id	sid	tid	token	lemma	pos
ap-3506	1	1	acta	acta	PROPN
ap-3506	1	2	polytechnica	polytechnica	PROPN
ap-3506	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3506	1	4	/	/	SYM
ap-3506	1	5	ap.2016.56.0173	ap.2016.56.0173	PROPN
ap-3506	1	6	acta	acta	PROPN
ap-3506	1	7	polytechnica	polytechnica	PROPN
ap-3506	1	8	56(3):173–179	56(3):173–179	PROPN
ap-3506	1	9	,	,	PUNCT
ap-3506	1	10	2016	2016	NUM
ap-3506	1	11	©	©	PROPN
ap-3506	1	12	czech	czech	PROPN
ap-3506	1	13	technical	technical	PROPN
ap-3506	1	14	university	university	PROPN
ap-3506	1	15	in	in	ADP
ap-3506	1	16	prague	prague	PROPN
ap-3506	1	17	,	,	PUNCT
ap-3506	1	18	2016	2016	NUM
ap-3506	1	19	available	available	ADJ
ap-3506	1	20	online	online	ADV
ap-3506	1	21	at	at	ADP
ap-3506	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3506	1	23	covariant	covariant	ADJ
ap-3506	1	24	integral	integral	ADJ
ap-3506	1	25	quantizations	quantization	NOUN
ap-3506	1	26	and	and	CCONJ
ap-3506	1	27	their	their	PRON
ap-3506	1	28	applications	application	NOUN
ap-3506	1	29	to	to	ADP
ap-3506	1	30	quantum	quantum	PROPN
ap-3506	1	31	cosmology	cosmology	NOUN
ap-3506	1	32	jean	jean	PROPN
ap-3506	1	33	pierre	pierre	PROPN
ap-3506	1	34	gazeau	gazeau	PROPN
ap-3506	1	35	astroparticle	astroparticle	PROPN
ap-3506	1	36	and	and	CCONJ
ap-3506	1	37	cosmology	cosmology	PROPN
ap-3506	1	38	,	,	PUNCT
ap-3506	1	39	univ	univ	PROPN
ap-3506	1	40	paris	paris	PROPN
ap-3506	1	41	diderot	diderot	PROPN
ap-3506	1	42	,	,	PUNCT
ap-3506	1	43	sorbonne	sorbonne	PROPN
ap-3506	1	44	paris	paris	PROPN
ap-3506	1	45	cité	cité	PROPN
ap-3506	1	46	,	,	PUNCT
ap-3506	1	47	paris	paris	PROPN
ap-3506	1	48	75205	75205	NUM
ap-3506	1	49	,	,	PUNCT
ap-3506	1	50	france	france	PROPN
ap-3506	1	51	correspondence	correspondence	NOUN
ap-3506	1	52	:	:	PUNCT
ap-3506	1	53	gazeau@apc.univ-paris7.fr	gazeau@apc.univ-paris7.fr	PROPN
ap-3506	1	54	abstract	abstract	NOUN
ap-3506	1	55	.	.	PUNCT
ap-3506	2	1	we	we	PRON
ap-3506	2	2	present	present	VERB
ap-3506	2	3	a	a	DET
ap-3506	2	4	general	general	ADJ
ap-3506	2	5	formalism	formalism	NOUN
ap-3506	2	6	for	for	ADP
ap-3506	2	7	giving	give	VERB
ap-3506	2	8	a	a	DET
ap-3506	2	9	measure	measure	NOUN
ap-3506	2	10	space	space	NOUN
ap-3506	2	11	paired	pair	VERB
ap-3506	2	12	with	with	ADP
ap-3506	2	13	a	a	DET
ap-3506	2	14	separable	separable	ADJ
ap-3506	2	15	hilbert	hilbert	NOUN
ap-3506	2	16	space	space	NOUN
ap-3506	2	17	a	a	DET
ap-3506	2	18	quantum	quantum	NOUN
ap-3506	2	19	version	version	NOUN
ap-3506	2	20	based	base	VERB
ap-3506	2	21	on	on	ADP
ap-3506	2	22	a	a	DET
ap-3506	2	23	normalized	normalize	VERB
ap-3506	2	24	positive	positive	ADJ
ap-3506	2	25	operator	operator	NOUN
ap-3506	2	26	-	-	PUNCT
ap-3506	2	27	valued	value	VERB
ap-3506	2	28	measure	measure	NOUN
ap-3506	2	29	.	.	PUNCT
ap-3506	3	1	the	the	DET
ap-3506	3	2	latter	latter	ADJ
ap-3506	3	3	are	be	AUX
ap-3506	3	4	built	build	VERB
ap-3506	3	5	from	from	ADP
ap-3506	3	6	families	family	NOUN
ap-3506	3	7	of	of	ADP
ap-3506	3	8	density	density	NOUN
ap-3506	3	9	operators	operator	NOUN
ap-3506	3	10	labeled	label	VERB
ap-3506	3	11	by	by	ADP
ap-3506	3	12	points	point	NOUN
ap-3506	3	13	of	of	ADP
ap-3506	3	14	the	the	DET
ap-3506	3	15	measure	measure	NOUN
ap-3506	3	16	space	space	NOUN
ap-3506	3	17	.	.	PUNCT
ap-3506	4	1	we	we	PRON
ap-3506	4	2	especially	especially	ADV
ap-3506	4	3	focus	focus	VERB
ap-3506	4	4	on	on	ADP
ap-3506	4	5	group	group	NOUN
ap-3506	4	6	representation	representation	NOUN
ap-3506	4	7	and	and	CCONJ
ap-3506	4	8	probabilistic	probabilistic	ADJ
ap-3506	4	9	aspects	aspect	NOUN
ap-3506	4	10	of	of	ADP
ap-3506	4	11	these	these	DET
ap-3506	4	12	constructions	construction	NOUN
ap-3506	4	13	.	.	PUNCT
ap-3506	5	1	simple	simple	ADJ
ap-3506	5	2	phase	phase	NOUN
ap-3506	5	3	space	space	NOUN
ap-3506	5	4	examples	example	NOUN
ap-3506	5	5	illustrate	illustrate	VERB
ap-3506	5	6	the	the	DET
ap-3506	5	7	procedure	procedure	NOUN
ap-3506	5	8	:	:	PUNCT
ap-3506	5	9	plane	plane	NOUN
ap-3506	5	10	(	(	PUNCT
ap-3506	5	11	weyl	weyl	PROPN
ap-3506	5	12	-	-	PUNCT
ap-3506	5	13	heisenberg	heisenberg	PROPN
ap-3506	5	14	symmetry	symmetry	PROPN
ap-3506	5	15	)	)	PUNCT
ap-3506	5	16	,	,	PUNCT
ap-3506	5	17	half	half	ADJ
ap-3506	5	18	-	-	PUNCT
ap-3506	5	19	plane	plane	NOUN
ap-3506	5	20	(	(	PUNCT
ap-3506	5	21	affine	affine	NOUN
ap-3506	5	22	symmetry	symmetry	PROPN
ap-3506	5	23	)	)	PUNCT
ap-3506	5	24	.	.	PUNCT
ap-3506	6	1	interesting	interesting	ADJ
ap-3506	6	2	applications	application	NOUN
ap-3506	6	3	to	to	ADP
ap-3506	6	4	quantum	quantum	ADJ
ap-3506	6	5	cosmology	cosmology	NOUN
ap-3506	6	6	(	(	PUNCT
ap-3506	6	7	“	"	PUNCT
ap-3506	6	8	smooth	smooth	ADJ
ap-3506	6	9	bouncing	bounce	VERB
ap-3506	6	10	”	"	PUNCT
ap-3506	6	11	)	)	PUNCT
ap-3506	6	12	for	for	ADP
ap-3506	6	13	friedmann	friedmann	NOUN
ap-3506	6	14	-	-	PUNCT
ap-3506	6	15	robertson	robertson	PROPN
ap-3506	6	16	-	-	PUNCT
ap-3506	6	17	walker	walker	PROPN
ap-3506	6	18	metric	metric	PROPN
ap-3506	6	19	are	be	AUX
ap-3506	6	20	presented	present	VERB
ap-3506	6	21	and	and	CCONJ
ap-3506	6	22	those	those	PRON
ap-3506	6	23	for	for	ADP
ap-3506	6	24	bianchi	bianchi	NOUN
ap-3506	7	1	i	i	PRON
ap-3506	7	2	and	and	CCONJ
ap-3506	7	3	ix	ix	PROPN
ap-3506	7	4	models	model	NOUN
ap-3506	7	5	are	be	AUX
ap-3506	7	6	mentioned	mention	VERB
ap-3506	7	7	.	.	PUNCT
ap-3506	8	1	keywords	keyword	NOUN
ap-3506	8	2	:	:	PUNCT
ap-3506	8	3	integral	integral	ADJ
ap-3506	8	4	quantization	quantization	NOUN
ap-3506	8	5	;	;	PUNCT
ap-3506	8	6	covariance	covariance	NOUN
ap-3506	8	7	;	;	PUNCT
ap-3506	8	8	povm	povm	NOUN
ap-3506	8	9	;	;	PUNCT
ap-3506	8	10	affine	affine	NOUN
ap-3506	8	11	group	group	NOUN
ap-3506	8	12	;	;	PUNCT
ap-3506	8	13	weyl	weyl	PROPN
ap-3506	8	14	-	-	PUNCT
ap-3506	8	15	heisenberg	heisenberg	PROPN
ap-3506	8	16	group	group	NOUN
ap-3506	8	17	;	;	PUNCT
ap-3506	8	18	coherent	coherent	ADJ
ap-3506	8	19	states	state	NOUN
ap-3506	8	20	;	;	PUNCT
ap-3506	8	21	frw	frw	NOUN
ap-3506	8	22	model	model	NOUN
ap-3506	8	23	;	;	PUNCT
ap-3506	8	24	smooth	smooth	ADJ
ap-3506	8	25	bouncing	bounce	VERB
ap-3506	8	26	.	.	PUNCT
ap-3506	9	1	1	1	X
ap-3506	9	2	.	.	X
ap-3506	9	3	introduction	introduction	NOUN
ap-3506	9	4	group	group	NOUN
ap-3506	9	5	theory	theory	NOUN
ap-3506	9	6	is	be	AUX
ap-3506	9	7	one	one	NUM
ap-3506	9	8	of	of	ADP
ap-3506	9	9	the	the	DET
ap-3506	9	10	favorite	favorite	ADJ
ap-3506	9	11	domains	domain	NOUN
ap-3506	9	12	of	of	ADP
ap-3506	9	13	j.	j.	PROPN
ap-3506	9	14	patera	patera	PROPN
ap-3506	9	15	and	and	CCONJ
ap-3506	9	16	p.	p.	PROPN
ap-3506	9	17	winternitz	winternitz	PROPN
ap-3506	9	18	.	.	PUNCT
ap-3506	10	1	this	this	DET
ap-3506	10	2	contribution	contribution	NOUN
ap-3506	10	3	to	to	ADP
ap-3506	10	4	the	the	DET
ap-3506	10	5	celebration	celebration	NOUN
ap-3506	10	6	of	of	ADP
ap-3506	10	7	the	the	DET
ap-3506	10	8	jiri	jiri	PROPN
ap-3506	10	9	and	and	CCONJ
ap-3506	10	10	pavel	pavel	PROPN
ap-3506	10	11	80th	80th	ADJ
ap-3506	10	12	birthday	birthday	NOUN
ap-3506	10	13	emphasizes	emphasize	VERB
ap-3506	10	14	the	the	DET
ap-3506	10	15	role	role	NOUN
ap-3506	10	16	of	of	ADP
ap-3506	10	17	group	group	NOUN
ap-3506	10	18	representation	representation	NOUN
ap-3506	10	19	theory	theory	NOUN
ap-3506	10	20	in	in	ADP
ap-3506	10	21	a	a	DET
ap-3506	10	22	certain	certain	ADJ
ap-3506	10	23	type	type	NOUN
ap-3506	10	24	of	of	ADP
ap-3506	10	25	quantization	quantization	NOUN
ap-3506	10	26	procedures	procedure	NOUN
ap-3506	10	27	.	.	PUNCT
ap-3506	11	1	these	these	DET
ap-3506	11	2	methods	method	NOUN
ap-3506	11	3	[	[	X
ap-3506	11	4	1–9	1–9	NOUN
ap-3506	11	5	]	]	X
ap-3506	11	6	are	be	AUX
ap-3506	11	7	named	name	VERB
ap-3506	11	8	(	(	PUNCT
ap-3506	11	9	covariant	covariant	ADJ
ap-3506	11	10	)	)	PUNCT
ap-3506	11	11	integral	integral	ADJ
ap-3506	11	12	quantizations	quantization	NOUN
ap-3506	11	13	and	and	CCONJ
ap-3506	11	14	offer	offer	VERB
ap-3506	11	15	a	a	DET
ap-3506	11	16	large	large	ADJ
ap-3506	11	17	scope	scope	NOUN
ap-3506	11	18	of	of	ADP
ap-3506	11	19	possibilities	possibility	NOUN
ap-3506	11	20	for	for	ADP
ap-3506	11	21	mapping	map	VERB
ap-3506	11	22	a	a	DET
ap-3506	11	23	classical	classical	ADJ
ap-3506	11	24	mathematical	mathematical	ADJ
ap-3506	11	25	model	model	NOUN
ap-3506	11	26	of	of	ADP
ap-3506	11	27	a	a	DET
ap-3506	11	28	physical	physical	ADJ
ap-3506	11	29	system	system	NOUN
ap-3506	11	30	to	to	ADP
ap-3506	11	31	a	a	DET
ap-3506	11	32	quantum	quantum	ADJ
ap-3506	11	33	model	model	NOUN
ap-3506	11	34	.	.	PUNCT
ap-3506	12	1	they	they	PRON
ap-3506	12	2	are	be	AUX
ap-3506	12	3	based	base	VERB
ap-3506	12	4	on	on	ADP
ap-3506	12	5	normalized	normalize	VERB
ap-3506	12	6	positive	positive	ADJ
ap-3506	12	7	operator	operator	NOUN
ap-3506	12	8	-	-	PUNCT
ap-3506	12	9	valued	value	VERB
ap-3506	12	10	measures	measure	NOUN
ap-3506	12	11	(	(	PUNCT
ap-3506	12	12	povm	povm	NOUN
ap-3506	12	13	)	)	PUNCT
ap-3506	12	14	and	and	CCONJ
ap-3506	12	15	present	present	ADJ
ap-3506	12	16	at	at	ADV
ap-3506	12	17	least	least	ADV
ap-3506	12	18	two	two	NUM
ap-3506	12	19	attractive	attractive	ADJ
ap-3506	12	20	advantages	advantage	NOUN
ap-3506	12	21	:	:	PUNCT
ap-3506	12	22	(	(	PUNCT
ap-3506	12	23	1	1	NUM
ap-3506	12	24	.	.	PUNCT
ap-3506	12	25	)	)	PUNCT
ap-3506	12	26	by	by	ADP
ap-3506	12	27	employing	employ	VERB
ap-3506	12	28	all	all	DET
ap-3506	12	29	resources	resource	NOUN
ap-3506	12	30	of	of	ADP
ap-3506	12	31	integration	integration	NOUN
ap-3506	12	32	and	and	CCONJ
ap-3506	12	33	distributions	distribution	NOUN
ap-3506	12	34	,	,	PUNCT
ap-3506	12	35	they	they	PRON
ap-3506	12	36	are	be	AUX
ap-3506	12	37	most	most	ADV
ap-3506	12	38	appropriate	appropriate	ADJ
ap-3506	12	39	when	when	SCONJ
ap-3506	12	40	we	we	PRON
ap-3506	12	41	have	have	VERB
ap-3506	12	42	to	to	PART
ap-3506	12	43	deal	deal	VERB
ap-3506	12	44	with	with	ADP
ap-3506	12	45	some	some	DET
ap-3506	12	46	geometric	geometric	ADJ
ap-3506	12	47	singularities	singularity	NOUN
ap-3506	12	48	.	.	PUNCT
ap-3506	13	1	(	(	PUNCT
ap-3506	13	2	2	2	NUM
ap-3506	13	3	.	.	PUNCT
ap-3506	13	4	)	)	PUNCT
ap-3506	14	1	they	they	PRON
ap-3506	14	2	afford	afford	VERB
ap-3506	14	3	a	a	DET
ap-3506	14	4	semi	semi	ADJ
ap-3506	14	5	-	-	ADJ
ap-3506	14	6	classical	classical	ADJ
ap-3506	14	7	phase	phase	NOUN
ap-3506	14	8	space	space	NOUN
ap-3506	14	9	portrait	portrait	NOUN
ap-3506	14	10	of	of	ADP
ap-3506	14	11	quantum	quantum	ADJ
ap-3506	14	12	states	state	NOUN
ap-3506	14	13	and	and	CCONJ
ap-3506	14	14	quantum	quantum	NOUN
ap-3506	14	15	dynamics	dynamic	NOUN
ap-3506	14	16	together	together	ADV
ap-3506	14	17	with	with	ADP
ap-3506	14	18	a	a	DET
ap-3506	14	19	probabilistic	probabilistic	ADJ
ap-3506	14	20	interpretation	interpretation	NOUN
ap-3506	14	21	.	.	PUNCT
ap-3506	15	1	moreover	moreover	ADV
ap-3506	15	2	,	,	PUNCT
ap-3506	15	3	their	their	PRON
ap-3506	15	4	recent	recent	ADJ
ap-3506	15	5	applications	application	NOUN
ap-3506	15	6	to	to	ADP
ap-3506	15	7	quantum	quantum	ADJ
ap-3506	15	8	cosmology	cosmology	NOUN
ap-3506	15	9	[	[	X
ap-3506	15	10	10–15	10–15	NUM
ap-3506	15	11	]	]	PUNCT
ap-3506	15	12	has	have	AUX
ap-3506	15	13	yielded	yield	VERB
ap-3506	15	14	interesting	interesting	ADJ
ap-3506	15	15	results	result	NOUN
ap-3506	15	16	as	as	ADP
ap-3506	15	17	:	:	PUNCT
ap-3506	15	18	•	•	NUM
ap-3506	15	19	consistent	consistent	ADJ
ap-3506	15	20	quantum	quantum	NOUN
ap-3506	15	21	dynamics	dynamic	NOUN
ap-3506	15	22	of	of	ADP
ap-3506	15	23	isotropic	isotropic	NOUN
ap-3506	15	24	,	,	PUNCT
ap-3506	15	25	anisotropic	anisotropic	NOUN
ap-3506	15	26	non	non	ADJ
ap-3506	15	27	-	-	ADJ
ap-3506	15	28	oscillatory	oscillatory	ADJ
ap-3506	15	29	and	and	CCONJ
ap-3506	15	30	anisotropic	anisotropic	NOUN
ap-3506	15	31	models	model	NOUN
ap-3506	15	32	of	of	ADP
ap-3506	15	33	universe	universe	NOUN
ap-3506	15	34	;	;	PUNCT
ap-3506	15	35	•	•	NUM
ap-3506	15	36	singularity	singularity	NOUN
ap-3506	15	37	resolution	resolution	NOUN
ap-3506	15	38	;	;	PUNCT
ap-3506	15	39	•	•	NUM
ap-3506	15	40	unitary	unitary	ADJ
ap-3506	15	41	dynamics	dynamic	NOUN
ap-3506	15	42	without	without	ADP
ap-3506	15	43	boundary	boundary	ADJ
ap-3506	15	44	conditions	condition	NOUN
ap-3506	15	45	;	;	PUNCT
ap-3506	15	46	•	•	NOUN
ap-3506	15	47	consistent	consistent	ADJ
ap-3506	15	48	semi	semi	ADJ
ap-3506	15	49	-	-	ADJ
ap-3506	15	50	classical	classical	ADJ
ap-3506	15	51	description	description	NOUN
ap-3506	15	52	of	of	ADP
ap-3506	15	53	involved	involved	ADJ
ap-3506	15	54	quantum	quantum	ADJ
ap-3506	15	55	dynamics	dynamic	NOUN
ap-3506	15	56	.	.	PUNCT
ap-3506	16	1	the	the	DET
ap-3506	16	2	aim	aim	NOUN
ap-3506	16	3	of	of	ADP
ap-3506	16	4	the	the	DET
ap-3506	16	5	present	present	ADJ
ap-3506	16	6	article	article	NOUN
ap-3506	16	7	is	be	AUX
ap-3506	16	8	to	to	PART
ap-3506	16	9	give	give	VERB
ap-3506	16	10	an	an	DET
ap-3506	16	11	overview	overview	NOUN
ap-3506	16	12	of	of	ADP
ap-3506	16	13	the	the	DET
ap-3506	16	14	methods	method	NOUN
ap-3506	16	15	,	,	PUNCT
ap-3506	16	16	their	their	PRON
ap-3506	16	17	main	main	ADJ
ap-3506	16	18	characteristics	characteristic	NOUN
ap-3506	16	19	,	,	PUNCT
ap-3506	16	20	and	and	CCONJ
ap-3506	16	21	their	their	PRON
ap-3506	16	22	promising	promising	ADJ
ap-3506	16	23	applications	application	NOUN
ap-3506	16	24	to	to	ADP
ap-3506	16	25	early	early	ADJ
ap-3506	16	26	cosmology	cosmology	NOUN
ap-3506	16	27	.	.	PUNCT
ap-3506	17	1	in	in	ADP
ap-3506	17	2	section	section	NOUN
ap-3506	17	3	2	2	NUM
ap-3506	17	4	we	we	PRON
ap-3506	17	5	give	give	VERB
ap-3506	17	6	a	a	DET
ap-3506	17	7	rapid	rapid	ADJ
ap-3506	17	8	survey	survey	NOUN
ap-3506	17	9	of	of	ADP
ap-3506	17	10	canonical	canonical	ADJ
ap-3506	17	11	quantization	quantization	NOUN
ap-3506	17	12	with	with	ADP
ap-3506	17	13	the	the	DET
ap-3506	17	14	problems	problem	NOUN
ap-3506	17	15	raised	raise	VERB
ap-3506	17	16	by	by	ADP
ap-3506	17	17	this	this	DET
ap-3506	17	18	procedure	procedure	NOUN
ap-3506	17	19	,	,	PUNCT
ap-3506	17	20	and	and	CCONJ
ap-3506	17	21	we	we	PRON
ap-3506	17	22	define	define	VERB
ap-3506	17	23	a	a	DET
ap-3506	17	24	few	few	ADJ
ap-3506	17	25	basic	basic	ADJ
ap-3506	17	26	requirements	requirement	NOUN
ap-3506	17	27	that	that	SCONJ
ap-3506	17	28	any	any	DET
ap-3506	17	29	quantization	quantization	NOUN
ap-3506	17	30	procedure	procedure	NOUN
ap-3506	17	31	should	should	AUX
ap-3506	17	32	fullfill	fullfill	VERB
ap-3506	17	33	.	.	PUNCT
ap-3506	18	1	in	in	ADP
ap-3506	18	2	section	section	NOUN
ap-3506	18	3	3	3	NUM
ap-3506	18	4	we	we	PRON
ap-3506	18	5	define	define	VERB
ap-3506	18	6	povm	povm	NOUN
ap-3506	18	7	-	-	PUNCT
ap-3506	18	8	based	base	VERB
ap-3506	18	9	integral	integral	ADJ
ap-3506	18	10	quantizations	quantization	NOUN
ap-3506	18	11	of	of	ADP
ap-3506	18	12	functions	function	NOUN
ap-3506	18	13	defined	define	VERB
ap-3506	18	14	on	on	ADP
ap-3506	18	15	a	a	DET
ap-3506	18	16	measure	measure	NOUN
ap-3506	18	17	space	space	NOUN
ap-3506	18	18	,	,	PUNCT
ap-3506	18	19	their	their	PRON
ap-3506	18	20	subsequent	subsequent	ADJ
ap-3506	18	21	semi	semi	ADJ
ap-3506	18	22	-	-	ADJ
ap-3506	18	23	classical	classical	ADJ
ap-3506	18	24	counterparts	counterpart	NOUN
ap-3506	18	25	(	(	PUNCT
ap-3506	18	26	i.e.	i.e.	X
ap-3506	18	27	,	,	PUNCT
ap-3506	18	28	lower	low	ADJ
ap-3506	18	29	symbols	symbol	NOUN
ap-3506	18	30	)	)	PUNCT
ap-3506	18	31	and	and	CCONJ
ap-3506	18	32	discuss	discuss	VERB
ap-3506	18	33	their	their	PRON
ap-3506	18	34	possibilities	possibility	NOUN
ap-3506	18	35	when	when	SCONJ
ap-3506	18	36	they	they	PRON
ap-3506	18	37	are	be	AUX
ap-3506	18	38	compared	compare	VERB
ap-3506	18	39	with	with	ADP
ap-3506	18	40	other	other	ADJ
ap-3506	18	41	methods	method	NOUN
ap-3506	18	42	.	.	PUNCT
ap-3506	19	1	covariant	covariant	ADJ
ap-3506	19	2	integral	integral	ADJ
ap-3506	19	3	quantizations	quantization	NOUN
ap-3506	19	4	are	be	AUX
ap-3506	19	5	then	then	ADV
ap-3506	19	6	considered	consider	VERB
ap-3506	19	7	when	when	SCONJ
ap-3506	19	8	the	the	DET
ap-3506	19	9	measure	measure	NOUN
ap-3506	19	10	space	space	NOUN
ap-3506	19	11	is	be	AUX
ap-3506	19	12	homogeneous	homogeneous	ADJ
ap-3506	19	13	for	for	ADP
ap-3506	19	14	some	some	DET
ap-3506	19	15	group	group	NOUN
ap-3506	19	16	,	,	PUNCT
ap-3506	19	17	and	and	CCONJ
ap-3506	19	18	we	we	PRON
ap-3506	19	19	give	give	VERB
ap-3506	19	20	the	the	DET
ap-3506	19	21	example	example	NOUN
ap-3506	19	22	of	of	ADP
ap-3506	19	23	the	the	DET
ap-3506	19	24	half	half	ADJ
ap-3506	19	25	-	-	PUNCT
ap-3506	19	26	plane	plane	NOUN
ap-3506	19	27	viewed	view	VERB
ap-3506	19	28	as	as	ADP
ap-3506	19	29	the	the	DET
ap-3506	19	30	affine	affine	ADJ
ap-3506	19	31	group	group	NOUN
ap-3506	19	32	of	of	ADP
ap-3506	19	33	the	the	DET
ap-3506	19	34	real	real	ADJ
ap-3506	19	35	line	line	NOUN
ap-3506	19	36	.	.	PUNCT
ap-3506	20	1	section	section	NOUN
ap-3506	20	2	4	4	NUM
ap-3506	20	3	is	be	AUX
ap-3506	20	4	devoted	devote	VERB
ap-3506	20	5	to	to	ADP
ap-3506	20	6	another	another	DET
ap-3506	20	7	example	example	NOUN
ap-3506	20	8	,	,	PUNCT
ap-3506	20	9	the	the	DET
ap-3506	20	10	integral	integral	ADJ
ap-3506	20	11	quantization	quantization	NOUN
ap-3506	20	12	of	of	ADP
ap-3506	20	13	functions	function	NOUN
ap-3506	20	14	on	on	ADP
ap-3506	20	15	the	the	DET
ap-3506	20	16	plane	plane	NOUN
ap-3506	20	17	viewed	view	VERB
ap-3506	20	18	as	as	ADP
ap-3506	20	19	a	a	DET
ap-3506	20	20	coset	coset	NOUN
ap-3506	20	21	of	of	ADP
ap-3506	20	22	the	the	DET
ap-3506	20	23	weyl	weyl	PROPN
ap-3506	20	24	-	-	PUNCT
ap-3506	20	25	heisenberg	heisenberg	PROPN
ap-3506	20	26	group	group	NOUN
ap-3506	20	27	.	.	PUNCT
ap-3506	21	1	in	in	ADP
ap-3506	21	2	section	section	NOUN
ap-3506	21	3	5	5	NUM
ap-3506	21	4	we	we	PRON
ap-3506	21	5	illustrate	illustrate	VERB
ap-3506	21	6	the	the	DET
ap-3506	21	7	method	method	NOUN
ap-3506	21	8	with	with	ADP
ap-3506	21	9	recent	recent	ADJ
ap-3506	21	10	applications	application	NOUN
ap-3506	21	11	to	to	ADP
ap-3506	21	12	quantum	quantum	ADJ
ap-3506	21	13	cosmology	cosmology	NOUN
ap-3506	21	14	where	where	SCONJ
ap-3506	21	15	the	the	DET
ap-3506	21	16	initial	initial	ADJ
ap-3506	21	17	singularity	singularity	NOUN
ap-3506	21	18	is	be	AUX
ap-3506	21	19	regularized	regularize	VERB
ap-3506	21	20	by	by	ADP
ap-3506	21	21	using	use	VERB
ap-3506	21	22	the	the	DET
ap-3506	21	23	affine	affine	ADJ
ap-3506	21	24	integral	integral	ADJ
ap-3506	21	25	quantization	quantization	NOUN
ap-3506	21	26	.	.	PUNCT
ap-3506	22	1	finally	finally	ADV
ap-3506	22	2	we	we	PRON
ap-3506	22	3	sketch	sketch	VERB
ap-3506	22	4	in	in	ADP
ap-3506	22	5	section	section	NOUN
ap-3506	22	6	6	6	NUM
ap-3506	22	7	a	a	DET
ap-3506	22	8	more	more	ADV
ap-3506	22	9	philosophical	philosophical	ADJ
ap-3506	22	10	point	point	NOUN
ap-3506	22	11	of	of	ADP
ap-3506	22	12	view	view	NOUN
ap-3506	22	13	on	on	ADP
ap-3506	22	14	the	the	DET
ap-3506	22	15	approaches	approach	NOUN
ap-3506	22	16	described	describe	VERB
ap-3506	22	17	in	in	ADP
ap-3506	22	18	this	this	DET
ap-3506	22	19	contribution	contribution	NOUN
ap-3506	22	20	.	.	PUNCT
ap-3506	23	1	a	a	DET
ap-3506	23	2	large	large	ADJ
ap-3506	23	3	part	part	NOUN
ap-3506	23	4	of	of	ADP
ap-3506	23	5	the	the	DET
ap-3506	23	6	content	content	NOUN
ap-3506	23	7	has	have	AUX
ap-3506	23	8	already	already	ADV
ap-3506	23	9	been	be	AUX
ap-3506	23	10	published	publish	VERB
ap-3506	23	11	,	,	PUNCT
ap-3506	23	12	as	as	SCONJ
ap-3506	23	13	exemplified	exemplify	VERB
ap-3506	23	14	by	by	ADP
ap-3506	23	15	the	the	DET
ap-3506	23	16	above	above	ADJ
ap-3506	23	17	citations	citation	NOUN
ap-3506	23	18	.	.	PUNCT
ap-3506	24	1	on	on	ADP
ap-3506	24	2	the	the	DET
ap-3506	24	3	other	other	ADJ
ap-3506	24	4	hand	hand	NOUN
ap-3506	24	5	the	the	DET
ap-3506	24	6	original	original	ADJ
ap-3506	24	7	side	side	NOUN
ap-3506	24	8	of	of	ADP
ap-3506	24	9	the	the	DET
ap-3506	24	10	paper	paper	NOUN
ap-3506	24	11	lies	lie	VERB
ap-3506	24	12	in	in	ADP
ap-3506	24	13	the	the	DET
ap-3506	24	14	synthetic	synthetic	ADJ
ap-3506	24	15	presentation	presentation	NOUN
ap-3506	24	16	of	of	ADP
ap-3506	24	17	the	the	DET
ap-3506	24	18	method	method	NOUN
ap-3506	24	19	together	together	ADV
ap-3506	24	20	with	with	ADP
ap-3506	24	21	some	some	DET
ap-3506	24	22	new	new	ADJ
ap-3506	24	23	ideas	idea	NOUN
ap-3506	24	24	like	like	ADP
ap-3506	24	25	the	the	DET
ap-3506	24	26	general	general	ADJ
ap-3506	24	27	(	(	PUNCT
ap-3506	24	28	and	and	CCONJ
ap-3506	24	29	promising	promising	ADJ
ap-3506	24	30	)	)	PUNCT
ap-3506	24	31	construction	construction	NOUN
ap-3506	24	32	sketched	sketched	NOUN
ap-3506	24	33	in	in	ADP
ap-3506	24	34	section	section	NOUN
ap-3506	24	35	3.2	3.2	NUM
ap-3506	24	36	.	.	PUNCT
ap-3506	25	1	2	2	NUM
ap-3506	25	2	.	.	X
ap-3506	26	1	what	what	PRON
ap-3506	26	2	is	be	AUX
ap-3506	26	3	quantization	quantization	NOUN
ap-3506	26	4	?	?	PUNCT
ap-3506	27	1	2.1	2.1	NUM
ap-3506	27	2	.	.	PUNCT
ap-3506	27	3	canonical	canonical	ADJ
ap-3506	27	4	quantization	quantization	NOUN
ap-3506	27	5	the	the	DET
ap-3506	27	6	basic	basic	ADJ
ap-3506	27	7	procedure	procedure	NOUN
ap-3506	27	8	of	of	ADP
ap-3506	27	9	quantization	quantization	NOUN
ap-3506	27	10	of	of	ADP
ap-3506	27	11	a	a	DET
ap-3506	27	12	classical	classical	ADJ
ap-3506	27	13	mechanical	mechanical	ADJ
ap-3506	27	14	model	model	NOUN
ap-3506	27	15	is	be	AUX
ap-3506	27	16	well	well	ADV
ap-3506	27	17	known	know	VERB
ap-3506	27	18	and	and	CCONJ
ap-3506	27	19	is	be	AUX
ap-3506	27	20	named	name	VERB
ap-3506	27	21	“	"	PUNCT
ap-3506	27	22	canonical	canonical	ADJ
ap-3506	27	23	"	"	PUNCT
ap-3506	27	24	(	(	PUNCT
ap-3506	27	25	heisenberg	heisenberg	PROPN
ap-3506	27	26	,	,	PUNCT
ap-3506	27	27	born	bear	VERB
ap-3506	27	28	,	,	PUNCT
ap-3506	27	29	jordan	jordan	PROPN
ap-3506	27	30	,	,	PUNCT
ap-3506	27	31	dirac	dirac	PROPN
ap-3506	27	32	,	,	PUNCT
ap-3506	27	33	weyl	weyl	VERB
