id	sid	tid	token	lemma	pos
ap-1402	1	1	acta	acta	PROPN
ap-1402	1	2	polytechnica	polytechnica	PROPN
ap-1402	1	3	vol	vol	NOUN
ap-1402	1	4	.	.	PUNCT
ap-1402	2	1	51	51	NUM
ap-1402	2	2	no	no	NOUN
ap-1402	2	3	.	.	PUNCT
ap-1402	3	1	4/2011	4/2011	NUM
ap-1402	3	2	erlangen	erlangen	PROPN
ap-1402	3	3	programme	programme	PROPN
ap-1402	3	4	at	at	ADP
ap-1402	3	5	large	large	ADJ
ap-1402	3	6	3.2	3.2	NUM
ap-1402	3	7	ladder	ladder	NOUN
ap-1402	3	8	operators	operator	NOUN
ap-1402	3	9	in	in	ADP
ap-1402	3	10	hypercomplex	hypercomplex	ADJ
ap-1402	3	11	mechanics	mechanic	NOUN
ap-1402	3	12	v.	v.	ADP
ap-1402	3	13	v.	v.	CCONJ
ap-1402	3	14	kisil	kisil	PROPN
ap-1402	3	15	abstract	abstract	NOUN
ap-1402	3	16	we	we	PRON
ap-1402	3	17	revise	revise	VERB
ap-1402	3	18	the	the	DET
ap-1402	3	19	construction	construction	NOUN
ap-1402	3	20	of	of	ADP
ap-1402	3	21	creation	creation	NOUN
ap-1402	3	22	/	/	SYM
ap-1402	3	23	annihilation	annihilation	NOUN
ap-1402	3	24	operators	operator	NOUN
ap-1402	3	25	in	in	ADP
ap-1402	3	26	quantum	quantum	ADJ
ap-1402	3	27	mechanics	mechanic	NOUN
ap-1402	3	28	based	base	VERB
ap-1402	3	29	on	on	ADP
ap-1402	3	30	the	the	DET
ap-1402	3	31	representation	representation	NOUN
ap-1402	3	32	theory	theory	NOUN
ap-1402	3	33	of	of	ADP
ap-1402	3	34	the	the	DET
ap-1402	3	35	heisenberg	heisenberg	PROPN
ap-1402	3	36	and	and	CCONJ
ap-1402	3	37	symplectic	symplectic	ADJ
ap-1402	3	38	groups	group	NOUN
ap-1402	3	39	.	.	PUNCT
ap-1402	4	1	besides	besides	SCONJ
ap-1402	4	2	the	the	DET
ap-1402	4	3	standard	standard	ADJ
ap-1402	4	4	harmonic	harmonic	ADJ
ap-1402	4	5	oscillator	oscillator	NOUN
ap-1402	4	6	(	(	PUNCT
ap-1402	4	7	the	the	DET
ap-1402	4	8	elliptic	elliptic	ADJ
ap-1402	4	9	case	case	NOUN
ap-1402	4	10	)	)	PUNCT
ap-1402	4	11	we	we	PRON
ap-1402	4	12	similarly	similarly	ADV
ap-1402	4	13	treat	treat	VERB
ap-1402	4	14	the	the	DET
ap-1402	4	15	repulsive	repulsive	ADJ
ap-1402	4	16	oscillator	oscillator	NOUN
ap-1402	4	17	(	(	PUNCT
ap-1402	4	18	hyperbolic	hyperbolic	ADJ
ap-1402	4	19	case	case	NOUN
ap-1402	4	20	)	)	PUNCT
ap-1402	4	21	and	and	CCONJ
ap-1402	4	22	the	the	DET
ap-1402	4	23	free	free	ADJ
ap-1402	4	24	particle	particle	NOUN
ap-1402	4	25	(	(	PUNCT
ap-1402	4	26	the	the	DET
ap-1402	4	27	parabolic	parabolic	ADJ
ap-1402	4	28	case	case	NOUN
