	−	−	NOUN
ap-1205	82	17	n	n	PRON
ap-1205	82	18	2b	2b	NUM
ap-1205	82	19	,	,	PUNCT
ap-1205	82	20	σ1	σ1	NOUN
ap-1205	82	21	)	)	PUNCT
ap-1205	82	22	=	=	PRON
ap-1205	82	23	(	(	PUNCT
ap-1205	82	24	−1)(k+1)(n+1)b(σ1	−1)(k+1)(n+1)b(σ1	PROPN
ap-1205	82	25	,	,	PUNCT
ap-1205	82	26	σ2)(k;p(n	σ2)(k;p(n	NUM
ap-1205	82	27	)	)	PUNCT
ap-1205	82	28	)	)	PUNCT
ap-1205	82	29	.	.	PUNCT
ap-1205	83	1	(	(	PUNCT
ap-1205	83	2	2.10	2.10	NUM
ap-1205	83	3	)	)	PUNCT
ap-1205	83	4	applying	apply	VERB
ap-1205	83	5	(	(	PUNCT
ap-1205	83	6	2.9	2.9	NUM
ap-1205	83	7	)	)	PUNCT
ap-1205	83	8	,	,	PUNCT
ap-1205	83	9	the	the	DET
ap-1205	83	10	ratio	ratio	NOUN
ap-1205	83	11	(	(	PUNCT
ap-1205	83	12	2.10	2.10	NUM
ap-1205	83	13	)	)	PUNCT
ap-1205	83	14	is	be	AUX
ap-1205	83	15	expressed	express	VERB
ap-1205	83	16	as	as	ADP
ap-1205	83	17	a	a	DET
ap-1205	83	18	k	k	PROPN
ap-1205	83	19	+	+	CCONJ
ap-1205	83	20	1	1	NUM
ap-1205	83	21	order	order	NOUN
ap-1205	83	22	polynomial	polynomial	ADJ
ap-1205	83	23	in	in	ADP
ap-1205	83	24	{	{	PUNCT
ap-1205	83	25	ci	ci	NOUN
ap-1205	83	26	}	}	PUNCT
ap-1205	83	27	using	use	VERB
ap-1205	83	28	that	that	PRON
ap-1205	83	29	for	for	ADP
ap-1205	83	30	k	k	PROPN
ap-1205	83	31	�	�	PROPN
ap-1205	83	32	=	=	SYM
ap-1205	83	33	0	0	NUM
ap-1205	83	34	g−	g−	PROPN
ap-1205	83	35	(	(	PUNCT
ap-1205	83	36	σ2	σ2	NOUN
ap-1205	83	37	,	,	PUNCT
ap-1205	83	38	b	b	PROPN
ap-1205	83	39	2	2	NUM
ap-1205	83	40	−	−	PROPN
ap-1205	84	1	k	k	NOUN
ap-1205	84	2	b	b	PROPN
ap-1205	84	3	2	2	NUM
ap-1205	84	4	+	+	NUM
ap-1205	84	5	n	n	PRON
ap-1205	84	6	2b	2b	NOUN
ap-1205	84	7	,	,	PUNCT
ap-1205	84	8	σ1	σ1	NOUN
ap-1205	84	9	)	)	PUNCT
ap-1205	84	10	g−	g−	PROPN
ap-1205	84	11	(	(	PUNCT
ap-1205	84	12	σ2	σ2	PROPN
ap-1205	84	13	,	,	PUNCT
ap-1205	84	14	b	b	PROPN
ap-1205	84	15	2	2	NUM
ap-1205	84	16	+	+	CCONJ
ap-1205	84	17	k	k	PROPN
ap-1205	84	18	b	b	PROPN
ap-1205	84	19	2	2	NUM
ap-1205	84	20	+	+	NUM
ap-1205	84	21	n	n	PRON
ap-1205	84	22	2b	2b	NOUN
ap-1205	84	23	,	,	PUNCT
ap-1205	84	24	σ1	σ1	NOUN
ap-1205	84	25	)	)	PUNCT
ap-1205	84	26	=	=	PUNCT
ap-1205	85	1	c21	c21	NOUN
ap-1205	85	2	+	+	CCONJ
ap-1205	85	3	c22	c22	PROPN
ap-1205	85	4	−	−	PROPN
ap-1205	85	5	c1c2(−1)n2	c1c2(−1)n2	X
ap-1205	85	6	cosπkb2	cosπkb2	NOUN
ap-1205	86	1	−	−	NOUN
ap-1205	86	2	(	(	PUNCT
ap-1205	86	3	2	2	NUM
ap-1205	86	4	sinπkb2)2	sinπkb2)2	NOUN
ap-1205	86	5	(	(	PUNCT
ap-1205	86	6	2.11	2.11	NUM
ap-1205	86	7	)	)	PUNCT
ap-1205	86	8	while	while	SCONJ
ap-1205	86	9	b(σ2	b(σ2	ADJ
ap-1205	86	10	,	,	PUNCT
ap-1205	86	11	σ1)(0;p(n	σ1)(0;p(n	NOUN
ap-1205	86	12	)	)	PUNCT
ap-1205	86	13	)	)	PUNCT
ap-1205	87	1	=	=	SYM
ap-1205	87	2	(	(	PUNCT
ap-1205	87	3	−1)nc2	−1)nc2	ADJ
ap-1205	87	4	−	−	PROPN
ap-1205	87	5	c1	c1	PROPN
ap-1205	87	6	.	.	PUNCT
ap-1205	88	1	similarly	similarly	ADV
ap-1205	88	2	,	,	PUNCT
ap-1205	88	3	we	we	PRON
ap-1205	88	4	define	define	VERB
ap-1205	88	5	the	the	DET
ap-1205	88	6	dual	dual	ADJ
ap-1205	88	7	b̃(σ2	b̃(σ2	VERB
ap-1205	88	8	,	,	PUNCT
ap-1205	88	9	σ1)(n;p(k	σ1)(n;p(k	NOUN
ap-1205	88	10	)	)	PUNCT
ap-1205	88	11	)	)	PUNCT
ap-1205	88	12	b̃(σ2	b̃(σ2	VERB
ap-1205	88	13	,	,	PUNCT
ap-1205	88	14	σ1	σ1	PROPN
ap-1205	88	15	)	)	PUNCT
ap-1205	88	16	(	(	PUNCT
ap-1205	88	17	n;p(k	n;p(k	PROPN
ap-1205	88	18	)	)	PUNCT
ap-1205	88	19	)	)	PUNCT
ap-1205	89	1	:	:	PUNCT
ap-1205	89	2	=	=	SYM
ap-1205	89	3	g(−)(σ2,−	g(−)(σ2,−	PROPN
ap-1205	89	4	n	n	CCONJ
ap-1205	89	5	2b	2b	NOUN
ap-1205	89	6	−	−	PROPN
ap-1205	89	7	kb	kb	PROPN
ap-1205	89	8	2	2	NUM
ap-1205	89	9	,	,	PUNCT
ap-1205	89	10	σ1	σ1	NOUN
ap-1205	89	11	)	)	PUNCT
ap-1205	89	12	g(−)(σ2	g(−)(σ2	VERB
ap-1205	89	13	,	,	PUNCT
ap-1205	89	14	1b	1b	NUM
ap-1205	89	15	+	+	CCONJ
ap-1205	89	16	n	n	CCONJ
ap-1205	89	17	2b	2b	NUM
ap-1205	89	18	−	−	PROPN
ap-1205	89	19	kb	kb	PROPN
ap-1205	89	20	2	2	NUM
ap-1205	89	21	,	,	PUNCT
ap-1205	89	22	σ1	σ1	PROPN
ap-1205	89	23	)	)	PUNCT
ap-1205	89	24	=	=	PUNCT
ap-1205	89	25	(	(	PUNCT
ap-1205	89	26	−1)(k+1)(n+1)b̃(σ1	−1)(k+1)(n+1)b̃(σ1	PROPN
ap-1205	89	27	,	,	PUNCT
ap-1205	89	28	σ2)(n;p(k	σ2)(n;p(k	NUM
ap-1205	89	29	)	)	PUNCT
ap-1205	89	30	)	)	PUNCT
ap-1205	89	31	(	(	PUNCT
ap-1205	89	32	2.12	2.12	NUM
ap-1205	89	33	)	)	PUNCT
ap-1205	89	34	so	so	SCONJ
ap-1205	89	35	that	that	SCONJ
ap-1205	89	36	the	the	DET
ap-1205	89	37	reflection	reflection	NOUN
ap-1205	89	38	amplitude	amplitude	NOUN
ap-1205	89	39	is	be	AUX
ap-1205	89	40	expressed	express	VERB
ap-1205	89	41	as	as	ADP
ap-1205	89	42	the	the	DET
ap-1205	89	43	ratio	ratio	NOUN
ap-1205	89	44	of	of	ADP
ap-1205	89	45	polynomials	polynomial	NOUN
ap-1205	89	46	λ	λ	PROPN
ap-1205	89	47	2β2−q	2β2−q	NUM
ap-1205	89	48	2b	2b	NUM
ap-1205	89	49	l	l	NOUN
ap-1205	89	50	g2(σ2	g2(σ2	X
ap-1205	89	51	,	,	PUNCT
ap-1205	89	52	β2	β2	NOUN
ap-1205	89	53	=	=	SYM
ap-1205	89	54	b+m2b−	b+m2b−	PROPN
ap-1205	89	55	n2	n2	PROPN
ap-1205	89	56	b	b	PROPN
ap-1205	89	57	,	,	PUNCT
ap-1205	89	58	σ1	σ1	PROPN
ap-1205	89	59	)	)	PUNCT
ap-1205	89	60	sb(2β2	sb(2β2	NOUN
ap-1205	89	61	−q	−q	NOUN
ap-1205	89	62	)	)	PUNCT
ap-1205	89	63	=	=	SYM
ap-1205	89	64	g(−)(σ2	g(−)(σ2	VERB
ap-1205	89	65	,	,	PUNCT
ap-1205	89	66	β2	β2	NOUN
ap-1205	89	67	,	,	PUNCT
ap-1205	89	68	σ1	σ1	PROPN
ap-1205	89	69	)	)	PUNCT
ap-1205	89	70	g(−)(σ2	g(−)(σ2	VERB
ap-1205	89	71	,	,	PUNCT
ap-1205	89	72	q−	q−	PROPN
ap-1205	89	73	β2	β2	PROPN
ap-1205	89	74	,	,	PUNCT
ap-1205	89	75	σ1	σ1	PROPN
ap-1205	89	76	)	)	PUNCT
ap-1205	89	77	=	=	PUNCT
ap-1205	89	78	b̃(σ2	b̃(σ2	PROPN
ap-1205	89	79	,	,	PUNCT
ap-1205	89	80	σ1)(2n2;p(2m2	σ1)(2n2;p(2m2	NOUN
ap-1205	89	81	)	)	PUNCT
ap-1205	89	82	)	)	PUNCT
ap-1205	89	83	b(σ2	b(σ2	ADJ
ap-1205	89	84	,	,	PUNCT
ap-1205	89	85	σ1)(2m2;p(2n2	σ1)(2m2;p(2n2	NOUN
ap-1205	89	86	)	)	PUNCT
ap-1205	89	87	)	)	PUNCT
ap-1205	89	88	.	.	PUNCT
ap-1205	90	1	(	(	PUNCT
ap-1205	90	2	2.13	2.13	NUM
ap-1205	90	3	)	)	PUNCT
ap-1205	90	4	86	86	NUM
ap-1205	90	5	acta	acta	PROPN
ap-1205	90	6	polytechnica	polytechnica	PROPN
ap-1205	90	7	vol	vol	NOUN
ap-1205	90	8	.	.	PROPN
ap-1205	91	1	50	50	NUM
ap-1205	91	2	no	no	NOUN
ap-1205	91	3	.	.	PUNCT
ap-1205	92	1	3/2010	3/2010	NUM
ap-1205	92	2	finally	finally	ADV
ap-1205	92	3	we	we	PRON
ap-1205	92	4	introduce	introduce	VERB
ap-1205	92	5	p2	p2	NOUN
ap-1205	92	6	≡	≡	PROPN
ap-1205	92	7	p	p	PROPN
ap-1205	92	8	σ3,σ2,σ1	σ3,σ2,σ1	ADV
ap-1205	92	9	β3,β2,β1	β3,β2,β1	ADV
ap-1205	92	10	:	:	PUNCT
ap-1205	92	11	=	=	SYM
ap-1205	92	12	(	(	PUNCT
ap-1205	92	13	−1)m	−1)m	PROPN
ap-1205	92	14	3	3	NUM
ap-1205	92	15	12	12	NUM
ap-1205	92	16	+	+	NUM
ap-1205	92	17	2m2λ	2m2λ	NUM
ap-1205	92	18	−	−	PROPN
ap-1205	92	19	m3	m3	PROPN
ap-1205	92	20	12	12	NUM
ap-1205	92	21	2	2	NUM
ap-1205	92	22	l	l	NOUN
ap-1205	92	23	sb((2m1	sb((2m1	PRON
ap-1205	92	24	+	+	NOUN
ap-1205	92	25	1)b)sb((2m2	1)b)sb((2m2	NUM
ap-1205	92	26	+	+	CCONJ
ap-1205	92	27	1)b	1)b	NOUN
ap-1205	92	28	)	)	PUNCT
ap-1205	92	29	sb(b	sb(b	NOUN
ap-1205	92	30	)	)	PUNCT
ap-1205	92	31	·	·	PUNCT
ap-1205	93	1	m3	m3	PROPN
ap-1205	93	2	12∑	12∑	NUM
ap-1205	94	1	p=0	p=0	PROPN
ap-1205	94	2	sb((m312	sb((m312	VERB
ap-1205	94	3	+	+	CCONJ
ap-1205	94	4	1)b	1)b	NOUN
ap-1205	94	5	)	)	PUNCT
ap-1205	94	6	sb((p+	sb((p+	PROPN
ap-1205	94	7	1)b)sb((m312	1)b)sb((m312	NUM
ap-1205	94	8	+	+	CCONJ
ap-1205	94	9	1−	1−	NUM
ap-1205	94	10	p)b	p)b	NOUN
ap-1205	94	11	)	)	PUNCT
ap-1205	94	12	×	×	NOUN
ap-1205	94	13	g2(σ2	g2(σ2	NUM
ap-1205	95	1	+	+	CCONJ
ap-1205	95	2	p	p	X
ap-1205	95	3	b	b	PROPN
ap-1205	95	4	2	2	NUM
ap-1205	95	5	,	,	PUNCT
ap-1205	95	6	β2	β2	NOUN
ap-1205	95	7	−	−	PROPN
ap-1205	95	8	p	p	NOUN
ap-1205	95	9	b	b	PROPN
ap-1205	95	10	2	2	NUM
ap-1205	95	11	,	,	PUNCT
ap-1205	95	12	σ3	σ3	NOUN
ap-1205	95	13	)	)	PUNCT