ap-3506	27	34	,	,	PUNCT
ap-3506	27	35	etc	etc	X
ap-3506	27	36	)	)	PUNCT
ap-3506	27	37	.	.	PUNCT
ap-3506	28	1	starting	start	VERB
ap-3506	28	2	from	from	ADP
ap-3506	28	3	a	a	DET
ap-3506	28	4	phase	phase	NOUN
ap-3506	28	5	space	space	NOUN
ap-3506	28	6	or	or	CCONJ
ap-3506	28	7	symplectic	symplectic	ADJ
ap-3506	28	8	manifold	manifold	NOUN
ap-3506	28	9	,	,	PUNCT
ap-3506	28	10	e.g.	e.g.	ADV
ap-3506	28	11	r2	r2	NOUN
ap-3506	28	12	,	,	PUNCT
ap-3506	28	13	e.g.	e.g.	ADV
ap-3506	28	14	the	the	DET
ap-3506	28	15	phase	phase	NOUN
ap-3506	28	16	space	space	NOUN
ap-3506	28	17	for	for	ADP
ap-3506	28	18	the	the	DET
ap-3506	28	19	motion	motion	NOUN
ap-3506	28	20	of	of	ADP
ap-3506	28	21	particle	particle	NOUN
ap-3506	28	22	on	on	ADP
ap-3506	28	23	the	the	DET
ap-3506	28	24	line	line	NOUN
ap-3506	28	25	,	,	PUNCT
ap-3506	28	26	it	it	PRON
ap-3506	28	27	consists	consist	VERB
ap-3506	28	28	in	in	ADP
ap-3506	28	29	the	the	DET
ap-3506	28	30	maps	map	NOUN
ap-3506	28	31	r2	r2	PROPN
ap-3506	28	32	3	3	NUM
ap-3506	28	33	(	(	PUNCT
ap-3506	28	34	q	q	NOUN
ap-3506	28	35	,	,	PUNCT
ap-3506	28	36	p	p	NOUN
ap-3506	28	37	)	)	PUNCT
ap-3506	28	38	,	,	PUNCT
ap-3506	28	39	{	{	PUNCT
ap-3506	28	40	q	q	X
ap-3506	28	41	,	,	PUNCT
ap-3506	28	42	p	p	NOUN
ap-3506	28	43	}	}	PUNCT
ap-3506	28	44	=	=	SYM
ap-3506	28	45	1	1	NUM
ap-3506	28	46	7→	7→	NUM
ap-3506	28	47	self	self	NOUN
ap-3506	28	48	-	-	PUNCT
ap-3506	28	49	adjoint	adjoint	NOUN
ap-3506	28	50	(	(	PUNCT
ap-3506	28	51	q	q	NOUN
ap-3506	28	52	,	,	PUNCT
ap-3506	28	53	p	p	NOUN
ap-3506	28	54	)	)	PUNCT
ap-3506	28	55	,	,	PUNCT
ap-3506	28	56	(	(	PUNCT
ap-3506	28	57	1	1	X
ap-3506	28	58	)	)	PUNCT
ap-3506	28	59	with	with	ADP
ap-3506	28	60	the	the	DET
ap-3506	28	61	canonical	canonical	ADJ
ap-3506	28	62	commutation	commutation	NOUN
ap-3506	28	63	rule	rule	NOUN
ap-3506	28	64	(	(	PUNCT
ap-3506	28	65	ccr	ccr	PROPN
ap-3506	28	66	)	)	PUNCT
ap-3506	29	1	[	[	X
ap-3506	29	2	q	q	X
ap-3506	29	3	,	,	PUNCT
ap-3506	29	4	p	p	X
ap-3506	29	5	]	]	X
ap-3506	29	6	=	=	PUNCT
ap-3506	29	7	i	i	X
ap-3506	29	8	~	~	PUNCT
ap-3506	29	9	i	i	PROPN
ap-3506	29	10	,	,	PUNCT
ap-3506	29	11	and	and	CCONJ
ap-3506	29	12	f(q	f(q	PROPN
ap-3506	29	13	,	,	PUNCT
ap-3506	29	14	p	p	NOUN
ap-3506	29	15	)	)	PUNCT
ap-3506	29	16	7→	7→	PROPN
ap-3506	29	17	f(q	f(q	PROPN
ap-3506	29	18	,	,	PUNCT
ap-3506	29	19	p	p	NOUN
ap-3506	29	20	)	)	PUNCT
ap-3506	29	21	7→	7→	PROPN
ap-3506	29	22	(	(	PUNCT
ap-3506	29	23	sym	sym	PROPN
ap-3506	29	24	f)(q	f)(q	PROPN
ap-3506	29	25	,	,	PUNCT
ap-3506	29	26	p	p	NOUN
ap-3506	29	27	)	)	PUNCT
ap-3506	29	28	.	.	PUNCT
ap-3506	30	1	(	(	PUNCT
ap-3506	30	2	2	2	X
ap-3506	30	3	)	)	PUNCT
ap-3506	30	4	173	173	NUM
ap-3506	30	5	http://dx.doi.org/10.14311/ap.2016.56.0173	http://dx.doi.org/10.14311/ap.2016.56.0173	NOUN
ap-3506	30	6	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3506	30	7	jean	jean	PROPN
ap-3506	30	8	pierre	pierre	PROPN
ap-3506	30	9	gazeau	gazeau	PROPN
ap-3506	30	10	acta	acta	PROPN
ap-3506	30	11	polytechnica	polytechnica	PROPN
ap-3506	30	12	beyond	beyond	ADP
ap-3506	30	13	the	the	DET
ap-3506	30	14	ordering	ordering	NOUN
ap-3506	30	15	problem	problem	NOUN
ap-3506	30	16	[	[	X
ap-3506	30	17	16–18	16–18	NUM
ap-3506	30	18	]	]	PUNCT
ap-3506	30	19	raised	raise	VERB
ap-3506	30	20	by	by	ADP
ap-3506	30	21	the	the	DET
ap-3506	30	22	second	second	ADJ
ap-3506	30	23	step	step	NOUN
ap-3506	30	24	(	(	PUNCT
ap-3506	30	25	symmetrisation	symmetrisation	NOUN
ap-3506	30	26	)	)	PUNCT
ap-3506	30	27	,	,	PUNCT
ap-3506	30	28	one	one	PRON
ap-3506	30	29	should	should	AUX
ap-3506	30	30	keep	keep	VERB
ap-3506	30	31	in	in	ADP
ap-3506	30	32	mind	mind	NOUN
ap-3506	30	33	that	that	SCONJ
ap-3506	31	1	[	[	X
ap-3506	31	2	q	q	X
ap-3506	31	3	,	,	PUNCT
ap-3506	31	4	p	p	X
ap-3506	31	5	]	]	X
ap-3506	31	6	=	=	PUNCT
ap-3506	31	7	i	i	PRON
ap-3506	31	8	~	~	PUNCT
ap-3506	31	9	i	i	PRON
ap-3506	31	10	holds	hold	VERB
ap-3506	31	11	true	true	ADJ
ap-3506	31	12	with	with	ADP
ap-3506	31	13	self	self	NOUN
ap-3506	31	14	-	-	PUNCT
ap-3506	31	15	adjoint	adjoint	NOUN
ap-3506	31	16	q	q	NOUN
ap-3506	31	17	,	,	PUNCT
ap-3506	31	18	p	p	X
ap-3506	31	19	,	,	PUNCT
ap-3506	31	20	only	only	ADV
ap-3506	31	21	if	if	SCONJ
ap-3506	31	22	both	both	PRON
ap-3506	31	23	have	have	VERB
ap-3506	31	24	continuous	continuous	ADJ
ap-3506	31	25	spectrum	spectrum	NOUN
ap-3506	31	26	(	(	PUNCT
ap-3506	31	27	−∞,+∞	−∞,+∞	NUM
ap-3506	31	28	)	)	PUNCT
ap-3506	31	29	,	,	PUNCT
ap-3506	31	30	and	and	CCONJ
ap-3506	31	31	there	there	PRON
ap-3506	31	32	is	be	VERB
ap-3506	31	33	uniqueness	uniqueness	NOUN
ap-3506	31	34	of	of	ADP
ap-3506	31	35	the	the	DET
ap-3506	31	36	solution	solution	NOUN
ap-3506	31	37	,	,	PUNCT
ap-3506	31	38	up	up	ADP
ap-3506	31	39	to	to	ADP
ap-3506	31	40	unitary	unitary	ADJ
ap-3506	31	41	equivalence	equivalence	NOUN
ap-3506	31	42	(	(	PUNCT
ap-3506	31	43	von	von	PROPN
ap-3506	31	44	neumann	neumann	PROPN
ap-3506	31	45	)	)	PUNCT
ap-3506	31	46	.	.	PUNCT
ap-3506	32	1	but	but	CCONJ
ap-3506	32	2	then	then	ADV
ap-3506	32	3	what	what	PRON
ap-3506	32	4	about	about	ADP
ap-3506	32	5	singular	singular	PROPN
ap-3506	32	6	f	f	PROPN
ap-3506	32	7	,	,	PUNCT
ap-3506	32	8	e.g.	e.g.	ADV
ap-3506	32	9	,	,	PUNCT
ap-3506	32	10	the	the	DET
ap-3506	32	11	angle	angle	NOUN
ap-3506	32	12	arctan(p	arctan(p	PROPN
ap-3506	32	13	/	/	SYM
ap-3506	32	14	q	q	NOUN
ap-3506	32	15	)	)	PUNCT
ap-3506	32	16	?	?	PUNCT
ap-3506	33	1	what	what	PRON
ap-3506	33	2	about	about	ADP
ap-3506	33	3	barriers	barrier	NOUN
ap-3506	33	4	or	or	CCONJ
ap-3506	33	5	other	other	ADJ
ap-3506	33	6	impassable	impassable	ADJ
ap-3506	33	7	boundaries	boundary	NOUN
ap-3506	33	8	?	?	PUNCT
ap-3506	34	1	the	the	DET
ap-3506	34	2	motion	motion	NOUN
ap-3506	34	3	on	on	ADP
ap-3506	34	4	a	a	DET
ap-3506	34	5	circle	circle	NOUN
ap-3506	34	6	?	?	PUNCT
ap-3506	35	1	in	in	ADP
ap-3506	35	2	a	a	DET
ap-3506	35	3	bounded	bounded	ADJ
ap-3506	35	4	interval	interval	NOUN
ap-3506	35	5	?	?	PUNCT
ap-3506	36	1	on	on	ADP
ap-3506	36	2	the	the	DET
ap-3506	36	3	half	half	ADJ
ap-3506	36	4	-	-	PUNCT
ap-3506	36	5	line	line	NOUN
ap-3506	36	6	?	?	PUNCT
ap-3506	37	1	despite	despite	SCONJ
ap-3506	37	2	their	their	PRON
ap-3506	37	3	elementary	elementary	ADJ
ap-3506	37	4	aspects	aspect	NOUN
ap-3506	37	5	,	,	PUNCT
ap-3506	37	6	these	these	DET
ap-3506	37	7	examples	example	NOUN
ap-3506	37	8	leave	leave	VERB
ap-3506	37	9	open	open	ADJ
ap-3506	37	10	many	many	ADJ
ap-3506	37	11	questions	question	NOUN
ap-3506	37	12	both	both	CCONJ
ap-3506	37	13	on	on	ADP
ap-3506	37	14	mathematical	mathematical	ADJ
ap-3506	37	15	and	and	CCONJ
ap-3506	37	16	physical	physical	ADJ
ap-3506	37	17	levels	level	NOUN
ap-3506	37	18	,	,	PUNCT
ap-3506	37	19	irrespective	irrespective	ADV
ap-3506	37	20	of	of	ADP
ap-3506	37	21	the	the	DET
ap-3506	37	22	manifold	manifold	ADJ
ap-3506	37	23	quantization	quantization	NOUN
ap-3506	37	24	procedures	procedure	NOUN
ap-3506	37	25	,	,	PUNCT
ap-3506	37	26	like	like	ADP
ap-3506	37	27	path	path	NOUN
ap-3506	37	28	integral	integral	ADJ
ap-3506	37	29	quantization	quantization	NOUN
ap-3506	37	30	(	(	PUNCT
ap-3506	37	31	feynman	feynman	PROPN
ap-3506	37	32	,	,	PUNCT
ap-3506	37	33	thesis	thesis	NOUN
ap-3506	37	34	,	,	PUNCT
ap-3506	37	35	1942	1942	NUM
ap-3506	37	36	)	)	PUNCT
ap-3506	37	37	,	,	PUNCT
ap-3506	37	38	geometric	geometric	ADJ
ap-3506	37	39	quantization	quantization	NOUN
ap-3506	37	40	with	with	ADP
ap-3506	37	41	weyl	weyl	PROPN
ap-3506	37	42	(	(	PUNCT
ap-3506	37	43	1927	1927	NUM
ap-3506	37	44	)	)	PUNCT
ap-3506	37	45	,	,	PUNCT
ap-3506	37	46	groenewold	groenewold	VERB
ap-3506	37	47	(	(	PUNCT
ap-3506	37	48	1946	1946	NUM
ap-3506	37	49	)	)	PUNCT
ap-3506	37	50	,	,	PUNCT
ap-3506	37	51	kirillov	kirillov	PROPN
ap-3506	37	52	(	(	PUNCT
ap-3506	37	53	1961	1961	NUM
ap-3506	37	54	)	)	PUNCT
ap-3506	37	55	,	,	PUNCT
ap-3506	37	56	souriau	souriau	NOUN
ap-3506	37	57	(	(	PUNCT
ap-3506	37	58	1966	1966	NUM
ap-3506	37	59	)	)	PUNCT
ap-3506	37	60	,	,	PUNCT
ap-3506	37	61	kostant	kostant	NOUN
ap-3506	37	62	(	(	PUNCT
ap-3506	37	63	1970	1970	NUM
ap-3506	37	64	)	)	PUNCT
ap-3506	37	65	,	,	PUNCT
ap-3506	37	66	deformation	deformation	NOUN
ap-3506	37	67	quantization	quantization	NOUN
ap-3506	37	68	with	with	ADP
ap-3506	37	69	moyal	moyal	ADJ
ap-3506	37	70	(	(	PUNCT
ap-3506	37	71	1947	1947	NUM
ap-3506	37	72	)	)	PUNCT
ap-3506	37	73	,	,	PUNCT
ap-3506	37	74	bayen	bayen	NOUN
ap-3506	37	75	,	,	PUNCT
ap-3506	37	76	flato	flato	NOUN
ap-3506	37	77	,	,	PUNCT
ap-3506	37	78	fronsdal	fronsdal	ADJ
ap-3506	37	79	,	,	PUNCT
ap-3506	37	80	lichnerowicz	lichnerowicz	NOUN
ap-3506	37	81	,	,	PUNCT
ap-3506	37	82	sternheimer	sternheimer	NOUN
ap-3506	37	83	(	(	PUNCT
ap-3506	37	84	1978	1978	NUM
ap-3506	37	85	)	)	PUNCT
ap-3506	37	86	,	,	PUNCT
ap-3506	37	87	fedosov	fedosov	NOUN
ap-3506	37	88	(	(	PUNCT
ap-3506	37	89	1985	1985	NUM
ap-3506	37	90	)	)	PUNCT
ap-3506	37	91	,	,	PUNCT
ap-3506	37	92	kontsevich	kontsevich	X
ap-3506	37	93	(	(	PUNCT
ap-3506	37	94	2003	2003	NUM
ap-3506	37	95	)	)	PUNCT
ap-3506	37	96	,	,	PUNCT
ap-3506	37	97	coherent	coherent	ADJ
ap-3506	37	98	state	state	NOUN
ap-3506	37	99	or	or	CCONJ
ap-3506	37	100	anti	anti	ADJ
ap-3506	37	101	-	-	ADJ
ap-3506	37	102	wick	wick	ADJ
ap-3506	37	103	or	or	CCONJ
ap-3506	37	104	toeplitz	toeplitz	NOUN
ap-3506	37	105	quantization	quantization	NOUN
ap-3506	37	106	with	with	ADP
ap-3506	37	107	klauder	klauder	PROPN
ap-3506	37	108	(	(	PUNCT
ap-3506	37	109	1961	1961	NUM
ap-3506	37	110	)	)	PUNCT
ap-3506	37	111	,	,	PUNCT
ap-3506	37	112	berezin	berezin	PROPN
ap-3506	37	113	(	(	PUNCT
ap-3506	37	114	1974	1974	NUM
ap-3506	37	115	)	)	PUNCT
ap-3506	37	116	.	.	PUNCT
ap-3506	38	1	of	of	ADP
ap-3506	38	2	course	course	NOUN
ap-3506	38	3	,	,	PUNCT
ap-3506	38	4	the	the	DET
ap-3506	38	5	canonical	canonical	ADJ
ap-3506	38	6	procedure	procedure	NOUN
ap-3506	38	7	is	be	AUX
ap-3506	38	8	universally	universally	ADV
ap-3506	38	9	accepted	accept	VERB
ap-3506	38	10	in	in	ADP
ap-3506	38	11	view	view	NOUN
ap-3506	38	12	of	of	ADP
ap-3506	38	13	its	its	PRON
ap-3506	38	14	numerous	numerous	ADJ
ap-3506	38	15	experimental	experimental	ADJ
ap-3506	38	16	validations	validation	NOUN
ap-3506	38	17	,	,	PUNCT
ap-3506	38	18	one	one	NUM
ap-3506	38	19	of	of	ADP
ap-3506	38	20	the	the	DET
ap-3506	38	21	most	most	ADV
ap-3506	38	22	famous	famous	ADJ
ap-3506	38	23	and	and	CCONJ
ap-3506	38	24	simplest	simple	ADJ
ap-3506	38	25	one	one	NOUN
ap-3506	38	26	going	go	VERB
ap-3506	38	27	back	back	ADV
ap-3506	38	28	to	to	ADP
ap-3506	38	29	the	the	DET
ap-3506	38	30	early	early	ADJ
ap-3506	38	31	period	period	NOUN
ap-3506	38	32	of	of	ADP
ap-3506	38	33	quantum	quantum	ADJ
ap-3506	38	34	mechanics	mechanic	NOUN
ap-3506	38	35	with	with	ADP
ap-3506	38	36	the	the	DET
ap-3506	38	37	quantitative	quantitative	ADJ
ap-3506	38	38	prediction	prediction	NOUN
ap-3506	38	39	of	of	ADP
ap-3506	38	40	the	the	DET
ap-3506	38	41	isotopic	isotopic	ADJ
ap-3506	38	42	effect	effect	NOUN
ap-3506	38	43	in	in	ADP
ap-3506	38	44	vibrational	vibrational	ADJ
ap-3506	38	45	spectra	spectra	NOUN
ap-3506	38	46	of	of	ADP
ap-3506	38	47	diatomic	diatomic	ADJ
ap-3506	38	48	molecules	molecule	NOUN
ap-3506	38	49	[	[	X
ap-3506	38	50	19	19	NUM
ap-3506	38	51	]	]	PUNCT
ap-3506	38	52	.	.	PUNCT
ap-3506	39	1	these	these	DET
ap-3506	39	2	data	datum	NOUN
ap-3506	39	3	validated	validate	VERB
ap-3506	39	4	the	the	DET
ap-3506	39	5	canonical	canonical	ADJ
ap-3506	39	6	quantization	quantization	NOUN
ap-3506	39	7	,	,	PUNCT
ap-3506	39	8	contrary	contrary	ADV
ap-3506	39	9	to	to	ADP
ap-3506	39	10	the	the	DET
ap-3506	39	11	bohr	bohr	NOUN
ap-3506	39	12	-	-	PUNCT
ap-3506	39	13	sommerfeld	sommerfeld	NOUN
ap-3506	39	14	ansatz	ansatz	ADJ
ap-3506	39	15	(	(	PUNCT
ap-3506	39	16	which	which	PRON
ap-3506	39	17	predicts	predict	VERB
ap-3506	39	18	no	no	DET
ap-3506	39	19	isotopic	isotopic	ADJ
ap-3506	39	20	effect	effect	NOUN
ap-3506	39	21	)	)	PUNCT
ap-3506	39	22	.	.	PUNCT
ap-3506	40	1	nevertheless	nevertheless	ADV
ap-3506	40	2	this	this	PRON
ap-3506	40	3	does	do	AUX
ap-3506	40	4	not	not	PART
ap-3506	40	5	prove	prove	VERB
ap-3506	40	6	that	that	SCONJ
ap-3506	40	7	another	another	DET
ap-3506	40	8	method	method	NOUN
ap-3506	40	9	of	of	ADP
ap-3506	40	10	quantization	quantization	NOUN
ap-3506	40	11	fails	fail	VERB
ap-3506	40	12	to	to	PART
ap-3506	40	13	yield	yield	VERB
ap-3506	40	14	the	the	DET
ap-3506	40	15	same	same	ADJ
ap-3506	40	16	prediction	prediction	NOUN
ap-3506	40	17	[	[	X
ap-3506	40	18	3	3	NUM
ap-3506	40	19	]	]	PUNCT
ap-3506	40	20	.	.	PUNCT
ap-3506	41	1	moreover	moreover	ADV
ap-3506	41	2	,	,	PUNCT
ap-3506	41	3	as	as	SCONJ
ap-3506	41	4	already	already	ADV
ap-3506	41	5	mentioned	mention	VERB
ap-3506	41	6	above	above	ADV
ap-3506	41	7	,	,	PUNCT
ap-3506	41	8	the	the	DET
ap-3506	41	9	canonical	canonical	ADJ
ap-3506	41	10	quantization	quantization	NOUN
ap-3506	41	11	is	be	AUX
ap-3506	41	12	difficult	difficult	ADJ
ap-3506	41	13	,	,	PUNCT
ap-3506	41	14	if	if	SCONJ
ap-3506	41	15	not	not	PART
ap-3506	41	16	impossible	impossible	ADJ
ap-3506	41	17	,	,	PUNCT
ap-3506	41	18	in	in	ADP
ap-3506	41	19	many	many	ADJ
ap-3506	41	20	circumstances	circumstance	NOUN
ap-3506	41	21	.	.	PUNCT
ap-3506	42	1	as	as	ADP
ap-3506	42	2	a	a	DET
ap-3506	42	3	matter	matter	NOUN
ap-3506	42	4	of	of	ADP
ap-3506	42	5	fact	fact	NOUN
ap-3506	42	6	,	,	PUNCT
ap-3506	42	7	the	the	DET
ap-3506	42	8	canonical	canonical	NOUN
ap-3506	42	9	or	or	CCONJ
ap-3506	42	10	the	the	DET
ap-3506	42	11	weyl	weyl	VERB
ap-3506	42	12	-	-	PUNCT
ap-3506	42	13	wigner	wigner	ADJ
ap-3506	42	14	integral	integral	ADJ
ap-3506	42	15	quantization	quantization	NOUN
ap-3506	42	16	maps	map	NOUN
ap-3506	42	17	f(q	f(q	PROPN
ap-3506	42	18	)	)	PUNCT
ap-3506	42	19	to	to	ADP
ap-3506	42	20	f(q	f(q	PROPN
ap-3506	42	21	)	)	PUNCT
ap-3506	42	22	(	(	PUNCT
ap-3506	42	23	resp	resp	NOUN
ap-3506	42	24	.	.	PUNCT
ap-3506	43	1	f(p	f(p	NOUN
ap-3506	43	2	)	)	PUNCT
ap-3506	43	3	to	to	ADP
ap-3506	43	4	f(p	f(p	PROPN
ap-3506	43	5	)	)	PUNCT
ap-3506	43	6	)	)	PUNCT
ap-3506	44	1	,	,	PUNCT
ap-3506	44	2	and	and	CCONJ
ap-3506	44	3	so	so	ADV
ap-3506	44	4	are	be	AUX
ap-3506	44	5	unable	unable	ADJ
ap-3506	44	6	to	to	PART
ap-3506	44	7	cure	cure	VERB
ap-3506	44	8	any	any	DET
ap-3506	44	9	kind	kind	NOUN
ap-3506	44	10	of	of	ADP
ap-3506	44	11	classical	classical	ADJ
ap-3506	44	12	singularity	singularity	NOUN
ap-3506	44	13	.	.	PUNCT
ap-3506	45	1	clearly	clearly	ADV
ap-3506	45	2	,	,	PUNCT
ap-3506	45	3	quantization	quantization	NOUN
ap-3506	45	4	procedures	procedure	NOUN
ap-3506	45	5	may	may	AUX
ap-3506	45	6	be	be	AUX
ap-3506	45	7	intractable	intractable	ADJ
ap-3506	45	8	when	when	SCONJ
ap-3506	45	9	different	different	ADJ
ap-3506	45	10	phase	phase	NOUN
ap-3506	45	11	space	space	NOUN
ap-3506	45	12	geometries	geometry	NOUN
ap-3506	45	13	and/or	and/or	CCONJ
ap-3506	45	14	topologies	topology	NOUN
ap-3506	45	15	are	be	AUX
ap-3506	45	16	considered	consider	VERB
ap-3506	45	17	.	.	PUNCT
ap-3506	46	1	self	self	NOUN
ap-3506	46	2	-	-	PUNCT
ap-3506	46	3	adjointness	adjointness	NOUN
ap-3506	46	4	of	of	ADP
ap-3506	46	5	basic	basic	ADJ
ap-3506	46	6	operators	operator	NOUN
ap-3506	46	7	is	be	AUX
ap-3506	46	8	not	not	PART
ap-3506	46	9	guaranteed	guarantee	VERB
ap-3506	46	10	anymore	anymore	ADV
ap-3506	46	11	.	.	PUNCT
ap-3506	47	1	2.2	2.2	NUM
ap-3506	47	2	.	.	PUNCT
ap-3506	47	3	quantization	quantization	NOUN
ap-3506	47	4	:	:	PUNCT
ap-3506	47	5	minimal	minimal	ADJ
ap-3506	47	6	requirements	requirement	NOUN
ap-3506	47	7	in	in	ADP
ap-3506	47	8	our	our	PRON
ap-3506	47	9	viewpoint	viewpoint	NOUN
ap-3506	47	10	,	,	PUNCT
ap-3506	47	11	any	any	DET
ap-3506	47	12	quantization	quantization	NOUN
ap-3506	47	13	of	of	ADP
ap-3506	47	14	a	a	DET
ap-3506	47	15	set	set	NOUN
ap-3506	47	16	x	x	INTJ
ap-3506	47	17	(	(	PUNCT
ap-3506	47	18	e.g.	e.g.	ADV
ap-3506	47	19	,	,	PUNCT
ap-3506	47	20	a	a	DET
ap-3506	47	21	phase	phase	NOUN
ap-3506	47	22	space	space	NOUN
ap-3506	47	23	or	or	CCONJ
ap-3506	47	24	something	something	PRON
ap-3506	47	25	else	else	ADV
ap-3506	47	26	)	)	PUNCT
ap-3506	47	27	and	and	CCONJ
ap-3506	47	28	functions	function	NOUN
ap-3506	47	29	on	on	ADP
ap-3506	47	30	it	it	PRON
ap-3506	47	31	should	should	AUX
ap-3506	47	32	meet	meet	VERB
ap-3506	47	33	four	four	NUM
ap-3506	47	34	basic	basic	ADJ
ap-3506	47	35	requirements	requirement	NOUN
ap-3506	47	36	:	:	PUNCT
ap-3506	47	37	(	(	PUNCT
ap-3506	47	38	1	1	NUM
ap-3506	47	39	.	.	NUM
ap-3506	47	40	)	)	PUNCT
ap-3506	47	41	linearity	linearity	NOUN
ap-3506	47	42	—	—	PUNCT
ap-3506	47	43	it	it	PRON
ap-3506	47	44	is	be	AUX
ap-3506	47	45	a	a	DET
ap-3506	47	46	linear	linear	ADJ
ap-3506	47	47	map	map	NOUN
ap-3506	47	48	q	q	NOUN
ap-3506	47	49	:	:	PUNCT
ap-3506	47	50	c(x	c(x	NOUN
ap-3506	47	51	)	)	PUNCT
ap-3506	47	52	7→	7→	NUM
ap-3506	47	53	a(h	a(h	PROPN
ap-3506	47	54	)	)	PUNCT
ap-3506	47	55	,	,	PUNCT
ap-3506	47	56	q(f	q(f	PROPN
ap-3506	47	57	)	)	PUNCT
ap-3506	47	58	≡	≡	PROPN
ap-3506	47	59	af	af	PROPN
ap-3506	47	60	,	,	PUNCT
ap-3506	47	61	(	(	PUNCT
ap-3506	47	62	3	3	X
ap-3506	47	63	)	)	PUNCT
ap-3506	47	64	where	where	SCONJ
ap-3506	47	65	:	:	PUNCT
ap-3506	47	66	•	•	NUM
ap-3506	47	67	c(x	c(x	NOUN
ap-3506	47	68	)	)	PUNCT
ap-3506	47	69	is	be	AUX
ap-3506	47	70	a	a	DET
ap-3506	47	71	vector	vector	NOUN
ap-3506	47	72	space	space	NOUN
ap-3506	47	73	of	of	ADP
ap-3506	47	74	complex	complex	ADJ
ap-3506	47	75	-	-	PUNCT
ap-3506	47	76	valued	value	VERB
ap-3506	47	77	functions	function	NOUN
ap-3506	47	78	f(x	f(x	PROPN
ap-3506	47	79	)	)	PUNCT
ap-3506	47	80	on	on	ADP
ap-3506	47	81	set	set	NOUN
ap-3506	47	82	x	x	SYM
ap-3506	47	83	,	,	PUNCT
ap-3506	47	84	i.e.	i.e.	X
ap-3506	47	85	,	,	PUNCT
ap-3506	47	86	a	a	DET
ap-3506	47	87	“	"	PUNCT
ap-3506	47	88	classical	classical	ADJ
ap-3506	47	89	”	"	PUNCT
ap-3506	47	90	mathematical	mathematical	ADJ
ap-3506	47	91	model	model	NOUN
ap-3506	47	92	;	;	PUNCT
ap-3506	47	93	•	•	DET
ap-3506	47	94	a(h	a(h	PROPN
ap-3506	47	95	)	)	PUNCT
ap-3506	47	96	is	be	AUX
ap-3506	47	97	a	a	DET
ap-3506	47	98	vector	vector	NOUN
ap-3506	47	99	space	space	NOUN
ap-3506	47	100	of	of	ADP
ap-3506	47	101	linear	linear	PROPN
ap-3506	47	102	operators	operator	NOUN
ap-3506	47	103	(	(	PUNCT
ap-3506	47	104	ignoring	ignore	VERB
ap-3506	47	105	domain	domain	NOUN
ap-3506	47	106	limitations	limitation	NOUN
ap-3506	47	107	)	)	PUNCT
ap-3506	47	108	in	in	ADP
ap-3506	47	109	some	some	DET
ap-3506	47	110	complex	complex	ADJ
ap-3506	47	111	hilbert	hilbert	NOUN
ap-3506	47	112	space	space	NOUN
ap-3506	47	113	h	h	PROPN
ap-3506	47	114	,	,	PUNCT
ap-3506	47	115	i.e	i.e	PROPN
ap-3506	47	116	,	,	PUNCT
ap-3506	47	117	a	a	DET
ap-3506	47	118	“	"	PUNCT
ap-3506	47	119	quantum	quantum	NOUN
ap-3506	47	120	”	"	PUNCT
ap-3506	47	121	mathematical	mathematical	ADJ
ap-3506	47	122	model	model	NOUN
ap-3506	47	123	.	.	PUNCT
ap-3506	48	1	(	(	PUNCT
ap-3506	48	2	2	2	NUM
ap-3506	48	3	.	.	NUM
ap-3506	48	4	)	)	PUNCT
ap-3506	48	5	unity	unity	NOUN
ap-3506	48	6	—	—	PUNCT
ap-3506	48	7	the	the	DET
ap-3506	48	8	map	map	NOUN
ap-3506	48	9	(	(	PUNCT
ap-3506	48	10	3	3	X
ap-3506	48	11	)	)	PUNCT
ap-3506	48	12	is	be	AUX
ap-3506	48	13	such	such	ADJ
ap-3506	48	14	that	that	SCONJ
ap-3506	48	15	the	the	DET
ap-3506	48	16	function	function	NOUN
ap-3506	48	17	f	f	NOUN
ap-3506	48	18	=	=	SYM
ap-3506	48	19	1	1	NUM
ap-3506	48	20	is	be	AUX
ap-3506	48	21	mapped	map	VERB
ap-3506	48	22	to	to	ADP
ap-3506	48	23	the	the	DET
ap-3506	48	24	identity	identity	NOUN
ap-3506	48	25	operator	operator	NOUN
ap-3506	48	26	i	i	PRON
ap-3506	48	27	on	on	ADP
ap-3506	48	28	h.	h.	PROPN
ap-3506	48	29	(	(	PUNCT
ap-3506	48	30	3	3	NUM
ap-3506	48	31	.	.	NUM
ap-3506	48	32	)	)	PUNCT
ap-3506	48	33	reality	reality	NOUN
ap-3506	48	34	—	—	PUNCT
ap-3506	48	35	a	a	DET
ap-3506	48	36	real	real	ADJ
ap-3506	48	37	f	f	NOUN
ap-3506	48	38	is	be	AUX
ap-3506	48	39	mapped	map	VERB
ap-3506	48	40	to	to	ADP
ap-3506	48	41	a	a	DET
ap-3506	48	42	self	self	NOUN
ap-3506	48	43	-	-	PUNCT
ap-3506	48	44	adjoint	adjoint	NOUN
ap-3506	48	45	operator	operator	NOUN
ap-3506	48	46	af	af	VERB
ap-3506	48	47	in	in	ADP
ap-3506	48	48	h	h	NOUN
ap-3506	48	49	or	or	CCONJ
ap-3506	48	50	,	,	PUNCT
ap-3506	48	51	at	at	ADP
ap-3506	48	52	least	least	ADJ
ap-3506	48	53	,	,	PUNCT
ap-3506	48	54	a	a	DET
ap-3506	48	55	symmetric	symmetric	ADJ
ap-3506	48	56	operator	operator	NOUN
ap-3506	48	57	,	,	PUNCT
ap-3506	48	58	(	(	PUNCT
ap-3506	48	59	4	4	NUM
ap-3506	48	60	.	.	PUNCT
ap-3506	48	61	)	)	PUNCT
ap-3506	49	1	covariance	covariance	NOUN
ap-3506	49	2	—	—	PUNCT
ap-3506	49	3	if	if	SCONJ
ap-3506	49	4	x	x	PRON
ap-3506	49	5	is	be	AUX
ap-3506	49	6	endowed	endow	VERB
ap-3506	49	7	with	with	ADP
ap-3506	49	8	symmetry	symmetry	NOUN
ap-3506	49	9	,	,	PUNCT
ap-3506	49	10	the	the	DET
ap-3506	49	11	latter	latter	ADJ
ap-3506	49	12	should	should	AUX
ap-3506	49	13	be	be	AUX
ap-3506	49	14	preserved	preserve	VERB
ap-3506	49	15	in	in	ADP
ap-3506	49	16	a	a	DET
ap-3506	49	17	“	"	PUNCT
ap-3506	49	18	certain	certain	ADJ
ap-3506	49	19	”	"	PUNCT
ap-3506	49	20	sense	sense	NOUN
ap-3506	49	21	.	.	PUNCT
ap-3506	50	1	of	of	ADP
ap-3506	50	2	course	course	NOUN
ap-3506	50	3	,	,	PUNCT
ap-3506	50	4	further	further	ADJ
ap-3506	50	5	requirements	requirement	NOUN
ap-3506	50	6	are	be	AUX
ap-3506	50	7	necessarily	necessarily	ADV
ap-3506	50	8	added	add	VERB
ap-3506	50	9	,	,	PUNCT
ap-3506	50	10	depending	depend	VERB
ap-3506	50	11	on	on	ADP
ap-3506	50	12	the	the	DET
ap-3506	50	13	mathematical	mathematical	ADJ
ap-3506	50	14	structures	structure	NOUN
ap-3506	50	15	equipping	equip	VERB
ap-3506	50	16	x	x	X
ap-3506	50	17	and	and	CCONJ
ap-3506	50	18	c(x	c(x	NOUN
ap-3506	50	19	)	)	PUNCT
ap-3506	50	20	(	(	PUNCT
ap-3506	50	21	e.g.	e.g.	ADV
ap-3506	50	22	,	,	PUNCT
ap-3506	50	23	measure	measure	NOUN
ap-3506	50	24	,	,	PUNCT