ap-1402	4	29	)	)	PUNCT
ap-1402	4	30	.	.	PUNCT
ap-1402	5	1	the	the	DET
ap-1402	5	2	respective	respective	ADJ
ap-1402	5	3	hypercomplex	hypercomplex	NOUN
ap-1402	5	4	numbers	number	NOUN
ap-1402	5	5	turn	turn	VERB
ap-1402	5	6	out	out	ADP
ap-1402	5	7	to	to	PART
ap-1402	5	8	be	be	AUX
ap-1402	5	9	handy	handy	ADJ
ap-1402	5	10	on	on	ADP
ap-1402	5	11	this	this	DET
ap-1402	5	12	occasion	occasion	NOUN
ap-1402	5	13	.	.	PUNCT
ap-1402	6	1	this	this	PRON
ap-1402	6	2	provides	provide	VERB
ap-1402	6	3	a	a	DET
ap-1402	6	4	further	further	ADJ
ap-1402	6	5	illustration	illustration	NOUN
ap-1402	6	6	to	to	ADP
ap-1402	6	7	the	the	DET
ap-1402	6	8	similarity	similarity	NOUN
ap-1402	6	9	and	and	CCONJ
ap-1402	6	10	correspondence	correspondence	NOUN
ap-1402	6	11	principle	principle	NOUN
ap-1402	6	12	.	.	PUNCT
ap-1402	7	1	keywords	keyword	NOUN
ap-1402	7	2	:	:	PUNCT
ap-1402	7	3	heisenberg	heisenberg	PROPN
ap-1402	7	4	group	group	PROPN
ap-1402	7	5	,	,	PUNCT
ap-1402	7	6	kirillov	kirillov	PROPN
ap-1402	7	7	’s	’s	PART
ap-1402	7	8	method	method	NOUN
ap-1402	7	9	of	of	ADP
ap-1402	7	10	orbits	orbit	NOUN
ap-1402	7	11	,	,	PUNCT
ap-1402	7	12	geometric	geometric	ADJ
ap-1402	7	13	quantisation	quantisation	NOUN
ap-1402	7	14	,	,	PUNCT
ap-1402	7	15	quantum	quantum	NOUN
ap-1402	7	16	mechanics	mechanic	NOUN
ap-1402	7	17	,	,	PUNCT
ap-1402	7	18	classical	classical	ADJ
ap-1402	7	19	mechanics	mechanic	NOUN
ap-1402	7	20	,	,	PUNCT
ap-1402	7	21	planck	planck	NOUN
ap-1402	7	22	constant	constant	ADJ
ap-1402	7	23	,	,	PUNCT
ap-1402	7	24	dual	dual	ADJ
ap-1402	7	25	numbers	number	NOUN
ap-1402	7	26	,	,	PUNCT
ap-1402	7	27	double	double	ADJ
ap-1402	7	28	numbers	number	NOUN
ap-1402	7	29	,	,	PUNCT
ap-1402	7	30	hypercomplex	hypercomplex	NOUN
ap-1402	7	31	,	,	PUNCT
ap-1402	7	32	jet	jet	NOUN
ap-1402	7	33	spaces	space	NOUN
ap-1402	7	34	,	,	PUNCT
ap-1402	7	35	hyperbolic	hyperbolic	ADJ
ap-1402	7	36	mechanics	mechanic	NOUN
ap-1402	7	37	,	,	PUNCT
ap-1402	7	38	interference	interference	NOUN
ap-1402	7	39	,	,	PUNCT
ap-1402	7	40	fock	fock	ADJ
ap-1402	7	41	-	-	PUNCT
ap-1402	7	42	segal	segal	NOUN
ap-1402	7	43	-	-	PUNCT
ap-1402	7	44	bargmann	bargmann	PROPN
ap-1402	7	45	representation	representation	NOUN
ap-1402	7	46	,	,	PUNCT
ap-1402	7	47	schrödinger	schrödinger	NOUN