ap-1205	95	14	g2(σ2	g2(σ2	PROPN
ap-1205	95	15	,	,	PUNCT
ap-1205	95	16	β2	β2	NOUN
ap-1205	95	17	,	,	PUNCT
ap-1205	95	18	σ3	σ3	PROPN
ap-1205	95	19	)	)	PUNCT
ap-1205	95	20	(	(	PUNCT
ap-1205	95	21	2.14	2.14	NUM
ap-1205	95	22	)	)	PUNCT
ap-1205	95	23	g2(σ2	g2(σ2	NUM
ap-1205	95	24	−	−	PROPN
ap-1205	96	1	(	(	PUNCT
ap-1205	96	2	m312	m312	PROPN
ap-1205	96	3	−	−	PROPN
ap-1205	96	4	p	p	NOUN
ap-1205	96	5	)	)	PUNCT
ap-1205	96	6	b2	b2	NOUN
ap-1205	96	7	,	,	PUNCT
ap-1205	96	8	β1	β1	PROPN
ap-1205	96	9	−	−	PROPN
ap-1205	96	10	(	(	PUNCT
ap-1205	96	11	m312	m312	PROPN
ap-1205	96	12	−	−	PROPN
ap-1205	96	13	p	p	NOUN
ap-1205	96	14	)	)	PUNCT
ap-1205	96	15	b2	b2	NOUN
ap-1205	96	16	,	,	PUNCT
ap-1205	96	17	σ1	σ1	PROPN
ap-1205	96	18	)	)	PUNCT
ap-1205	96	19	g2(σ2	g2(σ2	PROPN
ap-1205	96	20	,	,	PUNCT
ap-1205	96	21	β1	β1	PROPN
ap-1205	96	22	,	,	PUNCT
ap-1205	96	23	σ1	σ1	PROPN
ap-1205	96	24	)	)	PUNCT
ap-1205	96	25	and	and	CCONJ
ap-1205	96	26	similarly	similarly	ADV
ap-1205	96	27	p1	p1	PROPN
ap-1205	96	28	and	and	CCONJ
ap-1205	96	29	p3	p3	PROPN
ap-1205	96	30	,	,	PUNCT
ap-1205	96	31	which	which	PRON
ap-1205	96	32	are	be	AUX
ap-1205	96	33	obtained	obtain	VERB
ap-1205	96	34	from	from	ADP
ap-1205	96	35	(	(	PUNCT
ap-1205	96	36	2.14	2.14	NUM
ap-1205	96	37	)	)	PUNCT
ap-1205	96	38	by	by	ADP
ap-1205	96	39	cyclic	cyclic	ADJ
ap-1205	96	40	permutations	permutation	NOUN
ap-1205	96	41	.	.	PUNCT
ap-1205	97	1	the	the	DET
ap-1205	97	2	finite	finite	PROPN
ap-1205	97	3	sum	sum	NOUN
ap-1205	97	4	(	(	PUNCT
ap-1205	97	5	2.14	2.14	NUM
ap-1205	97	6	)	)	PUNCT
ap-1205	97	7	is	be	AUX
ap-1205	97	8	proportional	proportional	ADJ
ap-1205	97	9	to	to	ADP
ap-1205	97	10	a	a	DET
ap-1205	97	11	truncated	truncated	ADJ
ap-1205	97	12	basic	basic	ADJ
ap-1205	97	13	hypergeometric	hypergeometric	ADJ
ap-1205	97	14	function	function	NOUN
ap-1205	97	15	4φ3	4φ3	NUM
ap-1205	97	16	(	(	PUNCT
ap-1205	97	17	.	.	PUNCT
ap-1205	97	18	.	.	PUNCT
ap-1205	97	19	.	.	PUNCT
ap-1205	98	1	;	;	PUNCT
ap-1205	98	2	q	q	X
ap-1205	98	3	,	,	PUNCT
ap-1205	98	4	q	q	NOUN
ap-1205	98	5	)	)	PUNCT
ap-1205	98	6	.	.	PUNCT
ap-1205	99	1	it	it	PRON
ap-1205	99	2	can	can	AUX
ap-1205	99	3	be	be	AUX
ap-1205	99	4	expanded	expand	VERB
ap-1205	99	5	as	as	ADP
ap-1205	99	6	a	a	DET
ap-1205	99	7	polynomial	polynomial	NOUN
ap-1205	99	8	in	in	ADP
ap-1205	99	9	the	the	DET
ap-1205	99	10	variables	variable	NOUN
ap-1205	99	11	{	{	PUNCT
ap-1205	99	12	ci	ci	NOUN
ap-1205	99	13	}	}	PUNCT
ap-1205	99	14	(	(	PUNCT
ap-1205	99	15	a	a	DET
ap-1205	99	16	special	special	ADJ
ap-1205	99	17	case	case	NOUN
ap-1205	99	18	of	of	ADP
ap-1205	99	19	askey	askey	NOUN
ap-1205	99	20	-	-	PUNCT
ap-1205	99	21	wilson	wilson	NOUN
ap-1205	99	22	polynomials	polynomial	NOUN
ap-1205	99	23	)	)	PUNCT
ap-1205	99	24	.	.	PUNCT
ap-1205	100	1	we	we	PRON
ap-1205	100	2	begin	begin	VERB
ap-1205	100	3	with	with	ADP
ap-1205	100	4	the	the	DET
ap-1205	100	5	“	"	PUNCT
ap-1205	100	6	thermal	thermal	ADJ
ap-1205	100	7	”	"	PUNCT
ap-1205	100	8	case	case	NOUN
ap-1205	100	9	with	with	ADP
ap-1205	100	10	all	all	DET
ap-1205	100	11	ni	ni	NOUN
ap-1205	100	12	=	=	NOUN
ap-1205	100	13	0	0	NUM
ap-1205	100	14	in	in	ADP
ap-1205	100	15	(	(	PUNCT
ap-1205	100	16	1.1	1.1	NUM
ap-1205	100	17	)	)	PUNCT
ap-1205	100	18	.	.	PUNCT
ap-1205	101	1	we	we	PRON
ap-1205	101	2	first	first	ADV
ap-1205	101	3	use	use	VERB
ap-1205	101	4	such	such	DET
ap-1205	101	5	a	a	DET
ap-1205	101	6	regularised	regularise	VERB
ap-1205	101	7	equation	equation	NOUN
ap-1205	101	8	in	in	ADP
ap-1205	101	9	which	which	PRON
ap-1205	101	10	the	the	DET
ap-1205	101	11	first	first	ADJ
ap-1205	101	12	term	term	NOUN
ap-1205	101	13	on	on	ADP
ap-1205	101	14	the	the	DET
ap-1205	101	15	r.h.s	r.h.s	NOUN
ap-1205	101	16	.	.	PUNCT
ap-1205	102	1	of	of	ADP
ap-1205	102	2	(	(	PUNCT
ap-1205	102	3	2.4	2.4	NUM
ap-1205	102	4	)	)	PUNCT
ap-1205	102	5	reduces	reduce	VERB
ap-1205	102	6	to	to	ADP
ap-1205	102	7	a	a	DET
ap-1205	102	8	2	2	NUM
ap-1205	102	9	-	-	PUNCT
ap-1205	102	10	point	point	NOUN
ap-1205	102	11	function	function	NOUN
ap-1205	102	12	in	in	ADP
ap-1205	102	13	order	order	NOUN
ap-1205	102	14	to	to	PART
ap-1205	102	15	obtain	obtain	VERB
ap-1205	102	16	recursively	recursively	ADV
ap-1205	102	17	the	the	DET
ap-1205	102	18	most	most	ADV
ap-1205	102	19	general	general	ADJ
ap-1205	102	20	correlator	correlator	NOUN
ap-1205	102	21	with	with	ADP
ap-1205	102	22	m213	m213	PROPN
ap-1205	102	23	=	=	SYM
ap-1205	102	24	0	0	PROPN
ap-1205	102	25	.	.	PUNCT
ap-1205	103	1	then	then	ADV
ap-1205	103	2	using	use	VERB
ap-1205	103	3	the	the	DET
ap-1205	103	4	analog	analog	NOUN
ap-1205	103	5	of	of	ADP
ap-1205	103	6	the	the	DET
ap-1205	103	7	general	general	ADJ
ap-1205	103	8	equation	equation	NOUN
ap-1205	103	9	(	(	PUNCT
ap-1205	103	10	2.4	2.4	NUM
ap-1205	103	11	)	)	PUNCT
ap-1205	103	12	for	for	ADP
ap-1205	103	13	shifts	shift	NOUN
ap-1205	103	14	of	of	ADP
ap-1205	103	15	the	the	DET
ap-1205	103	16	pair	pair	NOUN
ap-1205	103	17	(	(	PUNCT
ap-1205	103	18	β3	β3	ADJ
ap-1205	103	19	,	,	PUNCT
ap-1205	103	20	β2	β2	NOUN
ap-1205	103	21	)	)	PUNCT
ap-1205	103	22	,	,	PUNCT
ap-1205	103	23	we	we	PRON
ap-1205	103	24	obtain	obtain	VERB
ap-1205	103	25	cσ3,σ2,σ1	cσ3,σ2,σ1	ADV
ap-1205	103	26	β3,β2,β1	β3,β2,β1	ADV
ap-1205	103	27	=	=	SYM
ap-1205	103	28	−	−	NOUN
ap-1205	103	29	λ	λ	PROPN
ap-1205	103	30	q−β123	q−β123	NOUN
ap-1205	103	31	2b	2b	NUM
ap-1205	103	32	l	l	X
ap-1205	103	33	∏	∏	X
ap-1205	103	34	(	(	PUNCT
ap-1205	103	35	β3	β3	ADJ
ap-1205	103	36	,	,	PUNCT
ap-1205	103	37	β2	β2	NOUN
ap-1205	103	38	,	,	PUNCT
ap-1205	103	39	β1	β1	PROPN
ap-1205	103	40	)	)	PUNCT
ap-1205	103	41	b(σ1	b(σ1	ADV
ap-1205	103	42	,	,	PUNCT
ap-1205	103	43	σ2)(2m1;0)b(σ2	σ2)(2m1;0)b(σ2	PROPN
ap-1205	103	44	,	,	PUNCT
ap-1205	103	45	σ3)(2m2;0)b(σ3	σ3)(2m2;0)b(σ3	PROPN
ap-1205	103	46	,	,	PUNCT
ap-1205	103	47	σ1)(2m3;0	σ1)(2m3;0	NOUN
ap-1205	103	48	)	)	PUNCT
ap-1205	103	49	f	f	NOUN
ap-1205	103	50	σ3,σ2,σ1	σ3,σ2,σ1	ADV
ap-1205	103	51	β3,β2,β1	β3,β2,β1	VERB
ap-1205	103	52	,	,	PUNCT
ap-1205	103	53	f	f	X
ap-1205	103	54	σ3,σ2,σ1	σ3,σ2,σ1	ADV
ap-1205	103	55	β3,β2,β1	β3,β2,β1	VERB
ap-1205	103	56	=	=	PUNCT
ap-1205	103	57	(	(	PUNCT
ap-1205	103	58	−1)2m1((−1)2m2	−1)2m1((−1)2m2	PROPN
ap-1205	103	59	c̃2	c̃2	PROPN
ap-1205	103	60	−	−	PROPN
ap-1205	103	61	c̃3)b(σ3	c̃3)b(σ3	NOUN
ap-1205	103	62	,	,	PUNCT
ap-1205	103	63	σ1)(2m3;0)p	σ1)(2m3;0)p	PROPN
ap-1205	103	64	σ3,σ2,σ1	σ3,σ2,σ1	ADV
ap-1205	103	65	β3,β2,β1	β3,β2,β1	VERB
ap-1205	103	66	−	−	PROPN
ap-1205	103	67	(	(	PUNCT
ap-1205	103	68	−1)2m2((−1)2m3	−1)2m2((−1)2m3	NOUN
ap-1205	103	69	c̃3	c̃3	PROPN
ap-1205	103	70	−	−	PROPN
ap-1205	103	71	c̃1)b(σ2	c̃1)b(σ2	PROPN
ap-1205	103	72	,	,	PUNCT
ap-1205	103	73	σ3)(2m2;0)p	σ3)(2m2;0)p	PROPN
ap-1205	103	74	σ2,σ1,σ3	σ2,σ1,σ3	PROPN
ap-1205	103	75	β2,β1,β3	β2,β1,β3	NOUN
ap-1205	103	76	=	=	SYM
ap-1205	103	77	(	(	PUNCT
ap-1205	103	78	2.15	2.15	NUM
ap-1205	103	79	)	)	PUNCT
ap-1205	103	80	−	−	PROPN
ap-1205	104	1	(	(	PUNCT
ap-1205	104	2	c̃1b(σ3	c̃1b(σ3	PROPN
ap-1205	104	3	,	,	PUNCT
ap-1205	104	4	σ2)(2m2;0)p	σ2)(2m2;0)p	PROPN
ap-1205	104	5	σ2,σ1,σ3	σ2,σ1,σ3	PROPN
ap-1205	104	6	β2,β1,β3	β2,β1,β3	PUNCT
ap-1205	104	7	+	+	CCONJ
ap-1205	104	8	c̃2b(σ1	c̃2b(σ1	NOUN
ap-1205	104	9	,	,	PUNCT
ap-1205	104	10	σ3)(2m3;0)p	σ3)(2m3;0)p	PROPN
ap-1205	104	11	σ3,σ2,σ1	σ3,σ2,σ1	ADV
ap-1205	104	12	β3,β2,β1	β3,β2,β1	VERB
ap-1205	104	13	+	+	CCONJ
ap-1205	104	14	c̃3b(σ2	c̃3b(σ2	ADJ
ap-1205	104	15	,	,	PUNCT
ap-1205	104	16	σ1)(2m1;0)p	σ1)(2m1;0)p	PROPN
ap-1205	104	17	σ1,σ3,σ2	σ1,σ3,σ2	ADJ
ap-1205	104	18	β1,β3,β2	β1,β3,β2	NOUN
ap-1205	104	19	)	)	PUNCT
ap-1205	104	20	where	where	SCONJ