ap-3506	50	25	topology	topology	NOUN
ap-3506	50	26	,	,	PUNCT
ap-3506	50	27	manifold	manifold	ADJ
ap-3506	50	28	,	,	PUNCT
ap-3506	50	29	closure	closure	NOUN
ap-3506	50	30	under	under	ADP
ap-3506	50	31	algebraic	algebraic	ADJ
ap-3506	50	32	operations	operation	NOUN
ap-3506	50	33	,	,	PUNCT
ap-3506	50	34	time	time	NOUN
ap-3506	50	35	evolution	evolution	NOUN
ap-3506	50	36	or	or	CCONJ
ap-3506	50	37	dynamics	dynamic	NOUN
ap-3506	50	38	,	,	PUNCT
ap-3506	50	39	etc	etc	X
ap-3506	50	40	)	)	PUNCT
ap-3506	50	41	.	.	PUNCT
ap-3506	51	1	moreover	moreover	ADV
ap-3506	51	2	,	,	PUNCT
ap-3506	51	3	a	a	DET
ap-3506	51	4	physical	physical	ADJ
ap-3506	51	5	interpretation	interpretation	NOUN
ap-3506	51	6	should	should	AUX
ap-3506	51	7	be	be	AUX
ap-3506	51	8	advanced	advanced	ADJ
ap-3506	51	9	about	about	ADP
ap-3506	51	10	measurement	measurement	NOUN
ap-3506	51	11	of	of	ADP
ap-3506	51	12	spectra	spectra	NOUN
ap-3506	51	13	of	of	ADP
ap-3506	51	14	classical	classical	ADJ
ap-3506	51	15	f	f	PROPN
ap-3506	51	16	∈	∈	PROPN
ap-3506	51	17	c(x	c(x	NOUN
ap-3506	51	18	)	)	PUNCT
ap-3506	51	19	or	or	CCONJ
ap-3506	51	20	quantum	quantum	NOUN
ap-3506	51	21	af	af	PROPN
ap-3506	51	22	∈	∈	PROPN
ap-3506	51	23	a(h	a(h	PROPN
ap-3506	51	24	)	)	PUNCT
ap-3506	51	25	to	to	PART
ap-3506	51	26	which	which	PRON
ap-3506	51	27	are	be	AUX
ap-3506	51	28	given	give	VERB
ap-3506	51	29	the	the	DET
ap-3506	51	30	status	status	NOUN
ap-3506	51	31	of	of	ADP
ap-3506	51	32	observables	observable	NOUN
ap-3506	51	33	.	.	PUNCT
ap-3506	52	1	finally	finally	ADV
ap-3506	52	2	,	,	PUNCT
ap-3506	52	3	an	an	DET
ap-3506	52	4	unambiguous	unambiguous	ADJ
ap-3506	52	5	classical	classical	ADJ
ap-3506	52	6	limit	limit	NOUN
ap-3506	52	7	of	of	ADP
ap-3506	52	8	the	the	DET
ap-3506	52	9	quantum	quantum	ADJ
ap-3506	52	10	physical	physical	ADJ
ap-3506	52	11	quantities	quantity	NOUN
ap-3506	52	12	should	should	AUX
ap-3506	52	13	exist	exist	VERB
ap-3506	52	14	,	,	PUNCT
ap-3506	52	15	the	the	DET
ap-3506	52	16	limit	limit	NOUN
ap-3506	52	17	operation	operation	NOUN
ap-3506	52	18	being	be	AUX
ap-3506	52	19	associated	associate	VERB
ap-3506	52	20	to	to	ADP
ap-3506	52	21	a	a	DET
ap-3506	52	22	change	change	NOUN
ap-3506	52	23	of	of	ADP
ap-3506	52	24	scale	scale	NOUN
ap-3506	52	25	.	.	PUNCT
ap-3506	53	1	3	3	X
ap-3506	53	2	.	.	X
ap-3506	53	3	integral	integral	ADJ
ap-3506	53	4	quantization(s	quantization(s	NOUN
ap-3506	53	5	)	)	PUNCT
ap-3506	53	6	3.1	3.1	NUM
ap-3506	53	7	.	.	PUNCT
ap-3506	54	1	integral	integral	ADJ
ap-3506	54	2	quantization	quantization	NOUN
ap-3506	54	3	:	:	PUNCT
ap-3506	54	4	general	general	ADJ
ap-3506	54	5	setting	setting	NOUN
ap-3506	54	6	and	and	CCONJ
ap-3506	54	7	povm	povm	NOUN
ap-3506	54	8	let	let	VERB
ap-3506	54	9	(	(	PUNCT
ap-3506	54	10	x	x	NOUN
ap-3506	54	11	,	,	PUNCT
ap-3506	54	12	ν	ν	NOUN
ap-3506	54	13	)	)	PUNCT
ap-3506	54	14	be	be	AUX
ap-3506	54	15	a	a	DET
ap-3506	54	16	measure	measure	NOUN
ap-3506	54	17	space	space	NOUN
ap-3506	54	18	.	.	PUNCT
ap-3506	55	1	suppose	suppose	VERB
ap-3506	55	2	that	that	SCONJ
ap-3506	55	3	there	there	PRON
ap-3506	55	4	exists	exist	VERB
ap-3506	55	5	an	an	DET
ap-3506	55	6	x	x	X
ap-3506	55	7	-	-	ADJ
ap-3506	55	8	labeled	label	VERB
ap-3506	55	9	family	family	NOUN
ap-3506	55	10	of	of	ADP
ap-3506	55	11	bounded	bounded	ADJ
ap-3506	55	12	operators	operator	NOUN
ap-3506	55	13	on	on	ADP
ap-3506	55	14	a	a	DET
ap-3506	55	15	hilbert	hilbert	NOUN
ap-3506	55	16	space	space	NOUN
ap-3506	55	17	h	h	NOUN
ap-3506	55	18	resolving	resolve	VERB
ap-3506	55	19	the	the	DET
ap-3506	55	20	identity	identity	NOUN
ap-3506	55	21	i	i	PRON
ap-3506	55	22	:	:	PUNCT
ap-3506	55	23	x	x	SYM
ap-3506	55	24	3	3	NUM
ap-3506	55	25	x	x	SYM
ap-3506	55	26	7→	7→	NUM
ap-3506	55	27	m(x	m(x	NOUN
ap-3506	55	28	)	)	PUNCT
ap-3506	55	29	∈	∈	PROPN
ap-3506	55	30	l(h	l(h	PROPN
ap-3506	55	31	)	)	PUNCT
ap-3506	55	32	,	,	PUNCT
ap-3506	55	33	∫	∫	PROPN
ap-3506	55	34	x	x	SYM
ap-3506	55	35	m(x	m(x	PROPN
ap-3506	55	36	)	)	PUNCT
ap-3506	55	37	dν(x	dν(x	NOUN
ap-3506	55	38	)	)	PUNCT
ap-3506	56	1	=	=	SYM
ap-3506	56	2	i	i	PROPN
ap-3506	56	3	,	,	PUNCT
ap-3506	56	4	(	(	PUNCT
ap-3506	56	5	4	4	X
ap-3506	56	6	)	)	PUNCT
ap-3506	56	7	where	where	SCONJ
ap-3506	56	8	the	the	DET
ap-3506	56	9	equality	equality	NOUN
ap-3506	56	10	holds	hold	VERB
ap-3506	56	11	in	in	ADP
ap-3506	56	12	a	a	DET
ap-3506	56	13	weak	weak	ADJ
ap-3506	56	14	sense	sense	NOUN
ap-3506	56	15	.	.	PUNCT
ap-3506	57	1	the	the	DET
ap-3506	57	2	case	case	NOUN
ap-3506	57	3	we	we	PRON
ap-3506	57	4	are	be	AUX
ap-3506	57	5	specially	specially	ADV
ap-3506	57	6	interested	interested	ADJ
ap-3506	57	7	in	in	ADP
ap-3506	57	8	occurs	occur	NOUN
ap-3506	57	9	when	when	SCONJ
ap-3506	57	10	the	the	DET
ap-3506	57	11	m(x	m(x	NOUN
ap-3506	57	12	)	)	PUNCT
ap-3506	57	13	’s	’	VERB
ap-3506	57	14	are	be	AUX
ap-3506	57	15	positive	positive	ADJ
ap-3506	57	16	semi	semi	ADJ
ap-3506	57	17	-	-	ADJ
ap-3506	57	18	definite	definite	ADJ
ap-3506	57	19	and	and	CCONJ
ap-3506	57	20	unit	unit	NOUN
ap-3506	57	21	trace	trace	NOUN
ap-3506	57	22	,	,	PUNCT
ap-3506	57	23	i.e.	i.e.	X
ap-3506	57	24	,	,	PUNCT
ap-3506	57	25	when	when	SCONJ
ap-3506	57	26	m(x	m(x	X
ap-3506	57	27	)	)	PUNCT
ap-3506	57	28	≡	≡	PROPN
ap-3506	57	29	ρ(x	ρ(x	PROPN
ap-3506	57	30	)	)	PUNCT
ap-3506	57	31	(	(	PUNCT
ap-3506	57	32	density	density	NOUN
ap-3506	57	33	operator	operator	NOUN
ap-3506	57	34	)	)	PUNCT
ap-3506	57	35	.	.	PUNCT
ap-3506	58	1	(	(	PUNCT
ap-3506	58	2	5	5	NUM
ap-3506	58	3	)	)	PUNCT
ap-3506	58	4	then	then	ADV
ap-3506	58	5	,	,	PUNCT
ap-3506	58	6	if	if	SCONJ
ap-3506	58	7	x	x	PRON
ap-3506	58	8	is	be	AUX
ap-3506	58	9	a	a	DET
ap-3506	58	10	space	space	NOUN
ap-3506	58	11	with	with	ADP
ap-3506	58	12	suitable	suitable	ADJ
ap-3506	58	13	topology	topology	NOUN
ap-3506	58	14	,	,	PUNCT
ap-3506	58	15	the	the	DET
ap-3506	58	16	map	map	NOUN
ap-3506	58	17	b(x	b(x	NOUN
ap-3506	58	18	)	)	PUNCT
ap-3506	58	19	3	3	NUM
ap-3506	58	20	∆	∆	X
ap-3506	58	21	7→	7→	NUM
ap-3506	58	22	∫	∫	PROPN
ap-3506	58	23	∆	∆	PROPN
ap-3506	58	24	ρ(x	ρ(x	PROPN
ap-3506	58	25	)	)	PUNCT
ap-3506	58	26	dν(x	dν(x	NOUN
ap-3506	58	27	)	)	PUNCT
ap-3506	58	28	(	(	PUNCT
ap-3506	58	29	6	6	NUM
ap-3506	58	30	)	)	PUNCT
ap-3506	58	31	may	may	AUX
ap-3506	58	32	define	define	VERB
ap-3506	58	33	a	a	DET
ap-3506	58	34	normalized	normalize	VERB
ap-3506	58	35	positive	positive	ADJ
ap-3506	58	36	operator	operator	NOUN
ap-3506	58	37	-	-	PUNCT
ap-3506	58	38	valued	value	VERB
ap-3506	58	39	measure	measure	NOUN
ap-3506	58	40	(	(	PUNCT
ap-3506	58	41	povm	povm	NOUN
ap-3506	58	42	)	)	PUNCT
ap-3506	58	43	on	on	ADP
ap-3506	58	44	the	the	DET
ap-3506	58	45	σ	σ	PROPN
ap-3506	58	46	-	-	PUNCT
ap-3506	58	47	algebra	algebra	NOUN
ap-3506	58	48	b(x	b(x	NOUN
ap-3506	58	49	)	)	PUNCT
ap-3506	58	50	of	of	ADP
ap-3506	58	51	borel	borel	NOUN
ap-3506	58	52	sets	set	NOUN
ap-3506	58	53	.	.	PUNCT
ap-3506	59	1	the	the	DET
ap-3506	59	2	quantization	quantization	NOUN
ap-3506	59	3	of	of	ADP
ap-3506	59	4	complex	complex	ADV
ap-3506	59	5	-	-	PUNCT
ap-3506	59	6	valued	value	VERB
ap-3506	59	7	functions	function	NOUN
ap-3506	59	8	f(x	f(x	PROPN
ap-3506	59	9	)	)	PUNCT
ap-3506	59	10	on	on	ADP
ap-3506	59	11	x	x	X
ap-3506	59	12	is	be	AUX
ap-3506	59	13	the	the	DET
ap-3506	59	14	linear	linear	ADJ
ap-3506	59	15	map	map	NOUN
ap-3506	59	16	:	:	PUNCT
ap-3506	59	17	f	f	PROPN
ap-3506	60	1	7→	7→	NUM
ap-3506	60	2	af	af	PROPN
ap-3506	60	3	=	=	SYM
ap-3506	60	4	∫	∫	PROPN
ap-3506	60	5	x	x	SYM
ap-3506	60	6	m(x)f(x	m(x)f(x	PROPN
ap-3506	60	7	)	)	PUNCT
ap-3506	60	8	dν(x	dν(x	NOUN
ap-3506	60	9	)	)	PUNCT
ap-3506	60	10	,	,	PUNCT
ap-3506	60	11	(	(	PUNCT
ap-3506	60	12	7	7	X
ap-3506	60	13	)	)	PUNCT
ap-3506	60	14	understood	understand	VERB
ap-3506	60	15	as	as	ADP
ap-3506	60	16	the	the	DET
ap-3506	60	17	sesquilinear	sesquilinear	NOUN
ap-3506	60	18	form	form	NOUN
ap-3506	60	19	,	,	PUNCT
ap-3506	60	20	bf	bf	NOUN
ap-3506	60	21	(	(	PUNCT
ap-3506	60	22	ψ1	ψ1	NOUN
ap-3506	60	23	,	,	PUNCT
ap-3506	60	24	ψ2	ψ2	NOUN
ap-3506	60	25	)	)	PUNCT
ap-3506	60	26	=	=	SYM
ap-3506	61	1	∫	∫	PROPN
ap-3506	61	2	x	x	PUNCT
ap-3506	61	3	〈	〈	PROPN
ap-3506	61	4	ψ1|m(x)|ψ2〉f(x	ψ1|m(x)|ψ2〉f(x	NOUN
ap-3506	61	5	)	)	PUNCT
ap-3506	61	6	dν(x	dν(x	NOUN
ap-3506	61	7	)	)	PUNCT
ap-3506	61	8	,	,	PUNCT
ap-3506	61	9	(	(	PUNCT
ap-3506	61	10	8)	8)	NUM
ap-3506	61	11	defined	define	VERB
ap-3506	61	12	on	on	ADP
ap-3506	61	13	a	a	DET
ap-3506	61	14	dense	dense	ADJ
ap-3506	61	15	subspace	subspace	NOUN
ap-3506	61	16	of	of	ADP
ap-3506	61	17	h.	h.	PROPN
ap-3506	61	18	if	if	SCONJ
ap-3506	61	19	f	f	PROPN
ap-3506	61	20	is	be	AUX
ap-3506	61	21	real	real	ADJ
ap-3506	61	22	and	and	CCONJ
ap-3506	61	23	at	at	ADP
ap-3506	61	24	least	least	ADJ
ap-3506	61	25	semi	semi	ADJ
ap-3506	61	26	-	-	ADJ
ap-3506	61	27	bounded	bounded	ADJ
ap-3506	61	28	,	,	PUNCT
ap-3506	61	29	and	and	CCONJ
ap-3506	61	30	if	if	SCONJ
ap-3506	61	31	the	the	DET
ap-3506	61	32	m(x	m(x	NOUN
ap-3506	61	33	)	)	PUNCT
ap-3506	61	34	’s	’	VERB
ap-3506	61	35	are	be	AUX
ap-3506	61	36	positive	positive	ADJ
ap-3506	61	37	operators	operator	NOUN
ap-3506	61	38	,	,	PUNCT
ap-3506	61	39	then	then	ADV
ap-3506	61	40	the	the	DET
ap-3506	61	41	friedrich	friedrich	NOUN
ap-3506	61	42	’s	’s	PART
ap-3506	61	43	extension	extension	NOUN
ap-3506	61	44	of	of	ADP
ap-3506	61	45	bf	bf	NOUN
ap-3506	61	46	univocally	univocally	ADV
ap-3506	61	47	defines	define	VERB
ap-3506	61	48	a	a	DET
ap-3506	61	49	self	self	NOUN
ap-3506	61	50	-	-	PUNCT
ap-3506	61	51	adjoint	adjoint	NOUN
ap-3506	61	52	operator	operator	NOUN
ap-3506	61	53	.	.	PUNCT
ap-3506	62	1	if	if	SCONJ
ap-3506	62	2	f	f	PROPN
ap-3506	62	3	is	be	AUX
ap-3506	62	4	not	not	PART
ap-3506	62	5	semi	semi	ADJ
ap-3506	62	6	-	-	ADJ
ap-3506	62	7	bounded	bounded	ADJ
ap-3506	62	8	,	,	PUNCT
ap-3506	62	9	there	there	PRON
ap-3506	62	10	is	be	VERB
ap-3506	62	11	no	no	DET
ap-3506	62	12	natural	natural	ADJ
ap-3506	62	13	choice	choice	NOUN
ap-3506	62	14	of	of	ADP
ap-3506	62	15	a	a	DET
ap-3506	62	16	selfadjoint	selfadjoint	NOUN
ap-3506	62	17	operator	operator	NOUN
ap-3506	62	18	associated	associate	VERB
ap-3506	62	19	with	with	ADP
ap-3506	62	20	bf	bf	NOUN
ap-3506	62	21	.	.	PUNCT
ap-3506	63	1	we	we	PRON
ap-3506	63	2	then	then	ADV
ap-3506	63	3	need	need	VERB
ap-3506	63	4	more	more	ADJ
ap-3506	63	5	information	information	NOUN
ap-3506	63	6	on	on	ADP
ap-3506	63	7	h	h	NOUN
ap-3506	63	8	to	to	PART
ap-3506	63	9	solve	solve	VERB
ap-3506	63	10	this	this	DET
ap-3506	63	11	subtlety	subtlety	NOUN
ap-3506	63	12	.	.	PUNCT
ap-3506	64	1	covariance	covariance	NOUN
ap-3506	64	2	implies	imply	VERB
ap-3506	64	3	symmetry	symmetry	NOUN
ap-3506	64	4	.	.	PUNCT
ap-3506	65	1	symmetry	symmetry	NOUN
ap-3506	65	2	suggests	suggest	VERB
ap-3506	65	3	a	a	DET
ap-3506	65	4	mathematical	mathematical	ADJ
ap-3506	65	5	group	group	NOUN
ap-3506	65	6	g.	g.	PROPN
ap-3506	65	7	a	a	DET
ap-3506	65	8	symmetry	symmetry	NOUN
ap-3506	65	9	structure	structure	NOUN
ap-3506	65	10	on	on	ADP
ap-3506	65	11	x	x	SYM
ap-3506	65	12	presupposes	presuppose	VERB
ap-3506	65	13	that	that	SCONJ
ap-3506	65	14	some	some	DET
ap-3506	65	15	group	group	NOUN
ap-3506	65	16	g	g	PROPN
ap-3506	65	17	acts	act	VERB
ap-3506	65	18	on	on	ADP
ap-3506	65	19	x.	x.	NOUN
ap-3506	65	20	our	our	PRON
ap-3506	65	21	hypothesis	hypothesis	NOUN
ap-3506	65	22	here	here	ADV
ap-3506	65	23	is	be	AUX
ap-3506	65	24	that	that	SCONJ
ap-3506	65	25	x	x	PRON
ap-3506	65	26	is	be	AUX
ap-3506	65	27	an	an	DET
ap-3506	65	28	homogeneous	homogeneous	ADJ
ap-3506	65	29	space	space	NOUN
ap-3506	65	30	for	for	ADP
ap-3506	65	31	g	g	NOUN
ap-3506	65	32	,	,	PUNCT
ap-3506	65	33	which	which	PRON
ap-3506	65	34	means	mean	VERB
ap-3506	65	35	that	that	SCONJ
ap-3506	65	36	x	x	PUNCT
ap-3506	65	37	∼	∼	VERB
ap-3506	65	38	g	g	NOUN
ap-3506	65	39	/	/	SYM
ap-3506	65	40	h	h	NOUN
ap-3506	65	41	for	for	ADP
ap-3506	65	42	h	h	DET
ap-3506	65	43	a	a	DET
ap-3506	65	44	subgroup	subgroup	NOUN
ap-3506	65	45	of	of	ADP
ap-3506	65	46	g.	g.	PROPN
ap-3506	65	47	we	we	PRON
ap-3506	65	48	now	now	ADV
ap-3506	65	49	examine	examine	VERB
ap-3506	65	50	two	two	NUM
ap-3506	65	51	possible	possible	ADJ
ap-3506	65	52	cases	case	NOUN
ap-3506	65	53	.	.	PUNCT
ap-3506	66	1	174	174	NUM
ap-3506	66	2	vol	vol	NOUN
ap-3506	66	3	.	.	PUNCT
ap-3506	67	1	56	56	NUM
ap-3506	67	2	no	no	NOUN
ap-3506	67	3	.	.	PUNCT
ap-3506	68	1	3/2016	3/2016	NUM
ap-3506	68	2	covariant	covariant	ADJ
ap-3506	68	3	integral	integral	ADJ
ap-3506	68	4	quantizations	quantization	NOUN
ap-3506	68	5	and	and	CCONJ
ap-3506	68	6	quantum	quantum	ADJ
ap-3506	68	7	cosmology	cosmology	NOUN
ap-3506	68	8	3.1.1	3.1.1	NOUN
ap-3506	68	9	.	.	PUNCT
ap-3506	69	1	x	x	X
ap-3506	69	2	=	=	SYM
ap-3506	69	3	g	g	NOUN
ap-3506	69	4	:	:	PUNCT
ap-3506	69	5	quantizing	quantize	VERB
ap-3506	69	6	the	the	DET
ap-3506	69	7	group	group	NOUN
ap-3506	69	8	let	let	VERB
ap-3506	69	9	g	g	PRON
ap-3506	69	10	be	be	AUX
ap-3506	69	11	a	a	DET
ap-3506	69	12	lie	lie	NOUN
ap-3506	69	13	group	group	NOUN
ap-3506	69	14	with	with	ADP
ap-3506	69	15	left	left	ADJ
ap-3506	69	16	invariant	invariant	ADJ
ap-3506	69	17	haar	haar	PROPN
ap-3506	69	18	measure	measure	PROPN
ap-3506	69	19	dµ(g	dµ(g	PROPN
ap-3506	69	20	)	)	PUNCT
ap-3506	69	21	,	,	PUNCT
ap-3506	69	22	and	and	CCONJ
ap-3506	69	23	let	let	VERB
ap-3506	69	24	g	g	PROPN
ap-3506	69	25	7→	7→	NUM
ap-3506	69	26	u(g	u(g	PROPN
ap-3506	69	27	)	)	PUNCT
ap-3506	69	28	be	be	AUX
ap-3506	69	29	a	a	DET
ap-3506	69	30	unitary	unitary	ADJ
ap-3506	69	31	irreducible	irreducible	ADJ
ap-3506	69	32	representation	representation	NOUN
ap-3506	69	33	(	(	PUNCT
ap-3506	69	34	uir	uir	PROPN
ap-3506	69	35	)	)	PUNCT
ap-3506	69	36	of	of	ADP
ap-3506	69	37	g	g	PROPN
ap-3506	69	38	in	in	ADP
ap-3506	69	39	a	a	DET
ap-3506	69	40	hilbert	hilbert	NOUN
ap-3506	69	41	space	space	NOUN
ap-3506	69	42	h.	h.	PROPN
ap-3506	69	43	let	let	VERB
ap-3506	69	44	m	m	PRON
ap-3506	69	45	be	be	AUX
ap-3506	69	46	a	a	DET
ap-3506	69	47	bounded	bounded	ADJ
ap-3506	69	48	operator	operator	NOUN
ap-3506	69	49	on	on	ADP
ap-3506	69	50	h.	h.	PROPN
ap-3506	69	51	suppose	suppose	VERB
ap-3506	69	52	that	that	SCONJ
ap-3506	69	53	the	the	DET
ap-3506	69	54	operator	operator	NOUN
ap-3506	69	55	r	r	NOUN
ap-3506	69	56	:	:	PUNCT
ap-3506	69	57	=	=	SYM
ap-3506	69	58	∫	∫	PROPN
ap-3506	69	59	g	g	PROPN
ap-3506	69	60	m(g	m(g	PROPN
ap-3506	69	61	)	)	PUNCT
ap-3506	69	62	dµ(g	dµ(g	PROPN
ap-3506	69	63	)	)	PUNCT
ap-3506	69	64	,	,	PUNCT
ap-3506	69	65	m(g	m(g	PROPN
ap-3506	69	66	)	)	PUNCT
ap-3506	69	67	:	:	PUNCT
ap-3506	69	68	=	=	SYM
ap-3506	69	69	u(g)mu(g)†	u(g)mu(g)†	NOUN
ap-3506	69	70	,	,	PUNCT
ap-3506	69	71	(	(	PUNCT
ap-3506	69	72	9	9	X
ap-3506	69	73	)	)	PUNCT
ap-3506	69	74	is	be	AUX
ap-3506	69	75	defined	define	VERB
ap-3506	69	76	in	in	ADP
ap-3506	69	77	a	a	DET
ap-3506	69	78	weak	weak	ADJ
ap-3506	69	79	sense	sense	NOUN
ap-3506	69	80	.	.	PUNCT
ap-3506	70	1	from	from	ADP
ap-3506	70	2	the	the	DET
ap-3506	70	3	left	left	ADJ
ap-3506	70	4	invariance	invariance	NOUN
ap-3506	70	5	of	of	ADP
ap-3506	70	6	dµ(g	dµ(g	PROPN
ap-3506	70	7	)	)	PUNCT
ap-3506	70	8	the	the	DET
ap-3506	70	9	operator	operator	NOUN
ap-3506	70	10	r	r	NOUN
ap-3506	70	11	commutes	commute	NOUN
ap-3506	70	12	with	with	ADP
ap-3506	70	13	all	all	DET
ap-3506	70	14	operators	operator	NOUN
ap-3506	70	15	u(g	u(g	ADP
ap-3506	70	16	)	)	PUNCT
ap-3506	70	17	,	,	PUNCT
ap-3506	70	18	g	g	PROPN
ap-3506	70	19	∈	∈	PROPN
ap-3506	70	20	g	g	NOUN
ap-3506	70	21	,	,	PUNCT
ap-3506	70	22	and	and	CCONJ
ap-3506	70	23	so	so	ADV
ap-3506	70	24	,	,	PUNCT
ap-3506	70	25	from	from	ADP
ap-3506	70	26	schur	schur	PROPN
ap-3506	70	27	’s	’s	PART
ap-3506	70	28	lemma	lemma	PROPN
ap-3506	70	29	,	,	PUNCT
ap-3506	70	30	r	r	NOUN
ap-3506	70	31	=	=	SYM
ap-3506	70	32	cmi	cmi	NOUN
ap-3506	70	33	with	with	ADP
ap-3506	70	34	cm	cm	PROPN
ap-3506	70	35	=	=	SYM
ap-3506	70	36	∫	∫	PROPN
ap-3506	70	37	g	g	PROPN
ap-3506	70	38	tr	tr	PUNCT
ap-3506	70	39	(	(	PUNCT
ap-3506	70	40	ρ0m(g	ρ0m(g	PROPN
ap-3506	70	41	)	)	PUNCT
ap-3506	70	42	)	)	PUNCT
ap-3506	70	43	dµ(g	dµ(g	PROPN
ap-3506	70	44	)	)	PUNCT
ap-3506	70	45	,	,	PUNCT
ap-3506	70	46	(	(	PUNCT
ap-3506	70	47	10	10	NUM
ap-3506	70	48	)	)	PUNCT
ap-3506	70	49	where	where	SCONJ
ap-3506	70	50	the	the	DET
ap-3506	70	51	unit	unit	NOUN
ap-3506	70	52	trace	trace	VERB
ap-3506	70	53	positive	positive	ADJ
ap-3506	70	54	operator	operator	NOUN
ap-3506	70	55	ρ0	ρ0	PROPN
ap-3506	70	56	is	be	AUX
ap-3506	70	57	chosen	choose	VERB
ap-3506	70	58	in	in	ADP
ap-3506	70	59	order	order	NOUN
ap-3506	70	60	to	to	PART
ap-3506	70	61	make	make	VERB
ap-3506	70	62	the	the	DET
ap-3506	70	63	integral	integral	ADJ
ap-3506	70	64	convergent	convergent	NOUN
ap-3506	70	65	.	.	PUNCT
ap-3506	71	1	if	if	SCONJ
ap-3506	71	2	cm	cm	PROPN
ap-3506	71	3	is	be	AUX
ap-3506	71	4	finite	finite	ADJ
ap-3506	71	5	and	and	CCONJ
ap-3506	71	6	not	not	PART
ap-3506	71	7	zero	zero	NUM
ap-3506	71	8	,	,	PUNCT
ap-3506	71	9	then	then	ADV
ap-3506	71	10	we	we	PRON
ap-3506	71	11	get	get	VERB
ap-3506	71	12	the	the	DET
ap-3506	71	13	resolution	resolution	NOUN
ap-3506	71	14	of	of	ADP
ap-3506	71	15	the	the	DET
ap-3506	71	16	identity:∫	identity:∫	NOUN
ap-3506	71	17	g	g	PROPN
ap-3506	71	18	m(g	m(g	PROPN
ap-3506	71	19	)	)	PUNCT
ap-3506	71	20	dν(g	dν(g	PUNCT
ap-3506	71	21	)	)	PUNCT
ap-3506	72	1	=	=	SYM
ap-3506	72	2	i	i	PROPN
ap-3506	72	3	,	,	PUNCT
ap-3506	72	4	dν(g	dν(g	NOUN
ap-3506	72	5	)	)	PUNCT
ap-3506	72	6	:	:	PUNCT
ap-3506	72	7	=	=	PUNCT
ap-3506	72	8	dµ(g)/cm	dµ(g)/cm	PROPN
ap-3506	72	9	.	.	PUNCT
ap-3506	73	1	(	(	PUNCT
ap-3506	73	2	11	11	NUM
ap-3506	73	3	)	)	PUNCT
ap-3506	73	4	for	for	ADP
ap-3506	73	5	this	this	DET
ap-3506	73	6	reason	reason	NOUN
ap-3506	73	7	,	,	PUNCT
ap-3506	73	8	the	the	DET
ap-3506	73	9	operator	operator	NOUN
ap-3506	73	10	m	m	AUX
ap-3506	73	11	to	to	PART
ap-3506	73	12	be	be	AUX
ap-3506	73	13	u	u	NOUN
ap-3506	73	14	transported	transport	VERB
ap-3506	73	15	will	will	AUX
ap-3506	73	16	be	be	AUX
ap-3506	73	17	designated	designate	VERB
ap-3506	73	18	(	(	PUNCT
ap-3506	73	19	admissible	admissible	ADJ
ap-3506	73	20	)	)	PUNCT
ap-3506	73	21	fiducial	fiducial	ADJ
ap-3506	73	22	operator	operator	NOUN
ap-3506	73	23	.	.	PUNCT
ap-3506	74	1	the	the	DET
ap-3506	74	2	method	method	NOUN
ap-3506	74	3	becomes	become	VERB
ap-3506	74	4	more	more	ADV
ap-3506	74	5	apparent	apparent	ADJ
ap-3506	74	6	when	when	SCONJ
ap-3506	74	7	the	the	DET
ap-3506	74	8	representation	representation	NOUN
ap-3506	74	9	u	u	NOUN
ap-3506	74	10	is	be	AUX
ap-3506	74	11	square	square	ADV
ap-3506	74	12	-	-	PUNCT
ap-3506	74	13	integrable	integrable	ADJ
ap-3506	74	14	in	in	ADP
ap-3506	74	15	the	the	DET
ap-3506	74	16	following	follow	VERB
ap-3506	74	17	sense	sense	NOUN
ap-3506	74	18	(	(	PUNCT
ap-3506	74	19	for	for	ADP
ap-3506	74	20	example	example	NOUN
ap-3506	74	21	,	,	PUNCT
ap-3506	74	22	it	it	PRON
ap-3506	74	23	is	be	AUX
ap-3506	74	24	the	the	DET
ap-3506	74	25	case	case	NOUN
ap-3506	74	26	for	for	ADP
ap-3506	74	27	the	the	DET
ap-3506	74	28	affine	affine	ADJ
ap-3506	74	29	group	group	NOUN
ap-3506	74	30	of	of	ADP
ap-3506	74	31	the	the	DET
ap-3506	74	32	real	real	ADJ
ap-3506	74	33	line	line	NOUN
ap-3506	74	34	,	,	PUNCT
ap-3506	74	35	see	see	VERB
ap-3506	74	36	below	below	ADV
ap-3506	74	37	)	)	PUNCT
ap-3506	74	38	.	.	PUNCT
ap-3506	75	1	suppose	suppose	VERB
ap-3506	75	2	that	that	SCONJ
ap-3506	75	3	there	there	PRON
ap-3506	75	4	exists	exist	VERB
ap-3506	75	5	a	a	DET
ap-3506	75	6	density	density	NOUN
ap-3506	75	7	operator	operator	NOUN
ap-3506	75	8	ρ	ρ	NOUN
ap-3506	75	9	which	which	PRON
ap-3506	75	10	is	be	AUX
ap-3506	75	11	admissible	admissible	ADJ
ap-3506	75	12	in	in	ADP
ap-3506	75	13	the	the	DET
ap-3506	75	14	sense	sense	NOUN
ap-3506	75	15	that	that	SCONJ
ap-3506	75	16	cρ	cρ	PRON
ap-3506	75	17	=	=	SYM
ap-3506	75	18	∫	∫	PROPN
ap-3506	75	19	g	g	PROPN
ap-3506	75	20	dµ(g	dµ(g	PROPN
ap-3506	75	21	)	)	PUNCT
ap-3506	75	22	tr	tr	PUNCT
ap-3506	75	23	(	(	PUNCT
ap-3506	75	24	ρρ(g	ρρ(g	NUM
ap-3506	75	25	)	)	PUNCT
ap-3506	75	26	)	)	PUNCT
ap-3506	76	1	<	<	X
ap-3506	76	2	∞	∞	PROPN
ap-3506	76	3	,	,	PUNCT
ap-3506	76	4	(	(	PUNCT
ap-3506	76	5	12	12	NUM
ap-3506	76	6	)	)	PUNCT
ap-3506	76	7	with	with	ADP
ap-3506	76	8	ρ(g	ρ(g	NOUN
ap-3506	76	9	)	)	PUNCT
ap-3506	76	10	=	=	PUNCT
ap-3506	76	11	u(g)ρu†(g	u(g)ρu†(g	PROPN
ap-3506	76	12	)	)	PUNCT
ap-3506	76	13	.	.	PUNCT
ap-3506	77	1	then	then	ADV
ap-3506	77	2	the	the	DET
ap-3506	77	3	resolution	resolution	NOUN
ap-3506	77	4	of	of	ADP
ap-3506	77	5	the	the	DET
ap-3506	77	6	identity	identity	NOUN
ap-3506	77	7	(	(	PUNCT
ap-3506	77	8	11	11	NUM
ap-3506	77	9	)	)	PUNCT
ap-3506	77	10	holds	hold	VERB
ap-3506	77	11	with	with	ADP
ap-3506	77	12	m(g	m(g	NOUN
ap-3506	77	13	)	)	PUNCT
ap-3506	77	14	and	and	CCONJ
ap-3506	77	15	cm	cm	NOUN
ap-3506	77	16	=	=	SYM
ap-3506	77	17	cρ	cρ	PROPN
ap-3506	77	18	.	.	PUNCT
ap-3506	78	1	this	this	PRON
ap-3506	78	2	allows	allow	VERB
ap-3506	78	3	a	a	DET
ap-3506	78	4	covariant	covariant	ADJ
ap-3506	78	5	integral	integral	ADJ
ap-3506	78	6	quantization	quantization	NOUN
ap-3506	78	7	of	of	ADP
ap-3506	78	8	complexvalued	complexvalue	VERB
ap-3506	78	9	functions	function	NOUN
ap-3506	78	10	on	on	ADP
ap-3506	78	11	the	the	DET
ap-3506	78	12	group	group	NOUN
ap-3506	78	13	f	f	PROPN
ap-3506	78	14	7→	7→	NUM
ap-3506	78	15	af	af	PROPN
ap-3506	78	16	=	=	SYM
ap-3506	78	17	∫	∫	PROPN
ap-3506	78	18	g	g	PROPN
ap-3506	78	19	ρ(g)f(g	ρ(g)f(g	NUM
ap-3506	78	20	)	)	PUNCT
ap-3506	78	21	dν(g	dν(g	NOUN
ap-3506	78	22	)	)	PUNCT
ap-3506	78	23	,	,	PUNCT
ap-3506	78	24	dν(g	dν(g	PUNCT
ap-3506	78	25	)	)	PUNCT
ap-3506	78	26	:	:	PUNCT
ap-3506	79	1	=	=	SYM
ap-3506	79	2	dµ(g	dµ(g	X
ap-3506	79	3	)	)	PUNCT
ap-3506	79	4	cρ	cρ	X
ap-3506	79	5	,	,	PUNCT
ap-3506	79	6	(	(	PUNCT
ap-3506	79	7	13	13	NUM
ap-3506	79	8	)	)	PUNCT