ap-1402	7	48	representation	representation	NOUN
ap-1402	7	49	,	,	PUNCT
ap-1402	7	50	dynamics	dynamic	NOUN
ap-1402	7	51	equation	equation	NOUN
ap-1402	7	52	,	,	PUNCT
ap-1402	7	53	harmonic	harmonic	ADJ
ap-1402	7	54	and	and	CCONJ
ap-1402	7	55	unharmonic	unharmonic	ADJ
ap-1402	7	56	oscillator	oscillator	NOUN
ap-1402	7	57	,	,	PUNCT
ap-1402	7	58	contextual	contextual	ADJ
ap-1402	7	59	probability	probability	NOUN
ap-1402	7	60	,	,	PUNCT
ap-1402	7	61	symplectic	symplectic	ADJ
ap-1402	7	62	group	group	NOUN
ap-1402	7	63	,	,	PUNCT
ap-1402	7	64	metaplectic	metaplectic	ADJ
ap-1402	7	65	representation	representation	NOUN
ap-1402	7	66	,	,	PUNCT
ap-1402	7	67	shale	shale	NOUN
ap-1402	7	68	-	-	PUNCT
ap-1402	7	69	weil	weil	PROPN
ap-1402	7	70	representation	representation	NOUN
ap-1402	7	71	.	.	PUNCT
ap-1402	8	1	1	1	NUM
ap-1402	8	2	introduction	introduction	NOUN
ap-1402	8	3	harmonic	harmonic	ADJ
ap-1402	8	4	oscillators	oscillator	NOUN
ap-1402	8	5	are	be	AUX
ap-1402	8	6	treated	treat	VERB
ap-1402	8	7	in	in	ADP
ap-1402	8	8	most	most	ADJ
ap-1402	8	9	textbooks	textbook	NOUN
ap-1402	8	10	on	on	ADP
ap-1402	8	11	quantum	quantum	ADJ
ap-1402	8	12	mechanics	mechanic	NOUN
ap-1402	8	13	.	.	PUNCT
ap-1402	9	1	this	this	PRON
ap-1402	9	2	is	be	AUX
ap-1402	9	3	efficiently	efficiently	ADV
ap-1402	9	4	done	do	VERB
ap-1402	9	5	through	through	ADP
ap-1402	9	6	creation	creation	NOUN
ap-1402	9	7	/	/	SYM
ap-1402	9	8	annihilation	annihilation	NOUN
ap-1402	9	9	(	(	PUNCT
ap-1402	9	10	ladder	ladder	NOUN
ap-1402	9	11	)	)	PUNCT
ap-1402	9	12	operators	operator	NOUN
ap-1402	10	1	[	[	X
ap-1402	10	2	9	9	NUM
ap-1402	10	3	,	,	PUNCT
ap-1402	10	4	3	3	NUM
ap-1402	10	5	]	]	PUNCT
ap-1402	10	6	.	.	PUNCT
ap-1402	11	1	the	the	DET
ap-1402	11	2	underlying	underlie	VERB
ap-1402	11	3	structure	structure	NOUN
ap-1402	11	4	is	be	AUX
ap-1402	11	5	the	the	DET
ap-1402	11	6	representation	representation	NOUN
ap-1402	11	7	theory	theory	NOUN
ap-1402	11	8	of	of	ADP
ap-1402	11	9	the	the	DET
ap-1402	11	10	heisenberg	heisenberg	PROPN
ap-1402	11	11	and	and	CCONJ
ap-1402	11	12	symplectic	symplectic	ADJ
ap-1402	11	13	groups	group	NOUN
ap-1402	11	14	[	[	X
ap-1402	11	15	28	28	NUM
ap-1402	11	16	,	,	PUNCT
ap-1402	11	17	§	§	PROPN
ap-1402	11	18	vi.2	vi.2	PROPN
ap-1402	11	19	]	]	PUNCT
ap-1402	11	20	,	,	PUNCT