ap-1205	104	21	∏	∏	PROPN
ap-1205	104	22	(	(	PUNCT
ap-1205	104	23	β3	β3	ADJ
ap-1205	104	24	,	,	PUNCT
ap-1205	104	25	β2	β2	NOUN
ap-1205	104	26	,	,	PUNCT
ap-1205	104	27	β1	β1	PROPN
ap-1205	104	28	)	)	PUNCT
ap-1205	104	29	=	=	SYM
ap-1205	104	30	be0(q−β123)γb(2q	be0(q−β123)γb(2q	NOUN
ap-1205	104	31	−	−	PROPN
ap-1205	104	32	β123)γb(q−	β123)γb(q−	ADV
ap-1205	104	33	β123)γb(q−	β123)γb(q−	PROPN
ap-1205	104	34	β213)γb(q−	β213)γb(q−	PROPN
ap-1205	104	35	β312	β312	PROPN
ap-1205	104	36	)	)	PUNCT
ap-1205	104	37	sb(1b	sb(1b	NOUN
ap-1205	104	38	)	)	PUNCT
ap-1205	104	39	sb(2b	sb(2b	ADJ
ap-1205	104	40	)	)	PUNCT
ap-1205	104	41	γb(q)γb(q−	γb(q)γb(q−	PROPN
ap-1205	105	1	2β1)γb(q−	2β1)γb(q−	NUM
ap-1205	105	2	2β2)γb(q−	2β2)γb(q−	NUM
ap-1205	105	3	2β3	2β3	NUM
ap-1205	105	4	)	)	PUNCT
ap-1205	105	5	.	.	PUNCT
ap-1205	106	1	(	(	PUNCT
ap-1205	106	2	2.16	2.16	NUM
ap-1205	106	3	)	)	PUNCT
ap-1205	106	4	in	in	ADP
ap-1205	106	5	the	the	DET
ap-1205	106	6	last	last	ADJ
ap-1205	106	7	equality	equality	NOUN
ap-1205	106	8	of	of	ADP
ap-1205	106	9	(	(	PUNCT
ap-1205	106	10	2.15	2.15	NUM
ap-1205	106	11	)	)	PUNCT
ap-1205	106	12	we	we	PRON
ap-1205	106	13	have	have	AUX
ap-1205	106	14	exploited	exploit	VERB
ap-1205	106	15	(	(	PUNCT
ap-1205	106	16	2.10	2.10	NUM
ap-1205	106	17	)	)	PUNCT
ap-1205	106	18	and	and	CCONJ
ap-1205	106	19	the	the	DET
ap-1205	106	20	relation	relation	NOUN
ap-1205	106	21	.	.	PUNCT
ap-1205	107	1	b(σ3	b(σ3	PROPN
ap-1205	107	2	,	,	PUNCT
ap-1205	107	3	σ1)(2m3;0)p	σ1)(2m3;0)p	PROPN
ap-1205	107	4	σ3,σ2,σ1	σ3,σ2,σ1	ADV
ap-1205	107	5	β3,β2,β1	β3,β2,β1	VERB
ap-1205	107	6	+	+	CCONJ
ap-1205	107	7	cyclic	cyclic	ADJ
ap-1205	107	8	permutations	permutation	NOUN
ap-1205	107	9	=	=	SYM
ap-1205	107	10	0	0	PUNCT
ap-1205	107	11	(	(	PUNCT
ap-1205	107	12	2.17	2.17	NUM
ap-1205	107	13	)	)	PUNCT
ap-1205	107	14	which	which	PRON
ap-1205	107	15	is	be	AUX
ap-1205	107	16	equivalent	equivalent	ADJ
ap-1205	107	17	to	to	ADP
ap-1205	107	18	the	the	DET
ap-1205	107	19	cyclic	cyclic	ADJ
ap-1205	107	20	symmetry	symmetry	NOUN
ap-1205	107	21	of	of	ADP
ap-1205	107	22	the	the	DET
ap-1205	107	23	correlator	correlator	NOUN
ap-1205	107	24	,	,	PUNCT
ap-1205	107	25	now	now	ADV
ap-1205	107	26	explicit	explicit	ADJ
ap-1205	107	27	in	in	ADP
ap-1205	107	28	(	(	PUNCT
ap-1205	107	29	2.15	2.15	NUM
ap-1205	107	30	)	)	PUNCT
ap-1205	107	31	.	.	PUNCT
ap-1205	108	1	symmetry	symmetry	NOUN
ap-1205	108	2	is	be	AUX
ap-1205	108	3	ensured	ensure	VERB
ap-1205	108	4	by	by	ADP
ap-1205	108	5	the	the	DET
ap-1205	108	6	fact	fact	NOUN
ap-1205	108	7	that	that	SCONJ
ap-1205	108	8	the	the	DET
ap-1205	108	9	expression	expression	NOUN
ap-1205	108	10	given	give	VERB
ap-1205	108	11	by	by	ADP
ap-1205	108	12	the	the	DET
ap-1205	108	13	first	first	ADJ
ap-1205	108	14	equality	equality	NOUN
ap-1205	108	15	satisfies	satisfy	VERB
ap-1205	108	16	all	all	DET
ap-1205	108	17	the	the	DET
ap-1205	108	18	equations	equation	NOUN
ap-1205	108	19	related	relate	VERB
ap-1205	108	20	by	by	ADP
ap-1205	108	21	cyclic	cyclic	ADJ
ap-1205	108	22	permutations	permutation	NOUN
ap-1205	108	23	.	.	PUNCT
ap-1205	109	1	the	the	DET
ap-1205	109	2	composition	composition	NOUN
ap-1205	109	3	of	of	ADP
ap-1205	109	4	the	the	DET
ap-1205	109	5	reflection	reflection	NOUN
ap-1205	109	6	of	of	ADP
ap-1205	109	7	all	all	DET
ap-1205	109	8	three	three	NUM
ap-1205	109	9	fields	field	NOUN
ap-1205	109	10	with	with	ADP
ap-1205	109	11	the	the	DET
ap-1205	109	12	reflection	reflection	NOUN
ap-1205	109	13	amplitude	amplitude	NOUN
ap-1205	109	14	as	as	ADP
ap-1205	109	15	in	in	ADP
ap-1205	109	16	(	(	PUNCT
ap-1205	109	17	2.1	2.1	NUM
ap-1205	109	18	)	)	PUNCT
ap-1205	109	19	and	and	CCONJ
ap-1205	109	20	the	the	DET
ap-1205	109	21	duality	duality	NOUN
ap-1205	109	22	transformation	transformation	NOUN
ap-1205	109	23	b	b	PROPN
ap-1205	109	24	→	→	SYM
ap-1205	109	25	1	1	NUM
ap-1205	109	26	/	/	SYM
ap-1205	109	27	b	b	NOUN
ap-1205	109	28	(	(	PUNCT
ap-1205	109	29	changing	change	VERB
ap-1205	109	30	notation	notation	NOUN
ap-1205	109	31	mi	mi	PROPN
ap-1205	109	32	→	→	SYM
ap-1205	109	33	ni	ni	PROPN
ap-1205	109	34	)	)	PUNCT
ap-1205	109	35	gives	give	VERB
ap-1205	109	36	the	the	DET
ap-1205	109	37	correlator	correlator	NOUN
ap-1205	109	38	in	in	ADP
ap-1205	109	39	the	the	DET
ap-1205	109	40	other	other	ADJ
ap-1205	109	41	thermal	thermal	ADJ
ap-1205	109	42	case	case	NOUN
ap-1205	109	43	,	,	PUNCT
ap-1205	109	44	when	when	SCONJ
ap-1205	109	45	all	all	DET
ap-1205	109	46	mi	mi	X
ap-1205	109	47	=	=	NOUN
ap-1205	109	48	0	0	NUM
ap-1205	109	49	in	in	ADP
ap-1205	109	50	(	(	PUNCT
ap-1205	109	51	1.1	1.1	NUM
ap-1205	109	52	)	)	PUNCT
ap-1205	109	53	.	.	PUNCT
ap-1205	110	1	in	in	ADP
ap-1205	110	2	this	this	DET
ap-1205	110	3	case	case	NOUN
ap-1205	110	4	the	the	DET
ap-1205	110	5	product	product	NOUN
ap-1205	110	6	of	of	ADP
ap-1205	110	7	b(0;p(2ni	b(0;p(2ni	PROPN
ap-1205	110	8	)	)	PUNCT
ap-1205	110	9	)	)	PUNCT
ap-1205	110	10	replaces	replace	VERB
ap-1205	110	11	the	the	DET
ap-1205	110	12	denominator	denominator	NOUN
ap-1205	110	13	in	in	ADP
ap-1205	110	14	(	(	PUNCT
ap-1205	110	15	2.15	2.15	NUM
ap-1205	110	16	)	)	PUNCT
ap-1205	110	17	and	and	CCONJ
ap-1205	110	18	the	the	DET
ap-1205	110	19	formula	formula	NOUN
ap-1205	110	20	confirms	confirm	VERB
ap-1205	110	21	the	the	DET
ap-1205	110	22	structure	structure	NOUN
ap-1205	110	23	suggested	suggest	VERB
ap-1205	110	24	in	in	ADP
ap-1205	110	25	the	the	DET
ap-1205	110	26	microscopic	microscopic	ADJ
ap-1205	110	27	approach	approach	NOUN
ap-1205	110	28	of	of	ADP
ap-1205	110	29	[	[	X
ap-1205	110	30	5	5	NUM
ap-1205	110	31	]	]	PUNCT
ap-1205	110	32	.	.	PUNCT
ap-1205	111	1	the	the	DET
ap-1205	111	2	dual	dual	ADJ
ap-1205	111	3	polynomial	polynomial	ADJ
ap-1205	111	4	p̃	p̃	PROPN
ap-1205	111	5	σ3,σ2,σ1	σ3,σ2,σ1	ADV
ap-1205	111	6	β3,β2,β1	β3,β2,β1	VERB
ap-1205	111	7	is	be	AUX
ap-1205	111	8	defined	define	VERB
ap-1205	111	9	by	by	ADP
ap-1205	111	10	changing	change	VERB
ap-1205	111	11	in	in	ADP
ap-1205	111	12	(	(	PUNCT
ap-1205	111	13	2.14	2.14	NUM
ap-1205	111	14	)	)	PUNCT
ap-1205	111	15	βi	βi	PROPN
ap-1205	111	16	→	→	SYM
ap-1205	111	17	q−βi	q−βi	PROPN
ap-1205	111	18	,	,	PUNCT
ap-1205	111	19	b→	b→	PROPN
ap-1205	111	20	1	1	NUM
ap-1205	111	21	/	/	SYM
ap-1205	111	22	b	b	PROPN
ap-1205	111	23	,	,	PUNCT
ap-1205	111	24	mi	mi	PROPN
ap-1205	111	25	→	→	SYM
ap-1205	111	26	ni	ni	PROPN
ap-1205	111	27	.	.	PROPN
ap-1205	111	28	with	with	ADP
ap-1205	111	29	the	the	DET
ap-1205	111	30	help	help	NOUN
ap-1205	111	31	of	of	ADP
ap-1205	111	32	some	some	DET
ap-1205	111	33	identities	identity	NOUN
ap-1205	111	34	for	for	ADP
ap-1205	111	35	the	the	DET
ap-1205	111	36	basic	basic	ADJ
ap-1205	111	37	hypergeometric	hypergeometric	ADJ
ap-1205	111	38	functions	function	NOUN
ap-1205	111	39	one	one	NUM
ap-1205	111	40	reproduces	reproduce	VERB
ap-1205	111	41	the	the	DET
ap-1205	111	42	formula	formula	NOUN
ap-1205	111	43	in	in	ADP
ap-1205	111	44	[	[	X
ap-1205	111	45	6	6	NUM
ap-1205	111	46	]	]	PUNCT
ap-1205	111	47	for	for	ADP
ap-1205	111	48	the	the	DET
ap-1205	111	49	case	case	NOUN
ap-1205	111	50	{	{	PUNCT
ap-1205	111	51	mi	mi	PROPN
ap-1205	111	52	=	=	PROPN
ap-1205	111	53	0	0	PROPN
ap-1205	111	54	,	,	PUNCT
ap-1205	111	55	ni	ni	NOUN
ap-1205	111	56	–	–	PUNCT
ap-1205	111	57	integers	integer	NOUN
ap-1205	111	58	}	}	PUNCT
ap-1205	111	59	.	.	PUNCT
ap-1205	112	1	the	the	DET
ap-1205	112	2	expression	expression	NOUN
ap-1205	112	3	in	in	ADP
ap-1205	112	4	[	[	X
ap-1205	112	5	6	6	NUM
ap-1205	112	6	]	]	PUNCT
ap-1205	112	7	is	be	AUX
ap-1205	112	8	however	however	ADV