ap-3506	79	9	u(g)afu†(g	u(g)afu†(g	NOUN
ap-3506	79	10	)	)	PUNCT
ap-3506	79	11	=	=	SYM
ap-3506	79	12	au(g)f	au(g)f	PROPN
ap-3506	79	13	(	(	PUNCT
ap-3506	79	14	covariance	covariance	NOUN
ap-3506	79	15	)	)	PUNCT
ap-3506	79	16	,	,	PUNCT
ap-3506	79	17	(	(	PUNCT
ap-3506	79	18	14	14	NUM
ap-3506	79	19	)	)	PUNCT
ap-3506	79	20	where	where	SCONJ
ap-3506	79	21	(	(	PUNCT
ap-3506	79	22	u(g)f	u(g)f	PROPN
ap-3506	79	23	)	)	PUNCT
ap-3506	79	24	(	(	PUNCT
ap-3506	79	25	g′	g′	NOUN
ap-3506	79	26	)	)	PUNCT
ap-3506	79	27	:	:	PUNCT
ap-3506	79	28	=	=	SYM
ap-3506	79	29	f(g−1g′	f(g−1g′	X
ap-3506	79	30	)	)	PUNCT
ap-3506	79	31	(	(	PUNCT
ap-3506	79	32	15	15	NUM
ap-3506	79	33	)	)	PUNCT
ap-3506	79	34	is	be	AUX
ap-3506	79	35	the	the	DET
ap-3506	79	36	regular	regular	ADJ
ap-3506	79	37	representation	representation	NOUN
ap-3506	79	38	if	if	SCONJ
ap-3506	79	39	f	f	PROPN
ap-3506	79	40	∈	∈	PROPN
ap-3506	79	41	l2(g	l2(g	PROPN
ap-3506	79	42	,	,	PUNCT
ap-3506	79	43	dµ(g	dµ(g	NOUN
ap-3506	79	44	)	)	PUNCT
ap-3506	79	45	)	)	PUNCT
ap-3506	79	46	.	.	PUNCT
ap-3506	80	1	this	this	PRON
ap-3506	80	2	leads	lead	VERB
ap-3506	80	3	to	to	ADP
ap-3506	80	4	a	a	DET
ap-3506	80	5	non	non	ADJ
ap-3506	80	6	-	-	ADJ
ap-3506	80	7	commutative	commutative	ADJ
ap-3506	80	8	version	version	NOUN
ap-3506	80	9	of	of	ADP
ap-3506	80	10	the	the	DET
ap-3506	80	11	original	original	ADJ
ap-3506	80	12	manifold	manifold	ADJ
ap-3506	80	13	structure	structure	NOUN
ap-3506	80	14	for	for	ADP
ap-3506	80	15	g.	g.	PROPN
ap-3506	80	16	example	example	NOUN
ap-3506	80	17	:	:	PUNCT
ap-3506	80	18	affine	affine	VERB
ap-3506	80	19	cs	cs	ADJ
ap-3506	80	20	integral	integral	ADJ
ap-3506	80	21	quantization	quantization	NOUN
ap-3506	80	22	in	in	ADP
ap-3506	80	23	this	this	DET
ap-3506	80	24	example	example	NOUN
ap-3506	80	25	,	,	PUNCT
ap-3506	80	26	the	the	DET
ap-3506	80	27	group	group	NOUN
ap-3506	80	28	g	g	PROPN
ap-3506	80	29	is	be	AUX
ap-3506	80	30	the	the	DET
ap-3506	80	31	affine	affine	ADJ
ap-3506	80	32	group	group	NOUN
ap-3506	80	33	of	of	ADP
ap-3506	80	34	the	the	DET
ap-3506	80	35	real	real	ADJ
ap-3506	80	36	line	line	NOUN
ap-3506	80	37	and	and	CCONJ
ap-3506	80	38	is	be	AUX
ap-3506	80	39	also	also	ADV
ap-3506	80	40	viewed	view	VERB
ap-3506	80	41	as	as	ADP
ap-3506	80	42	the	the	DET
ap-3506	80	43	phase	phase	NOUN
ap-3506	80	44	space	space	NOUN
ap-3506	80	45	for	for	ADP
ap-3506	80	46	the	the	DET
ap-3506	80	47	motion	motion	NOUN
ap-3506	80	48	on	on	ADP
ap-3506	80	49	the	the	DET
ap-3506	80	50	half	half	ADJ
ap-3506	80	51	-	-	PUNCT
ap-3506	80	52	line	line	NOUN
ap-3506	80	53	,	,	PUNCT
ap-3506	80	54	i.e.	i.e.	X
ap-3506	80	55	,	,	PUNCT
ap-3506	80	56	the	the	DET
ap-3506	80	57	half	half	ADJ
ap-3506	80	58	-	-	PUNCT
ap-3506	80	59	plane	plane	NOUN
ap-3506	80	60	{	{	PUNCT
ap-3506	80	61	(	(	PUNCT
ap-3506	80	62	q	q	ADJ
ap-3506	80	63	,	,	PUNCT
ap-3506	80	64	p	p	NOUN
ap-3506	80	65	)	)	PUNCT
ap-3506	80	66	∈	∈	PROPN
ap-3506	80	67	r∗+	r∗+	PROPN
ap-3506	80	68	×	×	NOUN
ap-3506	80	69	r	r	NOUN
ap-3506	80	70	}	}	PUNCT
ap-3506	80	71	.	.	PUNCT
ap-3506	81	1	the	the	DET
ap-3506	81	2	group	group	NOUN
ap-3506	81	3	law	law	NOUN
ap-3506	81	4	is	be	AUX
ap-3506	81	5	defined	define	VERB
ap-3506	81	6	as	as	ADP
ap-3506	81	7	(	(	PUNCT
ap-3506	81	8	q	q	NOUN
ap-3506	81	9	,	,	PUNCT
ap-3506	81	10	p)(q0	p)(q0	NOUN
ap-3506	81	11	,	,	PUNCT
ap-3506	81	12	p0	p0	NOUN
ap-3506	81	13	)	)	PUNCT
ap-3506	81	14	=	=	SYM
ap-3506	81	15	(	(	PUNCT
ap-3506	81	16	qq0	qq0	PROPN
ap-3506	81	17	,	,	PUNCT
ap-3506	81	18	p0	p0	PROPN
ap-3506	81	19	q	q	NOUN
ap-3506	82	1	+	+	CCONJ
ap-3506	82	2	p	p	NOUN
ap-3506	82	3	)	)	PUNCT
ap-3506	82	4	,	,	PUNCT
ap-3506	82	5	(	(	PUNCT
ap-3506	82	6	16	16	NUM
ap-3506	82	7	)	)	PUNCT
ap-3506	82	8	and	and	CCONJ
ap-3506	82	9	the	the	DET
ap-3506	82	10	left	left	ADJ
ap-3506	82	11	invariant	invariant	ADJ
ap-3506	82	12	measure	measure	NOUN
ap-3506	82	13	is	be	AUX
ap-3506	82	14	the	the	DET
ap-3506	82	15	symplectic	symplectic	ADJ
ap-3506	82	16	dq	dq	NUM
ap-3506	82	17	dp	dp	NOUN
ap-3506	82	18	.	.	PUNCT
ap-3506	83	1	this	this	DET
ap-3506	83	2	group	group	NOUN
ap-3506	83	3	has	have	VERB
ap-3506	83	4	two	two	NUM
ap-3506	83	5	uir	uir	NOUN
ap-3506	83	6	’s	’s	PART
ap-3506	83	7	which	which	PRON
ap-3506	83	8	are	be	AUX
ap-3506	83	9	both	both	PRON
ap-3506	83	10	square	square	ADV
ap-3506	83	11	integrable	integrable	ADJ
ap-3506	83	12	.	.	PUNCT
ap-3506	84	1	we	we	PRON
ap-3506	84	2	choose	choose	VERB
ap-3506	84	3	the	the	DET
ap-3506	84	4	following	follow	VERB
ap-3506	84	5	one	one	NUM
ap-3506	84	6	.	.	PUNCT
ap-3506	85	1	l2(r∗+,dx	l2(r∗+,dx	X
ap-3506	85	2	)	)	PUNCT
ap-3506	85	3	3	3	NUM
ap-3506	85	4	ψ(x	ψ(x	NOUN
ap-3506	85	5	)	)	PUNCT
ap-3506	85	6	7→	7→	NUM
ap-3506	85	7	(	(	PUNCT
ap-3506	85	8	u(q	u(q	ADV
ap-3506	85	9	,	,	PUNCT
ap-3506	85	10	p)ψ	p)ψ	NOUN
ap-3506	85	11	)	)	PUNCT
ap-3506	85	12	(	(	PUNCT
ap-3506	85	13	x	x	X
ap-3506	85	14	)	)	PUNCT
ap-3506	85	15	=	=	PRON
ap-3506	85	16	eipx	eipx	VERB
ap-3506	85	17	√	√	NUM
ap-3506	85	18	q	q	NOUN
ap-3506	85	19	ψ	ψ	X
ap-3506	85	20	(	(	PUNCT
ap-3506	85	21	x	x	X
ap-3506	85	22	q	q	NOUN
ap-3506	85	23	)	)	PUNCT
ap-3506	85	24	(	(	PUNCT
ap-3506	85	25	17	17	NUM
ap-3506	85	26	)	)	PUNCT
ap-3506	85	27	as	as	ADP
ap-3506	85	28	a	a	DET
ap-3506	85	29	density	density	NOUN
ap-3506	85	30	operator	operator	NOUN
ap-3506	85	31	we	we	PRON
ap-3506	85	32	choose	choose	VERB
ap-3506	85	33	the	the	DET
ap-3506	85	34	rank	rank	NOUN
ap-3506	85	35	one	one	NUM
ap-3506	85	36	projector	projector	NOUN
ap-3506	85	37	ρ	ρ	NOUN
ap-3506	85	38	=	=	SYM
ap-3506	85	39	|ψ〉〈ψ|	|ψ〉〈ψ|	NOUN
ap-3506	85	40	where	where	SCONJ
ap-3506	85	41	the	the	DET
ap-3506	85	42	fiducial	fiducial	ADJ
ap-3506	85	43	vector	vector	NOUN
ap-3506	85	44	,	,	PUNCT
ap-3506	85	45	i.e.	i.e.	X
ap-3506	85	46	,	,	PUNCT
ap-3506	85	47	the	the	DET
ap-3506	85	48	‘	'	PUNCT
ap-3506	85	49	wavelet	wavelet	NOUN
ap-3506	85	50	”	"	PUNCT
ap-3506	85	51	ψ	ψ	NOUN
ap-3506	85	52	is	be	AUX
ap-3506	85	53	in	in	ADP
ap-3506	85	54	l2(r+,dx	l2(r+,dx	NOUN
ap-3506	85	55	)	)	PUNCT
ap-3506	85	56	∩	∩	NOUN
ap-3506	85	57	l2(r+,dx	l2(r+,dx	X
ap-3506	85	58	/	/	SYM
ap-3506	85	59	x	x	NOUN
ap-3506	85	60	)	)	PUNCT
ap-3506	85	61	and	and	CCONJ
ap-3506	85	62	its	its	PRON
ap-3506	85	63	affine	affine	NOUN
ap-3506	85	64	transport	transport	NOUN
ap-3506	85	65	produces	produce	VERB
ap-3506	85	66	the	the	DET
ap-3506	85	67	overcomplete	overcomplete	ADJ
ap-3506	85	68	family	family	NOUN
ap-3506	85	69	of	of	ADP
ap-3506	85	70	affine	affine	NOUN
ap-3506	85	71	coherent	coherent	ADJ
ap-3506	85	72	states	state	NOUN
ap-3506	85	73	(	(	PUNCT
ap-3506	85	74	acs	acs	NOUN
ap-3506	85	75	)	)	PUNCT
ap-3506	85	76	|q	|q	NOUN
ap-3506	85	77	,	,	PUNCT
ap-3506	85	78	p	p	X
ap-3506	85	79	〉	〉	NUM
ap-3506	85	80	=	=	SYM
ap-3506	85	81	u(q	u(q	PROPN
ap-3506	85	82	,	,	PUNCT
ap-3506	85	83	p)|ψ	p)|ψ	PROPN
ap-3506	85	84	〉	〉	PROPN
ap-3506	85	85	.	.	PUNCT
ap-3506	86	1	(	(	PUNCT
ap-3506	86	2	18	18	NUM
ap-3506	86	3	)	)	PUNCT
ap-3506	86	4	the	the	DET
ap-3506	86	5	acs	acs	PROPN
ap-3506	86	6	integral	integral	ADJ
ap-3506	86	7	quantization	quantization	NOUN
ap-3506	86	8	reads	read	VERB
ap-3506	86	9	as	as	ADP
ap-3506	86	10	f(q	f(q	PROPN
ap-3506	86	11	,	,	PUNCT
ap-3506	86	12	p	p	X
ap-3506	86	13	)	)	PUNCT
ap-3506	86	14	7→	7→	NUM
ap-3506	86	15	af	af	NOUN
ap-3506	86	16	=	=	SYM
ap-3506	87	1	∫	∫	PROPN
ap-3506	87	2	r+×r	r+×r	PROPN
ap-3506	88	1	dq	dq	ADP
ap-3506	89	1	dp	dp	NOUN
ap-3506	90	1	cρ	cρ	PROPN
ap-3506	90	2	f(q	f(q	PROPN
ap-3506	90	3	,	,	PUNCT
ap-3506	90	4	p)|q	p)|q	NOUN
ap-3506	90	5	,	,	PUNCT
ap-3506	90	6	p〉〈q	p〉〈q	NOUN
ap-3506	90	7	,	,	PUNCT
ap-3506	90	8	p|	p|	CCONJ
ap-3506	90	9	(	(	PUNCT
ap-3506	90	10	19	19	NUM
ap-3506	90	11	)	)	PUNCT
ap-3506	90	12	with	with	ADP
ap-3506	90	13	cρ	cρ	PROPN
ap-3506	90	14	=	=	PUNCT
ap-3506	90	15	∫∞	∫∞	NOUN
ap-3506	90	16	0	0	NUM
ap-3506	90	17	|ψ(x)|2	|ψ(x)|2	NUM
ap-3506	90	18	dx	dx	PROPN
ap-3506	90	19	x	x	X
ap-3506	90	20	.	.	PUNCT
ap-3506	91	1	more	more	ADJ
ap-3506	91	2	details	detail	NOUN
ap-3506	91	3	and	and	CCONJ
ap-3506	91	4	new	new	ADJ
ap-3506	91	5	developments	development	NOUN
ap-3506	91	6	are	be	AUX
ap-3506	91	7	given	give	VERB
ap-3506	91	8	in	in	ADP
ap-3506	91	9	the	the	DET
ap-3506	91	10	recent	recent	ADJ
ap-3506	91	11	[	[	X
ap-3506	91	12	20	20	NUM
ap-3506	91	13	]	]	PUNCT
ap-3506	91	14	.	.	PUNCT
ap-3506	92	1	applications	application	NOUN
ap-3506	92	2	of	of	ADP
ap-3506	92	3	this	this	DET
ap-3506	92	4	method	method	NOUN
ap-3506	92	5	to	to	ADP
ap-3506	92	6	the	the	DET
ap-3506	92	7	resolution	resolution	NOUN
ap-3506	92	8	of	of	ADP
ap-3506	92	9	the	the	DET
ap-3506	92	10	singularity	singularity	NOUN
ap-3506	92	11	problem	problem	NOUN
ap-3506	92	12	on	on	ADP
ap-3506	92	13	a	a	DET
ap-3506	92	14	quantum	quantum	ADJ
ap-3506	92	15	level	level	NOUN
ap-3506	92	16	for	for	ADP
ap-3506	92	17	a	a	DET
ap-3506	92	18	series	series	NOUN
ap-3506	92	19	of	of	ADP
ap-3506	92	20	cosmological	cosmological	ADJ
ap-3506	92	21	models	model	NOUN
ap-3506	92	22	(	(	PUNCT
ap-3506	92	23	frw	frw	PROPN
ap-3506	92	24	,	,	PUNCT
ap-3506	92	25	bianchi	bianchi	PROPN
ap-3506	92	26	i	i	PROPN
ap-3506	92	27	,	,	PUNCT
ap-3506	92	28	bianchi	bianchi	NOUN
ap-3506	92	29	ix	ix	PROPN
ap-3506	92	30	)	)	PUNCT
ap-3506	92	31	,	,	PUNCT
ap-3506	92	32	for	for	ADP
ap-3506	92	33	which	which	PRON
ap-3506	92	34	the	the	DET
ap-3506	92	35	volume	volume	NOUN
ap-3506	92	36	—	—	PUNCT
ap-3506	92	37	expansion	expansion	NOUN
ap-3506	92	38	pair	pair	NOUN
ap-3506	92	39	variables	variable	NOUN
ap-3506	92	40	form	form	VERB
ap-3506	92	41	the	the	DET
ap-3506	92	42	above	above	ADJ
ap-3506	92	43	half	half	ADJ
ap-3506	92	44	-	-	PUNCT
ap-3506	92	45	plane	plane	NOUN
ap-3506	92	46	,	,	PUNCT
ap-3506	92	47	are	be	AUX
ap-3506	92	48	given	give	VERB
ap-3506	92	49	in	in	ADP
ap-3506	92	50	the	the	DET
ap-3506	92	51	recent	recent	ADJ
ap-3506	92	52	papers	paper	NOUN
ap-3506	92	53	[	[	X
ap-3506	92	54	10–15	10–15	NUM
ap-3506	92	55	]	]	PUNCT
ap-3506	92	56	and	and	CCONJ
ap-3506	92	57	will	will	AUX
ap-3506	92	58	be	be	AUX
ap-3506	92	59	summarised	summarise	VERB
ap-3506	92	60	in	in	ADP
ap-3506	92	61	section	section	NOUN
ap-3506	92	62	5	5	NUM
ap-3506	92	63	.	.	PUNCT
ap-3506	93	1	3.1.2	3.1.2	NUM
ap-3506	93	2	.	.	PUNCT
ap-3506	94	1	x	x	X
ap-3506	94	2	=	=	PUNCT
ap-3506	94	3	g	g	NOUN
ap-3506	94	4	/	/	SYM
ap-3506	94	5	h	h	NOUN
ap-3506	94	6	:	:	PUNCT
ap-3506	94	7	quantizing	quantize	VERB
ap-3506	94	8	a	a	DET
ap-3506	94	9	non	non	ADJ
ap-3506	94	10	-	-	ADJ
ap-3506	94	11	trivial	trivial	ADJ
ap-3506	94	12	group	group	NOUN
ap-3506	94	13	coset	coset	NOUN
ap-3506	94	14	in	in	ADP
ap-3506	94	15	the	the	DET
ap-3506	94	16	absence	absence	NOUN
ap-3506	94	17	of	of	ADP
ap-3506	94	18	square	square	NOUN
ap-3506	94	19	-	-	PUNCT
ap-3506	94	20	integrability	integrability	NOUN
ap-3506	94	21	over	over	ADP
ap-3506	94	22	g	g	PROPN
ap-3506	94	23	(	(	PUNCT
ap-3506	94	24	the	the	DET
ap-3506	94	25	trivial	trivial	ADJ
ap-3506	94	26	illustration	illustration	NOUN
ap-3506	94	27	is	be	AUX
ap-3506	94	28	the	the	DET
ap-3506	94	29	weyl	weyl	PROPN
ap-3506	94	30	-	-	PUNCT
ap-3506	94	31	heisenberg	heisenberg	PROPN
ap-3506	94	32	group	group	NOUN
ap-3506	94	33	which	which	PRON
ap-3506	94	34	underlies	underlie	VERB
ap-3506	94	35	in	in	ADP
ap-3506	94	36	particular	particular	ADJ
ap-3506	94	37	the	the	DET
ap-3506	94	38	canonical	canonical	ADJ
ap-3506	94	39	quantization	quantization	NOUN
ap-3506	94	40	,	,	PUNCT
ap-3506	94	41	see	see	VERB
ap-3506	94	42	section	section	NOUN
ap-3506	94	43	4	4	NUM
ap-3506	94	44	)	)	PUNCT
ap-3506	94	45	,	,	PUNCT
ap-3506	94	46	there	there	PRON
ap-3506	94	47	exists	exist	VERB
ap-3506	94	48	a	a	DET
ap-3506	94	49	definition	definition	NOUN
ap-3506	94	50	of	of	ADP
ap-3506	94	51	square	square	ADJ
ap-3506	94	52	-	-	PUNCT
ap-3506	94	53	integrable	integrable	ADJ
ap-3506	94	54	representations	representation	NOUN
ap-3506	94	55	with	with	ADP
ap-3506	94	56	respect	respect	NOUN
ap-3506	94	57	to	to	ADP
ap-3506	94	58	a	a	DET
ap-3506	94	59	left	left	ADJ
ap-3506	94	60	coset	coset	NOUN
ap-3506	94	61	manifold	manifold	ADJ
ap-3506	94	62	x	x	X
ap-3506	94	63	=	=	SYM
ap-3506	94	64	g	g	PROPN
ap-3506	94	65	/	/	SYM
ap-3506	94	66	h	h	NOUN
ap-3506	94	67	,	,	PUNCT
ap-3506	94	68	with	with	ADP
ap-3506	94	69	h	h	PROPN
ap-3506	94	70	a	a	DET
ap-3506	94	71	closed	closed	ADJ
ap-3506	94	72	subgroup	subgroup	NOUN
ap-3506	94	73	of	of	ADP
ap-3506	94	74	g	g	PROPN
ap-3506	94	75	(	(	PUNCT
ap-3506	94	76	it	it	PRON
ap-3506	94	77	is	be	AUX
ap-3506	94	78	the	the	DET
ap-3506	94	79	center	center	NOUN
ap-3506	94	80	in	in	ADP
ap-3506	94	81	the	the	DET
ap-3506	94	82	weyl	weyl	PROPN
ap-3506	94	83	-	-	PUNCT
ap-3506	94	84	heisenberg	heisenberg	PROPN
ap-3506	94	85	case	case	NOUN
ap-3506	94	86	)	)	PUNCT
ap-3506	94	87	,	,	PUNCT
ap-3506	94	88	equipped	equip	VERB
ap-3506	94	89	with	with	ADP
ap-3506	94	90	a	a	DET
ap-3506	94	91	quasi	quasi	ADJ
ap-3506	94	92	-	-	ADJ
ap-3506	94	93	invariant	invariant	ADJ
ap-3506	94	94	measure	measure	NOUN
ap-3506	94	95	ν	ν	X
ap-3506	94	96	[	[	X
ap-3506	94	97	2	2	NUM
ap-3506	94	98	]	]	PUNCT
ap-3506	94	99	.	.	PUNCT
ap-3506	95	1	for	for	ADP
ap-3506	95	2	a	a	DET
ap-3506	95	3	global	global	PROPN
ap-3506	95	4	borel	borel	PROPN
ap-3506	95	5	section	section	NOUN
ap-3506	95	6	σ	σ	PROPN
ap-3506	95	7	:	:	PUNCT
ap-3506	95	8	x	x	X
ap-3506	95	9	→	→	SYM
ap-3506	95	10	g	g	NOUN
ap-3506	95	11	of	of	ADP
ap-3506	95	12	the	the	DET
ap-3506	95	13	group	group	NOUN
ap-3506	95	14	,	,	PUNCT
ap-3506	95	15	let	let	VERB
ap-3506	95	16	νσ	νσ	PART
ap-3506	95	17	be	be	AUX
ap-3506	95	18	the	the	DET
ap-3506	95	19	unique	unique	ADJ
ap-3506	95	20	quasi	quasi	ADJ
ap-3506	95	21	-	-	ADJ
ap-3506	95	22	invariant	invariant	ADJ
ap-3506	95	23	measure	measure	NOUN
ap-3506	95	24	defined	define	VERB
ap-3506	95	25	by	by	ADP
ap-3506	95	26	dνσ(x	dνσ(x	PROPN
ap-3506	95	27	)	)	PUNCT
ap-3506	96	1	=	=	SYM
ap-3506	96	2	λ	λ	PROPN
ap-3506	96	3	(	(	PUNCT
ap-3506	96	4	σ(x	σ(x	PROPN
ap-3506	96	5	)	)	PUNCT
ap-3506	96	6	,	,	PUNCT
ap-3506	96	7	x	x	X
ap-3506	96	8	)	)	PUNCT
ap-3506	96	9	dν(x	dν(x	NOUN
ap-3506	96	10	)	)	PUNCT
ap-3506	96	11	,	,	PUNCT
ap-3506	96	12	(	(	PUNCT
ap-3506	96	13	20	20	NUM
ap-3506	96	14	)	)	PUNCT
ap-3506	96	15	where	where	SCONJ
ap-3506	96	16	λ(g	λ(g	PROPN
ap-3506	96	17	,	,	PUNCT
ap-3506	96	18	x)dν(x	x)dν(x	PROPN
ap-3506	96	19	)	)	PUNCT
ap-3506	96	20	=	=	SYM
ap-3506	96	21	dν(g−1x	dν(g−1x	NOUN
ap-3506	96	22	)	)	PUNCT
ap-3506	96	23	for	for	ADP
ap-3506	96	24	g	g	PROPN
ap-3506	96	25	∈	∈	PROPN
ap-3506	96	26	g	g	PROPN
ap-3506	96	27	with	with	ADP
ap-3506	96	28	λ(g	λ(g	PROPN
ap-3506	96	29	,	,	PUNCT
ap-3506	96	30	x	x	NOUN
ap-3506	96	31	)	)	PUNCT
ap-3506	96	32	obeying	obey	VERB
ap-3506	96	33	the	the	DET
ap-3506	96	34	cocycle	cocycle	NOUN
ap-3506	96	35	condition	condition	NOUN
ap-3506	96	36	λ(g1g2	λ(g1g2	PROPN
ap-3506	96	37	,	,	PUNCT
ap-3506	96	38	x	x	X
ap-3506	96	39	)	)	PUNCT
ap-3506	96	40	=	=	SYM
ap-3506	96	41	λ(g1	λ(g1	NOUN
ap-3506	96	42	,	,	PUNCT
ap-3506	96	43	x)λ(g2	x)λ(g2	ADV
ap-3506	96	44	,	,	PUNCT
ap-3506	96	45	g	g	PROPN
ap-3506	96	46	−1	−1	NOUN
ap-3506	96	47	1	1	NUM
ap-3506	96	48	x	x	NOUN
ap-3506	96	49	)	)	PUNCT
ap-3506	96	50	.	.	PUNCT
ap-3506	97	1	let	let	VERB
ap-3506	97	2	u	u	PRON
ap-3506	97	3	be	be	AUX
ap-3506	97	4	a	a	DET
ap-3506	97	5	uir	uir	NOUN
ap-3506	97	6	which	which	PRON
ap-3506	97	7	is	be	AUX
ap-3506	97	8	square	square	ADJ
ap-3506	97	9	integrable	integrable	ADJ
ap-3506	97	10	mod(h	mod(h	NOUN
ap-3506	97	11	)	)	PUNCT
ap-3506	97	12	with	with	ADP
ap-3506	97	13	an	an	DET
ap-3506	97	14	admissible	admissible	ADJ
ap-3506	97	15	ρ	ρ	NOUN
ap-3506	97	16	,	,	PUNCT
ap-3506	97	17	i.e.	i.e.	X
ap-3506	97	18	,	,	PUNCT
ap-3506	97	19	cρ	cρ	X
ap-3506	97	20	:	:	PUNCT
ap-3506	97	21	=	=	SYM
ap-3506	97	22	∫	∫	PROPN
ap-3506	97	23	x	x	SYM
ap-3506	97	24	tr(ρρσ(x	tr(ρρσ(x	NOUN
ap-3506	97	25	)	)	PUNCT
ap-3506	97	26	)	)	PUNCT
ap-3506	98	1	dνσ(x	dνσ(x	X
ap-3506	98	2	)	)	PUNCT
ap-3506	98	3	<	<	X
ap-3506	98	4	∞	∞	PROPN
ap-3506	98	5	,	,	PUNCT
ap-3506	98	6	with	with	ADP
ap-3506	98	7	ρσ(x	ρσ(x	NOUN
ap-3506	98	8	)	)	PUNCT
ap-3506	98	9	=	=	SYM
ap-3506	99	1	u(σ(x))ρu(σ(x))†.	u(σ(x))ρu(σ(x))†.	NOUN
ap-3506	99	2	then	then	ADV
ap-3506	99	3	we	we	PRON
ap-3506	99	4	have	have	VERB
ap-3506	99	5	the	the	DET
ap-3506	99	6	resolution	resolution	NOUN
ap-3506	99	7	of	of	ADP
ap-3506	99	8	the	the	DET
ap-3506	99	9	identity	identity	NOUN
ap-3506	99	10	and	and	CCONJ
ap-3506	99	11	the	the	DET
ap-3506	99	12	resulting	result	VERB
ap-3506	99	13	quantization	quantization	NOUN
ap-3506	99	14	f	f	PROPN
ap-3506	99	15	7→	7→	NUM
ap-3506	99	16	af	af	NOUN
ap-3506	100	1	=	=	NOUN
ap-3506	101	1	1	1	NUM
ap-3506	102	1	cρ	cρ	NOUN
ap-3506	103	1	∫	∫	PROPN
ap-3506	103	2	x	x	INTJ
ap-3506	103	3	f(x)ρσ(x	f(x)ρσ(x	PROPN
ap-3506	103	4	)	)	PUNCT
ap-3506	103	5	dνσ(x	dνσ(x	PROPN
ap-3506	103	6	)	)	PUNCT
ap-3506	103	7	(	(	PUNCT
ap-3506	103	8	21	21	NUM
ap-3506	103	9	)	)	PUNCT
ap-3506	103	10	covariance	covariance	NOUN
ap-3506	103	11	holds	hold	VERB
ap-3506	103	12	here	here	ADV
ap-3506	103	13	too	too	ADV
ap-3506	103	14	in	in	ADP
ap-3506	103	15	a	a	DET
ap-3506	103	16	certain	certain	ADJ
ap-3506	103	17	sense	sense	NOUN
ap-3506	103	18	(	(	PUNCT
ap-3506	103	19	see	see	VERB
ap-3506	103	20	[	[	X
ap-3506	103	21	2	2	NUM
ap-3506	103	22	,	,	PUNCT
ap-3506	103	23	chapter	chapter	NOUN
ap-3506	103	24	11	11	NUM
ap-3506	103	25	]	]	PUNCT
ap-3506	103	26	)	)	PUNCT
ap-3506	103	27	.	.	PUNCT
ap-3506	104	1	besides	besides	SCONJ
ap-3506	104	2	the	the	DET
ap-3506	104	3	weyl	weyl	PROPN
ap-3506	104	4	-	-	PUNCT
ap-3506	104	5	heisenberg	heisenberg	PROPN
ap-3506	104	6	group	group	NOUN
ap-3506	104	7	,	,	PUNCT
ap-3506	104	8	another	another	DET
ap-3506	104	9	example	example	NOUN
ap-3506	104	10	concerns	concern	VERB
ap-3506	104	11	the	the	DET
ap-3506	104	12	motion	motion	NOUN
ap-3506	104	13	on	on	ADP
ap-3506	104	14	the	the	DET
ap-3506	104	15	circle	circle	NOUN
ap-3506	104	16	for	for	ADP
ap-3506	104	17	which	which	PRON
ap-3506	104	18	g	g	NOUN
ap-3506	104	19	is	be	AUX
ap-3506	104	20	the	the	DET
ap-3506	104	21	group	group	NOUN
ap-3506	104	22	of	of	ADP
ap-3506	104	23	euclidean	euclidean	ADJ
ap-3506	104	24	displacements	displacement	NOUN
ap-3506	104	25	in	in	ADP
ap-3506	104	26	the	the	DET
ap-3506	104	27	plane	plane	NOUN
ap-3506	104	28	,	,	PUNCT
ap-3506	104	29	i.e.	i.e.	X
ap-3506	104	30	,	,	PUNCT
ap-3506	104	31	the	the	DET
ap-3506	104	32	semi	semi	ADJ
ap-3506	104	33	-	-	ADJ
ap-3506	104	34	direct	direct	ADJ
ap-3506	104	35	product	product	NOUN
ap-3506	104	36	r2oso(2	r2oso(2	ADJ
ap-3506	104	37	)	)	PUNCT
ap-3506	104	38	,	,	PUNCT
ap-3506	104	39	and	and	CCONJ
ap-3506	104	40	the	the	DET
ap-3506	104	41	subgroup	subgroup	NOUN
ap-3506	104	42	h	h	NOUN
ap-3506	104	43	is	be	AUX
ap-3506	104	44	isomorphic	isomorphic	ADJ
ap-3506	104	45	to	to	ADP
ap-3506	104	46	r	r	NOUN
ap-3506	105	1	[	[	X
ap-3506	105	2	22	22	NUM
ap-3506	105	3	]	]	PUNCT
ap-3506	105	4	.	.	PUNCT
ap-3506	106	1	other	other	ADJ
ap-3506	106	2	examples	example	NOUN
ap-3506	106	3	involve	involve	VERB
ap-3506	106	4	the	the	DET
ap-3506	106	5	relativity	relativity	NOUN
ap-3506	106	6	groups	group	NOUN
ap-3506	106	7	,	,	PUNCT
ap-3506	106	8	galileo	galileo	PROPN
ap-3506	106	9	,	,	PUNCT
ap-3506	106	10	poincaré	poincaré	PROPN
ap-3506	107	1	[	[	X
ap-3506	107	2	2	2	NUM
ap-3506	107	3	]	]	PUNCT
ap-3506	107	4	,	,	PUNCT
ap-3506	107	5	1	1	NUM
ap-3506	107	6	+	+	SYM
ap-3506	107	7	1	1	NUM
ap-3506	107	8	anti	anti	X
ap-3506	107	9	de	de	X
ap-3506	107	10	sitter	sitter	NOUN
ap-3506	107	11	(	(	PUNCT
ap-3506	107	12	unit	unit	NOUN
ap-3506	107	13	disk	disk	NOUN
ap-3506	107	14	and	and	CCONJ
ap-3506	107	15	su(1	su(1	NOUN
ap-3506	107	16	,	,	PUNCT
ap-3506	107	17	1	1	NUM
ap-3506	107	18	)	)	PUNCT
ap-3506	107	19	)	)	PUNCT
ap-3506	108	1	[	[	X
ap-3506	108	2	21	21	NUM
ap-3506	108	3	]	]	PUNCT
ap-3506	108	4	,	,	PUNCT
ap-3506	108	5	1	1	NUM
ap-3506	108	6	+	+	SYM
ap-3506	108	7	1	1	NUM
ap-3506	108	8	and	and	CCONJ
ap-3506	108	9	3	3	NUM
ap-3506	108	10	+	+	SYM
ap-3506	108	11	1	1	NUM
ap-3506	108	12	de	de	NOUN
ap-3506	108	13	sitter	sitter	NOUN
ap-3506	108	14	[	[	X
ap-3506	108	15	23	23	NUM
ap-3506	108	16	]	]	PUNCT
ap-3506	108	17	.	.	PUNCT
ap-3506	109	1	175	175	NUM
ap-3506	109	2	jean	jean	PROPN
ap-3506	109	3	pierre	pierre	PROPN
ap-3506	109	4	gazeau	gazeau	PROPN
ap-3506	109	5	acta	acta	PROPN
ap-3506	109	6	polytechnica	polytechnica	PROPN
ap-3506	109	7	3.2	3.2	NUM
ap-3506	109	8	.	.	PUNCT
ap-3506	110	1	an	an	DET
ap-3506	110	2	example	example	NOUN
ap-3506	110	3	of	of	ADP
ap-3506	110	4	construction	construction	NOUN
ap-3506	110	5	of	of	ADP
ap-3506	110	6	original	original	ADJ
ap-3506	110	7	operator	operator	NOUN
ap-3506	110	8	m	m	PROPN
ap-3506	110	9	or	or	CCONJ
ap-3506	110	10	ρ	ρ	NOUN
ap-3506	110	11	let	let	VERB
ap-3506	110	12	u	u	PRON
ap-3506	110	13	be	be	AUX
ap-3506	110	14	a	a	DET
ap-3506	110	15	uir	uir	NOUN
ap-3506	110	16	of	of	ADP
ap-3506	110	17	g	g	NOUN
ap-3506	110	18	and	and	CCONJ
ap-3506	110	19	$	$	SYM
ap-3506	110	20	(	(	PUNCT
ap-3506	110	21	x	x	X
ap-3506	110	22	)	)	PUNCT
ap-3506	110	23	be	be	AUX
ap-3506	110	24	a	a	DET
ap-3506	110	25	function	function	NOUN
ap-3506	110	26	on	on	ADP
ap-3506	110	27	the	the	DET
ap-3506	110	28	coset	coset	NOUN
ap-3506	110	29	x	x	NOUN
ap-3506	110	30	=	=	SYM
ap-3506	110	31	g	g	PROPN
ap-3506	110	32	/	/	SYM
ap-3506	110	33	h.	h.	PROPN
ap-3506	110	34	suppose	suppose	VERB
ap-3506	110	35	that	that	SCONJ
ap-3506	110	36	it	it	PRON
ap-3506	110	37	allows	allow	VERB
ap-3506	110	38	to	to	PART
ap-3506	110	39	define	define	VERB
ap-3506	110	40	a	a	DET
ap-3506	110	41	bounded	bounded	ADJ
ap-3506	110	42	operator	operator	NOUN
ap-3506	110	43	m$	m$	ADP
ap-3506	110	44	σ	σ	NOUN
ap-3506	110	45	on	on	ADP
ap-3506	110	46	h	h	PROPN
ap-3506	110	47	through	through	ADP