ap-1402	11	21	[	[	X
ap-1402	11	22	34	34	NUM
ap-1402	11	23	,	,	PUNCT
ap-1402	11	24	§	§	PROPN
ap-1402	11	25	8.2	8.2	NUM
ap-1402	11	26	]	]	PUNCT
ap-1402	11	27	,	,	PUNCT
ap-1402	11	28	[	[	X
ap-1402	11	29	12	12	NUM
ap-1402	11	30	,	,	PUNCT
ap-1402	11	31	8	8	NUM
ap-1402	11	32	]	]	PUNCT
ap-1402	11	33	.	.	PUNCT
ap-1402	12	1	it	it	PRON
ap-1402	12	2	is	be	AUX
ap-1402	12	3	also	also	ADV
ap-1402	12	4	known	know	VERB
ap-1402	12	5	that	that	SCONJ
ap-1402	12	6	quantum	quantum	ADJ
ap-1402	12	7	mechanics	mechanic	NOUN
ap-1402	12	8	and	and	CCONJ
ap-1402	12	9	field	field	NOUN
ap-1402	12	10	theory	theory	NOUN
ap-1402	12	11	can	can	AUX
ap-1402	12	12	benefit	benefit	VERB
ap-1402	12	13	from	from	ADP
ap-1402	12	14	the	the	DET
ap-1402	12	15	introduction	introduction	NOUN
ap-1402	12	16	of	of	ADP
ap-1402	12	17	clifford	clifford	PROPN
ap-1402	12	18	algebra	algebra	PROPN
ap-1402	12	19	-	-	PUNCT
ap-1402	12	20	valued	value	VERB
ap-1402	12	21	group	group	NOUN
ap-1402	12	22	representations	representation	VERB
ap-1402	12	23	[	[	X
ap-1402	12	24	20	20	NUM
ap-1402	12	25	,	,	PUNCT
ap-1402	12	26	5	5	NUM
ap-1402	12	27	,	,	PUNCT
ap-1402	12	28	4	4	NUM
ap-1402	12	29	,	,	PUNCT
ap-1402	12	30	10	10	NUM
ap-1402	12	31	]	]	PUNCT
ap-1402	12	32	.	.	PUNCT
ap-1402	13	1	the	the	DET
ap-1402	13	2	dynamics	dynamic	NOUN
ap-1402	13	3	of	of	ADP
ap-1402	13	4	a	a	DET
ap-1402	13	5	harmonic	harmonic	ADJ
ap-1402	13	6	oscillator	oscillator	NOUN
ap-1402	13	7	generates	generate	VERB
ap-1402	13	8	the	the	DET
ap-1402	13	9	symplectic	symplectic	ADJ
ap-1402	13	10	transformation	transformation	NOUN
ap-1402	13	11	of	of	ADP
ap-1402	13	12	the	the	DET
ap-1402	13	13	phase	phase	NOUN
ap-1402	13	14	space	space	NOUN
ap-1402	13	15	of	of	ADP
ap-1402	13	16	the	the	DET
ap-1402	13	17	elliptic	elliptic	ADJ
ap-1402	13	18	type	type	NOUN
ap-1402	13	19	.	.	PUNCT
ap-1402	14	1	the	the	DET
ap-1402	14	2	respective	respective	ADJ
ap-1402	14	3	parabolic	parabolic	NOUN
ap-1402	14	4	and	and	CCONJ
ap-1402	14	5	hyperbolic	hyperbolic	ADJ
ap-1402	14	6	counterparts	counterpart	NOUN
ap-1402	14	7	are	be	AUX
ap-1402	14	8	also	also	ADV
ap-1402	14	9	of	of	ADP
ap-1402	14	10	interest	interest	NOUN
ap-1402	14	11	[	[	X
ap-1402	14	12	37	37	NUM
ap-1402	14	13	,	,	PUNCT
ap-1402	14	14	§	§	PROPN
ap-1402	14	15	3.8	3.8	NUM