ap-1205	112	9	not	not	PART
ap-1205	112	10	explicitly	explicitly	ADV
ap-1205	112	11	symmetric	symmetric	ADJ
ap-1205	112	12	under	under	ADP
ap-1205	112	13	cyclic	cyclic	ADJ
ap-1205	112	14	permutations	permutation	NOUN
ap-1205	112	15	,	,	PUNCT
ap-1205	112	16	rather	rather	ADV
ap-1205	112	17	this	this	DET
ap-1205	112	18	symmetry	symmetry	NOUN
ap-1205	112	19	is	be	AUX
ap-1205	112	20	checked	check	VERB
ap-1205	112	21	to	to	PART
ap-1205	112	22	hold	hold	VERB
ap-1205	112	23	on	on	ADP
ap-1205	112	24	examples	example	NOUN
ap-1205	112	25	.	.	PUNCT
ap-1205	113	1	2.3	2.3	NUM
ap-1205	113	2	the	the	DET
ap-1205	113	3	general	general	ADJ
ap-1205	113	4	correlator	correlator	NOUN
ap-1205	113	5	to	to	PART
ap-1205	113	6	obtain	obtain	VERB
ap-1205	113	7	the	the	DET
ap-1205	113	8	liouville	liouville	NOUN
ap-1205	113	9	correlator	correlator	NOUN
ap-1205	113	10	defined	define	VERB
ap-1205	113	11	for	for	ADP
ap-1205	113	12	general	general	ADJ
ap-1205	113	13	values	value	NOUN
ap-1205	113	14	(	(	PUNCT
ap-1205	113	15	1.1	1.1	NUM
ap-1205	113	16	)	)	PUNCT
ap-1205	113	17	,	,	PUNCT
ap-1205	113	18	we	we	PRON
ap-1205	113	19	can	can	AUX
ap-1205	113	20	either	either	CCONJ
ap-1205	113	21	use	use	VERB
ap-1205	113	22	the	the	DET
ap-1205	113	23	dual	dual	ADJ
ap-1205	113	24	pentagon	pentagon	PROPN
ap-1205	113	25	equations	equation	NOUN
ap-1205	113	26	,	,	PUNCT
ap-1205	113	27	or	or	CCONJ
ap-1205	113	28	we	we	PRON
ap-1205	113	29	can	can	AUX
ap-1205	113	30	start	start	VERB
ap-1205	113	31	from	from	ADP
ap-1205	113	32	the	the	DET
ap-1205	113	33	correlator	correlator	NOUN
ap-1205	113	34	with	with	ADP
ap-1205	113	35	all	all	PRON
ap-1205	113	36	mi	mi	X
ap-1205	114	1	=	=	PROPN
ap-1205	114	2	0	0	PROPN
ap-1205	114	3	.	.	PUNCT
ap-1205	115	1	in	in	ADP
ap-1205	115	2	one	one	NUM
ap-1205	115	3	of	of	ADP
ap-1205	115	4	the	the	DET
ap-1205	115	5	steps	step	NOUN
ap-1205	115	6	,	,	PUNCT
ap-1205	115	7	the	the	DET
ap-1205	115	8	pentagon	pentagon	PROPN
ap-1205	115	9	equation	equation	NOUN
ap-1205	115	10	(	(	PUNCT
ap-1205	115	11	2.4	2.4	NUM
ap-1205	115	12	)	)	PUNCT
ap-1205	115	13	is	be	AUX
ap-1205	115	14	regularised	regularise	VERB
ap-1205	115	15	again	again	ADV
ap-1205	115	16	so	so	SCONJ
ap-1205	115	17	that	that	SCONJ
ap-1205	115	18	the	the	DET
ap-1205	115	19	second	second	ADJ
ap-1205	115	20	term	term	NOUN
ap-1205	115	21	on	on	ADP
ap-1205	115	22	the	the	DET
ap-1205	115	23	r.h.s	r.h.s	NOUN
ap-1205	115	24	.	.	PUNCT
ap-1205	115	25	is	be	AUX
ap-1205	115	26	given	give	VERB
ap-1205	115	27	by	by	ADP
ap-1205	115	28	g2	g2	PROPN
ap-1205	115	29	times	times	PROPN
ap-1205	115	30	a	a	DET
ap-1205	115	31	non	non	ADJ
ap-1205	115	32	-	-	ADJ
ap-1205	115	33	trivial	trivial	ADJ
ap-1205	115	34	coulomb	coulomb	NOUN
ap-1205	115	35	gas	gas	NOUN
ap-1205	115	36	liouville	liouville	NOUN
ap-1205	115	37	correlator	correlator	NOUN
ap-1205	115	38	.	.	PUNCT
ap-1205	116	1	the	the	DET
ap-1205	116	2	final	final	ADJ
ap-1205	116	3	result	result	NOUN
ap-1205	116	4	is	be	AUX
ap-1205	116	5	an	an	DET
ap-1205	116	6	expression	expression	NOUN
ap-1205	116	7	generalising	generalise	VERB
ap-1205	116	8	the	the	DET
ap-1205	116	9	first	first	ADJ
ap-1205	116	10	line	line	NOUN
ap-1205	116	11	in	in	ADP
ap-1205	116	12	(	(	PUNCT
ap-1205	116	13	2.15	2.15	NUM
ap-1205	116	14	)	)	PUNCT
ap-1205	116	15	,	,	PUNCT
ap-1205	116	16	cσ3,σ2,σ1	cσ3,σ2,σ1	ADV
ap-1205	116	17	β3,β2,β1	β3,β2,β1	ADV
ap-1205	116	18	=	=	SYM
ap-1205	116	19	λ	λ	PROPN
ap-1205	116	20	q−β123	q−β123	NOUN
ap-1205	116	21	2b	2b	NUM
ap-1205	116	22	l	l	NOUN
ap-1205	116	23	∏′(β3	∏′(β3	ADJ
ap-1205	116	24	,	,	PUNCT
ap-1205	116	25	β2	β2	NOUN
ap-1205	116	26	,	,	PUNCT
ap-1205	116	27	β1	β1	PROPN
ap-1205	116	28	)	)	PUNCT
ap-1205	116	29	b(σ1	b(σ1	ADV
ap-1205	116	30	,	,	PUNCT
ap-1205	116	31	σ2)(2m1;p(2n1))b(σ2	σ2)(2m1;p(2n1))b(σ2	NOUN
ap-1205	116	32	,	,	PUNCT
ap-1205	116	33	σ3)(2m2;p(2n2))b(σ3	σ3)(2m2;p(2n2))b(σ3	NOUN
ap-1205	116	34	,	,	PUNCT
ap-1205	116	35	σ1)(2m3;p(2n3	σ1)(2m3;p(2n3	ADJ
ap-1205	116	36	)	)	PUNCT
ap-1205	116	37	)	)	PUNCT
ap-1205	116	38	×	×	NOUN
ap-1205	116	39	(	(	PUNCT
ap-1205	116	40	−1)2m22n1	−1)2m22n1	PROPN
ap-1205	116	41	(	(	PUNCT
ap-1205	116	42	(	(	PUNCT
ap-1205	116	43	−1)2m1	−1)2m1	PRON
ap-1205	116	44	+	+	NOUN
ap-1205	116	45	2n2b̃(σ2	2n2b̃(σ2	NUM
ap-1205	116	46	,	,	PUNCT
ap-1205	116	47	σ3)(2n2;p(2m2))p̃	σ3)(2n2;p(2m2))p̃	ADJ
ap-1205	116	48	σ2,σ1,σ3	σ2,σ1,σ3	PROPN
ap-1205	116	49	β2,β1,β3	β2,β1,β3	PUNCT
ap-1205	116	50	b(σ3	b(σ3	NOUN
ap-1205	116	51	,	,	PUNCT
ap-1205	116	52	σ1)(2m3;p(2n3))p	σ1)(2m3;p(2n3))p	VERB
ap-1205	116	53	σ3,σ2,σ1	σ3,σ2,σ1	ADV
ap-1205	116	54	β3,β2,β1	β3,β2,β1	ADP
ap-1205	116	55	−	−	PROPN
ap-1205	116	56	(	(	PUNCT
ap-1205	116	57	2.18	2.18	NUM
ap-1205	116	58	)	)	PUNCT
ap-1205	116	59	(	(	PUNCT
ap-1205	116	60	−1)2m2	−1)2m2	NOUN
ap-1205	116	61	+	+	NOUN
ap-1205	116	62	2n1b̃(σ3	2n1b̃(σ3	NUM
ap-1205	116	63	,	,	PUNCT
ap-1205	116	64	σ1)(2n3;p(2m3))p̃	σ1)(2n3;p(2m3))p̃	PROPN
ap-1205	116	65	σ3,σ2,σ1	σ3,σ2,σ1	ADV
ap-1205	116	66	β3,β2,β1	β3,β2,β1	VERB
ap-1205	116	67	b(σ2	b(σ2	ADJ
ap-1205	116	68	,	,	PUNCT
ap-1205	116	69	σ3)(2m2;p(2n2))p	σ3)(2m2;p(2n2))p	PROPN
ap-1205	116	70	σ2,σ1,σ3	σ2,σ1,σ3	PROPN
ap-1205	116	71	β2,β1,β3	β2,β1,β3	PUNCT
ap-1205	116	72	)	)	PUNCT
ap-1205	116	73	with	with	ADP
ap-1205	116	74	the	the	DET
ap-1205	116	75	prefactor	prefactor	NOUN
ap-1205	116	76	∏′	∏′	PROPN
ap-1205	116	77	(	(	PUNCT
ap-1205	116	78	β3	β3	ADJ
ap-1205	116	79	,	,	PUNCT
ap-1205	116	80	β2	β2	NOUN
ap-1205	116	81	,	,	PUNCT
ap-1205	116	82	β1	β1	PROPN
ap-1205	116	83	)	)	PUNCT
ap-1205	116	84	=	=	PUNCT
ap-1205	117	1	(	(	PUNCT
ap-1205	117	2	−1)m123n123	−1)m123n123	X
ap-1205	117	3	∏	∏	PROPN
ap-1205	117	4	(	(	PUNCT
ap-1205	117	5	β3	β3	ADJ
ap-1205	117	6	,	,	PUNCT
ap-1205	117	7	β2	β2	NOUN
ap-1205	117	8	,	,	PUNCT
ap-1205	117	9	β1)s3b	β1)s3b	PUNCT
ap-1205	117	10	(	(	PUNCT
ap-1205	117	11	1	1	NUM
ap-1205	117	12	b	b	NOUN
ap-1205	117	13	)	)	PUNCT
ap-1205	117	14	sb(2b	sb(2b	VERB
ap-1205	117	15	−	−	PROPN
ap-1205	117	16	b	b	X
ap-1205	117	17	)	)	PUNCT
ap-1205	117	18	sb	sb	PROPN
ap-1205	117	19	(	(	PUNCT
ap-1205	117	20	n312	n312	PROPN
ap-1205	117	21	+	+	PROPN
ap-1205	117	22	1	1	NUM
ap-1205	117	23	b	b	X
ap-1205	117	24	)	)	PUNCT
ap-1205	117	25	sb	sb	PROPN
ap-1205	117	26	(	(	PUNCT
ap-1205	117	27	n123	n123	PROPN
ap-1205	117	28	+	+	PROPN
ap-1205	117	29	1	1	NUM
ap-1205	117	30	b	b	X
ap-1205	117	31	)	)	PUNCT
ap-1205	117	32	sb	sb	PROPN
ap-1205	117	33	(	(	PUNCT
ap-1205	117	34	n213	n213	PROPN
ap-1205	117	35	+	+	PROPN
ap-1205	117	36	1	1	NUM
ap-1205	117	37	b	b	NOUN
ap-1205	117	38	)	)	PUNCT
ap-1205	117	39	sb(n123	sb(n123	PROPN
ap-1205	118	1	+	+	SYM
ap-1205	118	2	2b	2b	NUM
ap-1205	118	3	−	−	PROPN
ap-1205	118	4	b	b	NOUN
ap-1205	118	5	)	)	PUNCT
ap-1205	118	6	.	.	PUNCT
ap-1205	119	1	(	(	PUNCT
ap-1205	119	2	2.19	2.19	NUM
ap-1205	119	3	)	)	PUNCT
ap-1205	119	4	87	87	NUM
ap-1205	119	5	acta	acta	PROPN
ap-1205	119	6	polytechnica	polytechnica	PROPN
ap-1205	119	7	vol	vol	NOUN
ap-1205	119	8	.	.	PROPN
ap-1205	120	1	50	50	NUM
ap-1205	120	2	no	no	NOUN
ap-1205	120	3	.	.	PUNCT
ap-1205	121	1	3/2010	3/2010	NUM
ap-1205	121	2	here	here	ADV
ap-1205	121	3	,	,	PUNCT
ap-1205	121	4	say	say	INTJ
ap-1205	121	5	,	,	PUNCT
ap-1205	121	6	the	the	DET
ap-1205	121	7	polynomial	polynomial	ADJ
ap-1205	121	8	p2	p2	NOUN
ap-1205	121	9	is	be	AUX
ap-1205	121	10	given	give	VERB
ap-1205	121	11	by	by	ADP
ap-1205	121	12	the	the	DET
ap-1205	121	13	first	first	ADJ
ap-1205	121	14	formula	formula	NOUN
ap-1205	121	15	(	(	PUNCT
ap-1205	121	16	2.14	2.14	NUM
ap-1205	121	17	)	)	PUNCT
ap-1205	121	18	,	,	PUNCT
ap-1205	121	19	where	where	SCONJ