ap-3506	110	48	the	the	DET
ap-3506	110	49	operatorvalued	operatorvalue	VERB
ap-3506	110	50	integral	integral	ADJ
ap-3506	110	51	m$	m$	NOUN
ap-3506	110	52	σ	σ	PROPN
ap-3506	110	53	=	=	SYM
ap-3506	110	54	∫	∫	PROPN
ap-3506	110	55	x	x	SYM
ap-3506	110	56	$	$	SYM
ap-3506	110	57	(	(	PUNCT
ap-3506	110	58	x)u(σ(x	x)u(σ(x	ADJ
ap-3506	110	59	)	)	PUNCT
ap-3506	110	60	)	)	PUNCT
ap-3506	111	1	dνσ(x	dνσ(x	PROPN
ap-3506	111	2	)	)	PUNCT
ap-3506	111	3	.	.	PUNCT
ap-3506	112	1	(	(	PUNCT
ap-3506	112	2	22	22	NUM
ap-3506	112	3	)	)	PUNCT
ap-3506	112	4	then	then	ADV
ap-3506	112	5	,	,	PUNCT
ap-3506	112	6	under	under	ADP
ap-3506	112	7	appropriate	appropriate	ADJ
ap-3506	112	8	conditions	condition	NOUN
ap-3506	112	9	on	on	ADP
ap-3506	112	10	the	the	DET
ap-3506	112	11	“	"	PUNCT
ap-3506	112	12	weight	weight	NOUN
ap-3506	112	13	”	"	PUNCT
ap-3506	112	14	function	function	NOUN
ap-3506	112	15	$	$	SYM
ap-3506	112	16	(	(	PUNCT
ap-3506	112	17	σ(x	σ(x	PROPN
ap-3506	112	18	)	)	PUNCT
ap-3506	112	19	)	)	PUNCT
ap-3506	112	20	such	such	ADJ
ap-3506	112	21	that	that	SCONJ
ap-3506	112	22	u	u	PROPN
ap-3506	112	23	be	be	VERB
ap-3506	112	24	a	a	DET
ap-3506	112	25	uir	uir	NOUN
ap-3506	112	26	which	which	PRON
ap-3506	112	27	is	be	AUX
ap-3506	112	28	square	square	ADJ
ap-3506	112	29	integrable	integrable	ADJ
ap-3506	112	30	mod(h	mod(h	NOUN
ap-3506	112	31	)	)	PUNCT
ap-3506	112	32	and	and	CCONJ
ap-3506	112	33	m$	m$	NOUN
ap-3506	112	34	σ	σ	PROPN
ap-3506	112	35	is	be	AUX
ap-3506	112	36	admissible	admissible	ADJ
ap-3506	112	37	in	in	ADP
ap-3506	112	38	the	the	DET
ap-3506	112	39	above	above	ADJ
ap-3506	112	40	sense	sense	NOUN
ap-3506	112	41	,	,	PUNCT
ap-3506	112	42	the	the	DET
ap-3506	112	43	family	family	NOUN
ap-3506	112	44	of	of	ADP
ap-3506	112	45	transported	transport	VERB
ap-3506	112	46	operators	operator	NOUN
ap-3506	112	47	m$	m$	ADP
ap-3506	112	48	σ	σ	PROPN
ap-3506	112	49	(	(	PUNCT
ap-3506	112	50	x	x	NOUN
ap-3506	112	51	)	)	PUNCT
ap-3506	112	52	:	:	PUNCT
ap-3506	113	1	=	=	SYM
ap-3506	113	2	u(σ(x))m$	u(σ(x))m$	PROPN
ap-3506	113	3	σ	σ	NUM
ap-3506	113	4	u	u	NOUN
ap-3506	113	5	†(σ(x	†(σ(x	PROPN
ap-3506	113	6	)	)	PUNCT
ap-3506	113	7	)	)	PUNCT
ap-3506	113	8	resolves	resolve	VERB
ap-3506	113	9	the	the	DET
ap-3506	113	10	identity	identity	NOUN
ap-3506	113	11	.	.	PUNCT
ap-3506	114	1	3.3	3.3	NUM
ap-3506	114	2	.	.	PUNCT
ap-3506	115	1	semi	semi	ADJ
ap-3506	115	2	-	-	ADJ
ap-3506	115	3	classical	classical	ADJ
ap-3506	115	4	portraits	portrait	NOUN
ap-3506	115	5	some	some	DET
ap-3506	115	6	quantization	quantization	NOUN
ap-3506	115	7	features	feature	NOUN
ap-3506	115	8	,	,	PUNCT
ap-3506	115	9	e.g.	e.g.	ADV
ap-3506	115	10	,	,	PUNCT
ap-3506	115	11	spectral	spectral	ADJ
ap-3506	115	12	properties	property	NOUN
ap-3506	115	13	of	of	ADP
ap-3506	115	14	af	af	PROPN
ap-3506	115	15	,	,	PUNCT
ap-3506	115	16	may	may	AUX
ap-3506	115	17	be	be	AUX
ap-3506	115	18	derived	derive	VERB
ap-3506	115	19	or	or	CCONJ
ap-3506	115	20	at	at	ADP
ap-3506	115	21	least	least	ADJ
ap-3506	115	22	well	well	ADV
ap-3506	115	23	grasped	grasp	VERB
ap-3506	115	24	from	from	ADP
ap-3506	115	25	functional	functional	ADJ
ap-3506	115	26	properties	property	NOUN
ap-3506	115	27	of	of	ADP
ap-3506	115	28	the	the	DET
ap-3506	115	29	lower	low	ADJ
ap-3506	115	30	(	(	PUNCT
ap-3506	115	31	lieb	lieb	X
ap-3506	115	32	)	)	PUNCT
ap-3506	115	33	or	or	CCONJ
ap-3506	115	34	covariant	covariant	ADJ
ap-3506	115	35	(	(	PUNCT
ap-3506	115	36	berezin	berezin	NOUN
ap-3506	115	37	)	)	PUNCT
ap-3506	115	38	symbol	symbol	NOUN
ap-3506	115	39	(	(	PUNCT
ap-3506	115	40	it	it	PRON
ap-3506	115	41	generalizes	generalize	VERB
ap-3506	115	42	husimi	husimi	ADJ
ap-3506	115	43	function	function	NOUN
ap-3506	115	44	or	or	CCONJ
ap-3506	115	45	wigner	wigner	ADJ
ap-3506	115	46	function	function	NOUN
ap-3506	115	47	)	)	PUNCT
ap-3506	115	48	af	af	PROPN
ap-3506	115	49	7→	7→	NUM
ap-3506	115	50	f̌(x	f̌(x	NUM
ap-3506	115	51	)	)	PUNCT
ap-3506	115	52	:	:	PUNCT
ap-3506	116	1	=	=	PUNCT
ap-3506	116	2	tr	tr	VERB
ap-3506	116	3	(	(	PUNCT
ap-3506	116	4	m(x)af	m(x)af	NOUN
ap-3506	116	5	)	)	PUNCT
ap-3506	116	6	,	,	PUNCT
ap-3506	116	7	(	(	PUNCT
ap-3506	116	8	23	23	NUM
ap-3506	116	9	)	)	PUNCT
ap-3506	116	10	when	when	SCONJ
ap-3506	116	11	m	m	VERB
ap-3506	116	12	=	=	SYM
ap-3506	116	13	ρ	ρ	PROPN
ap-3506	116	14	(	(	PUNCT
ap-3506	116	15	density	density	NOUN
ap-3506	116	16	operator	operator	NOUN
ap-3506	116	17	)	)	PUNCT
ap-3506	116	18	this	this	DET
ap-3506	116	19	new	new	ADJ
ap-3506	116	20	function	function	NOUN
ap-3506	116	21	is	be	AUX
ap-3506	116	22	the	the	DET
ap-3506	116	23	local	local	ADJ
ap-3506	116	24	average	average	NOUN
ap-3506	116	25	of	of	ADP
ap-3506	116	26	the	the	DET
ap-3506	116	27	original	original	ADJ
ap-3506	116	28	f	f	NOUN
ap-3506	116	29	with	with	ADP
ap-3506	116	30	respect	respect	NOUN
ap-3506	116	31	to	to	ADP
ap-3506	116	32	the	the	DET
ap-3506	116	33	probability	probability	NOUN
ap-3506	116	34	distribution	distribution	NOUN
ap-3506	116	35	tr(ρ(x)ρ(x′	tr(ρ(x)ρ(x′	ADJ
ap-3506	116	36	)	)	PUNCT
ap-3506	116	37	)	)	PUNCT
ap-3506	117	1	f(x	f(x	PROPN
ap-3506	117	2	)	)	PUNCT
ap-3506	117	3	7→	7→	NOUN
ap-3506	117	4	f̌(x	f̌(x	PROPN
ap-3506	117	5	)	)	PUNCT
ap-3506	117	6	=	=	SYM
ap-3506	118	1	∫	∫	PROPN
ap-3506	118	2	x	x	SYM
ap-3506	118	3	f(x′	f(x′	PROPN
ap-3506	118	4	)	)	PUNCT
ap-3506	118	5	tr	tr	PUNCT
ap-3506	118	6	(	(	PUNCT
ap-3506	118	7	ρ(x)ρ(x′	ρ(x)ρ(x′	ADV
ap-3506	118	8	)	)	PUNCT
ap-3506	118	9	)	)	PUNCT
ap-3506	119	1	dν(x′	dν(x′	PROPN
ap-3506	119	2	)	)	PUNCT
ap-3506	119	3	.	.	PUNCT
ap-3506	120	1	(	(	PUNCT
ap-3506	120	2	24	24	NUM
ap-3506	120	3	)	)	PUNCT
ap-3506	120	4	the	the	DET
ap-3506	120	5	bargmann	bargmann	PROPN
ap-3506	120	6	-	-	PUNCT
ap-3506	120	7	segal	segal	NOUN
ap-3506	120	8	-	-	PUNCT
ap-3506	120	9	like	like	NOUN
ap-3506	120	10	map	map	NOUN
ap-3506	120	11	f	f	PROPN
ap-3506	120	12	7→	7→	NUM
ap-3506	120	13	f̌	f̌	PROPN
ap-3506	120	14	which	which	PRON
ap-3506	120	15	,	,	PUNCT
ap-3506	120	16	generalizes	generalize	VERB
ap-3506	120	17	the	the	DET
ap-3506	120	18	berezin	berezin	NOUN
ap-3506	120	19	or	or	CCONJ
ap-3506	120	20	heat	heat	NOUN
ap-3506	120	21	kernel	kernel	NOUN
ap-3506	120	22	transform	transform	VERB
ap-3506	120	23	when	when	SCONJ
ap-3506	120	24	x	x	PROPN
ap-3506	120	25	=	=	PRON
ap-3506	120	26	g	g	PROPN
ap-3506	120	27	is	be	AUX
ap-3506	120	28	a	a	DET
ap-3506	120	29	lie	lie	NOUN
ap-3506	120	30	group	group	NOUN
ap-3506	120	31	,	,	PUNCT
ap-3506	120	32	is	be	AUX
ap-3506	120	33	in	in	ADP
ap-3506	120	34	general	general	ADJ
ap-3506	120	35	a	a	DET
ap-3506	120	36	regularization	regularization	NOUN
ap-3506	120	37	of	of	ADP
ap-3506	120	38	the	the	DET
ap-3506	120	39	original	original	ADJ
ap-3506	120	40	,	,	PUNCT
ap-3506	120	41	possibly	possibly	ADV
ap-3506	120	42	extremely	extremely	ADV
ap-3506	120	43	singular	singular	ADJ
ap-3506	120	44	,	,	PUNCT
ap-3506	120	45	f	f	PROPN
ap-3506	120	46	,	,	PUNCT
ap-3506	120	47	and	and	CCONJ
ap-3506	120	48	the	the	DET
ap-3506	120	49	classical	classical	ADJ
ap-3506	120	50	limit	limit	NOUN
ap-3506	120	51	itself	itself	PRON
ap-3506	120	52	means	mean	VERB
ap-3506	120	53	that	that	SCONJ
ap-3506	120	54	,	,	PUNCT
ap-3506	120	55	given	give	VERB
ap-3506	120	56	one	one	NUM
ap-3506	120	57	or	or	CCONJ
ap-3506	120	58	more	more	ADJ
ap-3506	120	59	scale	scale	NOUN
ap-3506	120	60	parameter(s	parameter(s	NOUN
ap-3506	120	61	)	)	PUNCT
ap-3506	120	62	ε(i	ε(i	NOUN
ap-3506	120	63	)	)	PUNCT
ap-3506	120	64	and	and	CCONJ
ap-3506	120	65	a	a	DET
ap-3506	120	66	distance	distance	NOUN
ap-3506	120	67	d(f	d(f	NOUN
ap-3506	120	68	,	,	PUNCT
ap-3506	120	69	f̌	f̌	NOUN
ap-3506	120	70	)	)	PUNCT
ap-3506	120	71	,	,	PUNCT
ap-3506	120	72	we	we	PRON
ap-3506	120	73	have	have	VERB
ap-3506	120	74	d(f	d(f	NOUN
ap-3506	120	75	,	,	PUNCT
ap-3506	120	76	f̌)→	f̌)→	PROPN
ap-3506	120	77	0	0	NUM
ap-3506	120	78	as	as	ADP
ap-3506	120	79	ε(i	ε(i	NOUN
ap-3506	120	80	)	)	PUNCT
ap-3506	120	81	→	→	SYM
ap-3506	120	82	0	0	X
ap-3506	120	83	.	.	PUNCT
ap-3506	121	1	(	(	PUNCT
ap-3506	121	2	25	25	NUM
ap-3506	121	3	)	)	PUNCT
ap-3506	121	4	3.4	3.4	NUM
ap-3506	121	5	.	.	PUNCT
ap-3506	122	1	comments	comment	NOUN
ap-3506	122	2	beyond	beyond	ADP
ap-3506	122	3	the	the	DET
ap-3506	122	4	freedom	freedom	NOUN
ap-3506	122	5	(	(	PUNCT
ap-3506	122	6	think	think	VERB
ap-3506	122	7	of	of	ADP
ap-3506	122	8	analogy	analogy	NOUN
ap-3506	122	9	with	with	ADP
ap-3506	122	10	signal	signal	ADJ
ap-3506	122	11	analysis	analysis	NOUN
ap-3506	122	12	where	where	SCONJ
ap-3506	122	13	different	different	ADJ
ap-3506	122	14	techniques	technique	NOUN
ap-3506	122	15	are	be	AUX
ap-3506	122	16	complementary	complementary	ADJ
ap-3506	122	17	)	)	PUNCT
ap-3506	122	18	allowed	allow	VERB
ap-3506	122	19	by	by	ADP
ap-3506	122	20	integral	integral	ADJ
ap-3506	122	21	quantization	quantization	NOUN
ap-3506	122	22	,	,	PUNCT
ap-3506	122	23	the	the	DET
ap-3506	122	24	advantages	advantage	NOUN
ap-3506	122	25	of	of	ADP
ap-3506	122	26	the	the	DET
ap-3506	122	27	method	method	NOUN
ap-3506	122	28	with	with	ADP
ap-3506	122	29	regard	regard	NOUN
ap-3506	122	30	to	to	ADP
ap-3506	122	31	other	other	ADJ
ap-3506	122	32	quantization	quantization	NOUN
ap-3506	122	33	procedures	procedure	NOUN
ap-3506	122	34	in	in	ADP
ap-3506	122	35	use	use	NOUN
ap-3506	122	36	are	be	AUX
ap-3506	122	37	of	of	ADP
ap-3506	122	38	four	four	NUM
ap-3506	122	39	types	type	NOUN
ap-3506	122	40	.	.	PUNCT
ap-3506	123	1	(	(	PUNCT
ap-3506	123	2	i)the	i)the	DET
ap-3506	123	3	minimal	minimal	ADJ
ap-3506	123	4	amount	amount	NOUN
ap-3506	123	5	of	of	ADP
ap-3506	123	6	constraints	constraint	NOUN
ap-3506	123	7	imposed	impose	VERB
ap-3506	123	8	on	on	ADP
ap-3506	123	9	the	the	DET
ap-3506	123	10	classical	classical	ADJ
ap-3506	123	11	objects	object	NOUN
ap-3506	123	12	to	to	PART
ap-3506	123	13	be	be	AUX
ap-3506	123	14	quantized	quantize	VERB
ap-3506	123	15	.	.	PUNCT
ap-3506	124	1	(	(	PUNCT
ap-3506	124	2	ii)once	ii)once	VERB
ap-3506	124	3	a	a	DET
ap-3506	124	4	choice	choice	NOUN
ap-3506	124	5	of	of	ADP
ap-3506	124	6	(	(	PUNCT
ap-3506	124	7	positive	positive	ADJ
ap-3506	124	8	)	)	PUNCT
ap-3506	124	9	operator	operator	NOUN
ap-3506	124	10	-	-	PUNCT
ap-3506	124	11	valued	value	VERB
ap-3506	124	12	measure	measure	NOUN
ap-3506	124	13	has	have	AUX
ap-3506	124	14	been	be	AUX
ap-3506	124	15	made	make	VERB
ap-3506	124	16	,	,	PUNCT
ap-3506	124	17	which	which	PRON
ap-3506	124	18	must	must	AUX
ap-3506	124	19	be	be	AUX
ap-3506	124	20	consistent	consistent	ADJ
ap-3506	124	21	with	with	ADP
ap-3506	124	22	experiment	experiment	NOUN
ap-3506	124	23	,	,	PUNCT
ap-3506	124	24	there	there	PRON
ap-3506	124	25	is	be	VERB
ap-3506	124	26	no	no	DET
ap-3506	124	27	ambiguity	ambiguity	NOUN
ap-3506	124	28	in	in	ADP
ap-3506	124	29	the	the	DET
ap-3506	124	30	issue	issue	NOUN
ap-3506	124	31	,	,	PUNCT
ap-3506	124	32	contrarily	contrarily	ADV
ap-3506	124	33	to	to	ADP
ap-3506	124	34	other	other	ADJ
ap-3506	124	35	method(s	method(s	PROPN
ap-3506	124	36	)	)	PUNCT
ap-3506	124	37	in	in	ADP
ap-3506	124	38	use	use	NOUN
ap-3506	124	39	(	(	PUNCT
ap-3506	124	40	think	think	VERB
ap-3506	124	41	in	in	ADP
ap-3506	124	42	particular	particular	ADJ
ap-3506	124	43	of	of	ADP
ap-3506	124	44	the	the	DET
ap-3506	124	45	ordering	ordering	NOUN
ap-3506	124	46	problem	problem	NOUN
ap-3506	124	47	)	)	PUNCT
ap-3506	124	48	.	.	PUNCT
ap-3506	125	1	to	to	ADP
ap-3506	125	2	one	one	NUM
ap-3506	125	3	classical	classical	ADJ
ap-3506	125	4	model	model	NOUN
ap-3506	125	5	corresponds	correspond	VERB
ap-3506	125	6	one	one	NUM
ap-3506	125	7	and	and	CCONJ
ap-3506	125	8	only	only	ADV
ap-3506	125	9	one	one	NUM
ap-3506	125	10	quantum	quantum	NOUN
ap-3506	125	11	model	model	NOUN
ap-3506	125	12	.	.	PUNCT
ap-3506	126	1	of	of	ADP
ap-3506	126	2	course	course	VERB
ap-3506	126	3	different	different	ADJ
ap-3506	126	4	choices	choice	NOUN
ap-3506	126	5	of	of	ADP
ap-3506	126	6	(	(	PUNCT
ap-3506	126	7	p)ovm	p)ovm	NOUN
ap-3506	126	8	are	be	AUX
ap-3506	126	9	requested	request	VERB
ap-3506	126	10	to	to	PART
ap-3506	126	11	be	be	AUX
ap-3506	126	12	physically	physically	ADV
ap-3506	126	13	equivalent	equivalent	ADJ
ap-3506	126	14	,	,	PUNCT
ap-3506	126	15	e.g.	e.g.	ADV
ap-3506	126	16	,	,	PUNCT
ap-3506	126	17	leading	lead	VERB
ap-3506	126	18	to	to	ADP
ap-3506	126	19	the	the	DET
ap-3506	126	20	same	same	ADJ
ap-3506	126	21	experimental	experimental	ADJ
ap-3506	126	22	predictions	prediction	NOUN
ap-3506	126	23	,	,	PUNCT
ap-3506	126	24	if	if	SCONJ
ap-3506	126	25	they	they	PRON
ap-3506	126	26	are	be	AUX
ap-3506	126	27	aimed	aim	VERB
ap-3506	126	28	to	to	PART
ap-3506	126	29	describe	describe	VERB
ap-3506	126	30	one	one	NUM
ap-3506	126	31	specific	specific	ADJ
ap-3506	126	32	system	system	NOUN
ap-3506	126	33	.	.	PUNCT
ap-3506	127	1	(	(	PUNCT
ap-3506	127	2	iii)the	iii)the	DET
ap-3506	127	3	method	method	NOUN
ap-3506	127	4	produces	produce	VERB
ap-3506	127	5	in	in	ADP
ap-3506	127	6	essence	essence	NOUN
ap-3506	127	7	a	a	DET
ap-3506	127	8	regularizing	regularize	VERB
ap-3506	127	9	effect	effect	NOUN
ap-3506	127	10	,	,	PUNCT
ap-3506	127	11	at	at	ADP
ap-3506	127	12	the	the	DET
ap-3506	127	13	exception	exception	NOUN
ap-3506	127	14	of	of	ADP
ap-3506	127	15	certain	certain	ADJ
ap-3506	127	16	choices	choice	NOUN
ap-3506	127	17	,	,	PUNCT
ap-3506	127	18	like	like	ADP
ap-3506	127	19	the	the	DET
ap-3506	127	20	weyl	weyl	NOUN
ap-3506	127	21	-	-	PUNCT
ap-3506	127	22	wigner	wigner	NOUN
ap-3506	127	23	(	(	PUNCT
ap-3506	127	24	i.e.	i.e.	X
ap-3506	127	25	,	,	PUNCT
ap-3506	127	26	canonical	canonical	ADJ
ap-3506	127	27	)	)	PUNCT
ap-3506	127	28	integral	integral	ADJ
ap-3506	127	29	quantization	quantization	NOUN
ap-3506	127	30	.	.	PUNCT
ap-3506	128	1	(	(	PUNCT
ap-3506	128	2	iv)the	iv)the	DET
ap-3506	128	3	method	method	NOUN
ap-3506	128	4	,	,	PUNCT
ap-3506	128	5	through	through	ADP
ap-3506	128	6	povm	povm	ADJ
ap-3506	128	7	choices	choice	NOUN
ap-3506	128	8	,	,	PUNCT
ap-3506	128	9	offers	offer	VERB
ap-3506	128	10	the	the	DET
ap-3506	128	11	possibility	possibility	NOUN
ap-3506	128	12	to	to	PART
ap-3506	128	13	keep	keep	VERB
ap-3506	128	14	a	a	DET
ap-3506	128	15	fully	fully	ADV
ap-3506	128	16	probabilistic	probabilistic	ADJ
ap-3506	128	17	content	content	NOUN
ap-3506	128	18	.	.	PUNCT
ap-3506	129	1	as	as	ADP
ap-3506	129	2	a	a	DET
ap-3506	129	3	matter	matter	NOUN
ap-3506	129	4	of	of	ADP
ap-3506	129	5	fact	fact	NOUN
ap-3506	129	6	,	,	PUNCT
ap-3506	129	7	the	the	DET
ap-3506	129	8	weyl	weyl	VERB
ap-3506	129	9	-	-	PUNCT
ap-3506	129	10	wigner	wigner	ADJ
ap-3506	129	11	integral	integral	ADJ
ap-3506	129	12	quantization	quantization	NOUN
ap-3506	129	13	does	do	AUX
ap-3506	129	14	not	not	PART
ap-3506	129	15	rest	rest	VERB
ap-3506	129	16	on	on	ADP
ap-3506	129	17	a	a	DET
ap-3506	129	18	povm	povm	NOUN
ap-3506	129	19	.	.	PUNCT
ap-3506	130	1	4	4	X
ap-3506	130	2	.	.	X
ap-3506	130	3	weyl	weyl	PROPN
ap-3506	130	4	-	-	PUNCT
ap-3506	130	5	heisenberg	heisenberg	PROPN
ap-3506	130	6	covariant	covariant	PROPN
ap-3506	130	7	integral	integral	ADJ
ap-3506	130	8	quantization(s	quantization(s	NOUN
ap-3506	130	9	)	)	PUNCT
ap-3506	130	10	the	the	DET
ap-3506	130	11	weyl	weyl	PROPN
ap-3506	130	12	-	-	PUNCT
ap-3506	130	13	heisenberg	heisenberg	PROPN
ap-3506	130	14	group	group	NOUN
ap-3506	130	15	is	be	AUX
ap-3506	130	16	defined	define	VERB
ap-3506	130	17	as	as	ADP
ap-3506	130	18	gwh	gwh	NOUN
ap-3506	130	19	=	=	SYM
ap-3506	130	20	{	{	PUNCT
ap-3506	130	21	(	(	PUNCT
ap-3506	130	22	s	s	X
ap-3506	130	23	,	,	PUNCT
ap-3506	130	24	z	z	NOUN
ap-3506	130	25	)	)	PUNCT
ap-3506	131	1	|	|	ADV
ap-3506	131	2	s	s	VERB
ap-3506	131	3	∈	∈	PROPN
ap-3506	131	4	r	r	NOUN
ap-3506	131	5	,	,	PUNCT
ap-3506	131	6	z	z	PROPN
ap-3506	131	7	∈	∈	PROPN
ap-3506	131	8	c	c	NOUN
ap-3506	131	9	}	}	PUNCT
ap-3506	131	10	with	with	ADP
ap-3506	131	11	multiplication	multiplication	NOUN
ap-3506	131	12	law	law	NOUN
ap-3506	131	13	(	(	PUNCT
ap-3506	131	14	s	s	PROPN
ap-3506	131	15	,	,	PUNCT
ap-3506	131	16	z)(s′	z)(s′	PROPN
ap-3506	131	17	,	,	PUNCT
ap-3506	131	18	z′	z′	NUM
ap-3506	131	19	)	)	PUNCT
ap-3506	131	20	=	=	NOUN
ap-3506	131	21	(	(	PUNCT
ap-3506	131	22	s+	s+	X
ap-3506	131	23	s′	s′	X
ap-3506	131	24	+	+	CCONJ
ap-3506	131	25	im(zz̄′	im(zz̄′	PROPN
ap-3506	131	26	)	)	PUNCT
ap-3506	131	27	,	,	PUNCT
ap-3506	131	28	z	z	PROPN
ap-3506	131	29	+	+	CCONJ
ap-3506	131	30	z′	z′	NUM
ap-3506	131	31	)	)	PUNCT
ap-3506	131	32	(	(	PUNCT
ap-3506	131	33	26	26	NUM
ap-3506	131	34	)	)	PUNCT
ap-3506	131	35	let	let	VERB
ap-3506	131	36	h	h	NOUN
ap-3506	131	37	be	be	AUX
ap-3506	131	38	a	a	DET
ap-3506	131	39	separable	separable	ADJ
ap-3506	131	40	(	(	PUNCT
ap-3506	131	41	complex	complex	ADJ
ap-3506	131	42	)	)	PUNCT
ap-3506	131	43	hilbert	hilbert	NOUN
ap-3506	131	44	space	space	NOUN
ap-3506	131	45	with	with	ADP
ap-3506	131	46	orthonormal	orthonormal	ADJ
ap-3506	131	47	basis	basis	NOUN
ap-3506	131	48	e0	e0	NOUN
ap-3506	131	49	,	,	PUNCT
ap-3506	131	50	e1	e1	PROPN
ap-3506	131	51	,	,	PUNCT
ap-3506	131	52	.	.	PUNCT
ap-3506	131	53	.	.	PUNCT
ap-3506	132	1	.	.	PUNCT
ap-3506	133	1	,	,	PUNCT
ap-3506	133	2	en	en	PROPN
ap-3506	133	3	≡	≡	PROPN
ap-3506	133	4	|en	|en	PROPN
ap-3506	133	5	〉	〉	PROPN
ap-3506	133	6	,	,	PUNCT
ap-3506	133	7	.	.	PUNCT
ap-3506	133	8	.	.	PUNCT
ap-3506	133	9	.	.	PUNCT
ap-3506	134	1	,	,	PUNCT
ap-3506	135	1	and	and	CCONJ
ap-3506	135	2	corresponding	correspond	VERB
ap-3506	135	3	lowering	lowering	NOUN
ap-3506	135	4	and	and	CCONJ
ap-3506	135	5	raising	raise	VERB
ap-3506	135	6	operators	operator	NOUN
ap-3506	135	7	defined	define	VERB
ap-3506	135	8	in	in	ADP
ap-3506	135	9	the	the	DET
ap-3506	135	10	usual	usual	ADJ
ap-3506	135	11	way	way	NOUN
ap-3506	135	12	a|en	a|en	X
ap-3506	135	13	〉	〉	NOUN
ap-3506	135	14	=	=	SYM
ap-3506	135	15	√	√	PROPN
ap-3506	135	16	n|en−1	n|en−1	PROPN
ap-3506	135	17	〉	〉	PROPN
ap-3506	135	18	,	,	PUNCT
ap-3506	135	19	a|e0	a|e0	NOUN
ap-3506	135	20	〉	〉	NOUN
ap-3506	135	21	=	=	SYM
ap-3506	135	22	0	0	NUM
ap-3506	135	23	,	,	PUNCT
ap-3506	135	24	a†|en	a†|en	VERB
ap-3506	135	25	〉	〉	NOUN
ap-3506	135	26	=	=	SYM
ap-3506	135	27	√	√	PROPN
ap-3506	135	28	n+	n+	NUM
ap-3506	135	29	1|en+1	1|en+1	NUM
ap-3506	135	30	〉	〉	NUM
ap-3506	135	31	,	,	PUNCT
ap-3506	135	32	[	[	X
ap-3506	135	33	a	a	X
ap-3506	135	34	,	,	PUNCT
ap-3506	135	35	a†	a†	NOUN
ap-3506	135	36	]	]	PUNCT
ap-3506	136	1	=	=	SYM
ap-3506	136	2	i	i	PROPN
ap-3506	136	3	,	,	PUNCT
ap-3506	136	4	it	it	PRON
ap-3506	136	5	is	be	AUX
ap-3506	136	6	well	well	ADV
ap-3506	136	7	known	know	VERB
ap-3506	136	8	that	that	SCONJ
ap-3506	136	9	the	the	DET
ap-3506	136	10	weyl	weyl	PROPN
ap-3506	136	11	-	-	PUNCT
ap-3506	136	12	heisenberg	heisenberg	PROPN
ap-3506	136	13	group	group	NOUN
ap-3506	136	14	has	have	VERB
ap-3506	136	15	a	a	DET
ap-3506	136	16	unique	unique	ADJ
ap-3506	136	17	non	non	ADJ
ap-3506	136	18	-	-	ADJ
ap-3506	136	19	trivial	trivial	ADJ
ap-3506	136	20	uir	uir	NOUN
ap-3506	136	21	u	u	NOUN
ap-3506	136	22	,	,	PUNCT
ap-3506	136	23	up	up	ADP
ap-3506	136	24	to	to	ADP
ap-3506	136	25	unitary	unitary	ADJ
ap-3506	136	26	equivalence	equivalence	NOUN
ap-3506	136	27	,	,	PUNCT
ap-3506	136	28	each	each	DET
ap-3506	136	29	element	element	NOUN
ap-3506	136	30	in	in	ADP
ap-3506	136	31	this	this	DET
ap-3506	136	32	equivalence	equivalence	NOUN
ap-3506	136	33	class	class	NOUN
ap-3506	136	34	corresponding	correspond	VERB
ap-3506	136	35	to	to	ADP
ap-3506	136	36	a	a	DET
ap-3506	136	37	non	non	ADJ
ap-3506	136	38	-	-	ADJ
ap-3506	136	39	zero	zero	ADJ
ap-3506	136	40	real	real	ADJ
ap-3506	136	41	number	number	NOUN
ap-3506	136	42	like	like	ADP
ap-3506	136	43	the	the	DET
ap-3506	136	44	planck	planck	NOUN
ap-3506	136	45	constant	constant	ADJ
ap-3506	136	46	.	.	PUNCT
ap-3506	137	1	consider	consider	VERB
ap-3506	137	2	the	the	DET
ap-3506	137	3	center	center	NOUN
ap-3506	137	4	c	c	NOUN
ap-3506	138	1	=	=	PRON
ap-3506	138	2	{	{	PUNCT
ap-3506	138	3	(	(	PUNCT
ap-3506	138	4	s	s	X
ap-3506	138	5	,	,	PUNCT
ap-3506	138	6	0	0	NUM
ap-3506	138	7	)	)	PUNCT
ap-3506	139	1	|	|	ADV
ap-3506	139	2	s	s	X
ap-3506	139	3	∈	∈	PROPN
ap-3506	139	4	r	r	NOUN
ap-3506	139	5	}	}	PUNCT
ap-3506	139	6	of	of	ADP
ap-3506	139	7	gwh	gwh	PROPN
ap-3506	139	8	.	.	PUNCT
ap-3506	140	1	then	then	ADV
ap-3506	140	2	,	,	PUNCT
ap-3506	140	3	the	the	DET
ap-3506	140	4	set	set	NOUN
ap-3506	140	5	x	x	PUNCT
ap-3506	140	6	is	be	AUX
ap-3506	140	7	the	the	DET
ap-3506	140	8	coset	coset	NOUN
ap-3506	140	9	x	x	NOUN
ap-3506	140	10	=	=	SYM
ap-3506	140	11	gwh	gwh	NOUN
ap-3506	140	12	/	/	SYM
ap-3506	140	13	c	c	NOUN
ap-3506	140	14	∼	∼	NOUN
ap-3506	140	15	c	c	NOUN
ap-3506	140	16	with	with	ADP
ap-3506	140	17	measure	measure	NOUN
ap-3506	140	18	d2z	d2z	X
ap-3506	140	19	/	/	SYM
ap-3506	140	20	π	π	PROPN
ap-3506	140	21	.	.	PUNCT
ap-3506	141	1	choosing	choose	VERB
ap-3506	141	2	the	the	DET
ap-3506	141	3	trivial	trivial	ADJ
ap-3506	141	4	section	section	NOUN
ap-3506	141	5	c	c	PROPN
ap-3506	141	6	3	3	NUM
ap-3506	141	7	z	z	SYM
ap-3506	141	8	7→	7→	NUM
ap-3506	141	9	σ(z	σ(z	NOUN
ap-3506	141	10	)	)	PUNCT
ap-3506	141	11	=	=	PUNCT
ap-3506	141	12	(	(	PUNCT
ap-3506	141	13	0	0	NUM
ap-3506	141	14	,	,	PUNCT
ap-3506	141	15	z	z	NOUN
ap-3506	141	16	)	)	PUNCT
ap-3506	141	17	,	,	PUNCT
ap-3506	141	18	to	to	ADP
ap-3506	141	19	each	each	DET
ap-3506	141	20	z	z	NOUN
ap-3506	141	21	corresponds	correspond	VERB
ap-3506	141	22	the	the	DET
ap-3506	141	23	(	(	PUNCT
ap-3506	141	24	unitary	unitary	ADJ
ap-3506	141	25	)	)	PUNCT
ap-3506	141	26	displacement	displacement	NOUN
ap-3506	141	27	(	(	PUNCT
ap-3506	141	28	∼	∼	NOUN
ap-3506	141	29	weyl	weyl	VERB
ap-3506	141	30	)	)	PUNCT
ap-3506	141	31	operator	operator	NOUN
ap-3506	141	32	d(z	d(z	NOUN
ap-3506	141	33	)	)	PUNCT
ap-3506	141	34	:	:	PUNCT
ap-3506	141	35	=	=	PUNCT
ap-3506	141	36	u(σ(z	u(σ(z	NOUN