ap-1402	14	16	]	]	PUNCT
ap-1402	14	17	,	,	PUNCT
ap-1402	14	18	[	[	X
ap-1402	14	19	35	35	NUM
ap-1402	14	20	]	]	PUNCT
ap-1402	14	21	.	.	PUNCT
ap-1402	15	1	as	as	SCONJ
ap-1402	15	2	we	we	PRON
ap-1402	15	3	will	will	AUX
ap-1402	15	4	see	see	VERB
ap-1402	15	5	,	,	PUNCT
ap-1402	15	6	they	they	PRON
ap-1402	15	7	are	be	AUX
ap-1402	15	8	naturally	naturally	ADV
ap-1402	15	9	connected	connect	VERB
ap-1402	15	10	with	with	ADP
ap-1402	15	11	the	the	DET
ap-1402	15	12	respective	respective	ADJ
ap-1402	15	13	hypercomplex	hypercomplex	NOUN
ap-1402	15	14	numbers	number	NOUN
ap-1402	15	15	.	.	PUNCT
ap-1402	16	1	to	to	PART
ap-1402	16	2	make	make	VERB
ap-1402	16	3	this	this	DET
ap-1402	16	4	correspondence	correspondence	NOUN
ap-1402	16	5	explicit	explicit	ADJ
ap-1402	16	6	we	we	PRON
ap-1402	16	7	recall	recall	VERB
ap-1402	16	8	that	that	SCONJ
ap-1402	16	9	the	the	DET
ap-1402	16	10	symplectic	symplectic	ADJ
ap-1402	16	11	group	group	NOUN
ap-1402	16	12	sp(2	sp(2	NOUN
ap-1402	16	13	)	)	PUNCT
ap-1402	17	1	[	[	X
ap-1402	17	2	8	8	NUM
ap-1402	17	3	,	,	PUNCT
ap-1402	17	4	§	§	NOUN
ap-1402	17	5	1.2	1.2	NUM
ap-1402	17	6	]	]	PUNCT
ap-1402	17	7	consists	consist	VERB
ap-1402	17	8	of	of	ADP
ap-1402	17	9	2×2	2×2	NUM
ap-1402	17	10	matrices	matrix	NOUN
ap-1402	17	11	with	with	ADP
ap-1402	17	12	real	real	ADJ
ap-1402	17	13	entries	entry	NOUN
ap-1402	17	14	and	and	CCONJ
ap-1402	17	15	the	the	DET
ap-1402	17	16	unit	unit	NOUN
ap-1402	17	17	determinant	determinant	ADJ
ap-1402	17	18	.	.	PUNCT
ap-1402	18	1	it	it	PRON
ap-1402	18	2	is	be	AUX
ap-1402	18	3	isomorphic	isomorphic	ADJ
ap-1402	18	4	to	to	ADP
ap-1402	18	5	the	the	DET
ap-1402	18	6	group	group	NOUN
ap-1402	18	7	sl2(r	sl2(r	PROPN
ap-1402	18	8	)	)	PUNCT
ap-1402	19	1	[	[	X
ap-1402	19	2	28,13,30	28,13,30	NUM
ap-1402	19	3	]	]	PUNCT
ap-1402	19	4	and	and	CCONJ
ap-1402	19	5	provides	provide	VERB
ap-1402	19	6	linear	linear	ADJ
ap-1402	19	7	symplectomorphisms	symplectomorphism	NOUN
ap-1402	19	8	of	of	ADP
ap-1402	19	9	the	the	DET
ap-1402	19	10	twodimensional	twodimensional	ADJ
ap-1402	19	11	phase	phase	NOUN
ap-1402	19	12	space	space	NOUN
ap-1402	19	13	.	.	PUNCT
ap-1402	20	1	it	it	PRON
ap-1402	20	2	has	have	VERB
ap-1402	20	3	three	three	NUM
ap-1402	20	4	types	type	NOUN
ap-1402	20	5	of	of	ADP
ap-1402	20	6	nonisomorphic	nonisomorphic	ADJ