ap-1205	121	20	now	now	ADV
ap-1205	121	21	all	all	DET
ap-1205	121	22	βi	βi	PRON
ap-1205	121	23	are	be	AUX
ap-1205	121	24	given	give	VERB
ap-1205	121	25	by	by	ADP
ap-1205	121	26	(	(	PUNCT
ap-1205	121	27	1.1	1.1	NUM
ap-1205	121	28	)	)	PUNCT
ap-1205	121	29	,	,	PUNCT
ap-1205	121	30	with	with	ADP
ap-1205	121	31	only	only	ADV
ap-1205	121	32	the	the	DET
ap-1205	121	33	sign	sign	NOUN
ap-1205	121	34	in	in	ADP
ap-1205	121	35	front	front	NOUN
ap-1205	121	36	of	of	ADP
ap-1205	121	37	(	(	PUNCT
ap-1205	121	38	2.14	2.14	NUM
ap-1205	121	39	)	)	PUNCT
ap-1205	121	40	modified	modify	VERB
ap-1205	121	41	to	to	ADP
ap-1205	121	42	(	(	PUNCT
ap-1205	121	43	−1)m3	−1)m3	NOUN
ap-1205	121	44	12(1	12(1	NOUN
ap-1205	121	45	+	+	NOUN
ap-1205	121	46	2n3)+2m32n3	2n3)+2m32n3	NUM
ap-1205	121	47	+	+	SYM
ap-1205	121	48	2m2	2m2	NUM
ap-1205	121	49	=	=	SYM
ap-1205	121	50	(	(	PUNCT
ap-1205	121	51	−1)m123(1	−1)m123(1	NUM
ap-1205	121	52	+	+	NOUN
ap-1205	121	53	2n3)+2m1	2n3)+2m1	NUM
ap-1205	121	54	.	.	PUNCT
ap-1205	122	1	let	let	VERB
ap-1205	122	2	us	we	PRON
ap-1205	122	3	also	also	ADV
ap-1205	122	4	write	write	VERB
ap-1205	122	5	down	down	ADP
ap-1205	122	6	the	the	DET
ap-1205	122	7	expression	expression	NOUN
ap-1205	122	8	for	for	ADP
ap-1205	122	9	one	one	NUM
ap-1205	122	10	of	of	ADP
ap-1205	122	11	the	the	DET
ap-1205	122	12	dual	dual	ADJ
ap-1205	122	13	polynomials	polynomial	NOUN
ap-1205	123	1	p̃1	p̃1	PROPN
ap-1205	123	2	≡	≡	PROPN
ap-1205	123	3	p̃	p̃	PROPN
ap-1205	123	4	σ2,σ1,σ3	σ2,σ1,σ3	PROPN
ap-1205	123	5	β2,β1,β3	β2,β1,β3	PUNCT
ap-1205	123	6	(	(	PUNCT
ap-1205	123	7	−1)n123(1	−1)n123(1	X
ap-1205	123	8	+	+	NOUN
ap-1205	123	9	2m2)+2n3λ	2m2)+2n3λ	PROPN
ap-1205	123	10	−n213/2	−n213/2	NUM
ap-1205	123	11	l	l	PROPN
ap-1205	123	12	sb(2n1	sb(2n1	NOUN
ap-1205	123	13	+	+	PROPN
ap-1205	123	14	1b	1b	NUM
ap-1205	123	15	)	)	PUNCT
ap-1205	123	16	sb(2n3	sb(2n3	PROPN
ap-1205	123	17	+	+	NOUN
ap-1205	123	18	1b	1b	NUM
ap-1205	123	19	)	)	PUNCT
ap-1205	124	1	sb(1b	sb(1b	NOUN
ap-1205	124	2	)	)	PUNCT
ap-1205	125	1	n213∑	n213∑	PROPN
ap-1205	125	2	u=0	u=0	SYM
ap-1205	125	3	sb	sb	PROPN
ap-1205	125	4	(	(	PUNCT
ap-1205	125	5	n213	n213	PROPN
ap-1205	125	6	+	+	PROPN
ap-1205	125	7	1	1	NUM
ap-1205	125	8	b	b	NOUN
ap-1205	125	9	)	)	PUNCT
ap-1205	125	10	sb(1+u	sb(1+u	PROPN
ap-1205	125	11	b	b	PROPN
ap-1205	125	12	)	)	PUNCT
ap-1205	125	13	sb	sb	PROPN
ap-1205	125	14	(	(	PUNCT
ap-1205	125	15	n213	n213	PROPN
ap-1205	125	16	+	+	PROPN
ap-1205	125	17	1−u	1−u	NUM
ap-1205	125	18	b	b	NOUN
ap-1205	125	19	)	)	PUNCT
ap-1205	125	20	×	×	NOUN
ap-1205	125	21	(	(	PUNCT
ap-1205	125	22	2.20	2.20	NUM
ap-1205	125	23	)	)	PUNCT
ap-1205	125	24	g2(σ1	g2(σ1	NOUN
ap-1205	125	25	+	+	CCONJ
ap-1205	125	26	u	u	NOUN
ap-1205	125	27	2b	2b	NOUN
ap-1205	125	28	,	,	PUNCT
ap-1205	125	29	q−	q−	PROPN
ap-1205	125	30	β1	β1	PROPN
ap-1205	125	31	−	−	PROPN
ap-1205	125	32	u	u	PROPN
ap-1205	125	33	2b	2b	NOUN
ap-1205	125	34	,	,	PUNCT
ap-1205	125	35	σ2	σ2	NOUN
ap-1205	125	36	)	)	PUNCT
ap-1205	125	37	g2(σ1	g2(σ1	NOUN
ap-1205	125	38	,	,	PUNCT
ap-1205	125	39	q−	q−	PROPN
ap-1205	125	40	β1	β1	PROPN
ap-1205	125	41	,	,	PUNCT
ap-1205	125	42	σ2	σ2	NOUN
ap-1205	125	43	)	)	PUNCT
ap-1205	125	44	g2(σ1	g2(σ1	NOUN
ap-1205	125	45	−	−	PROPN
ap-1205	125	46	n213−u	n213−u	PROPN
ap-1205	125	47	2b	2b	NOUN
ap-1205	125	48	,	,	PUNCT
ap-1205	125	49	q−	q−	PROPN
ap-1205	125	50	β3	β3	VERB
ap-1205	125	51	−	−	PROPN
ap-1205	125	52	n213−u	n213−u	PROPN
ap-1205	125	53	2b	2b	NUM
ap-1205	125	54	σ3	σ3	PROPN
ap-1205	125	55	)	)	PUNCT
ap-1205	125	56	g2(σ1	g2(σ1	NOUN
ap-1205	125	57	,	,	PUNCT
ap-1205	125	58	q−	q−	PROPN
ap-1205	125	59	β3	β3	PROPN
ap-1205	125	60	,	,	PUNCT
ap-1205	125	61	σ3	σ3	PROPN
ap-1205	125	62	)	)	PUNCT
ap-1205	125	63	.	.	PUNCT
ap-1205	126	1	the	the	DET
ap-1205	126	2	cyclic	cyclic	ADJ
ap-1205	126	3	symmetry	symmetry	NOUN
ap-1205	126	4	of	of	ADP
ap-1205	126	5	the	the	DET
ap-1205	126	6	full	full	ADJ
ap-1205	126	7	correlator	correlator	NOUN
ap-1205	126	8	is	be	AUX
ap-1205	126	9	ensured	ensure	VERB
ap-1205	126	10	by	by	ADP
ap-1205	126	11	construction	construction	NOUN
ap-1205	126	12	and	and	CCONJ
ap-1205	126	13	is	be	AUX
ap-1205	126	14	equivalent	equivalent	ADJ
ap-1205	126	15	to	to	ADP
ap-1205	126	16	a	a	DET
ap-1205	126	17	relation	relation	NOUN
ap-1205	126	18	generalising	generalise	VERB
ap-1205	126	19	(	(	PUNCT
ap-1205	126	20	2.17	2.17	NUM
ap-1205	126	21	)	)	PUNCT
ap-1205	126	22	,	,	PUNCT
ap-1205	126	23	(	(	PUNCT
ap-1205	126	24	−1)2n2(2m2	−1)2n2(2m2	PROPN
ap-1205	126	25	+	+	NOUN
ap-1205	126	26	1)b(σ3	1)b(σ3	PROPN
ap-1205	126	27	,	,	PUNCT
ap-1205	126	28	σ1	σ1	PROPN
ap-1205	126	29	)	)	PUNCT
ap-1205	126	30	(	(	PUNCT
ap-1205	126	31	2m3;p(2n3))p2	2m3;p(2n3))p2	NUM
ap-1205	126	32	+	+	CCONJ
ap-1205	126	33	cyclic	cyclic	ADJ
ap-1205	126	34	permutations	permutation	NOUN
ap-1205	126	35	=	=	SYM
ap-1205	126	36	0	0	PUNCT
ap-1205	126	37	(	(	PUNCT
ap-1205	126	38	2.21	2.21	NUM
ap-1205	126	39	)	)	PUNCT
ap-1205	126	40	and	and	CCONJ
ap-1205	126	41	its	its	PRON
ap-1205	126	42	dual	dual	ADJ
ap-1205	126	43	with	with	ADP
ap-1205	126	44	the	the	DET
ap-1205	126	45	dual	dual	ADJ
ap-1205	126	46	polynomials	polynomial	NOUN
ap-1205	126	47	and	and	CCONJ
ap-1205	126	48	mi	mi	PROPN
ap-1205	126	49	↔	↔	PROPN
ap-1205	126	50	ni	ni	PROPN
ap-1205	126	51	.	.	PROPN
ap-1205	126	52	in	in	ADP
ap-1205	126	53	particular	particular	ADJ
ap-1205	126	54	,	,	PUNCT
ap-1205	126	55	when	when	SCONJ
ap-1205	126	56	all	all	PRON
ap-1205	126	57	mi	mi	X
ap-1205	126	58	=	=	SYM
ap-1205	126	59	0	0	PROPN
ap-1205	127	1	the	the	DET
ap-1205	127	2	dual	dual	ADJ
ap-1205	127	3	relation	relation	NOUN
ap-1205	127	4	reproduces	reproduce	VERB
ap-1205	127	5	the	the	DET
ap-1205	127	6	cyclic	cyclic	ADJ
ap-1205	127	7	identity	identity	NOUN
ap-1205	127	8	satisfied	satisfy	VERB
ap-1205	127	9	by	by	ADP
ap-1205	127	10	the	the	DET
ap-1205	127	11	first	first	ADJ
ap-1205	127	12	order	order	NOUN
ap-1205	127	13	dual	dual	ADJ
ap-1205	127	14	polynomials	polynomial	NOUN
ap-1205	127	15	b̃(σ2	b̃(σ2	VERB
ap-1205	127	16	,	,	PUNCT
ap-1205	127	17	σ3	σ3	NOUN
ap-1205	127	18	)	)	PUNCT
ap-1205	127	19	(	(	PUNCT
ap-1205	127	20	0;p(2m2	0;p(2m2	PROPN
ap-1205	127	21	)	)	PUNCT
ap-1205	127	22	)	)	PUNCT
ap-1205	128	1	=	=	PUNCT
ap-1205	128	2	(	(	PUNCT
ap-1205	128	3	−1)2m2	−1)2m2	X
ap-1205	128	4	c̃2	c̃2	PROPN
ap-1205	128	5	−	−	PROPN
ap-1205	128	6	c̃3	c̃3	PROPN
ap-1205	128	7	,	,	PUNCT
ap-1205	128	8	etc	etc	X
ap-1205	128	9	.	.	X
ap-1205	128	10	,	,	PUNCT
ap-1205	128	11	which	which	PRON
ap-1205	128	12	appear	appear	VERB
ap-1205	128	13	in	in	ADP
ap-1205	128	14	the	the	DET
ap-1205	128	15	numerator	numerator	NOUN
ap-1205	128	16	in	in	ADP
ap-1205	128	17	(	(	PUNCT
ap-1205	128	18	2.15	2.15	NUM
ap-1205	128	19	)	)	PUNCT
ap-1205	128	20	.	.	PUNCT
ap-1205	129	1	the	the	DET
ap-1205	129	2	composition	composition	NOUN
ap-1205	129	3	of	of	ADP
ap-1205	129	4	the	the	DET
ap-1205	129	5	duality	duality	NOUN
ap-1205	129	6	transformation	transformation	NOUN
ap-1205	129	7	b	b	PROPN
ap-1205	129	8	→	→	SYM
ap-1205	129	9	1	1	NUM
ap-1205	129	10	/	/	SYM
ap-1205	129	11	b	b	NOUN
ap-1205	129	12	,	,	PUNCT
ap-1205	129	13	mi	mi	PROPN
ap-1205	129	14	↔	↔	PROPN
ap-1205	129	15	ni	ni	PROPN
ap-1205	129	16	with	with	ADP
ap-1205	129	17	reflection	reflection	NOUN
ap-1205	129	18	of	of	ADP
ap-1205	129	19	all	all	DET
ap-1205	129	20	three	three	NUM
ap-1205	129	21	fields	field	NOUN
ap-1205	129	22	keeps	keep	VERB
ap-1205	129	23	(	(	PUNCT
ap-1205	129	24	2.18	2.18	NUM
ap-1205	129	25	)	)	PUNCT
ap-1205	129	26	invariant	invariant	ADJ
ap-1205	129	27	.	.	PUNCT
ap-1205	130	1	3	3	NUM