ap-3506	141	37	)	)	PUNCT
ap-3506	141	38	)	)	PUNCT
ap-3506	142	1	=	=	SYM
ap-3506	142	2	eza	eza	PROPN
ap-3506	142	3	†−z̄a	†−z̄a	PROPN
ap-3506	142	4	,	,	PUNCT
ap-3506	142	5	d(−z	d(−z	NOUN
ap-3506	142	6	)	)	PUNCT
ap-3506	142	7	=	=	SYM
ap-3506	142	8	(	(	PUNCT
ap-3506	142	9	d(z))−1	d(z))−1	NOUN
ap-3506	142	10	=	=	PUNCT
ap-3506	142	11	d(z)†.	d(z)†.	PROPN
ap-3506	142	12	(	(	PUNCT
ap-3506	142	13	27	27	NUM
ap-3506	142	14	)	)	PUNCT
ap-3506	142	15	the	the	DET
ap-3506	142	16	noncommutativity	noncommutativity	NOUN
ap-3506	142	17	of	of	ADP
ap-3506	142	18	quantum	quantum	ADJ
ap-3506	142	19	mechanics	mechanic	NOUN
ap-3506	142	20	is	be	AUX
ap-3506	142	21	encoded	encode	VERB
ap-3506	142	22	in	in	ADP
ap-3506	142	23	the	the	DET
ap-3506	142	24	relation	relation	NOUN
ap-3506	142	25	d(z)d(z′	d(z)d(z′	NOUN
ap-3506	142	26	)	)	PUNCT
ap-3506	142	27	=	=	SYM
ap-3506	143	1	e	e	NOUN
ap-3506	143	2	1	1	NUM
ap-3506	143	3	2	2	NUM
ap-3506	143	4	(	(	PUNCT
ap-3506	143	5	zz̄′−z̄z′)d(z	zz̄′−z̄z′)d(z	NOUN
ap-3506	143	6	+	+	CCONJ
ap-3506	143	7	z′	z′	NUM
ap-3506	143	8	)	)	PUNCT
ap-3506	143	9	=	=	PUNCT
ap-3506	144	1	e(zz̄′−z̄z′)d(z′)d(z	e(zz̄′−z̄z′)d(z′)d(z	NOUN
ap-3506	144	2	)	)	PUNCT
ap-3506	144	3	,	,	PUNCT
ap-3506	144	4	(	(	PUNCT
ap-3506	144	5	28	28	NUM
ap-3506	144	6	)	)	PUNCT
ap-3506	144	7	i.e.	i.e.	X
ap-3506	144	8	,	,	PUNCT
ap-3506	144	9	z	z	PROPN
ap-3506	144	10	7→	7→	NUM
ap-3506	144	11	d(z	d(z	PROPN
ap-3506	144	12	)	)	PUNCT
ap-3506	144	13	is	be	AUX
ap-3506	144	14	a	a	DET
ap-3506	144	15	projective	projective	ADJ
ap-3506	144	16	representation	representation	NOUN
ap-3506	144	17	of	of	ADP
ap-3506	144	18	the	the	DET
ap-3506	144	19	abelian	abelian	PROPN
ap-3506	144	20	group	group	PROPN
ap-3506	144	21	c.	c.	PROPN
ap-3506	145	1	the	the	DET
ap-3506	145	2	standard	standard	PROPN
ap-3506	145	3	(	(	PUNCT
ap-3506	145	4	i.e.	i.e.	X
ap-3506	145	5	,	,	PUNCT
ap-3506	145	6	schrödingerklauder	schrödingerklauder	NOUN
ap-3506	145	7	-	-	PUNCT
ap-3506	145	8	glauber	glauber	PROPN
ap-3506	145	9	-	-	PUNCT
ap-3506	145	10	sudarshan	sudarshan	PROPN
ap-3506	145	11	)	)	PUNCT
ap-3506	145	12	cs	cs	PROPN
ap-3506	145	13	are	be	AUX
ap-3506	145	14	defined	define	VERB
ap-3506	145	15	as	as	ADP
ap-3506	145	16	|z	|z	PROPN
ap-3506	145	17	〉	〉	PROPN
ap-3506	145	18	=	=	PUNCT
ap-3506	146	1	d(z)|e0	d(z)|e0	VERB
ap-3506	146	2	〉	〉	PROPN
ap-3506	146	3	.	.	PUNCT
ap-3506	147	1	(	(	PUNCT
ap-3506	147	2	29	29	NUM
ap-3506	147	3	)	)	PUNCT
ap-3506	147	4	we	we	PRON
ap-3506	147	5	now	now	ADV
ap-3506	147	6	adopt	adopt	VERB
ap-3506	147	7	the	the	DET
ap-3506	147	8	construction	construction	NOUN
ap-3506	147	9	sketched	sketched	NOUN
ap-3506	147	10	in	in	ADP
ap-3506	147	11	section	section	NOUN
ap-3506	147	12	3.2	3.2	NUM
ap-3506	147	13	.	.	PUNCT
ap-3506	148	1	let	let	VERB
ap-3506	148	2	$	$	SYM
ap-3506	148	3	(	(	PUNCT
ap-3506	148	4	z	z	NOUN
ap-3506	148	5	)	)	PUNCT
ap-3506	148	6	be	be	AUX
ap-3506	148	7	a	a	DET
ap-3506	148	8	function	function	NOUN
ap-3506	148	9	on	on	ADP
ap-3506	148	10	the	the	DET
ap-3506	148	11	complex	complex	ADJ
ap-3506	148	12	plane	plane	NOUN
ap-3506	148	13	obeying	obey	VERB
ap-3506	148	14	$	$	SYM
ap-3506	148	15	(	(	PUNCT
ap-3506	148	16	0	0	NUM
ap-3506	148	17	)	)	PUNCT
ap-3506	148	18	=	=	SYM
ap-3506	149	1	1	1	X
ap-3506	149	2	.	.	PUNCT
ap-3506	149	3	suppose	suppose	VERB
ap-3506	149	4	that	that	SCONJ
ap-3506	149	5	it	it	PRON
ap-3506	149	6	allows	allow	VERB
ap-3506	149	7	to	to	PART
ap-3506	149	8	define	define	VERB
ap-3506	149	9	a	a	DET
ap-3506	149	10	fiducial	fiducial	ADJ
ap-3506	149	11	operator	operator	NOUN
ap-3506	149	12	m$	m$	NOUN
ap-3506	149	13	on	on	ADP
ap-3506	149	14	h	h	NOUN
ap-3506	149	15	through	through	ADP
ap-3506	149	16	the	the	DET
ap-3506	149	17	operator	operator	NOUN
ap-3506	149	18	-	-	PUNCT
ap-3506	149	19	valued	value	VERB
ap-3506	149	20	integral	integral	ADJ
ap-3506	149	21	m$	m$	NOUN
ap-3506	149	22	=	=	SYM
ap-3506	149	23	∫	∫	PROPN
ap-3506	149	24	c	c	NOUN
ap-3506	149	25	$	$	SYM
ap-3506	149	26	(	(	PUNCT
ap-3506	149	27	z)d(z)d2z	z)d(z)d2z	PROPN
ap-3506	149	28	π	π	NOUN
ap-3506	149	29	.	.	PUNCT
ap-3506	150	1	(	(	PUNCT
ap-3506	150	2	30	30	NUM
ap-3506	150	3	)	)	PUNCT
ap-3506	150	4	then	then	ADV
ap-3506	150	5	,	,	PUNCT
ap-3506	150	6	the	the	DET
ap-3506	150	7	family	family	NOUN
ap-3506	150	8	of	of	ADP
ap-3506	150	9	displaced	displace	VERB
ap-3506	150	10	m$(z	m$(z	NOUN
ap-3506	150	11	)	)	PUNCT
ap-3506	150	12	:	:	PUNCT
ap-3506	151	1	=	=	SYM
ap-3506	151	2	d(z)m$d(z)†	d(z)m$d(z)†	NOUN
ap-3506	151	3	under	under	ADP
ap-3506	151	4	the	the	DET
ap-3506	151	5	unitary	unitary	ADJ
ap-3506	151	6	action	action	NOUN
ap-3506	151	7	d(z	d(z	NOUN
ap-3506	151	8	)	)	PUNCT
ap-3506	151	9	resolves	resolve	VERB
ap-3506	151	10	the	the	DET
ap-3506	151	11	identity	identity	NOUN
ap-3506	151	12	∫	∫	PROPN
ap-3506	151	13	c	c	PROPN
ap-3506	151	14	m$(z)d2z	m$(z)d2z	PROPN
ap-3506	151	15	π	π	X
ap-3506	151	16	=	=	PUNCT
ap-3506	151	17	i.	i.	PROPN
ap-3506	151	18	(	(	PUNCT
ap-3506	151	19	31	31	NUM
ap-3506	151	20	)	)	PUNCT
ap-3506	151	21	176	176	NUM
ap-3506	151	22	vol	vol	NOUN
ap-3506	151	23	.	.	PUNCT
ap-3506	152	1	56	56	NUM
ap-3506	152	2	no	no	NOUN
ap-3506	152	3	.	.	PUNCT
ap-3506	153	1	3/2016	3/2016	NUM
ap-3506	153	2	covariant	covariant	ADJ
ap-3506	153	3	integral	integral	ADJ
ap-3506	153	4	quantizations	quantization	NOUN
ap-3506	153	5	and	and	CCONJ
ap-3506	153	6	quantum	quantum	ADJ
ap-3506	153	7	cosmology	cosmology	NOUN
ap-3506	153	8	it	it	PRON
ap-3506	153	9	is	be	AUX
ap-3506	153	10	a	a	DET
ap-3506	153	11	direct	direct	ADJ
ap-3506	153	12	consequence	consequence	NOUN
ap-3506	153	13	of	of	ADP
ap-3506	153	14	d(z)d(z′)d(z)†	d(z)d(z′)d(z)†	NOUN
ap-3506	153	15	=	=	SYM
ap-3506	153	16	ezz̄	ezz̄	NOUN
ap-3506	153	17	′−z̄z′	′−z̄z′	PROPN
ap-3506	153	18	d(z′	d(z′	PROPN
ap-3506	153	19	)	)	PUNCT
ap-3506	153	20	,	,	PUNCT
ap-3506	153	21	of	of	ADP
ap-3506	153	22	∫	∫	PROPN
ap-3506	153	23	c	c	PROPN
ap-3506	153	24	e	e	PROPN
ap-3506	153	25	zξ̄−z̄ξ	zξ̄−z̄ξ	PROPN
ap-3506	153	26	d2ξ	d2ξ	PROPN
ap-3506	153	27	π	π	NOUN
ap-3506	153	28	=	=	PUNCT
ap-3506	153	29	πδ2(z	πδ2(z	PROPN
ap-3506	153	30	)	)	PUNCT
ap-3506	153	31	,	,	PUNCT
ap-3506	153	32	and	and	CCONJ
ap-3506	153	33	of	of	ADP
ap-3506	153	34	$	$	SYM
ap-3506	153	35	(	(	PUNCT
ap-3506	153	36	0	0	NUM
ap-3506	153	37	)	)	PUNCT
ap-3506	153	38	=	=	SYM
ap-3506	153	39	1	1	NUM
ap-3506	153	40	with	with	ADP
ap-3506	153	41	d(0	d(0	NOUN
ap-3506	153	42	)	)	PUNCT
ap-3506	154	1	=	=	SYM
ap-3506	154	2	i.	i.	NOUN
ap-3506	154	3	the	the	DET
ap-3506	154	4	resulting	result	VERB
ap-3506	154	5	quantization	quantization	NOUN
ap-3506	154	6	map	map	NOUN
ap-3506	154	7	is	be	AUX
ap-3506	154	8	given	give	VERB
ap-3506	154	9	by	by	ADP
ap-3506	154	10	f	f	PROPN
ap-3506	154	11	7→	7→	NUM
ap-3506	154	12	a$f	a$f	NOUN
ap-3506	154	13	=	=	SYM
ap-3506	154	14	∫	∫	PROPN
ap-3506	154	15	c	c	NOUN
ap-3506	154	16	m$(z)f(z)d2z	m$(z)f(z)d2z	PROPN
ap-3506	155	1	π	π	X
ap-3506	155	2	=	=	SYM
ap-3506	155	3	∫	∫	PROPN
ap-3506	155	4	c	c	NOUN
ap-3506	155	5	$	$	SYM
ap-3506	155	6	(	(	PUNCT
ap-3506	155	7	z)d(z)fs[f	z)d(z)fs[f	NOUN
ap-3506	155	8	]	]	X
ap-3506	155	9	(	(	PUNCT
ap-3506	155	10	z)d2z	z)d2z	PROPN
ap-3506	155	11	π	π	PROPN
ap-3506	155	12	,	,	PUNCT
ap-3506	155	13	(	(	PUNCT
ap-3506	155	14	32	32	NUM
ap-3506	155	15	)	)	PUNCT
ap-3506	155	16	where	where	SCONJ
ap-3506	155	17	are	be	AUX
ap-3506	155	18	involved	involve	VERB
ap-3506	155	19	the	the	DET
ap-3506	155	20	symplectic	symplectic	ADJ
ap-3506	155	21	fourier	fourier	NOUN
ap-3506	155	22	transforms	transform	VERB
ap-3506	155	23	fs	fs	ADP
ap-3506	155	24	and	and	CCONJ
ap-3506	155	25	its	its	PRON
ap-3506	155	26	space	space	NOUN
ap-3506	155	27	reverse	reverse	NOUN
ap-3506	155	28	fs	fs	ADP
ap-3506	155	29	fs[f	fs[f	PROPN
ap-3506	155	30	]	]	PUNCT
ap-3506	155	31	(	(	PUNCT
ap-3506	155	32	z	z	NOUN
ap-3506	155	33	)	)	PUNCT
ap-3506	155	34	=	=	SYM
ap-3506	156	1	∫	∫	PROPN
ap-3506	156	2	c	c	X
ap-3506	156	3	ezξ̄−z̄ξf(ξ)d2ξ	ezξ̄−z̄ξf(ξ)d2ξ	PROPN
ap-3506	156	4	π	π	PROPN
ap-3506	156	5	,	,	PUNCT
ap-3506	156	6	fs[f	fs[f	PROPN
ap-3506	156	7	]	]	PUNCT
ap-3506	156	8	(	(	PUNCT
ap-3506	156	9	z	z	NOUN
ap-3506	156	10	)	)	PUNCT
ap-3506	156	11	=	=	SYM
ap-3506	156	12	fs[f	fs[f	NOUN
ap-3506	156	13	]	]	PUNCT
ap-3506	156	14	(	(	PUNCT
ap-3506	156	15	−z	−z	NOUN
ap-3506	156	16	)	)	PUNCT
ap-3506	156	17	both	both	PRON
ap-3506	156	18	are	be	AUX
ap-3506	156	19	unipotent	unipotent	ADJ
ap-3506	156	20	fs[fs[f	fs[fs[f	NOUN
ap-3506	156	21	]	]	X
ap-3506	156	22	]	]	PUNCT
ap-3506	156	23	=	=	SYM
ap-3506	156	24	f	f	PROPN
ap-3506	156	25	and	and	CCONJ
ap-3506	156	26	fs[fs[f	fs[fs[f	NOUN
ap-3506	156	27	]	]	PUNCT
ap-3506	156	28	]	]	PUNCT
ap-3506	157	1	=	=	SYM
ap-3506	157	2	f	f	X
ap-3506	157	3	.	.	PUNCT
ap-3506	158	1	we	we	PRON
ap-3506	158	2	have	have	VERB
ap-3506	158	3	the	the	DET
ap-3506	158	4	following	follow	VERB
ap-3506	158	5	covariance	covariance	NOUN
ap-3506	158	6	properties	property	NOUN
ap-3506	158	7	•	•	NUM
ap-3506	158	8	translation	translation	NOUN
ap-3506	158	9	covariance	covariance	NOUN
ap-3506	158	10	:	:	PUNCT
ap-3506	158	11	a$f(z−z0	a$f(z−z0	NOUN
ap-3506	158	12	)	)	PUNCT
ap-3506	158	13	=	=	SYM
ap-3506	159	1	d(z0)a$f(z)d(z0)†.	d(z0)a$f(z)d(z0)†.	PROPN
ap-3506	159	2	(	(	PUNCT
ap-3506	159	3	33	33	NUM
ap-3506	159	4	)	)	PUNCT
ap-3506	159	5	•	•	NOUN
ap-3506	159	6	parity	parity	NOUN
ap-3506	159	7	covariance	covariance	NOUN
ap-3506	159	8	a$f(−z	a$f(−z	PUNCT
ap-3506	159	9	)	)	PUNCT
ap-3506	160	1	=	=	PUNCT
ap-3506	160	2	pa$f(z)p	pa$f(z)p	PROPN
ap-3506	160	3	∀f	∀f	VERB
ap-3506	160	4	⇐	⇐	ADJ
ap-3506	160	5	⇒	⇒	NOUN
ap-3506	160	6	$	$	SYM
ap-3506	160	7	(	(	PUNCT
ap-3506	160	8	z	z	NOUN
ap-3506	160	9	)	)	PUNCT
ap-3506	160	10	=	=	SYM
ap-3506	160	11	$	$	SYM
ap-3506	160	12	(	(	PUNCT
ap-3506	160	13	−z	−z	NOUN
ap-3506	160	14	)	)	PUNCT
ap-3506	160	15	∀z	∀z	PROPN
ap-3506	160	16	,	,	PUNCT
ap-3506	160	17	(	(	PUNCT
ap-3506	160	18	34	34	NUM
ap-3506	160	19	)	)	PUNCT
ap-3506	160	20	where	where	SCONJ
ap-3506	160	21	p	p	NOUN
ap-3506	160	22	=	=	NOUN
ap-3506	160	23	∑∞	∑∞	NOUN
ap-3506	160	24	n=0(−1)n|en〉〈en|	n=0(−1)n|en〉〈en|	PROPN
ap-3506	160	25	is	be	AUX
ap-3506	160	26	the	the	DET
ap-3506	160	27	parity	parity	NOUN
ap-3506	160	28	operator	operator	NOUN
ap-3506	160	29	.	.	PUNCT
ap-3506	161	1	•	•	NUM
ap-3506	161	2	complex	complex	ADJ
ap-3506	161	3	conjugation	conjugation	NOUN
ap-3506	161	4	covariance	covariance	NOUN
ap-3506	161	5	a$	a$	ADV
ap-3506	161	6	f(z	f(z	PROPN
ap-3506	161	7	)	)	PUNCT
ap-3506	162	1	=	=	SYM
ap-3506	162	2	(	(	PUNCT
ap-3506	162	3	a$f(z	a$f(z	PROPN
ap-3506	162	4	)	)	PUNCT
ap-3506	162	5	)	)	PUNCT
ap-3506	163	1	†	†	PROPN
ap-3506	163	2	∀f	∀f	NUM
ap-3506	163	3	⇐	⇐	PROPN
ap-3506	163	4	⇒	⇒	NOUN
ap-3506	163	5	$	$	SYM
ap-3506	163	6	(	(	PUNCT
ap-3506	163	7	−z	−z	NOUN
ap-3506	163	8	)	)	PUNCT
ap-3506	163	9	=	=	PUNCT
ap-3506	163	10	$	$	SYM
ap-3506	163	11	(	(	PUNCT
ap-3506	163	12	z	z	NOUN
ap-3506	163	13	)	)	PUNCT
ap-3506	163	14	∀z	∀z	PROPN
ap-3506	163	15	,	,	PUNCT
ap-3506	163	16	(	(	PUNCT
ap-3506	163	17	35	35	NUM
ap-3506	163	18	)	)	PUNCT
ap-3506	163	19	•	•	NOUN
ap-3506	163	20	for	for	ADP
ap-3506	163	21	rotational	rotational	ADJ
ap-3506	163	22	covariance	covariance	NOUN
ap-3506	163	23	we	we	PRON
ap-3506	163	24	define	define	VERB
ap-3506	163	25	the	the	DET
ap-3506	163	26	unitary	unitary	ADJ
ap-3506	163	27	representation	representation	NOUN
ap-3506	163	28	θ	θ	PROPN
ap-3506	163	29	7→	7→	NUM
ap-3506	163	30	ut(θ	ut(θ	PUNCT
ap-3506	163	31	)	)	PUNCT
ap-3506	163	32	of	of	ADP
ap-3506	163	33	s1	s1	NOUN
ap-3506	163	34	on	on	ADP
ap-3506	163	35	the	the	DET
ap-3506	163	36	hilbert	hilbert	PROPN
ap-3506	163	37	space	space	NOUN
ap-3506	163	38	h	h	NOUN
ap-3506	163	39	as	as	ADP
ap-3506	163	40	the	the	DET
ap-3506	163	41	diagonal	diagonal	ADJ
ap-3506	163	42	operator	operator	NOUN
ap-3506	163	43	ut(θ)|en	ut(θ)|en	PROPN
ap-3506	163	44	〉	〉	NOUN
ap-3506	163	45	=	=	PUNCT
ap-3506	163	46	ei(n+ν)θ|en	ei(n+ν)θ|en	PROPN
ap-3506	163	47	〉	〉	NOUN
ap-3506	163	48	,	,	PUNCT
ap-3506	163	49	where	where	SCONJ
ap-3506	163	50	ν	ν	NOUN
ap-3506	163	51	is	be	AUX
ap-3506	163	52	arbitrary	arbitrary	ADJ
ap-3506	163	53	real	real	ADJ
ap-3506	163	54	.	.	PUNCT
ap-3506	164	1	from	from	ADP
ap-3506	164	2	the	the	DET
ap-3506	164	3	matrix	matrix	NOUN
ap-3506	164	4	elements	element	NOUN
ap-3506	164	5	of	of	ADP
ap-3506	164	6	d(z	d(z	NOUN
ap-3506	164	7	)	)	PUNCT
ap-3506	164	8	one	one	PRON
ap-3506	164	9	proves	prove	VERB
ap-3506	164	10	easily	easily	ADV
ap-3506	164	11	the	the	DET
ap-3506	164	12	rotational	rotational	ADJ
ap-3506	164	13	covariance	covariance	NOUN
ap-3506	164	14	property	property	NOUN
ap-3506	164	15	ut(θ)d(z)ut(θ)†	ut(θ)d(z)ut(θ)†	NOUN
ap-3506	164	16	=	=	SYM
ap-3506	164	17	d(eiθz	d(eiθz	NOUN
ap-3506	164	18	)	)	PUNCT
ap-3506	164	19	,	,	PUNCT
ap-3506	164	20	(	(	PUNCT
ap-3506	164	21	36	36	NUM
ap-3506	164	22	)	)	PUNCT
ap-3506	164	23	and	and	CCONJ
ap-3506	164	24	its	its	PRON
ap-3506	164	25	immediate	immediate	ADJ
ap-3506	164	26	consequence	consequence	NOUN
ap-3506	164	27	on	on	ADP
ap-3506	164	28	the	the	DET
ap-3506	164	29	nature	nature	NOUN
ap-3506	164	30	of	of	ADP
ap-3506	164	31	m$	m$	NOUN
ap-3506	164	32	and	and	CCONJ
ap-3506	164	33	the	the	DET
ap-3506	164	34	covariance	covariance	NOUN
ap-3506	164	35	of	of	ADP
ap-3506	164	36	a$f	a$f	NOUN
ap-3506	164	37	:	:	PUNCT
ap-3506	164	38	the	the	DET
ap-3506	164	39	equality	equality	NOUN
ap-3506	164	40	ut(θ)a$f	ut(θ)a$f	PROPN
ap-3506	164	41	ut(−θ	ut(−θ	NOUN
ap-3506	164	42	)	)	PUNCT
ap-3506	165	1	=	=	SYM
ap-3506	165	2	a$t	a$t	NOUN
ap-3506	165	3	(	(	PUNCT
ap-3506	165	4	θ)f	θ)f	NOUN
ap-3506	165	5	,	,	PUNCT
ap-3506	165	6	(	(	PUNCT
ap-3506	165	7	37	37	NUM
ap-3506	165	8	)	)	PUNCT
ap-3506	165	9	with	with	ADP
ap-3506	165	10	t	t	PROPN
ap-3506	165	11	(	(	PUNCT
ap-3506	165	12	θ)f(z	θ)f(z	PROPN
ap-3506	165	13	)	)	PUNCT
ap-3506	165	14	:	:	PUNCT
ap-3506	166	1	=	=	SYM
ap-3506	166	2	f	f	X
ap-3506	166	3	(	(	PUNCT
ap-3506	166	4	e−iθz	e−iθz	PROPN
ap-3506	166	5	)	)	PUNCT
ap-3506	166	6	,	,	PUNCT
ap-3506	166	7	holds	hold	VERB
ap-3506	166	8	true	true	ADJ
ap-3506	166	9	if	if	SCONJ
ap-3506	166	10	and	and	CCONJ
ap-3506	166	11	only	only	ADV
ap-3506	166	12	if	if	SCONJ
ap-3506	166	13	$	$	SYM
ap-3506	166	14	(	(	PUNCT
ap-3506	166	15	eiθz	eiθz	NOUN
ap-3506	166	16	)	)	PUNCT
ap-3506	166	17	=	=	SYM
ap-3506	166	18	$	$	SYM
ap-3506	166	19	(	(	PUNCT
ap-3506	166	20	z	z	NOUN
ap-3506	166	21	)	)	PUNCT
ap-3506	166	22	∀z	∀z	PROPN
ap-3506	166	23	,	,	PUNCT
ap-3506	166	24	θ	θ	PROPN
ap-3506	166	25	,	,	PUNCT
ap-3506	166	26	i.e.	i.e.	X
ap-3506	166	27	,	,	PUNCT
ap-3506	166	28	if	if	SCONJ
ap-3506	166	29	and	and	CCONJ
ap-3506	166	30	only	only	ADV
ap-3506	166	31	if	if	SCONJ
ap-3506	166	32	m$	m$	NOUN
ap-3506	166	33	is	be	AUX
ap-3506	166	34	diagonal	diagonal	ADJ
ap-3506	166	35	.	.	PUNCT
ap-3506	167	1	5	5	X
ap-3506	167	2	.	.	X
ap-3506	167	3	applications	application	NOUN
ap-3506	167	4	of	of	ADP
ap-3506	167	5	acs	acs	NOUN
ap-3506	167	6	quantization	quantization	NOUN
ap-3506	167	7	in	in	ADP
ap-3506	167	8	quantum	quantum	ADJ
ap-3506	167	9	cosmology	cosmology	NOUN
ap-3506	167	10	let	let	VERB
ap-3506	167	11	us	we	PRON
ap-3506	167	12	consider	consider	VERB
ap-3506	167	13	the	the	DET
ap-3506	167	14	friedmann	friedmann	NOUN
ap-3506	167	15	-	-	PUNCT
ap-3506	167	16	robertson	robertson	PROPN
ap-3506	167	17	-	-	PUNCT
ap-3506	167	18	walker	walker	PROPN
ap-3506	167	19	model	model	NOUN
ap-3506	167	20	filled	fill	VERB
ap-3506	167	21	with	with	ADP
ap-3506	167	22	barotropic	barotropic	ADJ
ap-3506	167	23	fluid	fluid	NOUN
ap-3506	167	24	with	with	ADP
ap-3506	167	25	equation	equation	NOUN
ap-3506	167	26	of	of	ADP
ap-3506	167	27	state	state	NOUN
ap-3506	167	28	p	p	PROPN
ap-3506	167	29	=	=	PROPN
ap-3506	167	30	wρ	wρ	PROPN
ap-3506	167	31	.	.	PUNCT
ap-3506	168	1	the	the	DET
ap-3506	168	2	line	line	NOUN
ap-3506	168	3	element	element	NOUN
ap-3506	168	4	is	be	AUX
ap-3506	168	5	given	give	VERB
ap-3506	168	6	by	by	ADP
ap-3506	168	7	:	:	PUNCT
ap-3506	168	8	ds2	ds2	PROPN
ap-3506	168	9	=	=	SYM
ap-3506	168	10	−n(t)2dt2	−n(t)2dt2	PROPN
ap-3506	169	1	+	+	CCONJ
ap-3506	169	2	a(t)2δijω	a(t)2δijω	VERB
ap-3506	169	3	iωj	iωj	NOUN
ap-3506	169	4	,	,	PUNCT
ap-3506	169	5	(	(	PUNCT
ap-3506	169	6	38	38	NUM
ap-3506	169	7	)	)	PUNCT
ap-3506	169	8	where	where	SCONJ
ap-3506	169	9	a(t	a(t	NOUN
ap-3506	169	10	)	)	PUNCT
ap-3506	169	11	is	be	AUX
ap-3506	169	12	the	the	DET
ap-3506	169	13	scale	scale	NOUN
ap-3506	169	14	factor	factor	NOUN
ap-3506	169	15	and	and	CCONJ
ap-3506	169	16	the	the	DET
ap-3506	169	17	ωi	ωi	NOUN
ap-3506	169	18	’s	’s	PART
ap-3506	169	19	are	be	AUX
ap-3506	169	20	rightinvariant	rightinvariant	ADJ
ap-3506	169	21	dual	dual	ADJ
ap-3506	169	22	vectors	vector	NOUN
ap-3506	169	23	.	.	PUNCT
ap-3506	170	1	the	the	DET
ap-3506	170	2	resolving	resolving	NOUN
ap-3506	170	3	of	of	ADP
ap-3506	170	4	the	the	DET
ap-3506	170	5	hamiltonian	hamiltonian	ADJ
ap-3506	170	6	constraint	constraint	NOUN
ap-3506	170	7	leads	lead	VERB
ap-3506	170	8	to	to	ADP
ap-3506	170	9	a	a	DET
ap-3506	170	10	model	model	NOUN
ap-3506	170	11	of	of	ADP
ap-3506	170	12	singular	singular	ADJ
ap-3506	170	13	universe	universe	NOUN
ap-3506	170	14	analogous	analogous	ADJ
ap-3506	170	15	to	to	ADP
ap-3506	170	16	a	a	DET
ap-3506	170	17	particle	particle	NOUN
ap-3506	170	18	moving	move	VERB
ap-3506	170	19	on	on	ADP
ap-3506	170	20	the	the	DET
ap-3506	170	21	half	half	ADJ
ap-3506	170	22	-	-	PUNCT
ap-3506	170	23	line	line	NOUN
ap-3506	170	24	(	(	PUNCT
ap-3506	170	25	0,∞	0,∞	NUM
ap-3506	170	26	)	)	PUNCT
ap-3506	170	27	.	.	PUNCT
ap-3506	171	1	indeed	indeed	ADV
ap-3506	171	2	,	,	PUNCT
ap-3506	171	3	canonical	canonical	ADJ
ap-3506	171	4	coordinates	coordinate	NOUN
ap-3506	171	5	(	(	PUNCT
ap-3506	171	6	q	q	X
ap-3506	171	7	,	,	PUNCT
ap-3506	171	8	p	p	NOUN
ap-3506	171	9	)	)	PUNCT
ap-3506	171	10	can	can	AUX
ap-3506	171	11	be	be	AUX
ap-3506	171	12	introduced	introduce	VERB
ap-3506	171	13	in	in	ADP
ap-3506	171	14	terms	term	NOUN
ap-3506	171	15	of	of	ADP
ap-3506	171	16	the	the	DET
ap-3506	171	17	volume	volume	NOUN
ap-3506	171	18	v	v	ADP
ap-3506	171	19	∼	∼	NOUN
ap-3506	171	20	a3	a3	NOUN
ap-3506	171	21	and	and	CCONJ
ap-3506	171	22	the	the	DET
ap-3506	171	23	expansion	expansion	NOUN
ap-3506	171	24	rate	rate	NOUN
ap-3506	171	25	v̇	v̇	NOUN
ap-3506	171	26	/v	/v	PUNCT
ap-3506	171	27	∼	∼	NOUN
ap-3506	171	28	ȧ/a	ȧ/a	NOUN
ap-3506	171	29	through	through	ADP
ap-3506	171	30	the	the	DET
ap-3506	171	31	relations	relation	NOUN
ap-3506	171	32	v	v	ADP
ap-3506	171	33	=	=	SYM
ap-3506	171	34	q2/(1−w	q2/(1−w	NOUN
ap-3506	171	35	)	)	PUNCT
ap-3506	171	36	and	and	CCONJ
ap-3506	171	37	k	k	NOUN
ap-3506	171	38	=	=	SYM
ap-3506	171	39	(	(	PUNCT
ap-3506	171	40	3/8)(1−	3/8)(1−	NUM
ap-3506	171	41	w)pq−(1+w)/(1−w	w)pq−(1+w)/(1−w	NOUN
ap-3506	171	42	)	)	PUNCT
ap-3506	171	43	.	.	PUNCT
ap-3506	172	1	clearly	clearly	ADV
ap-3506	172	2	,	,	PUNCT
ap-3506	172	3	q	q	X
ap-3506	172	4	>	>	X
ap-3506	172	5	0	0	PUNCT
ap-3506	172	6	and	and	CCONJ
ap-3506	172	7	p	p	PROPN
ap-3506	172	8	∈	∈	PROPN
ap-3506	172	9	r.	r.	NOUN
ap-3506	172	10	then	then	ADV
ap-3506	172	11	the	the	DET
ap-3506	172	12	reduced	reduced	ADJ
ap-3506	172	13	hamiltonian	hamiltonian	ADJ
ap-3506	172	14	reads	read	NOUN
ap-3506	172	15	as	as	ADP
ap-3506	172	16	{	{	PUNCT
ap-3506	172	17	q	q	NOUN
ap-3506	172	18	,	,	PUNCT
ap-3506	172	19	p	p	NOUN
ap-3506	172	20	}	}	PUNCT
ap-3506	172	21	=	=	SYM
ap-3506	172	22	1	1	NUM
ap-3506	172	23	,	,	PUNCT
ap-3506	172	24	h(q	h(q	ADV
ap-3506	172	25	,	,	PUNCT
ap-3506	172	26	p	p	X
ap-3506	172	27	)	)	PUNCT
ap-3506	172	28	=	=	NOUN
ap-3506	172	29	α(w)p2	α(w)p2	NOUN
ap-3506	172	30	+	+	CCONJ
ap-3506	172	31	6k̃qβ(w	6k̃qβ(w	NUM
ap-3506	172	32	)	)	PUNCT
ap-3506	172	33	,	,	PUNCT
ap-3506	172	34	q	q	X
ap-3506	172	35	>	>	X
ap-3506	172	36	0	0	X
ap-3506	172	37	.	.	PUNCT
ap-3506	172	38	with	with	ADP
ap-3506	172	39	k̃	k̃	PROPN
ap-3506	172	40	=	=	PUNCT
ap-3506	172	41	(	(	PUNCT
ap-3506	172	42	∫	∫	PROPN
ap-3506	172	43	dω)2/3k	dω)2/3k	PROPN
ap-3506	172	44	,	,	PUNCT
ap-3506	172	45	α(w	α(w	NOUN
ap-3506	172	46	)	)	PUNCT
ap-3506	172	47	=	=	SYM
ap-3506	172	48	3(1−w)2/32	3(1−w)2/32	NUM
ap-3506	172	49	and	and	CCONJ
ap-3506	172	50	β(w	β(w	NOUN
ap-3506	172	51	)	)	PUNCT
ap-3506	172	52	=	=	SYM
ap-3506	172	53	2(3w+	2(3w+	NUM
ap-3506	172	54	1)/(3(1−w	1)/(3(1−w	NUM
ap-3506	172	55	)	)	PUNCT
ap-3506	172	56	)	)	PUNCT
ap-3506	172	57	.	.	PUNCT
ap-3506	173	1	k	k	X
ap-3506	174	1	=	=	PUNCT
ap-3506	174	2	0,−1	0,−1	PROPN
ap-3506	174	3	or	or	CCONJ
ap-3506	174	4	1	1	NUM
ap-3506	174	5	(	(	PUNCT
ap-3506	174	6	in	in	ADP
ap-3506	174	7	suitable	suitable	ADJ
ap-3506	174	8	unit	unit	NOUN
ap-3506	174	9	of	of	ADP
ap-3506	174	10	inverse	inverse	NOUN
ap-3506	174	11	area	area	NOUN
ap-3506	174	12	)	)	PUNCT
ap-3506	174	13	depending	depend	VERB
ap-3506	174	14	on	on	ADP
ap-3506	174	15	whether	whether	SCONJ
ap-3506	174	16	the	the	DET
ap-3506	174	17	universe	universe	NOUN
ap-3506	174	18	is	be	AUX
ap-3506	174	19	flat	flat	ADJ
ap-3506	174	20	,	,	PUNCT
ap-3506	174	21	open	open	ADJ
ap-3506	174	22	or	or	CCONJ
ap-3506	174	23	closed	closed	ADJ
ap-3506	174	24	.	.	PUNCT
ap-3506	175	1	assuming	assume	VERB
ap-3506	175	2	a	a	DET
ap-3506	175	3	closed	closed	ADJ
ap-3506	175	4	universe	universe	NOUN
ap-3506	175	5	with	with	ADP
ap-3506	175	6	radiation	radiation	NOUN
ap-3506	175	7	content	content	NOUN
ap-3506	175	8	w	w	PROPN
ap-3506	176	1	=	=	SYM
ap-3506	176	2	1/3	1/3	PROPN
ap-3506	176	3	and	and	CCONJ
ap-3506	176	4	k	k	PROPN
ap-3506	176	5	=	=	SYM
ap-3506	176	6	+1	+1	PROPN
ap-3506	176	7	,	,	PUNCT
ap-3506	176	8	the	the	DET
ap-3506	176	9	classical	classical	ADJ
ap-3506	176	10	isotropy	isotropy	VERB
ap-3506	176	11	singularity	singularity	NOUN
ap-3506	176	12	is	be	AUX
ap-3506	176	13	cured	cure	VERB
ap-3506	176	14	on	on	ADP