ap-1402	20	7	one	one	NUM
ap-1402	20	8	-	-	PUNCT
ap-1402	20	9	dimensional	dimensional	ADJ
ap-1402	20	10	subgroups	subgroup	NOUN
ap-1402	20	11	represented	represent	VERB
ap-1402	20	12	by	by	ADP
ap-1402	20	13	:	:	PUNCT
ap-1402	20	14	k	k	X
ap-1402	20	15	=	=	PUNCT
ap-1402	20	16	{	{	PUNCT
ap-1402	20	17	(	(	PUNCT
ap-1402	20	18	cos	cos	PROPN
ap-1402	20	19	t	t	PROPN
ap-1402	20	20	sin	sin	NOUN
ap-1402	20	21	t	t	PROPN
ap-1402	20	22	−	−	PROPN
ap-1402	20	23	sin	sin	PROPN
ap-1402	20	24	t	t	PROPN
ap-1402	20	25	cos	cos	PROPN
ap-1402	20	26	t	t	PROPN
ap-1402	20	27	)	)	PUNCT
ap-1402	21	1	=	=	NOUN
ap-1402	21	2	exp	exp	NOUN
ap-1402	21	3	(	(	PUNCT
ap-1402	21	4	0	0	NUM
ap-1402	21	5	t	t	PROPN
ap-1402	21	6	−t	−t	NOUN
ap-1402	21	7	0	0	NUM
ap-1402	21	8	)	)	PUNCT
ap-1402	21	9	,	,	PUNCT
ap-1402	21	10	t	t	PROPN
ap-1402	21	11	∈	∈	PROPN
ap-1402	21	12	(	(	PUNCT
ap-1402	21	13	−π	−π	PROPN
ap-1402	21	14	,	,	PUNCT
ap-1402	21	15	π	π	X
ap-1402	21	16	]	]	X
ap-1402	21	17	}	}	PUNCT
ap-1402	21	18	,	,	PUNCT
ap-1402	21	19	(	(	PUNCT
ap-1402	21	20	1	1	X
ap-1402	21	21	)	)	PUNCT
ap-1402	21	22	n	n	NOUN
ap-1402	21	23	=	=	PRON
ap-1402	21	24	{	{	PUNCT
ap-1402	21	25	(	(	PUNCT
ap-1402	21	26	1	1	NUM
ap-1402	21	27	t	t	NOUN
ap-1402	21	28	0	0	NUM
ap-1402	21	29	1	1	NUM
ap-1402	21	30	)	)	PUNCT
ap-1402	21	31	=	=	NOUN
ap-1402	21	32	exp	exp	NOUN
ap-1402	21	33	(	(	PUNCT
ap-1402	21	34	0	0	NUM
ap-1402	21	35	t	t	NOUN
ap-1402	21	36	0	0	NUM
ap-1402	21	37	0	0	NUM
ap-1402	21	38	)	)	PUNCT
ap-1402	21	39	,	,	PUNCT
ap-1402	21	40	t	t	PROPN
ap-1402	21	41	∈	∈	PROPN
ap-1402	21	42	r	r	NOUN
ap-1402	21	43	}	}	PUNCT
ap-1402	21	44	,	,	PUNCT
ap-1402	21	45	(	(	PUNCT
ap-1402	21	46	2	2	X
ap-1402	21	47	)	)	PUNCT
ap-1402	21	48	a	a	PRON
ap-1402	21	49	=	=	X
ap-1402	21	50	{	{	PUNCT
ap-1402	21	51	(	(	PUNCT
ap-1402	21	52	et	et	NOUN
ap-1402	21	53	0	0	NUM
ap-1402	21	54	0	0	NUM
ap-1402	21	55	e−t	e−t	NOUN
ap-1402	21	56	)	)	PUNCT
ap-1402	21	57	=	=	SYM
ap-1402	21	58	exp	exp	NOUN
ap-1402	21	59	(	(	PUNCT
ap-1402	21	60	t	t	PROPN
ap-1402	21	61	0	0	NUM
ap-1402	21	62	0	0	NUM
ap-1402	21	63	−t	−t	PROPN
ap-1402	21	64	)	)	PUNCT
ap-1402	21	65	,	,	PUNCT
ap-1402	21	66	t	t	PROPN
ap-1402	21	67	∈	∈	PROPN
ap-1402	21	68	r	r	NOUN
ap-1402	21	69	}	}	PUNCT
ap-1402	21	70	.	.	PUNCT
ap-1402	22	1	(	(	PUNCT