ap-1205	130	2	summary	summary	NOUN
ap-1205	130	3	and	and	CCONJ
ap-1205	130	4	discussion	discussion	NOUN
ap-1205	130	5	we	we	PRON
ap-1205	130	6	have	have	AUX
ap-1205	130	7	obtained	obtain	VERB
ap-1205	130	8	the	the	DET
ap-1205	130	9	general	general	ADJ
ap-1205	130	10	liouville	liouville	NOUN
ap-1205	130	11	dressing	dressing	NOUN
ap-1205	130	12	factor	factor	NOUN
ap-1205	130	13	in	in	ADP
ap-1205	130	14	the	the	DET
ap-1205	130	15	tachyon	tachyon	NOUN
ap-1205	130	16	3	3	NUM
ap-1205	130	17	-	-	PUNCT
ap-1205	130	18	point	point	NOUN
ap-1205	130	19	boundary	boundary	ADJ
ap-1205	130	20	correlator	correlator	NOUN
ap-1205	130	21	with	with	ADP
ap-1205	130	22	degenerate	degenerate	ADJ
ap-1205	130	23	c	c	NOUN
ap-1205	130	24	<	<	X
ap-1205	130	25	1	1	NUM
ap-1205	130	26	representations	representation	NOUN
ap-1205	130	27	.	.	PUNCT
ap-1205	131	1	formula	formula	NOUN
ap-1205	131	2	(	(	PUNCT
ap-1205	131	3	2.18	2.18	NUM
ap-1205	131	4	)	)	PUNCT
ap-1205	131	5	represents	represent	VERB
ap-1205	131	6	the	the	DET
ap-1205	131	7	liouville	liouville	NOUN
ap-1205	131	8	correlator	correlator	NOUN
ap-1205	131	9	as	as	ADP
ap-1205	131	10	a	a	DET
ap-1205	131	11	ratio	ratio	NOUN
ap-1205	131	12	of	of	ADP
ap-1205	131	13	polynomials	polynomial	NOUN
ap-1205	131	14	of	of	ADP
ap-1205	131	15	the	the	DET
ap-1205	131	16	boundary	boundary	ADJ
ap-1205	131	17	cosmological	cosmological	ADJ
ap-1205	131	18	parameters	parameter	NOUN
ap-1205	131	19	ci	ci	PROPN
ap-1205	131	20	,	,	PUNCT
ap-1205	131	21	c̃i	c̃i	NOUN
ap-1205	131	22	generalising	generalise	VERB
ap-1205	131	23	the	the	DET
ap-1205	131	24	partial	partial	ADJ
ap-1205	131	25	results	result	NOUN
ap-1205	131	26	in	in	ADP
ap-1205	131	27	[	[	X
ap-1205	131	28	5	5	NUM
ap-1205	131	29	,	,	PUNCT
ap-1205	131	30	6	6	NUM
ap-1205	131	31	]	]	PUNCT
ap-1205	131	32	.	.	PUNCT
ap-1205	132	1	this	this	DET
ap-1205	132	2	solution	solution	NOUN
ap-1205	132	3	of	of	ADP
ap-1205	132	4	the	the	DET
ap-1205	132	5	liouville	liouville	NOUN
ap-1205	132	6	pentagon	pentagon	PROPN
ap-1205	132	7	equations	equation	NOUN
ap-1205	132	8	extends	extend	VERB
ap-1205	132	9	to	to	ADP
ap-1205	132	10	the	the	DET
ap-1205	132	11	minimal	minimal	ADJ
ap-1205	132	12	gravity	gravity	NOUN
ap-1205	132	13	theory	theory	NOUN
ap-1205	132	14	with	with	ADP
ap-1205	132	15	rational	rational	ADJ
ap-1205	132	16	b2	b2	NOUN
ap-1205	132	17	,	,	PUNCT
ap-1205	132	18	in	in	ADP
ap-1205	132	19	which	which	DET
ap-1205	132	20	case	case	NOUN
ap-1205	132	21	there	there	PRON
ap-1205	132	22	may	may	AUX
ap-1205	132	23	appear	appear	VERB
ap-1205	132	24	further	further	ADJ
ap-1205	132	25	truncations	truncation	NOUN
ap-1205	132	26	of	of	ADP
ap-1205	132	27	the	the	DET
ap-1205	132	28	sums	sum	NOUN
ap-1205	132	29	.	.	PUNCT
ap-1205	133	1	the	the	DET
ap-1205	133	2	general	general	ADJ
ap-1205	133	3	3	3	NUM
ap-1205	133	4	-	-	PUNCT
ap-1205	133	5	point	point	NOUN
ap-1205	133	6	boundary	boundary	ADJ
ap-1205	133	7	tachyon	tachyon	NOUN
ap-1205	133	8	correlator	correlator	NOUN
ap-1205	133	9	is	be	AUX
ap-1205	133	10	a	a	DET
ap-1205	133	11	product	product	NOUN
ap-1205	133	12	of	of	ADP
ap-1205	133	13	(	(	PUNCT
ap-1205	133	14	2.18	2.18	NUM
ap-1205	133	15	)	)	PUNCT
ap-1205	133	16	and	and	CCONJ
ap-1205	133	17	the	the	DET
ap-1205	133	18	matter	matter	NOUN
ap-1205	133	19	3	3	NUM
ap-1205	133	20	-	-	PUNCT
ap-1205	133	21	point	point	NOUN
ap-1205	133	22	boundary	boundary	ADJ
ap-1205	133	23	correlator	correlator	NOUN
ap-1205	133	24	,	,	PUNCT
ap-1205	133	25	satisfying	satisfy	VERB
ap-1205	133	26	a	a	DET
ap-1205	133	27	4	4	NUM
ap-1205	133	28	-	-	PUNCT
ap-1205	133	29	term	term	NOUN
ap-1205	133	30	equation	equation	NOUN
ap-1205	133	31	,	,	PUNCT
ap-1205	133	32	see	see	VERB
ap-1205	133	33	[	[	X
ap-1205	133	34	11	11	NUM
ap-1205	133	35	]	]	PUNCT
ap-1205	133	36	for	for	ADP
ap-1205	133	37	an	an	DET
ap-1205	133	38	explicit	explicit	ADJ
ap-1205	133	39	formula	formula	NOUN
ap-1205	133	40	and	and	CCONJ
ap-1205	133	41	further	further	ADJ
ap-1205	133	42	discussion	discussion	NOUN
ap-1205	133	43	.	.	PUNCT
ap-1205	134	1	a	a	DET
ap-1205	134	2	possible	possible	ADJ
ap-1205	134	3	extension	extension	NOUN
ap-1205	134	4	of	of	ADP
ap-1205	134	5	our	our	PRON
ap-1205	134	6	result	result	NOUN
ap-1205	134	7	would	would	AUX
ap-1205	134	8	allow	allow	VERB
ap-1205	134	9	us	we	PRON
ap-1205	134	10	to	to	PART
ap-1205	134	11	describe	describe	VERB
ap-1205	134	12	also	also	ADV
ap-1205	134	13	the	the	DET
ap-1205	134	14	3	3	NUM
ap-1205	134	15	-	-	PUNCT
ap-1205	134	16	point	point	NOUN
ap-1205	134	17	boundary	boundary	ADJ
ap-1205	134	18	tachyon	tachyon	NOUN
ap-1205	134	19	correlators	correlator	NOUN
ap-1205	134	20	corresponding	correspond	VERB
ap-1205	134	21	to	to	ADP
ap-1205	134	22	the	the	DET
ap-1205	134	23	zz	zz	PROPN
ap-1205	134	24	branes	brane	NOUN
ap-1205	134	25	.	.	PUNCT
ap-1205	135	1	for	for	ADP
ap-1205	135	2	this	this	DET
ap-1205	135	3	purpose	purpose	NOUN
ap-1205	135	4	,	,	PUNCT
ap-1205	135	5	the	the	DET
ap-1205	135	6	roles	role	NOUN
ap-1205	135	7	of	of	ADP
ap-1205	135	8	the	the	DET
ap-1205	135	9	matter	matter	NOUN
ap-1205	135	10	and	and	CCONJ
ap-1205	135	11	liouville	liouville	VERB
ap-1205	135	12	spectra	spectra	NOUN
ap-1205	135	13	and	and	CCONJ
ap-1205	135	14	the	the	DET
ap-1205	135	15	corresponding	corresponding	ADJ
ap-1205	135	16	correlators	correlator	NOUN
ap-1205	135	17	are	be	AUX
ap-1205	135	18	essentially	essentially	ADV
ap-1205	135	19	inverted	invert	VERB
ap-1205	135	20	:	:	PUNCT
ap-1205	135	21	the	the	DET
ap-1205	135	22	coulomb	coulomb	NOUN
ap-1205	135	23	gas	gas	NOUN
ap-1205	135	24	liouville	liouville	NOUN
ap-1205	135	25	correlator	correlator	NOUN
ap-1205	135	26	for	for	ADP
ap-1205	135	27	degenerate	degenerate	ADJ
ap-1205	135	28	c	c	NOUN
ap-1205	135	29	>	>	X
ap-1205	135	30	25	25	NUM
ap-1205	135	31	representations	representation	NOUN
ap-1205	135	32	describing	describe	VERB
ap-1205	135	33	both	both	CCONJ
ap-1205	135	34	the	the	DET
ap-1205	135	35	charges	charge	NOUN
ap-1205	135	36	and	and	CCONJ
ap-1205	135	37	the	the	DET
ap-1205	135	38	boundaries	boundary	NOUN
ap-1205	135	39	should	should	AUX
ap-1205	135	40	be	be	AUX
ap-1205	135	41	combined	combine	VERB
ap-1205	135	42	with	with	ADP
ap-1205	135	43	a	a	DET
ap-1205	135	44	matter	matter	NOUN
ap-1205	135	45	factor	factor	NOUN
ap-1205	135	46	obtained	obtain	VERB
ap-1205	135	47	by	by	ADP
ap-1205	135	48	analytic	analytic	ADJ
ap-1205	135	49	continuation	continuation	NOUN
ap-1205	135	50	of	of	ADP
ap-1205	135	51	the	the	DET
ap-1205	135	52	solution	solution	NOUN
ap-1205	135	53	(	(	PUNCT
ap-1205	135	54	2.18	2.18	NUM
ap-1205	135	55	)	)	PUNCT
ap-1205	135	56	.	.	PUNCT
ap-1205	136	1	note	note	VERB
ap-1205	136	2	that	that	SCONJ
ap-1205	136	3	the	the	DET
ap-1205	136	4	corresponding	correspond	VERB
ap-1205	136	5	discrete	discrete	NOUN
ap-1205	136	6	c	c	NOUN
ap-1205	136	7	<	<	X
ap-1205	136	8	1	1	NUM
ap-1205	136	9	spectrum	spectrum	NOUN
ap-1205	136	10	parametrises	parametrise	NOUN
ap-1205	136	11	the	the	DET
ap-1205	136	12	irreducible	irreducible	ADJ
ap-1205	136	13	representations	representation	NOUN
ap-1205	136	14	embedded	embed	VERB
ap-1205	136	15	as	as	ADP
ap-1205	136	16	submodules	submodule	NOUN
ap-1205	136	17	of	of	ADP
ap-1205	136	18	the	the	DET
ap-1205	136	19	reducible	reducible	ADJ
ap-1205	136	20	virasoro	virasoro	NOUN
ap-1205	136	21	modules	module	NOUN
ap-1205	136	22	.	.	PUNCT
ap-1205	137	1	the	the	DET
ap-1205	137	2	analogous	analogous	ADJ
ap-1205	137	3	characteristics	characteristic	NOUN
ap-1205	137	4	of	of	ADP
ap-1205	137	5	the	the	DET