ap-3506	176	15	the	the	DET
ap-3506	176	16	quantum	quantum	ADJ
ap-3506	176	17	level	level	NOUN
ap-3506	176	18	by	by	ADP
ap-3506	176	19	using	use	VERB
ap-3506	176	20	affine	affine	NOUN
ap-3506	176	21	cs	cs	ADJ
ap-3506	176	22	quantization	quantization	NOUN
ap-3506	176	23	[	[	X
ap-3506	176	24	10	10	NUM
ap-3506	176	25	]	]	PUNCT
ap-3506	176	26	.	.	PUNCT
ap-3506	177	1	indeed	indeed	ADV
ap-3506	177	2	the	the	DET
ap-3506	177	3	latter	latter	ADJ
ap-3506	177	4	regularizes	regularize	VERB
ap-3506	177	5	the	the	DET
ap-3506	177	6	kinetic	kinetic	ADJ
ap-3506	177	7	term	term	NOUN
ap-3506	177	8	by	by	ADP
ap-3506	177	9	adding	add	VERB
ap-3506	177	10	a	a	DET
ap-3506	177	11	repulsive	repulsive	ADJ
ap-3506	177	12	centrifugal	centrifugal	ADJ
ap-3506	177	13	potential	potential	NOUN
ap-3506	177	14	which	which	PRON
ap-3506	177	15	prevents	prevent	VERB
ap-3506	177	16	the	the	DET
ap-3506	177	17	system	system	NOUN
ap-3506	177	18	from	from	ADP
ap-3506	177	19	reaching	reach	VERB
ap-3506	177	20	the	the	DET
ap-3506	177	21	value	value	NOUN
ap-3506	177	22	q	q	NOUN
ap-3506	178	1	=	=	NOUN
ap-3506	178	2	0	0	NUM
ap-3506	178	3	.	.	PUNCT
ap-3506	179	1	precisely	precisely	ADV
ap-3506	179	2	,	,	PUNCT
ap-3506	179	3	with	with	ADP
ap-3506	179	4	the	the	DET
ap-3506	179	5	choice	choice	NOUN
ap-3506	179	6	of	of	ADP
ap-3506	179	7	a	a	DET
ap-3506	179	8	fiducial	fiducial	ADJ
ap-3506	179	9	vector	vector	NOUN
ap-3506	179	10	ψ	ψ	NOUN
ap-3506	179	11	,	,	PUNCT
ap-3506	179	12	h	h	NOUN
ap-3506	179	13	=	=	SYM
ap-3506	179	14	1	1	NUM
ap-3506	179	15	24p	24p	NOUN
ap-3506	179	16	2	2	NUM
ap-3506	179	17	+	+	CCONJ
ap-3506	179	18	6q2	6q2	NUM
ap-3506	179	19	7→	7→	NUM
ap-3506	179	20	ah	ah	INTJ
ap-3506	179	21	=	=	SYM
ap-3506	179	22	1	1	NUM
ap-3506	179	23	24p	24p	NOUN
ap-3506	179	24	2	2	NUM
ap-3506	179	25	+	+	CCONJ
ap-3506	179	26	k(ψ	k(ψ	PROPN
ap-3506	179	27	)	)	PUNCT
ap-3506	179	28	24	24	NUM
ap-3506	179	29	1	1	NUM
ap-3506	179	30	q2	q2	NOUN
ap-3506	179	31	+	+	X
ap-3506	179	32	6m(ψ)q2	6m(ψ)q2	PROPN
ap-3506	179	33	,	,	PUNCT
ap-3506	179	34	(	(	PUNCT
ap-3506	179	35	39	39	NUM
ap-3506	179	36	)	)	PUNCT
ap-3506	179	37	p	p	PROPN
ap-3506	179	38	≡	≡	PROPN
ap-3506	179	39	−i	−i	PROPN
ap-3506	180	1	d	d	PROPN
ap-3506	180	2	dx	dx	PROPN
ap-3506	180	3	,	,	PUNCT
ap-3506	180	4	qφ(x	qφ(x	PROPN
ap-3506	180	5	)	)	PUNCT
ap-3506	180	6	≡	≡	PROPN
ap-3506	180	7	xφ(x	xφ(x	PUNCT
ap-3506	180	8	)	)	PUNCT
ap-3506	180	9	.	.	PUNCT
ap-3506	181	1	the	the	DET
ap-3506	181	2	constants	constant	NOUN
ap-3506	181	3	k(ψ	k(ψ	PROPN
ap-3506	181	4	)	)	PUNCT
ap-3506	181	5	and	and	CCONJ
ap-3506	181	6	m(ψ	m(ψ	PROPN
ap-3506	181	7	)	)	PUNCT
ap-3506	181	8	are	be	AUX
ap-3506	181	9	>	>	X
ap-3506	181	10	0	0	PUNCT
ap-3506	181	11	for	for	ADP
ap-3506	181	12	all	all	DET
ap-3506	181	13	ψ	ψ	NOUN
ap-3506	181	14	and	and	CCONJ
ap-3506	181	15	their	their	PRON
ap-3506	181	16	appearance	appearance	NOUN
ap-3506	181	17	is	be	AUX
ap-3506	181	18	due	due	ADJ
ap-3506	181	19	to	to	ADP
ap-3506	181	20	the	the	DET
ap-3506	181	21	affine	affine	NOUN
ap-3506	181	22	cs	cs	ADJ
ap-3506	181	23	quantization	quantization	NOUN
ap-3506	181	24	.	.	PUNCT
ap-3506	182	1	moreover	moreover	ADV
ap-3506	182	2	,	,	PUNCT
ap-3506	182	3	for	for	ADP
ap-3506	182	4	a	a	DET
ap-3506	182	5	ψ	ψ	NOUN
ap-3506	182	6	such	such	ADJ
ap-3506	182	7	that	that	SCONJ
ap-3506	182	8	k(ψ	k(ψ	PROPN
ap-3506	182	9	)	)	PUNCT
ap-3506	182	10	≥	≥	NOUN
ap-3506	182	11	3	3	NUM
ap-3506	182	12	4	4	NUM
ap-3506	182	13	the	the	DET
ap-3506	182	14	quantum	quantum	ADJ
ap-3506	182	15	hamiltonian	hamiltonian	NOUN
ap-3506	182	16	ah	ah	INTJ
ap-3506	182	17	is	be	AUX
ap-3506	182	18	essentially	essentially	ADV
ap-3506	182	19	self	self	NOUN
ap-3506	182	20	-	-	PUNCT
ap-3506	182	21	adjoint	adjoint	NOUN
ap-3506	182	22	,	,	PUNCT
ap-3506	182	23	giving	give	VERB
ap-3506	182	24	a	a	DET
ap-3506	182	25	unique	unique	ADJ
ap-3506	182	26	unitary	unitary	ADJ
ap-3506	182	27	evolution	evolution	NOUN
ap-3506	182	28	:	:	PUNCT
ap-3506	182	29	there	there	PRON
ap-3506	182	30	is	be	VERB
ap-3506	182	31	no	no	DET
ap-3506	182	32	need	need	NOUN
ap-3506	182	33	of	of	ADP
ap-3506	182	34	boundary	boundary	ADJ
ap-3506	182	35	conditions	condition	NOUN
ap-3506	182	36	.	.	PUNCT
ap-3506	183	1	the	the	DET
ap-3506	183	2	semi	semi	ADJ
ap-3506	183	3	-	-	ADJ
ap-3506	183	4	classical	classical	ADJ
ap-3506	183	5	dynamics	dynamic	NOUN
ap-3506	183	6	is	be	AUX
ap-3506	183	7	ruled	rule	VERB
ap-3506	183	8	by	by	ADP
ap-3506	183	9	the	the	DET
ap-3506	183	10	acs	acs	PROPN
ap-3506	183	11	mean	mean	NOUN
ap-3506	183	12	value	value	NOUN
ap-3506	183	13	of	of	ADP
ap-3506	183	14	the	the	DET
ap-3506	183	15	quantum	quantum	ADJ
ap-3506	183	16	hamiltonian	hamiltonian	NOUN
ap-3506	183	17	:	:	PUNCT
ap-3506	184	1	〈	〈	PROPN
ap-3506	184	2	q	q	PRON
ap-3506	184	3	,	,	PUNCT
ap-3506	184	4	p|ah|q	p|ah|q	NOUN
ap-3506	184	5	,	,	PUNCT
ap-3506	184	6	p	p	NOUN
ap-3506	184	7	〉	〉	NUM
ap-3506	184	8	=	=	SYM
ap-3506	184	9	c(ψ	c(ψ	PROPN
ap-3506	184	10	)	)	PUNCT
ap-3506	184	11	∫	∫	PROPN
ap-3506	184	12	r+×r	r+×r	PROPN
ap-3506	184	13	dq′dp′	dq′dp′	PROPN
ap-3506	184	14	∣∣〈q′	∣∣〈q′	PROPN
ap-3506	184	15	,	,	PUNCT
ap-3506	184	16	p′|q	p′|q	NOUN
ap-3506	184	17	,	,	PUNCT
ap-3506	184	18	p〉∣∣2h(q′	p〉∣∣2h(q′	PROPN
ap-3506	184	19	,	,	PUNCT
ap-3506	184	20	p′	p′	NOUN
ap-3506	184	21	)	)	PUNCT
ap-3506	184	22	,	,	PUNCT
ap-3506	184	23	(	(	PUNCT
ap-3506	184	24	40	40	NUM
ap-3506	184	25	)	)	PUNCT
ap-3506	184	26	with	with	ADP
ap-3506	184	27	a	a	DET
ap-3506	184	28	displacement	displacement	NOUN
ap-3506	184	29	of	of	ADP
ap-3506	184	30	the	the	DET
ap-3506	184	31	equilibrium	equilibrium	NOUN
ap-3506	184	32	point	point	NOUN
ap-3506	184	33	of	of	ADP
ap-3506	184	34	the	the	DET
ap-3506	184	35	potential	potential	NOUN
ap-3506	184	36	at	at	ADP
ap-3506	184	37	q4	q4	PROPN
ap-3506	184	38	eq	eq	NOUN
ap-3506	184	39	=	=	NOUN
ap-3506	184	40	1	1	NUM
ap-3506	184	41	144	144	NUM
ap-3506	184	42	k	k	NOUN
ap-3506	184	43	m	m	PROPN
ap-3506	184	44	.	.	PUNCT
ap-3506	185	1	the	the	DET
ap-3506	185	2	constant	constant	ADJ
ap-3506	185	3	c(ψ	c(ψ	NOUN
ap-3506	185	4	)	)	PUNCT
ap-3506	185	5	is	be	AUX
ap-3506	185	6	>	>	X
ap-3506	185	7	0	0	PUNCT
ap-3506	185	8	for	for	ADP
ap-3506	185	9	all	all	DET
ap-3506	185	10	ψ	ψ	NOUN
ap-3506	185	11	.	.	PUNCT
ap-3506	186	1	in	in	ADP
ap-3506	186	2	figure	figure	NOUN
ap-3506	186	3	1	1	NUM
ap-3506	186	4	contour	contour	NOUN
ap-3506	186	5	plots	plot	NOUN
ap-3506	186	6	of	of	ADP
ap-3506	186	7	phase	phase	NOUN
ap-3506	186	8	space	space	NOUN
ap-3506	186	9	trajectories	trajectory	NOUN
ap-3506	186	10	for	for	ADP
ap-3506	186	11	classical	classical	ADJ
ap-3506	186	12	hamiltonian	hamiltonian	NOUN
ap-3506	186	13	h(q	h(q	ADV
ap-3506	186	14	,	,	PUNCT
ap-3506	186	15	p	p	NOUN
ap-3506	186	16	)	)	PUNCT
ap-3506	186	17	(	(	PUNCT
ap-3506	186	18	left	leave	VERB
ap-3506	186	19	)	)	PUNCT
ap-3506	186	20	and	and	CCONJ
ap-3506	186	21	semi	semi	ADJ
ap-3506	186	22	-	-	ADJ
ap-3506	186	23	classical	classical	ADJ
ap-3506	186	24	hamiltonian	hamiltonian	NOUN
ap-3506	186	25	(	(	PUNCT
ap-3506	186	26	right	right	ADJ
ap-3506	186	27	)	)	PUNCT
ap-3506	186	28	defined	define	VERB
ap-3506	186	29	by	by	ADP
ap-3506	186	30	(	(	PUNCT
ap-3506	186	31	40	40	NUM
ap-3506	186	32	)	)	PUNCT
ap-3506	186	33	are	be	AUX
ap-3506	186	34	compared	compare	VERB
ap-3506	186	35	.	.	PUNCT
ap-3506	187	1	as	as	ADP
ap-3506	187	2	the	the	DET
ap-3506	187	3	result	result	NOUN
ap-3506	187	4	of	of	ADP
ap-3506	187	5	affine	affine	ADJ
ap-3506	187	6	quantization	quantization	NOUN
ap-3506	187	7	and	and	CCONJ
ap-3506	187	8	restoring	restore	VERB
ap-3506	187	9	arbitrariness	arbitrariness	NOUN
ap-3506	187	10	on	on	ADP
ap-3506	187	11	w	w	PROPN
ap-3506	187	12	and	and	CCONJ
ap-3506	187	13	k	k	NOUN
ap-3506	187	14	,	,	PUNCT
ap-3506	187	15	we	we	PRON
ap-3506	187	16	obtain	obtain	VERB
ap-3506	187	17	two	two	NUM
ap-3506	187	18	corrections	correction	NOUN
ap-3506	187	19	to	to	ADP
ap-3506	187	20	the	the	DET
ap-3506	187	21	friedmann	friedmann	NOUN
ap-3506	187	22	equation	equation	NOUN
ap-3506	187	23	which	which	PRON
ap-3506	187	24	reads	read	VERB
ap-3506	187	25	in	in	ADP
ap-3506	187	26	its	its	PRON
ap-3506	187	27	semiclassical	semiclassical	ADJ
ap-3506	187	28	version	version	NOUN
ap-3506	187	29	as	as	ADP
ap-3506	187	30	(	(	PUNCT
ap-3506	187	31	ȧ	ȧ	PROPN
ap-3506	187	32	a	a	NOUN
ap-3506	187	33	)	)	PUNCT
ap-3506	187	34	2	2	NUM
ap-3506	187	35	+	+	CCONJ
ap-3506	187	36	c2a2	c2a2	PRON
ap-3506	187	37	p	p	X
ap-3506	187	38	(	(	PUNCT
ap-3506	187	39	1−	1−	NUM
ap-3506	187	40	w)2a	w)2a	NOUN
ap-3506	187	41	1	1	NUM
ap-3506	187	42	v	v	ADP
ap-3506	187	43	2	2	NUM
ap-3506	187	44	+	+	NOUN
ap-3506	187	45	b	b	X
ap-3506	187	46	kc2	kc2	PROPN
ap-3506	187	47	a2	a2	PROPN
ap-3506	187	48	=	=	PROPN
ap-3506	187	49	8πg	8πg	ADJ
ap-3506	187	50	3c2	3c2	NUM
ap-3506	187	51	ρ	ρ	NOUN
ap-3506	187	52	,	,	PUNCT
ap-3506	187	53	(	(	PUNCT
ap-3506	187	54	41	41	NUM
ap-3506	187	55	)	)	PUNCT
ap-3506	187	56	where	where	SCONJ
ap-3506	187	57	a	a	PRON
ap-3506	187	58	and	and	CCONJ
ap-3506	187	59	b	b	NOUN
ap-3506	187	60	are	be	AUX
ap-3506	187	61	positive	positive	ADJ
ap-3506	187	62	factor	factor	NOUN
ap-3506	187	63	dependent	dependent	ADJ
ap-3506	187	64	on	on	ADP
ap-3506	187	65	ψ	ψ	X
ap-3506	187	66	and	and	CCONJ
ap-3506	187	67	can	can	AUX
ap-3506	187	68	be	be	AUX
ap-3506	187	69	adjusted	adjust	VERB
ap-3506	187	70	at	at	ADP
ap-3506	187	71	will	will	AUX
ap-3506	187	72	in	in	ADP
ap-3506	187	73	consistence	consistence	NOUN
ap-3506	187	74	with	with	ADP
ap-3506	187	75	(	(	PUNCT
ap-3506	187	76	so	so	ADV
ap-3506	187	77	far	far	ADV
ap-3506	187	78	very	very	ADV
ap-3506	187	79	hypothetical	hypothetical	ADJ
ap-3506	187	80	!	!	PUNCT
ap-3506	187	81	)	)	PUNCT
ap-3506	188	1	observations	observation	NOUN
ap-3506	188	2	.	.	PUNCT
ap-3506	189	1	the	the	DET
ap-3506	189	2	first	first	ADJ
ap-3506	189	3	correction	correction	NOUN
ap-3506	189	4	is	be	AUX
ap-3506	189	5	the	the	DET
ap-3506	189	6	repulsive	repulsive	ADJ
ap-3506	189	7	potential	potential	NOUN
ap-3506	189	8	,	,	PUNCT
ap-3506	189	9	which	which	PRON
ap-3506	189	10	depends	depend	VERB
ap-3506	189	11	on	on	ADP
ap-3506	189	12	the	the	DET
ap-3506	189	13	volume	volume	NOUN
ap-3506	189	14	,	,	PUNCT
ap-3506	189	15	177	177	NUM
ap-3506	189	16	jean	jean	PROPN
ap-3506	189	17	pierre	pierre	PROPN
ap-3506	189	18	gazeau	gazeau	PROPN
ap-3506	189	19	acta	acta	PROPN
ap-3506	189	20	polytechnica	polytechnica	PROPN
ap-3506	189	21	figure	figure	NOUN
ap-3506	189	22	1	1	NUM
ap-3506	189	23	.	.	PUNCT
ap-3506	190	1	contour	contour	NOUN
ap-3506	190	2	plots	plot	NOUN
ap-3506	190	3	of	of	ADP
ap-3506	190	4	the	the	DET
ap-3506	190	5	classical	classical	ADJ
ap-3506	190	6	and	and	CCONJ
ap-3506	190	7	semiclassical	semiclassical	ADJ
ap-3506	190	8	hamiltonians	hamiltonian	NOUN
ap-3506	190	9	for	for	ADP
ap-3506	190	10	the	the	DET
ap-3506	190	11	closed	closed	ADJ
ap-3506	190	12	friedmann	friedmann	NOUN
ap-3506	190	13	universe	universe	NOUN
ap-3506	190	14	.	.	PUNCT
ap-3506	191	1	the	the	DET
ap-3506	191	2	singularity	singularity	NOUN
ap-3506	191	3	q	q	NOUN
ap-3506	192	1	=	=	NOUN
ap-3506	192	2	0	0	NUM
ap-3506	192	3	on	on	ADP
ap-3506	192	4	the	the	DET
ap-3506	192	5	left	left	NOUN
ap-3506	192	6	is	be	AUX
ap-3506	192	7	replaced	replace	VERB
ap-3506	192	8	with	with	ADP
ap-3506	192	9	a	a	DET
ap-3506	192	10	bounce	bounce	NOUN
ap-3506	192	11	on	on	ADP
ap-3506	192	12	the	the	DET
ap-3506	192	13	right	right	NOUN
ap-3506	192	14	.	.	PUNCT
ap-3506	193	1	and	and	CCONJ
ap-3506	193	2	this	this	PRON
ap-3506	193	3	excludes	exclude	VERB
ap-3506	193	4	non	non	ADJ
ap-3506	193	5	-	-	ADJ
ap-3506	193	6	compact	compact	ADJ
ap-3506	193	7	universes	universe	NOUN
ap-3506	193	8	from	from	ADP
ap-3506	193	9	quantum	quantum	ADJ
ap-3506	193	10	modelling	modelling	NOUN
ap-3506	193	11	.	.	PUNCT
ap-3506	194	1	we	we	PRON
ap-3506	194	2	notice	notice	VERB
ap-3506	194	3	that	that	SCONJ
ap-3506	194	4	as	as	SCONJ
ap-3506	194	5	the	the	DET
ap-3506	194	6	singularity	singularity	NOUN
ap-3506	194	7	is	be	AUX
ap-3506	194	8	approached	approach	VERB
ap-3506	194	9	a→	a→	PUNCT
ap-3506	194	10	0	0	NUM
ap-3506	194	11	,	,	PUNCT
ap-3506	194	12	this	this	DET
ap-3506	194	13	potential	potential	NOUN
ap-3506	194	14	grows	grow	VERB
ap-3506	194	15	faster	fast	ADV
ap-3506	194	16	(	(	PUNCT
ap-3506	194	17	∼	∼	NOUN
ap-3506	194	18	a−6	a−6	NOUN
ap-3506	194	19	)	)	PUNCT
ap-3506	194	20	than	than	ADP
ap-3506	194	21	the	the	DET
ap-3506	194	22	density	density	NOUN
ap-3506	194	23	of	of	ADP
ap-3506	194	24	fluid	fluid	NOUN
ap-3506	194	25	(	(	PUNCT
ap-3506	194	26	∼	∼	NOUN
ap-3506	194	27	a−3(1+w	a−3(1+w	NOUN
ap-3506	194	28	)	)	PUNCT
ap-3506	194	29	)	)	PUNCT
ap-3506	194	30	and	and	CCONJ
ap-3506	194	31	therefore	therefore	ADV
ap-3506	194	32	at	at	ADP
ap-3506	194	33	some	some	DET
ap-3506	194	34	point	point	NOUN
ap-3506	194	35	the	the	DET
ap-3506	194	36	contraction	contraction	NOUN
ap-3506	194	37	must	must	AUX
ap-3506	194	38	come	come	VERB
ap-3506	194	39	to	to	ADP
ap-3506	194	40	a	a	DET
ap-3506	194	41	halt	halt	NOUN
ap-3506	194	42	.	.	PUNCT
ap-3506	195	1	second	second	ADJ
ap-3506	195	2	,	,	PUNCT
ap-3506	195	3	the	the	DET
ap-3506	195	4	curvature	curvature	NOUN
ap-3506	195	5	becomes	become	VERB
ap-3506	195	6	dressed	dress	VERB
ap-3506	195	7	by	by	ADP
ap-3506	195	8	the	the	DET
ap-3506	195	9	factor	factor	NOUN
ap-3506	195	10	b.	b.	PROPN
ap-3506	196	1	this	this	DET
ap-3506	196	2	effect	effect	NOUN
ap-3506	196	3	could	could	AUX
ap-3506	196	4	in	in	ADP
ap-3506	196	5	principle	principle	NOUN
ap-3506	196	6	be	be	AUX
ap-3506	196	7	observed	observe	VERB
ap-3506	196	8	far	far	ADV
ap-3506	196	9	away	away	ADV
ap-3506	196	10	from	from	ADP
ap-3506	196	11	the	the	DET
ap-3506	196	12	quantum	quantum	ADJ
ap-3506	196	13	phase	phase	NOUN
ap-3506	196	14	.	.	PUNCT
ap-3506	197	1	however	however	ADV
ap-3506	197	2	,	,	PUNCT
ap-3506	197	3	we	we	PRON
ap-3506	197	4	do	do	AUX
ap-3506	197	5	not	not	PART
ap-3506	197	6	observe	observe	VERB
ap-3506	197	7	the	the	DET
ap-3506	197	8	intrinsic	intrinsic	ADJ
ap-3506	197	9	curvature	curvature	NOUN
ap-3506	197	10	neither	neither	CCONJ
ap-3506	197	11	in	in	ADP
ap-3506	197	12	the	the	DET
ap-3506	197	13	geometry	geometry	NOUN
ap-3506	197	14	nor	nor	CCONJ
ap-3506	197	15	in	in	ADP
ap-3506	197	16	the	the	DET
ap-3506	197	17	dynamics	dynamic	NOUN
ap-3506	197	18	of	of	ADP
ap-3506	197	19	space	space	NOUN
ap-3506	197	20	.	.	PUNCT
ap-3506	198	1	nevertheless	nevertheless	ADV
ap-3506	198	2	,	,	PUNCT
ap-3506	198	3	for	for	ADP
ap-3506	198	4	a	a	DET
ap-3506	198	5	convenient	convenient	ADJ
ap-3506	198	6	choice	choice	NOUN
ap-3506	198	7	of	of	ADP
ap-3506	198	8	ψ	ψ	NOUN
ap-3506	198	9	,	,	PUNCT
ap-3506	198	10	this	this	DET
ap-3506	198	11	factor	factor	NOUN
ap-3506	198	12	≈	≈	PROPN
ap-3506	198	13	1	1	NUM
ap-3506	198	14	also	also	ADV
ap-3506	198	15	note	note	VERB
ap-3506	198	16	that	that	SCONJ
ap-3506	198	17	the	the	DET
ap-3506	198	18	form	form	NOUN
ap-3506	198	19	of	of	ADP
ap-3506	198	20	the	the	DET
ap-3506	198	21	repulsive	repulsive	ADJ
ap-3506	198	22	potential	potential	NOUN
ap-3506	198	23	does	do	AUX
ap-3506	198	24	not	not	PART
ap-3506	198	25	depend	depend	VERB
ap-3506	198	26	on	on	ADP
ap-3506	198	27	the	the	DET
ap-3506	198	28	state	state	NOUN
ap-3506	198	29	of	of	ADP
ap-3506	198	30	fluid	fluid	NOUN
ap-3506	198	31	filling	fill	VERB
ap-3506	198	32	the	the	DET
ap-3506	198	33	universe	universe	NOUN
ap-3506	198	34	:	:	PUNCT
ap-3506	198	35	the	the	DET
ap-3506	198	36	origin	origin	NOUN
ap-3506	198	37	of	of	ADP
ap-3506	198	38	singularity	singularity	NOUN
ap-3506	198	39	avoidance	avoidance	NOUN
ap-3506	198	40	is	be	AUX
ap-3506	198	41	quantum	quantum	ADJ
ap-3506	198	42	geometrical	geometrical	ADJ
ap-3506	198	43	.	.	PUNCT
ap-3506	199	1	the	the	DET
ap-3506	199	2	applications	application	NOUN
ap-3506	199	3	of	of	ADP
ap-3506	199	4	the	the	DET
ap-3506	199	5	same	same	ADJ
ap-3506	199	6	quantization	quantization	NOUN
ap-3506	199	7	methods	method	NOUN
ap-3506	199	8	to	to	ADP
ap-3506	199	9	more	more	ADV
ap-3506	199	10	involved	involved	ADJ
ap-3506	199	11	cosmological	cosmological	ADJ
ap-3506	199	12	models	model	NOUN
ap-3506	199	13	like	like	ADP
ap-3506	199	14	bianchi	bianchi	NOUN
ap-3506	199	15	i	i	PRON
ap-3506	199	16	and	and	CCONJ
ap-3506	199	17	bianchi	bianchi	PROPN
ap-3506	199	18	ix	ix	PRON
ap-3506	199	19	are	be	AUX
ap-3506	199	20	described	describe	VERB
ap-3506	199	21	in	in	ADP
ap-3506	199	22	[	[	X
ap-3506	199	23	11–15	11–15	NUM
ap-3506	199	24	]	]	X
ap-3506	199	25	.	.	PUNCT
ap-3506	200	1	for	for	ADP
ap-3506	200	2	other	other	ADJ
ap-3506	200	3	approaches	approach	NOUN
ap-3506	200	4	to	to	ADP
ap-3506	200	5	quantum	quantum	ADJ
ap-3506	200	6	cosmology	cosmology	NOUN
ap-3506	200	7	based	base	VERB
ap-3506	200	8	on	on	ADP
ap-3506	200	9	affine	affine	NOUN
ap-3506	200	10	symmetry	symmetry	NOUN
ap-3506	200	11	see	see	VERB
ap-3506	200	12	[	[	X
ap-3506	200	13	24–26	24–26	NUM
ap-3506	200	14	]	]	PUNCT
ap-3506	200	15	.	.	PUNCT
ap-3506	201	1	6	6	X
ap-3506	201	2	.	.	X
ap-3506	201	3	conclusion	conclusion	NOUN
ap-3506	201	4	to	to	PART
ap-3506	201	5	conclude	conclude	VERB
ap-3506	201	6	with	with	ADP
ap-3506	201	7	an	an	DET
ap-3506	201	8	allusion	allusion	NOUN
ap-3506	201	9	to	to	ADP
ap-3506	201	10	more	more	ADJ
ap-3506	201	11	“	"	PUNCT
ap-3506	201	12	philosophical	philosophical	ADJ
ap-3506	201	13	"	"	PUNCT
ap-3506	201	14	perspectives	perspective	NOUN
ap-3506	201	15	,	,	PUNCT
ap-3506	201	16	we	we	PRON
ap-3506	201	17	think	think	VERB
ap-3506	201	18	that	that	SCONJ
ap-3506	201	19	integral	integral	ADJ
ap-3506	201	20	quantization	quantization	NOUN
ap-3506	201	21	is	be	AUX
ap-3506	201	22	just	just	ADV
ap-3506	201	23	a	a	DET
ap-3506	201	24	part	part	NOUN
ap-3506	201	25	of	of	ADP
ap-3506	201	26	a	a	DET
ap-3506	201	27	world	world	NOUN
ap-3506	201	28	of	of	ADP
ap-3506	201	29	mathematical	mathematical	ADJ
ap-3506	201	30	models	model	NOUN
ap-3506	201	31	for	for	ADP
ap-3506	201	32	one	one	NUM
ap-3506	201	33	phenomenon	phenomenon	NOUN
ap-3506	201	34	.	.	PUNCT
ap-3506	202	1	indeed	indeed	ADV
ap-3506	202	2	,	,	PUNCT
ap-3506	202	3	the	the	DET
ap-3506	202	4	physical	physical	ADJ
ap-3506	202	5	laws	law	NOUN
ap-3506	202	6	are	be	AUX
ap-3506	202	7	expressed	express	VERB
ap-3506	202	8	in	in	ADP
ap-3506	202	9	terms	term	NOUN
ap-3506	202	10	of	of	ADP
ap-3506	202	11	combinations	combination	NOUN
ap-3506	202	12	of	of	ADP
ap-3506	202	13	mathematical	mathematical	ADJ
ap-3506	202	14	symbols	symbol	NOUN
ap-3506	202	15	,	,	PUNCT
ap-3506	202	16	and	and	CCONJ
ap-3506	202	17	these	these	DET
ap-3506	202	18	combinations	combination	NOUN
ap-3506	202	19	make	make	VERB
ap-3506	202	20	sense	sense	NOUN
ap-3506	202	21	for	for	ADP
ap-3506	202	22	people	people	NOUN
ap-3506	202	23	who	who	PRON
ap-3506	202	24	have	have	AUX
ap-3506	202	25	learnt	learn	VERB
ap-3506	202	26	these	these	DET
ap-3506	202	27	elements	element	NOUN
ap-3506	202	28	of	of	ADP
ap-3506	202	29	mathematical	mathematical	ADJ
ap-3506	202	30	language	language	NOUN
ap-3506	202	31	.	.	PUNCT
ap-3506	203	1	this	this	DET
ap-3506	203	2	language	language	NOUN
ap-3506	203	3	is	be	AUX
ap-3506	203	4	in	in	ADP
ap-3506	203	5	constant	constant	ADJ
ap-3506	203	6	development	development	NOUN
ap-3506	203	7	,	,	PUNCT
ap-3506	203	8	enhancement	enhancement	NOUN
ap-3506	203	9	,	,	PUNCT
ap-3506	203	10	since	since	SCONJ
ap-3506	203	11	the	the	DET
ap-3506	203	12	set	set	NOUN
ap-3506	203	13	of	of	ADP
ap-3506	203	14	phenomenons	phenomenon	NOUN
ap-3506	203	15	which	which	PRON
ap-3506	203	16	are	be	AUX
ap-3506	203	17	accessible	accessible	ADJ
ap-3506	203	18	to	to	ADP
ap-3506	203	19	our	our	PRON
ap-3506	203	20	understanding	understanding	NOUN
ap-3506	203	21	is	be	AUX
ap-3506	203	22	constantly	constantly	ADV
ap-3506	203	23	broadening	broaden	VERB
ap-3506	203	24	.	.	PUNCT
ap-3506	204	1	these	these	DET
ap-3506	204	2	combinations	combination	NOUN
ap-3506	204	3	take	take	VERB
ap-3506	204	4	place	place	NOUN
ap-3506	204	5	within	within	ADP
ap-3506	204	6	a	a	DET
ap-3506	204	7	mathematical	mathematical	ADJ
ap-3506	204	8	model	model	NOUN
ap-3506	204	9	.	.	PUNCT
ap-3506	205	1	a	a	DET
ap-3506	205	2	model	model	NOUN
ap-3506	205	3	is	be	AUX
ap-3506	205	4	usually	usually	ADV
ap-3506	205	5	scale	scale	NOUN
ap-3506	205	6	dependent	dependent	ADJ
ap-3506	205	7	.	.	PUNCT
ap-3506	206	1	it	it	PRON
ap-3506	206	2	depends	depend	VERB
ap-3506	206	3	on	on	ADP
ap-3506	206	4	a	a	DET
ap-3506	206	5	ratio	ratio	NOUN
ap-3506	206	6	of	of	ADP
ap-3506	206	7	physical	physical	ADJ
ap-3506	206	8	(	(	PUNCT
ap-3506	206	9	i.e.	i.e.	X
ap-3506	206	10	,	,	PUNCT
ap-3506	206	11	measurable	measurable	ADJ
ap-3506	206	12	)	)	PUNCT
ap-3506	206	13	quantities	quantity	NOUN
ap-3506	206	14	,	,	PUNCT
ap-3506	206	15	like	like	ADP
ap-3506	206	16	lengths	length	NOUN
ap-3506	206	17	,	,	PUNCT
ap-3506	206	18	time(s	time(s	NOUN
ap-3506	206	19	)	)	PUNCT
ap-3506	206	20	,	,	PUNCT
ap-3506	206	21	sizes	size	NOUN
ap-3506	206	22	,	,	PUNCT
ap-3506	206	23	impulsions	impulsion	NOUN
ap-3506	206	24	,	,	PUNCT
ap-3506	206	25	actions	action	NOUN
ap-3506	206	26	,	,	PUNCT
ap-3506	206	27	energies	energy	NOUN
ap-3506	206	28	,	,	PUNCT
ap-3506	206	29	etc	etc	X
ap-3506	206	30	.	.	X
ap-3506	206	31	changing	change	VERB
ap-3506	206	32	scale	scale	NOUN
ap-3506	206	33	for	for	ADP
ap-3506	206	34	a	a	DET
ap-3506	206	35	model	model	NOUN
ap-3506	206	36	amounts	amount	VERB
ap-3506	206	37	to	to	PART
ap-3506	206	38	“	"	PUNCT
ap-3506	206	39	quantize	quantize	VERB
ap-3506	206	40	”	"	PUNCT
ap-3506	206	41	or	or	CCONJ
ap-3506	206	42	“	"	PUNCT
ap-3506	206	43	de	de	X
ap-3506	206	44	-	-	NOUN
ap-3506	206	45	quantize	quantize	NOUN
ap-3506	206	46	”	"	PUNCT
ap-3506	206	47	toward	toward	ADP
ap-3506	206	48	(	(	PUNCT