ap-1402	22	2	3	3	X
ap-1402	22	3	)	)	PUNCT
ap-1402	22	4	we	we	PRON
ap-1402	22	5	will	will	AUX
ap-1402	22	6	refer	refer	VERB
ap-1402	22	7	to	to	ADP
ap-1402	22	8	them	they	PRON
ap-1402	22	9	as	as	ADP
ap-1402	22	10	elliptic	elliptic	ADJ
ap-1402	22	11	,	,	PUNCT
ap-1402	22	12	parabolic	parabolic	ADJ
ap-1402	22	13	and	and	CCONJ
ap-1402	22	14	hyperbolic	hyperbolic	ADJ
ap-1402	22	15	subgroups	subgroup	NOUN
ap-1402	22	16	,	,	PUNCT
ap-1402	22	17	respectively	respectively	ADV
ap-1402	22	18	.	.	PUNCT
ap-1402	23	1	on	on	ADP
ap-1402	23	2	the	the	DET
ap-1402	23	3	other	other	ADJ
ap-1402	23	4	hand	hand	NOUN
ap-1402	23	5	,	,	PUNCT
ap-1402	23	6	there	there	PRON
ap-1402	23	7	are	be	VERB
ap-1402	23	8	three	three	NUM
ap-1402	23	9	nonisomorphic	nonisomorphic	ADJ
ap-1402	23	10	types	type	NOUN
ap-1402	23	11	of	of	ADP
ap-1402	23	12	commutative	commutative	ADJ
ap-1402	23	13	,	,	PUNCT
ap-1402	23	14	associative	associative	ADJ
ap-1402	23	15	twodimensional	twodimensional	ADJ
ap-1402	23	16	algebras	algebra	NOUN
ap-1402	23	17	known	know	VERB
ap-1402	23	18	as	as	ADP
ap-1402	23	19	complex	complex	ADJ
ap-1402	23	20	,	,	PUNCT
ap-1402	23	21	dual	dual	ADJ
ap-1402	23	22	and	and	CCONJ
ap-1402	23	23	double	double	ADJ
ap-1402	23	24	numbers	number	NOUN
ap-1402	23	25	[	[	X
ap-1402	23	26	38	38	NUM
ap-1402	23	27	,	,	PUNCT
ap-1402	23	28	app	app	X
ap-1402	23	29	.	.	PUNCT
ap-1402	24	1	c	c	X
ap-1402	24	2	]	]	X
ap-1402	24	3	,	,	PUNCT
ap-1402	24	4	[	[	X
ap-1402	24	5	29	29	NUM
ap-1402	24	6	,	,	PUNCT
ap-1402	24	7	§	§	PROPN
ap-1402	24	8	5	5	NUM
ap-1402	24	9	]	]	PUNCT
ap-1402	24	10	.	.	PUNCT
ap-1402	25	1	they	they	PRON
ap-1402	25	2	are	be	AUX
ap-1402	25	3	represented	represent	VERB
ap-1402	25	4	by	by	ADP
ap-1402	25	5	expressions	expression	NOUN
ap-1402	25	6	x	x	PUNCT
ap-1402	26	1	+	+	CCONJ
ap-1402	26	2	ιy	ιy	CCONJ
ap-1402	26	3	,	,	PUNCT
ap-1402	26	4	where	where	SCONJ
ap-1402	26	5	ι	ι	PROPN
ap-1402	26	6	stands	stand	VERB
ap-1402	26	7	for	for	ADP
ap-1402	26	8	one	one	NUM
ap-1402	26	9	of	of	ADP
ap-1402	26	10	the	the	DET
ap-1402	26	11	hypercomplex	hypercomplex	NOUN
ap-1402	26	12	units	unit	NOUN
ap-1402	26	13	i	i	PRON
ap-1402	26	14	,	,	PUNCT
ap-1402	26	15	ε	ε	PROPN
ap-1402	26	16	or	or	CCONJ
ap-1402	26	17	j	j	PROPN
ap-1402	26	18	with	with	ADP
ap-1402	26	19	the	the	DET