ap-1205	137	6	c	c	PROPN
ap-1205	137	7	>	>	SYM
ap-1205	137	8	25	25	NUM
ap-1205	137	9	spectrum	spectrum	NOUN
ap-1205	137	10	(	(	PUNCT
ap-1205	137	11	1.1	1.1	NUM
ap-1205	137	12	)	)	PUNCT
ap-1205	137	13	have	have	AUX
ap-1205	137	14	been	be	AUX
ap-1205	137	15	exploited	exploit	VERB
ap-1205	137	16	in	in	ADP
ap-1205	137	17	the	the	DET
ap-1205	137	18	construction	construction	NOUN
ap-1205	137	19	of	of	ADP
ap-1205	137	20	the	the	DET
ap-1205	137	21	4	4	NUM
ap-1205	137	22	-	-	PUNCT
ap-1205	137	23	point	point	NOUN
ap-1205	137	24	bulk	bulk	ADJ
ap-1205	137	25	tachyon	tachyon	NOUN
ap-1205	137	26	correlators	correlator	NOUN
ap-1205	137	27	[	[	X
ap-1205	137	28	12	12	NUM
ap-1205	137	29	]	]	PUNCT
ap-1205	137	30	.	.	PUNCT
ap-1205	138	1	acknowledgement	acknowledgement	PROPN
ap-1205	138	2	p.	p.	PROPN
ap-1205	138	3	furlan	furlan	PROPN
ap-1205	138	4	acknowledges	acknowledge	VERB
ap-1205	138	5	support	support	NOUN
ap-1205	138	6	from	from	ADP
ap-1205	138	7	the	the	DET
ap-1205	138	8	italian	italian	ADJ
ap-1205	138	9	ministry	ministry	PROPN
ap-1205	138	10	of	of	ADP
ap-1205	138	11	education	education	PROPN
ap-1205	138	12	,	,	PUNCT
ap-1205	138	13	universities	university	NOUN
ap-1205	138	14	and	and	CCONJ
ap-1205	138	15	research	research	NOUN
ap-1205	138	16	(	(	PUNCT
ap-1205	138	17	miur	miur	NOUN
ap-1205	138	18	)	)	PUNCT
ap-1205	138	19	.	.	PUNCT
ap-1205	139	1	v.	v.	PROPN
ap-1205	139	2	b.	b.	PROPN
ap-1205	139	3	petkova	petkova	PROPN
ap-1205	139	4	acknowledges	acknowledge	VERB
ap-1205	139	5	hospitality	hospitality	NOUN
ap-1205	139	6	from	from	ADP
ap-1205	139	7	the	the	DET
ap-1205	139	8	service	service	NOUN
ap-1205	139	9	de	de	X
ap-1205	139	10	physique	physique	NOUN
ap-1205	139	11	thèorique	thèorique	PROPN
ap-1205	139	12	,	,	PUNCT
ap-1205	139	13	cea	cea	PROPN
ap-1205	139	14	-	-	PUNCT
ap-1205	139	15	saclay	saclay	NOUN
ap-1205	139	16	,	,	PUNCT
ap-1205	139	17	france	france	PROPN
ap-1205	139	18	,	,	PUNCT
ap-1205	139	19	and	and	CCONJ
ap-1205	139	20	ictp	ictp	ADJ
ap-1205	139	21	and	and	CCONJ
ap-1205	139	22	infn	infn	PROPN
ap-1205	139	23	,	,	PUNCT
ap-1205	139	24	italy	italy	PROPN
ap-1205	139	25	.	.	PUNCT
ap-1205	140	1	this	this	DET
ap-1205	140	2	research	research	NOUN
ap-1205	140	3	has	have	AUX
ap-1205	140	4	received	receive	VERB
ap-1205	140	5	some	some	DET
ap-1205	140	6	support	support	NOUN
ap-1205	140	7	from	from	ADP
ap-1205	140	8	the	the	DET
ap-1205	140	9	french	french	ADJ
ap-1205	140	10	-	-	PUNCT
ap-1205	140	11	bulgarian	bulgarian	ADJ
ap-1205	140	12	rila	rila	PROPN
ap-1205	140	13	project	project	PROPN
ap-1205	140	14	,	,	PUNCT
ap-1205	140	15	contract	contract	NOUN
ap-1205	140	16	3/8	3/8	NUM
ap-1205	140	17	-	-	SYM
ap-1205	140	18	2006	2006	NUM
ap-1205	140	19	.	.	PUNCT
ap-1205	141	1	references	reference	NOUN
ap-1205	141	2	[	[	X
ap-1205	141	3	1	1	NUM
ap-1205	141	4	]	]	PUNCT
ap-1205	141	5	ginsparg	ginsparg	NOUN
ap-1205	141	6	,	,	PUNCT
ap-1205	141	7	p.	p.	PROPN
ap-1205	141	8	,	,	PUNCT
ap-1205	141	9	moore	moore	PROPN
ap-1205	141	10	,	,	PUNCT
ap-1205	141	11	g.	g.	PROPN
ap-1205	141	12	:	:	PUNCT
ap-1205	141	13	lectures	lecture	NOUN
ap-1205	141	14	on	on	ADP
ap-1205	141	15	2d	2d	NUM
ap-1205	141	16	gravity	gravity	NOUN
ap-1205	141	17	and	and	CCONJ
ap-1205	141	18	2d	2d	NOUN
ap-1205	141	19	string	string	NOUN
ap-1205	141	20	theory	theory	NOUN
ap-1205	141	21	(	(	PUNCT
ap-1205	141	22	tasi	tasi	PROPN
ap-1205	141	23	1992	1992	NUM
ap-1205	141	24	)	)	PUNCT
ap-1205	141	25	,	,	PUNCT
ap-1205	141	26	hep	hep	NOUN
ap-1205	141	27	-	-	SYM
ap-1205	141	28	th/9304011	th/9304011	NUM
ap-1205	141	29	.	.	PUNCT
ap-1205	142	1	[	[	X
ap-1205	142	2	2	2	NUM
ap-1205	142	3	]	]	X
ap-1205	142	4	martinec	martinec	PROPN
ap-1205	142	5	,	,	PUNCT
ap-1205	142	6	e.	e.	PROPN
ap-1205	142	7	j.	j.	PROPN
ap-1205	142	8	:	:	PUNCT
ap-1205	142	9	the	the	DET
ap-1205	142	10	annular	annular	ADJ
ap-1205	142	11	report	report	NOUN
ap-1205	142	12	on	on	ADP
ap-1205	142	13	non	non	ADJ
ap-1205	142	14	-	-	ADJ
ap-1205	142	15	critical	critical	ADJ
ap-1205	142	16	string	string	NOUN
ap-1205	142	17	theory	theory	NOUN
ap-1205	142	18	,	,	PUNCT
ap-1205	142	19	hep	hep	NOUN
ap-1205	142	20	-	-	NOUN
ap-1205	142	21	th/0305148	th/0305148	NOUN
ap-1205	142	22	.	.	PUNCT
ap-1205	143	1	[	[	X
ap-1205	143	2	3	3	NUM
ap-1205	143	3	]	]	X
ap-1205	143	4	seiberg	seiberg	PROPN
ap-1205	143	5	,	,	PUNCT
ap-1205	143	6	n.	n.	NOUN
ap-1205	143	7	,	,	PUNCT
ap-1205	143	8	shih	shih	PROPN
ap-1205	143	9	,	,	PUNCT
ap-1205	143	10	d.	d.	PROPN
ap-1205	143	11	:	:	PUNCT
ap-1205	143	12	jhep	jhep	ADJ
ap-1205	143	13	0402	0402	NUM
ap-1205	143	14	(	(	PUNCT
ap-1205	143	15	2004	2004	NUM
ap-1205	143	16	)	)	PUNCT
ap-1205	143	17	021	021	NUM
ap-1205	143	18	,	,	PUNCT
ap-1205	143	19	hep	hep	NOUN
ap-1205	143	20	-	-	PROPN
ap-1205	143	21	th/0312170	th/0312170	NOUN
ap-1205	143	22	.	.	PUNCT
ap-1205	144	1	[	[	X
ap-1205	144	2	4	4	NUM
ap-1205	144	3	]	]	X
ap-1205	144	4	kostov	kostov	NOUN
ap-1205	144	5	,	,	PUNCT
ap-1205	144	6	i.	i.	PROPN
ap-1205	144	7	k.	k.	PROPN
ap-1205	144	8	:	:	PUNCT
ap-1205	144	9	nucl	nucl	PROPN
ap-1205	144	10	.	.	PUNCT
ap-1205	145	1	phys	phy	NOUN
ap-1205	145	2	.	.	PUNCT
ap-1205	146	1	b	b	X
ap-1205	146	2	689	689	NUM
ap-1205	146	3	,	,	PUNCT
ap-1205	146	4	3	3	NUM
ap-1205	146	5	(	(	PUNCT
ap-1205	146	6	2004	2004	NUM
ap-1205	146	7	)	)	PUNCT
ap-1205	146	8	,	,	PUNCT
ap-1205	146	9	hep	hep	NOUN
ap-1205	146	10	-	-	PROPN
ap-1205	146	11	th/0312301	th/0312301	NOUN
ap-1205	146	12	.	.	PUNCT
ap-1205	147	1	[	[	X
ap-1205	147	2	5	5	NUM
ap-1205	147	3	]	]	X
ap-1205	147	4	kostov	kostov	NOUN
ap-1205	147	5	,	,	PUNCT
ap-1205	147	6	i.	i.	PROPN
ap-1205	147	7	k.	k.	PROPN
ap-1205	147	8	,	,	PUNCT
ap-1205	147	9	ponsot	ponsot	PROPN
ap-1205	147	10	,	,	PUNCT
ap-1205	147	11	b.	b.	PROPN
ap-1205	147	12	,	,	PUNCT
ap-1205	147	13	serban	serban	PROPN
ap-1205	147	14	,	,	PUNCT
ap-1205	147	15	d.	d.	PROPN
ap-1205	147	16	:	:	PUNCT
ap-1205	147	17	nucl	nucl	PROPN
ap-1205	147	18	.	.	PUNCT
ap-1205	148	1	phys	phy	NOUN
ap-1205	148	2	.	.	PUNCT
ap-1205	149	1	b	b	ADP
ap-1205	149	2	683	683	NUM
ap-1205	149	3	,	,	PUNCT
ap-1205	149	4	309	309	NUM
ap-1205	149	5	(	(	PUNCT
ap-1205	149	6	2004	2004	NUM
ap-1205	149	7	)	)	PUNCT
ap-1205	149	8	,	,	PUNCT
ap-1205	149	9	hep	hep	NOUN
ap-1205	149	10	-	-	PROPN
ap-1205	149	11	th/0307189	th/0307189	NOUN
ap-1205	149	12	.	.	PUNCT
ap-1205	150	1	[	[	X
ap-1205	150	2	6	6	NUM
ap-1205	150	3	]	]	PUNCT
ap-1205	150	4	alexandrov	alexandrov	PROPN
ap-1205	150	5	,	,	PUNCT
ap-1205	150	6	s.	s.	PROPN
ap-1205	150	7	y.	y.	PROPN
ap-1205	150	8	,	,	PUNCT
ap-1205	150	9	imeroni	imeroni	NOUN
ap-1205	150	10	,	,	PUNCT
ap-1205	150	11	e.	e.	PROPN
ap-1205	150	12	:	:	PUNCT
ap-1205	150	13	nucl.phys	nucl.phy	NOUN
ap-1205	150	14	.	.	PUNCT
ap-1205	151	1	b	b	ADP
ap-1205	151	2	731	731	NUM
ap-1205	151	3	(	(	PUNCT
ap-1205	151	4	2005	2005	NUM
ap-1205	151	5	)	)	PUNCT
ap-1205	151	6	242	242	NUM
ap-1205	151	7	,	,	PUNCT
ap-1205	151	8	hep	hep	NOUN
ap-1205	151	9	-	-	NOUN
ap-1205	151	10	th/0504199	th/0504199	NOUN
ap-1205	151	11	.	.	PUNCT
ap-1205	152	1	[	[	X
ap-1205	152	2	7	7	NUM
ap-1205	152	3	]	]	X
ap-1205	152	4	basu	basu	PROPN
ap-1205	152	5	,	,	PUNCT
ap-1205	152	6	a.	a.	PROPN
ap-1205	152	7	,	,	PUNCT
ap-1205	152	8	martinec	martinec	PROPN
ap-1205	152	9	,	,	PUNCT
ap-1205	152	10	e.	e.	PROPN
ap-1205	152	11	j.	j.	PROPN
ap-1205	152	12	:	:	PUNCT
ap-1205	152	13	phys	phy	NOUN
ap-1205	152	14	.	.	PUNCT
ap-1205	152	15	rev	rev	PROPN
ap-1205	152	16	.	.	PUNCT
ap-1205	153	1	d	d	X
ap-1205	153	2	72	72	NUM
ap-1205	153	3	,	,	PUNCT
ap-1205	153	4	106007	106007	NUM
ap-1205	153	5	(	(	PUNCT
ap-1205	153	6	2005	2005	NUM