ap-3506	206	49	semi-)classicality	semi-)classicality	NOUN
ap-3506	206	50	.	.	PUNCT
ap-3506	207	1	one	one	NUM
ap-3506	207	2	changes	change	NOUN
ap-3506	207	3	perspective	perspective	VERB
ap-3506	207	4	like	like	SCONJ
ap-3506	207	5	one	one	PRON
ap-3506	207	6	would	would	AUX
ap-3506	207	7	change	change	VERB
ap-3506	207	8	glasses	glass	NOUN
ap-3506	207	9	to	to	PART
ap-3506	207	10	examine	examine	VERB
ap-3506	207	11	one	one	NUM
ap-3506	207	12	’s	’s	PART
ap-3506	207	13	environment	environment	NOUN
ap-3506	207	14	.	.	PUNCT
ap-3506	208	1	acknowledgements	acknowledgement	VERB
ap-3506	208	2	the	the	DET
ap-3506	208	3	author	author	NOUN
ap-3506	208	4	is	be	AUX
ap-3506	208	5	indebted	indebte	VERB
ap-3506	208	6	to	to	ADP
ap-3506	208	7	jiri	jiri	PROPN
ap-3506	208	8	patera	patera	PROPN
ap-3506	208	9	and	and	CCONJ
ap-3506	208	10	pavel	pavel	PROPN
ap-3506	208	11	winternitz	winternitz	PROPN
ap-3506	208	12	for	for	ADP
ap-3506	208	13	inviting	invite	VERB
ap-3506	208	14	him	he	PRON
ap-3506	208	15	at	at	ADP
ap-3506	208	16	many	many	ADJ
ap-3506	208	17	occasions	occasion	NOUN
ap-3506	208	18	to	to	PART
ap-3506	208	19	share	share	VERB
ap-3506	208	20	their	their	PRON
ap-3506	208	21	enthusiasm	enthusiasm	NOUN
ap-3506	208	22	in	in	ADP
ap-3506	208	23	search	search	NOUN
ap-3506	208	24	for	for	ADP
ap-3506	208	25	symmetry	symmetry	NOUN
ap-3506	208	26	.	.	PUNCT
ap-3506	209	1	he	he	PRON
ap-3506	209	2	is	be	AUX
ap-3506	209	3	also	also	ADV
ap-3506	209	4	indebted	indebted	ADJ
ap-3506	209	5	to	to	ADP
ap-3506	209	6	h.	h.	PROPN
ap-3506	209	7	bergeron	bergeron	PROPN
ap-3506	209	8	,	,	PUNCT
ap-3506	209	9	e.	e.	PROPN
ap-3506	209	10	czuchry	czuchry	PROPN
ap-3506	209	11	,	,	PUNCT
ap-3506	209	12	and	and	CCONJ
ap-3506	209	13	p.	p.	NOUN
ap-3506	209	14	małkiewicz	małkiewicz	NOUN
ap-3506	209	15	,	,	PUNCT
ap-3506	209	16	for	for	ADP
ap-3506	209	17	having	having	AUX
ap-3506	209	18	developed	develop	VERB
ap-3506	209	19	with	with	ADP
ap-3506	209	20	them	they	PRON
ap-3506	209	21	a	a	DET
ap-3506	209	22	large	large	ADJ
ap-3506	209	23	part	part	NOUN
ap-3506	209	24	of	of	ADP
ap-3506	209	25	the	the	DET
ap-3506	209	26	material	material	NOUN
ap-3506	209	27	exposed	expose	VERB
ap-3506	209	28	in	in	ADP
ap-3506	209	29	the	the	DET
ap-3506	209	30	present	present	ADJ
ap-3506	209	31	contribution	contribution	NOUN
ap-3506	209	32	.	.	PUNCT
ap-3506	210	1	references	reference	NOUN
ap-3506	210	2	[	[	X
ap-3506	210	3	1	1	NUM
ap-3506	210	4	]	]	PUNCT
ap-3506	210	5	j.-p	j.-p	PROPN
ap-3506	210	6	.	.	PUNCT
ap-3506	211	1	gazeau	gazeau	PROPN
ap-3506	211	2	,	,	PUNCT
ap-3506	211	3	coherent	coherent	ADJ
ap-3506	211	4	states	state	NOUN
ap-3506	211	5	in	in	ADP
ap-3506	211	6	quantum	quantum	ADJ
ap-3506	211	7	physics	physics	NOUN
ap-3506	211	8	,	,	PUNCT
ap-3506	211	9	wiley	wiley	PROPN
ap-3506	211	10	-	-	PUNCT
ap-3506	211	11	vch	vch	PROPN
ap-3506	211	12	,	,	PUNCT
ap-3506	211	13	berlin	berlin	PROPN
ap-3506	211	14	,	,	PUNCT
ap-3506	211	15	2009	2009	NUM
ap-3506	211	16	.	.	PUNCT
ap-3506	212	1	[	[	X
ap-3506	212	2	2	2	X
ap-3506	212	3	]	]	PUNCT
ap-3506	212	4	s.	s.	PROPN
ap-3506	212	5	t.	t.	PROPN
ap-3506	212	6	ali	ali	PROPN
ap-3506	212	7	,	,	PUNCT
ap-3506	212	8	j.-p	j.-p	PROPN
ap-3506	212	9	antoine	antoine	PROPN
ap-3506	212	10	,	,	PUNCT
ap-3506	212	11	and	and	CCONJ
ap-3506	212	12	j.-p	j.-p	PROPN
ap-3506	212	13	.	.	PUNCT
ap-3506	213	1	gazeau	gazeau	PROPN
ap-3506	213	2	,	,	PUNCT
ap-3506	213	3	coherent	coherent	ADJ
ap-3506	213	4	states	state	NOUN
ap-3506	213	5	,	,	PUNCT
ap-3506	213	6	wavelets	wavelet	NOUN
ap-3506	213	7	and	and	CCONJ
ap-3506	213	8	their	their	PRON
ap-3506	213	9	generalizations	generalization	NOUN
ap-3506	213	10	2d	2d	NUM
ap-3506	213	11	edition	edition	NOUN
ap-3506	213	12	,	,	PUNCT
ap-3506	213	13	theoretical	theoretical	ADJ
ap-3506	213	14	and	and	CCONJ
ap-3506	213	15	mathematical	mathematical	ADJ
ap-3506	213	16	physics	physics	NOUN
ap-3506	213	17	,	,	PUNCT
ap-3506	213	18	springer	springer	NOUN
ap-3506	213	19	,	,	PUNCT
ap-3506	213	20	new	new	PROPN
ap-3506	213	21	york	york	PROPN
ap-3506	213	22	(	(	PUNCT
ap-3506	213	23	2013	2013	NUM
ap-3506	213	24	)	)	PUNCT
ap-3506	213	25	,	,	PUNCT
ap-3506	213	26	specially	specially	ADV
ap-3506	213	27	chapter	chapter	NOUN
ap-3506	213	28	11	11	NUM
ap-3506	213	29	.	.	PUNCT
ap-3506	214	1	[	[	X
ap-3506	214	2	3	3	X
ap-3506	214	3	]	]	X
ap-3506	214	4	h.	h.	PROPN
ap-3506	214	5	bergeron	bergeron	PROPN
ap-3506	214	6	,	,	PUNCT
ap-3506	214	7	j.-p	j.-p	PROPN
ap-3506	214	8	.	.	PUNCT
ap-3506	215	1	gazeau	gazeau	PROPN
ap-3506	215	2	,	,	PUNCT
ap-3506	215	3	and	and	CCONJ
ap-3506	215	4	a.	a.	PROPN
ap-3506	215	5	youssef	youssef	PROPN
ap-3506	215	6	,	,	PUNCT
ap-3506	215	7	are	be	AUX
ap-3506	215	8	the	the	DET
ap-3506	215	9	weyl	weyl	ADJ
ap-3506	215	10	and	and	CCONJ
ap-3506	215	11	coherent	coherent	ADJ
ap-3506	215	12	state	state	NOUN
ap-3506	215	13	descriptions	description	NOUN
ap-3506	215	14	physically	physically	ADV
ap-3506	215	15	equivalent	equivalent	ADJ
ap-3506	215	16	?	?	PUNCT
ap-3506	216	1	phys	phy	NOUN
ap-3506	216	2	.	.	PUNCT
ap-3506	217	1	lett	lett	PROPN
ap-3506	217	2	.	.	PUNCT
ap-3506	218	1	a	a	DET
ap-3506	218	2	377	377	NUM
ap-3506	218	3	598(2013	598(2013	NUM
ap-3506	218	4	)	)	PUNCT
ap-3506	218	5	;	;	PUNCT
ap-3506	218	6	arxiv:1102.3556	arxiv:1102.3556	ADP
ap-3506	218	7	[	[	X
ap-3506	218	8	4	4	NUM
ap-3506	218	9	]	]	X
ap-3506	218	10	h	h	PROPN
ap-3506	218	11	bergeron	bergeron	PROPN
ap-3506	218	12	and	and	CCONJ
ap-3506	218	13	j.-p	j.-p	PROPN
ap-3506	218	14	gazeau	gazeau	NOUN
ap-3506	218	15	,	,	PUNCT
ap-3506	218	16	integral	integral	ADJ
ap-3506	218	17	quantizations	quantization	NOUN
ap-3506	218	18	with	with	ADP
ap-3506	218	19	two	two	NUM
ap-3506	218	20	basic	basic	ADJ
ap-3506	218	21	examples	example	NOUN
ap-3506	218	22	,	,	PUNCT
ap-3506	218	23	annals	annal	NOUN
ap-3506	218	24	of	of	ADP
ap-3506	218	25	physics	physics	NOUN
ap-3506	218	26	(	(	PUNCT
ap-3506	218	27	ny	ny	PROPN
ap-3506	218	28	)	)	PUNCT
ap-3506	218	29	344	344	NUM
ap-3506	218	30	43	43	NUM
ap-3506	218	31	(	(	PUNCT
ap-3506	218	32	2014	2014	NUM
ap-3506	218	33	)	)	PUNCT
ap-3506	218	34	;	;	PUNCT
ap-3506	218	35	arxiv:1308.2348	arxiv:1308.2348	PROPN
ap-3506	218	36	[	[	X
ap-3506	218	37	5	5	NUM
ap-3506	218	38	]	]	PUNCT
ap-3506	218	39	h.	h.	PROPN
ap-3506	218	40	bergeron	bergeron	PROPN
ap-3506	218	41	,	,	PUNCT
ap-3506	218	42	e.	e.	PROPN
ap-3506	218	43	m.	m.	PROPN
ap-3506	218	44	f.	f.	PROPN
ap-3506	218	45	curado	curado	PROPN
ap-3506	218	46	,	,	PUNCT
ap-3506	218	47	j.-p	j.-p	PROPN
ap-3506	218	48	.	.	PUNCT
ap-3506	219	1	gazeau	gazeau	PROPN
ap-3506	219	2	,	,	PUNCT
ap-3506	219	3	and	and	CCONJ
ap-3506	219	4	ligia	ligia	PROPN
ap-3506	219	5	m.	m.	PROPN
ap-3506	219	6	c.	c.	PROPN
ap-3506	219	7	s.	s.	PROPN
ap-3506	219	8	rodrigues	rodrigues	PROPN
ap-3506	219	9	,	,	PUNCT
ap-3506	219	10	quantizations	quantization	NOUN
ap-3506	219	11	from	from	ADP
ap-3506	219	12	(	(	PUNCT
ap-3506	219	13	p)ovm	p)ovm	NOUN
ap-3506	219	14	’s	’s	NOUN
ap-3506	219	15	,	,	PUNCT
ap-3506	219	16	j.	j.	PROPN
ap-3506	219	17	phys	phys	PROPN
ap-3506	219	18	.	.	PUNCT
ap-3506	219	19	:	:	PUNCT
ap-3506	220	1	conf	conf	PROPN
ap-3506	220	2	.	.	PUNCT
ap-3506	220	3	ser	ser	PROPN
ap-3506	220	4	.	.	PUNCT
ap-3506	221	1	(	(	PUNCT
ap-3506	221	2	2014	2014	NUM
ap-3506	221	3	)	)	PUNCT
ap-3506	221	4	;	;	PUNCT
ap-3506	221	5	arxiv:1310.3304	arxiv:1310.3304	VERB
ap-3506	221	6	[	[	X
ap-3506	221	7	6	6	NUM
ap-3506	221	8	]	]	PUNCT
ap-3506	221	9	m.	m.	NOUN
ap-3506	221	10	baldiotti	baldiotti	PROPN
ap-3506	221	11	,	,	PUNCT
ap-3506	221	12	r.	r.	PROPN
ap-3506	221	13	fresneda	fresneda	PROPN
ap-3506	221	14	,	,	PUNCT
ap-3506	221	15	and	and	CCONJ
ap-3506	221	16	j.-p	j.-p	PROPN
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ap-3506	222	15	)	)	PUNCT
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ap-3506	224	29	)	)	PUNCT
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ap-3506	225	12	.	.	PUNCT
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ap-3506	227	3	(	(	PUNCT
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ap-3506	227	5	)	)	PUNCT
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ap-3506	228	1	[	[	X
ap-3506	228	2	9	9	NUM
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ap-3506	228	4	r.	r.	X
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ap-3506	228	12	with	with	ADP
ap-3506	228	13	povm	povm	NOUN
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ap-3506	228	17	,	,	PUNCT
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ap-3506	228	19	proceedings	proceeding	NOUN
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ap-3506	228	21	the	the	DET
ap-3506	228	22	30th	30th	ADJ
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ap-3506	228	25	on	on	ADP
ap-3506	228	26	group	group	NOUN
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ap-3506	228	28	methods	method	NOUN
ap-3506	228	29	eds	ed	NOUN
ap-3506	228	30	.	.	PUNCT
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ap-3506	229	2	van	van	PROPN
ap-3506	229	3	der	der	PROPN
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ap-3506	229	5	et	et	PROPN
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ap-3506	229	15	(	(	PUNCT
ap-3506	229	16	2015	2015	NUM
ap-3506	229	17	)	)	PUNCT
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ap-3506	231	13	,	,	PUNCT
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ap-3506	231	17	.	.	PUNCT
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ap-3506	232	4	(	(	PUNCT
ap-3506	232	5	2014	2014	NUM
ap-3506	232	6	)	)	PUNCT
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ap-3506	232	17	,	,	PUNCT
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ap-3506	232	19	.	.	PUNCT
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ap-3506	233	2	,	,	PUNCT
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ap-3506	234	2	d	d	PROPN
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ap-3506	234	5	(	(	PUNCT
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ap-3506	234	7	)	)	PUNCT
ap-3506	234	8	;	;	PUNCT
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ap-3506	234	11	12	12	NUM
ap-3506	234	12	]	]	PUNCT
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ap-3506	234	14	bergeron	bergeron	PROPN
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ap-3506	235	2	,	,	PUNCT
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ap-3506	235	21	.	.	PUNCT
ap-3506	236	1	d	d	PROPN
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ap-3506	236	3	061302(r	061302(r	NOUN
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ap-3506	236	5	(	(	PUNCT
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ap-3506	236	13	h.	h.	PROPN
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ap-3506	237	7	w.	w.	PROPN
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ap-3506	238	20	.	.	PUNCT
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ap-3506	248	5	2187	2187	NUM
ap-3506	248	6	;	;	PUNCT
ap-3506	248	7	2206	2206	NUM
ap-3506	248	8	(	(	PUNCT
ap-3506	248	9	1970	1970	NUM
ap-3506	248	10	)	)	PUNCT
ap-3506	248	11	.	.	PUNCT
ap-3506	249	1	[	[	X
ap-3506	249	2	18	18	NUM
ap-3506	249	3	]	]	X
ap-3506	249	4	f.	f.	PROPN
ap-3506	249	5	a.	a.	PROPN
ap-3506	249	6	berezin	berezin	PROPN
ap-3506	249	7	and	and	CCONJ
ap-3506	249	8	m.	m.	PROPN
ap-3506	249	9	a.	a.	PROPN
ap-3506	249	10	shubin	shubin	PROPN
ap-3506	249	11	,	,	PUNCT
ap-3506	249	12	the	the	DET
ap-3506	249	13	schrödinger	schrödinger	ADJ
ap-3506	249	14	equation	equation	NOUN
ap-3506	249	15	,	,	PUNCT
ap-3506	249	16	kluwer	kluwer	NOUN
ap-3506	249	17	academic	academic	ADJ
ap-3506	249	18	publishers	publisher	NOUN
ap-3506	249	19	,	,	PUNCT
ap-3506	249	20	dordrecht	dordrecht	PROPN
ap-3506	249	21	,	,	PUNCT
ap-3506	249	22	1991	1991	NUM
ap-3506	249	23	.	.	PUNCT
ap-3506	250	1	[	[	X
ap-3506	250	2	19	19	NUM
ap-3506	250	3	]	]	X
ap-3506	250	4	g.	g.	PROPN
ap-3506	250	5	herzberg	herzberg	PROPN
ap-3506	250	6	,	,	PUNCT
ap-3506	250	7	molecular	molecular	ADJ
ap-3506	250	8	spectra	spectra	NOUN
ap-3506	250	9	and	and	CCONJ
ap-3506	250	10	molecular	molecular	ADJ
ap-3506	250	11	structure	structure	NOUN
ap-3506	250	12	:	:	PUNCT
ap-3506	250	13	spectra	spectra	NOUN
ap-3506	250	14	of	of	ADP
ap-3506	250	15	diatomic	diatomic	ADJ
ap-3506	250	16	molecules	molecule	NOUN
ap-3506	250	17	,	,	PUNCT
ap-3506	250	18	2nd	2nd	NOUN
ap-3506	250	19	.	.	PUNCT
ap-3506	251	1	ed	ed	NOUN
ap-3506	251	2	.	.	PROPN
ap-3506	251	3	,	,	PUNCT
ap-3506	251	4	krieger	krieger	PROPN
ap-3506	251	5	pub	pub	PROPN
ap-3506	251	6	.	.	PUNCT
ap-3506	251	7	,	,	PUNCT
ap-3506	251	8	malabar	malabar	PROPN
ap-3506	251	9	,	,	PUNCT
ap-3506	251	10	fl	fl	PROPN
ap-3506	251	11	,	,	PUNCT
ap-3506	251	12	1989	1989	NUM
ap-3506	251	13	.	.	PUNCT
ap-3506	252	1	[	[	X
ap-3506	252	2	20	20	NUM
ap-3506	252	3	]	]	PUNCT
ap-3506	252	4	j.-p	j.-p	PROPN
ap-3506	252	5	.	.	PUNCT
ap-3506	253	1	gazeau	gazeau	PROPN
ap-3506	253	2	and	and	CCONJ
ap-3506	253	3	r.	r.	PROPN
ap-3506	253	4	murenzi	murenzi	PROPN
ap-3506	253	5	,	,	PUNCT
ap-3506	253	6	covariant	covariant	PROPN
ap-3506	253	7	affine	affine	NOUN
ap-3506	253	8	integral	integral	ADJ
ap-3506	253	9	quantization(s	quantization(s	NOUN
ap-3506	253	10	)	)	PUNCT
ap-3506	253	11	,	,	PUNCT
ap-3506	253	12	accepted	accept	VERB
ap-3506	253	13	to	to	ADP
ap-3506	253	14	j.	j.	PROPN
ap-3506	253	15	math	math	PROPN
ap-3506	253	16	.	.	PUNCT
ap-3506	254	1	phys	phy	NOUN
ap-3506	254	2	.	.	PUNCT
ap-3506	255	1	(	(	PUNCT
ap-3506	255	2	2016	2016	NUM
ap-3506	255	3	)	)	PUNCT
ap-3506	255	4	,	,	PUNCT
ap-3506	255	5	arxiv:1512.08274	arxiv:1512.08274	PRON
ap-3506	255	6	[	[	X
ap-3506	255	7	21	21	NUM
ap-3506	255	8	]	]	PUNCT
ap-3506	255	9	j.-p	j.-p	PROPN
ap-3506	255	10	.	.	PUNCT
ap-3506	256	1	gazeau	gazeau	PROPN
ap-3506	256	2	and	and	CCONJ
ap-3506	256	3	m.	m.	PROPN
ap-3506	256	4	del	del	PROPN
ap-3506	256	5	olmo	olmo	PROPN
ap-3506	256	6	,	,	PUNCT
ap-3506	256	7	unit	unit	NOUN
ap-3506	256	8	disk	disk	NOUN
ap-3506	256	9	&	&	CCONJ
ap-3506	256	10	su(1,1	su(1,1	NOUN
ap-3506	256	11	)	)	PUNCT
ap-3506	256	12	integral	integral	ADJ
ap-3506	256	13	quantizations	quantization	NOUN
ap-3506	256	14	,	,	PUNCT
ap-3506	256	15	in	in	ADP
ap-3506	256	16	preparation	preparation	NOUN
ap-3506	256	17	.	.	PUNCT
ap-3506	257	1	[	[	X
ap-3506	257	2	22	22	NUM
ap-3506	257	3	]	]	X
ap-3506	257	4	r.	r.	PROPN
ap-3506	257	5	fresneda	fresneda	PROPN
ap-3506	257	6	,	,	PUNCT
ap-3506	257	7	j.-p	j.-p	PROPN
ap-3506	257	8	.	.	PUNCT
ap-3506	258	1	gazeau	gazeau	PROPN
ap-3506	258	2	,	,	PUNCT
ap-3506	258	3	and	and	CCONJ
ap-3506	258	4	d.	d.	PROPN
ap-3506	258	5	noguera	noguera	PROPN
ap-3506	258	6	,	,	PUNCT
ap-3506	258	7	covariant	covariant	ADJ
ap-3506	258	8	integral	integral	ADJ
ap-3506	258	9	quantization	quantization	NOUN
ap-3506	258	10	of	of	ADP
ap-3506	258	11	the	the	DET
ap-3506	258	12	motion	motion	NOUN
ap-3506	258	13	on	on	ADP
ap-3506	258	14	the	the	DET
ap-3506	258	15	circle	circle	NOUN
ap-3506	258	16	,	,	PUNCT
ap-3506	258	17	in	in	ADP
ap-3506	258	18	preparation	preparation	NOUN
ap-3506	258	19	.	.	PUNCT
ap-3506	259	1	[	[	X
ap-3506	259	2	23	23	NUM
ap-3506	259	3	]	]	PUNCT
ap-3506	259	4	j.-p	j.-p	PROPN
ap-3506	259	5	.	.	PUNCT
ap-3506	260	1	gazeau	gazeau	PROPN
ap-3506	260	2	,	,	PUNCT
ap-3506	260	3	a.	a.	NOUN
ap-3506	260	4	izadi	izadi	NOUN
ap-3506	260	5	,	,	PUNCT
ap-3506	260	6	a.	a.	NOUN
ap-3506	260	7	rabei	rabei	NOUN
ap-3506	260	8	,	,	PUNCT
ap-3506	260	9	and	and	CCONJ
ap-3506	260	10	m.	m.	NOUN
ap-3506	260	11	takook	takook	PROPN
ap-3506	260	12	,	,	PUNCT
ap-3506	260	13	covariant	covariant	ADJ
ap-3506	260	14	integral	integral	ADJ
ap-3506	260	15	quantization	quantization	NOUN
ap-3506	260	16	of	of	ADP
ap-3506	260	17	the	the	DET
ap-3506	260	18	motion	motion	NOUN
ap-3506	260	19	on	on	ADP
ap-3506	260	20	1	1	NUM
ap-3506	260	21	+	+	SYM
ap-3506	260	22	1	1	NUM
ap-3506	260	23	de	de	NOUN
ap-3506	260	24	sitter	sitter	NOUN
ap-3506	260	25	space	space	NOUN
ap-3506	260	26	-	-	PUNCT
ap-3506	260	27	time	time	NOUN
ap-3506	260	28	,	,	PUNCT
ap-3506	260	29	in	in	ADP
ap-3506	260	30	preparation	preparation	NOUN
ap-3506	260	31	.	.	PUNCT
ap-3506	261	1	[	[	X
ap-3506	261	2	24	24	NUM
ap-3506	261	3	]	]	PUNCT
ap-3506	261	4	m.	m.	NOUN
ap-3506	261	5	fanuel	fanuel	NOUN
ap-3506	261	6	and	and	CCONJ
ap-3506	261	7	s.	s.	PROPN
ap-3506	261	8	zonetti	zonetti	PROPN
ap-3506	261	9	,	,	PUNCT
ap-3506	261	10	affine	affine	ADJ
ap-3506	261	11	quantization	quantization	NOUN
ap-3506	261	12	and	and	CCONJ
ap-3506	261	13	the	the	DET
ap-3506	261	14	initial	initial	ADJ
ap-3506	261	15	cosmological	cosmological	ADJ
ap-3506	261	16	singularity	singularity	NOUN
ap-3506	261	17	,	,	PUNCT
ap-3506	261	18	eur	eur	NOUN
ap-3506	261	19	.	.	PUNCT
ap-3506	262	1	phys	phy	NOUN
ap-3506	262	2	.	.	PUNCT
ap-3506	263	1	lett	lett	PROPN
ap-3506	263	2	.	.	PUNCT
ap-3506	264	1	101	101	NUM
ap-3506	264	2	,	,	PUNCT
ap-3506	264	3	10001	10001	NUM
ap-3506	264	4	(	(	PUNCT
ap-3506	264	5	2013	2013	NUM
ap-3506	264	6	)	)	PUNCT
ap-3506	264	7	;	;	PUNCT
ap-3506	265	1	[	[	X
ap-3506	265	2	25	25	NUM
ap-3506	265	3	]	]	PUNCT
ap-3506	265	4	j.	j.	PROPN
ap-3506	265	5	r.	r.	PROPN
ap-3506	265	6	klauder	klauder	PROPN
ap-3506	265	7	,	,	PUNCT
ap-3506	265	8	an	an	DET
ap-3506	265	9	affinity	affinity	NOUN
ap-3506	265	10	for	for	ADP
ap-3506	265	11	affine	affine	ADJ
ap-3506	265	12	quantum	quantum	NOUN
ap-3506	265	13	gravity	gravity	NOUN
ap-3506	265	14	,	,	PUNCT
ap-3506	265	15	proc	proc	NOUN
ap-3506	265	16	.	.	PUNCT
ap-3506	265	17	steklov	steklov	PROPN
ap-3506	265	18	institute	institute	PROPN
ap-3506	265	19	of	of	ADP
ap-3506	265	20	mathematics	mathematics	PROPN
ap-3506	265	21	272	272	NUM
ap-3506	265	22	,	,	PUNCT
ap-3506	265	23	169	169	NUM
ap-3506	265	24	-	-	SYM
ap-3506	265	25	176	176	NUM
ap-3506	265	26	(	(	PUNCT
ap-3506	265	27	2011	2011	NUM
ap-3506	265	28	)	)	PUNCT
ap-3506	265	29	;	;	PUNCT
ap-3506	266	1	gr	gr	PROPN
ap-3506	266	2	-	-	NOUN
ap-3506	266	3	qc/1003.261	qc/1003.261	ADJ
ap-3506	266	4	[	[	X
ap-3506	266	5	26	26	NUM
ap-3506	266	6	]	]	PUNCT
ap-3506	266	7	j.	j.	PROPN
ap-3506	266	8	r.	r.	PROPN
ap-3506	266	9	klauder	klauder	PROPN
ap-3506	266	10	,	,	PUNCT
ap-3506	266	11	enhanced	enhanced	ADJ
ap-3506	266	12	quantization	quantization	NOUN
ap-3506	266	13	,	,	PUNCT
ap-3506	266	14	particles	particle	NOUN
ap-3506	266	15	,	,	PUNCT
ap-3506	266	16	fields	field	NOUN
ap-3506	266	17	&	&	CCONJ
ap-3506	266	18	gravity	gravity	NOUN
ap-3506	266	19	,	,	PUNCT
ap-3506	266	20	world	world	NOUN
ap-3506	266	21	scientific	scientific	PROPN
ap-3506	266	22	,	,	PUNCT
ap-3506	266	23	singapore	singapore	PROPN
ap-3506	266	24	,	,	PUNCT
ap-3506	266	25	2015	2015	NUM
ap-3506	266	26	.	.	PUNCT
ap-3506	267	1	179	179	NUM
ap-3506	267	2	http://arxiv.org/abs/1512.08274	http://arxiv.org/abs/1512.08274	PROPN
ap-3506	267	3	acta	acta	PROPN
ap-3506	267	4	polytechnica	polytechnica	PROPN
ap-3506	267	5	56(3):173–179	56(3):173–179	PROPN
ap-3506	267	6	,	,	PUNCT
ap-3506	267	7	2016	2016	NUM
ap-3506	267	8	1	1	NUM
ap-3506	267	9	introduction	introduction	NOUN
ap-3506	267	10	2	2	NUM
ap-3506	267	11	what	what	PRON
ap-3506	267	12	is	be	AUX
ap-3506	267	13	quantization	quantization	NOUN
ap-3506	267	14	?	?	PUNCT
ap-3506	268	1	2.1	2.1	NUM
ap-3506	268	2	canonical	canonical	ADJ
ap-3506	268	3	quantization	quantization	NOUN
ap-3506	268	4	2.2	2.2	NUM
ap-3506	268	5	quantization	quantization	NOUN
ap-3506	268	6	:	:	PUNCT
ap-3506	268	7	minimal	minimal	ADJ
ap-3506	268	8	requirements	requirement	NOUN
ap-3506	268	9	3	3	NUM
ap-3506	268	10	integral	integral	ADJ
ap-3506	268	11	quantization(s	quantization(s	NOUN
ap-3506	268	12	)	)	PUNCT
ap-3506	268	13	3.1	3.1	NUM
ap-3506	268	14	integral	integral	ADJ
ap-3506	268	15	quantization	quantization	NOUN
ap-3506	268	16	:	:	PUNCT
ap-3506	268	17	general	general	ADJ
ap-3506	268	18	setting	setting	NOUN
ap-3506	268	19	and	and	CCONJ
ap-3506	268	20	povm	povm	NOUN
ap-3506	268	21	3.1.1	3.1.1	NOUN
ap-3506	268	22	x	x	X
ap-3506	268	23	=	=	PRON
ap-3506	268	24	g	g	NOUN
ap-3506	268	25	:	:	PUNCT
ap-3506	268	26	quantizing	quantize	VERB
ap-3506	268	27	the	the	DET
ap-3506	268	28	group	group	NOUN
ap-3506	268	29	3.1.2	3.1.2	NUM
ap-3506	268	30	x	x	NOUN
ap-3506	268	31	=	=	PRON
ap-3506	268	32	g	g	NOUN
ap-3506	268	33	/	/	SYM
ap-3506	268	34	h	h	NOUN
ap-3506	268	35	:	:	PUNCT
ap-3506	268	36	quantizing	quantize	VERB
ap-3506	268	37	a	a	DET
ap-3506	268	38	non	non	ADJ
ap-3506	268	39	-	-	ADJ
ap-3506	268	40	trivial	trivial	ADJ
ap-3506	268	41	group	group	NOUN
ap-3506	268	42	coset	coset	NOUN
ap-3506	268	43	3.2	3.2	NUM
ap-3506	268	44	an	an	DET
ap-3506	268	45	example	example	NOUN
ap-3506	268	46	of	of	ADP
ap-3506	268	47	construction	construction	NOUN
ap-3506	268	48	of	of	ADP
ap-3506	268	49	original	original	ADJ
ap-3506	268	50	operator	operator	NOUN
ap-3506	268	51	m	m	PROPN
ap-3506	268	52	or	or	CCONJ
ap-3506	268	53	rho	rho	ADJ
ap-3506	268	54	3.3	3.3	NUM
ap-3506	268	55	semi	semi	ADJ
ap-3506	268	56	-	-	ADJ
ap-3506	268	57	classical	classical	ADJ
ap-3506	268	58	portraits	portrait	NOUN
ap-3506	268	59	3.4	3.4	NUM
ap-3506	268	60	comments	comment	NOUN
ap-3506	268	61	4	4	NUM
ap-3506	268	62	weyl	weyl	VERB
ap-3506	268	63	-	-	PUNCT
ap-3506	268	64	heisenberg	heisenberg	PROPN
ap-3506	268	65	covariant	covariant	PROPN
ap-3506	268	66	integral	integral	ADJ
ap-3506	268	67	quantization(s	quantization(s	NOUN
ap-3506	268	68	)	)	PUNCT
ap-3506	268	69	5	5	NUM
ap-3506	268	70	applications	application	NOUN
ap-3506	268	71	of	of	ADP
ap-3506	268	72	acs	acs	NOUN
ap-3506	268	73	quantization	quantization	NOUN
ap-3506	268	74	in	in	ADP
ap-3506	268	75	quantum	quantum	ADJ
ap-3506	268	76	cosmology	cosmology	NOUN
ap-3506	268	77	6	6	NUM
ap-3506	268	78	conclusion	conclusion	NOUN
ap-3506	268	79	acknowledgements	acknowledgement	NOUN
ap-3506	268	80	references	reference	NOUN