ap-1205	153	7	)	)	PUNCT
ap-1205	153	8	,	,	PUNCT
ap-1205	154	1	hep	hep	PROPN
ap-1205	154	2	-	-	PROPN
ap-1205	154	3	th/0509142	th/0509142	PROPN
ap-1205	154	4	.	.	PUNCT
ap-1205	155	1	[	[	X
ap-1205	155	2	8	8	NUM
ap-1205	155	3	]	]	SYM
ap-1205	155	4	fateev	fateev	PROPN
ap-1205	155	5	,	,	PUNCT
ap-1205	155	6	v.	v.	PROPN
ap-1205	155	7	,	,	PUNCT
ap-1205	155	8	zamolodchikov	zamolodchikov	PROPN
ap-1205	155	9	,	,	PUNCT
ap-1205	155	10	a.	a.	PROPN
ap-1205	155	11	,	,	PUNCT
ap-1205	155	12	zamolodchikov	zamolodchikov	PROPN
ap-1205	155	13	,	,	PUNCT
ap-1205	155	14	al	al	PROPN
ap-1205	155	15	.	.	PUNCT
ap-1205	155	16	:	:	PUNCT
ap-1205	155	17	boundary	boundary	ADJ
ap-1205	155	18	liouville	liouville	NOUN
ap-1205	155	19	field	field	NOUN
ap-1205	155	20	theory	theory	NOUN
ap-1205	155	21	.	.	PUNCT
ap-1205	156	1	i	i	PRON
ap-1205	156	2	:	:	PUNCT
ap-1205	156	3	boundary	boundary	ADJ
ap-1205	156	4	state	state	NOUN
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ap-1205	156	6	boundary	boundary	ADJ
ap-1205	156	7	two	two	NUM
ap-1205	156	8	-	-	PUNCT
ap-1205	156	9	point	point	NOUN
ap-1205	156	10	function	function	NOUN
ap-1205	156	11	,	,	PUNCT
ap-1205	156	12	hep	hep	NOUN
ap-1205	156	13	-	-	NOUN
ap-1205	156	14	th/0001012	th/0001012	NOUN
ap-1205	156	15	.	.	PROPN
ap-1205	156	16	88	88	NUM
ap-1205	156	17	acta	acta	PROPN
ap-1205	156	18	polytechnica	polytechnica	PROPN
ap-1205	156	19	vol	vol	NOUN
ap-1205	156	20	.	.	PROPN
ap-1205	157	1	50	50	NUM
ap-1205	157	2	no	no	NOUN
ap-1205	157	3	.	.	PUNCT
ap-1205	158	1	3/2010	3/2010	NUM
ap-1205	158	2	[	[	X
ap-1205	158	3	9	9	NUM
ap-1205	158	4	]	]	SYM
ap-1205	158	5	ponsot	ponsot	NOUN
ap-1205	158	6	,	,	PUNCT
ap-1205	158	7	b.	b.	PROPN
ap-1205	158	8	,	,	PUNCT
ap-1205	158	9	teschner	teschner	NOUN
ap-1205	158	10	,	,	PUNCT
ap-1205	158	11	j.	j.	PROPN
ap-1205	158	12	:	:	PUNCT
ap-1205	158	13	nucl	nucl	PROPN
ap-1205	158	14	.	.	PUNCT
ap-1205	159	1	phys	phy	NOUN
ap-1205	159	2	.	.	PUNCT
ap-1205	160	1	b	b	X
ap-1205	160	2	622	622	NUM
ap-1205	160	3	(	(	PUNCT
ap-1205	160	4	2002	2002	NUM
ap-1205	160	5	)	)	PUNCT
ap-1205	160	6	309	309	NUM
ap-1205	160	7	,	,	PUNCT
ap-1205	160	8	hep	hep	NOUN
ap-1205	160	9	-	-	PROPN
ap-1205	160	10	th/0110244	th/0110244	NOUN
ap-1205	160	11	.	.	PUNCT
ap-1205	161	1	[	[	X
ap-1205	161	2	10	10	NUM
ap-1205	161	3	]	]	SYM
ap-1205	161	4	ponsot	ponsot	NOUN
ap-1205	161	5	,	,	PUNCT
ap-1205	161	6	b.	b.	PROPN
ap-1205	161	7	,	,	PUNCT
ap-1205	161	8	teschner	teschner	NOUN
ap-1205	161	9	,	,	PUNCT
ap-1205	161	10	j.	j.	PROPN
ap-1205	161	11	:	:	PUNCT
ap-1205	161	12	liouville	liouville	PROPN
ap-1205	161	13	bootstrap	bootstrap	NOUN
ap-1205	161	14	via	via	ADP
ap-1205	161	15	harmonic	harmonic	ADJ
ap-1205	161	16	analysis	analysis	NOUN
ap-1205	161	17	on	on	ADP
ap-1205	161	18	a	a	DET
ap-1205	161	19	noncompact	noncompact	ADJ
ap-1205	161	20	quantum	quantum	NOUN
ap-1205	161	21	group	group	NOUN
ap-1205	161	22	,	,	PUNCT
ap-1205	161	23	hepth/99111110	hepth/99111110	PROPN
ap-1205	161	24	;	;	PUNCT
ap-1205	161	25	comm	comm	NOUN
ap-1205	161	26	.	.	PUNCT
ap-1205	161	27	math	math	NOUN
ap-1205	161	28	.	.	PUNCT
ap-1205	162	1	phys	phy	NOUN
ap-1205	162	2	.	.	PUNCT
ap-1205	163	1	224	224	NUM
ap-1205	163	2	,	,	PUNCT
ap-1205	163	3	3	3	NUM
ap-1205	163	4	(	(	PUNCT
ap-1205	163	5	2001	2001	NUM
ap-1205	163	6	)	)	PUNCT
ap-1205	163	7	613	613	NUM
ap-1205	163	8	,	,	PUNCT
ap-1205	163	9	math.qa/0007097	math.qa/0007097	NOUN
ap-1205	163	10	.	.	PUNCT
ap-1205	164	1	[	[	X
ap-1205	164	2	11	11	NUM
ap-1205	164	3	]	]	SYM
ap-1205	164	4	furlan	furlan	NOUN
ap-1205	164	5	,	,	PUNCT
ap-1205	164	6	p.	p.	PROPN
ap-1205	164	7	,	,	PUNCT
ap-1205	164	8	petkova	petkova	PROPN
ap-1205	164	9	,	,	PUNCT
ap-1205	164	10	v.	v.	PROPN
ap-1205	164	11	b.	b.	PROPN
ap-1205	164	12	,	,	PUNCT
ap-1205	164	13	stanishkov	stanishkov	PROPN
ap-1205	164	14	,	,	PUNCT
ap-1205	164	15	m.	m.	NOUN
ap-1205	164	16	:	:	PUNCT
ap-1205	164	17	non	non	ADJ
ap-1205	164	18	-	-	ADJ
ap-1205	164	19	critical	critical	ADJ
ap-1205	164	20	string	string	NOUN
ap-1205	164	21	pentagon	pentagon	PROPN
ap-1205	164	22	equations	equation	NOUN
ap-1205	164	23	and	and	CCONJ
ap-1205	164	24	their	their	PRON
ap-1205	164	25	solutions	solution	NOUN
ap-1205	164	26	,	,	PUNCT
ap-1205	164	27	to	to	PART
ap-1205	164	28	appear	appear	VERB
ap-1205	164	29	in	in	ADP
ap-1205	164	30	:	:	PUNCT
ap-1205	164	31	j.	j.	PROPN
ap-1205	164	32	phys	phys	PROPN
ap-1205	164	33	.	.	PUNCT
ap-1205	165	1	a	a	DET
ap-1205	165	2	,	,	PUNCT
ap-1205	165	3	arxiv:0805.0134	arxiv:0805.0134	PROPN
ap-1205	165	4	.	.	PUNCT
ap-1205	166	1	[	[	X
ap-1205	166	2	12	12	NUM
ap-1205	166	3	]	]	X
ap-1205	166	4	belavin	belavin	NOUN
ap-1205	166	5	,	,	PUNCT
ap-1205	166	6	a.	a.	PROPN
ap-1205	166	7	,	,	PUNCT
ap-1205	166	8	zamolodchikov	zamolodchikov	PROPN
ap-1205	166	9	,	,	PUNCT
ap-1205	166	10	al	al	PROPN
ap-1205	166	11	.	.	PROPN
ap-1205	166	12	:	:	PUNCT
ap-1205	166	13	theor	theor	PROPN
ap-1205	166	14	.	.	PUNCT
ap-1205	166	15	math	math	NOUN
ap-1205	166	16	.	.	PUNCT
ap-1205	167	1	phys	phy	NOUN
ap-1205	167	2	.	.	PUNCT
ap-1205	168	1	147	147	NUM
ap-1205	168	2	(	(	PUNCT
ap-1205	168	3	2006	2006	NUM
ap-1205	168	4	)	)	PUNCT
ap-1205	168	5	729	729	NUM
ap-1205	168	6	,	,	PUNCT
ap-1205	168	7	hep	hep	NOUN
ap-1205	168	8	-	-	SYM
ap-1205	168	9	th/0510214	th/0510214	PROPN
ap-1205	168	10	.	.	PUNCT
ap-1205	169	1	p.	p.	NOUN
ap-1205	169	2	furlan	furlan	PROPN
ap-1205	169	3	dipartimento	dipartimento	PROPN
ap-1205	169	4	di	di	PROPN
ap-1205	169	5	fisica	fisica	PROPN
ap-1205	169	6	teorica	teorica	PROPN
ap-1205	169	7	dell’università	dell’università	PROPN
ap-1205	169	8	di	di	NOUN
ap-1205	169	9	trieste	trieste	PROPN
ap-1205	169	10	,	,	PUNCT
ap-1205	169	11	italy	italy	PROPN
ap-1205	169	12	istituto	istituto	PROPN
ap-1205	169	13	nazionale	nazionale	PROPN
ap-1205	169	14	di	di	PROPN
ap-1205	169	15	fisica	fisica	PROPN
ap-1205	169	16	nucleare	nucleare	PROPN
ap-1205	169	17	(	(	PUNCT
ap-1205	169	18	infn	infn	PROPN
ap-1205	169	19	)	)	PUNCT
ap-1205	169	20	sezione	sezione	PROPN
ap-1205	169	21	di	di	X
ap-1205	169	22	trieste	trieste	PROPN
ap-1205	169	23	,	,	PUNCT
ap-1205	169	24	italy	italy	PROPN
ap-1205	169	25	v.	v.	PROPN
ap-1205	169	26	b.	b.	PROPN
ap-1205	169	27	petkova	petkova	PROPN
ap-1205	169	28	institute	institute	PROPN
ap-1205	169	29	for	for	ADP
ap-1205	169	30	nuclear	nuclear	ADJ
ap-1205	169	31	research	research	NOUN
ap-1205	169	32	and	and	CCONJ
ap-1205	169	33	nuclear	nuclear	ADJ
ap-1205	169	34	energy	energy	NOUN
ap-1205	169	35	(	(	PUNCT
ap-1205	169	36	inrne	inrne	VERB
ap-1205	169	37	)	)	PUNCT
ap-1205	169	38	,	,	PUNCT
ap-1205	169	39	bulgarian	bulgarian	PROPN
ap-1205	169	40	academy	academy	PROPN
ap-1205	169	41	of	of	ADP
ap-1205	169	42	sciences	sciences	PROPN
ap-1205	169	43	(	(	PUNCT
ap-1205	169	44	bas	bas	PROPN
ap-1205	169	45	)	)	PUNCT
ap-1205	169	46	,	,	PUNCT
ap-1205	169	47	bulgaria	bulgaria	PROPN
ap-1205	169	48	m.	m.	PROPN
ap-1205	169	49	stanishkov	stanishkov	PROPN
ap-1205	169	50	institute	institute	PROPN
ap-1205	169	51	for	for	ADP
ap-1205	169	52	nuclear	nuclear	ADJ
ap-1205	169	53	research	research	NOUN
ap-1205	169	54	and	and	CCONJ
ap-1205	169	55	nuclear	nuclear	ADJ
ap-1205	169	56	energy	energy	NOUN
ap-1205	169	57	(	(	PUNCT
ap-1205	169	58	inrne	inrne	VERB
ap-1205	169	59	)	)	PUNCT
ap-1205	169	60	,	,	PUNCT
ap-1205	169	61	bulgarian	bulgarian	PROPN
ap-1205	169	62	academy	academy	PROPN
ap-1205	169	63	of	of	ADP
ap-1205	169	64	sciences	sciences	PROPN
ap-1205	169	65	(	(	PUNCT
ap-1205	169	66	bas	bas	PROPN
ap-1205	169	67	)	)	PUNCT
ap-1205	169	68	,	,	PUNCT
ap-1205	169	69	bulgaria	bulgaria	PROPN
ap-1205	169	70	89	89	NUM