ap-1402	26	20	properties	property	NOUN
ap-1402	26	21	:	:	PUNCT
ap-1402	26	22	i2	i2	PROPN
ap-1402	26	23	=	=	SYM
ap-1402	26	24	−1	−1	NOUN
ap-1402	26	25	,	,	PUNCT
ap-1402	26	26	ε2	ε2	PROPN
ap-1402	26	27	=	=	SYM
ap-1402	26	28	0	0	NUM
ap-1402	26	29	,	,	PUNCT
ap-1402	26	30	j2	j2	NOUN
ap-1402	26	31	=	=	SYM
ap-1402	26	32	1	1	X
ap-1402	26	33	.	.	PUNCT
ap-1402	27	1	these	these	DET
ap-1402	27	2	units	unit	NOUN
ap-1402	27	3	can	can	AUX
ap-1402	27	4	also	also	ADV
ap-1402	27	5	be	be	AUX
ap-1402	27	6	labelled	label	VERB
ap-1402	27	7	as	as	ADP
ap-1402	27	8	elliptic	elliptic	ADJ
ap-1402	27	9	,	,	PUNCT
ap-1402	27	10	parabolic	parabolic	ADJ
ap-1402	27	11	and	and	CCONJ
ap-1402	27	12	hyperbolic	hyperbolic	ADJ
ap-1402	27	13	.	.	PUNCT
ap-1402	28	1	in	in	ADP
ap-1402	28	2	an	an	DET
ap-1402	28	3	earlier	early	ADJ
ap-1402	28	4	paper	paper	NOUN
ap-1402	28	5	[	[	X
ap-1402	28	6	25	25	NUM
ap-1402	28	7	]	]	PUNCT
ap-1402	28	8	,	,	PUNCT
ap-1402	28	9	we	we	PRON
ap-1402	28	10	considered	consider	VERB
ap-1402	28	11	representations	representation	NOUN
ap-1402	28	12	of	of	ADP
ap-1402	28	13	the	the	DET
ap-1402	28	14	heisenberg	heisenberg	PROPN
ap-1402	28	15	group	group	NOUN
ap-1402	28	16	which	which	PRON
ap-1402	28	17	are	be	AUX
ap-1402	28	18	induced	induce	VERB
ap-1402	28	19	by	by	ADP
ap-1402	28	20	hypercomplex	hypercomplex	NOUN
ap-1402	28	21	characters	character	NOUN
ap-1402	28	22	of	of	ADP
ap-1402	28	23	its	its	PRON
ap-1402	28	24	centre	centre	NOUN
ap-1402	28	25	.	.	PUNCT
ap-1402	29	1	the	the	DET
ap-1402	29	2	elliptic	elliptic	ADJ
ap-1402	29	3	case	case	NOUN
ap-1402	29	4	(	(	PUNCT
ap-1402	29	5	complex	complex	ADJ
ap-1402	29	6	numbers	number	NOUN
ap-1402	29	7	)	)	PUNCT
ap-1402	29	8	describes	describe	VERB
ap-1402	29	9	the	the	DET
ap-1402	29	10	traditional	traditional	ADJ
ap-1402	29	11	framework	framework	NOUN
ap-1402	29	12	of	of	ADP
ap-1402	29	13	quantum	quantum	ADJ
ap-1402	29	14	mechanics	mechanic	NOUN
ap-1402	29	15	,	,	PUNCT
ap-1402	29	16	of	of	ADP
ap-1402	29	17	course	course	NOUN
ap-1402	29	18	.	.	PUNCT
ap-1402	30	1	double	double	ADJ
ap-1402	30	2	-	-	PUNCT
ap-1402	30	3	valued	value	VERB
ap-1402	30	4	representations	representation	NOUN
ap-1402	30	5	,	,	PUNCT
ap-1402	30	6	with	with	ADP
ap-1402	30	7	the	the	DET
ap-1402	30	8	imaginary	imaginary	ADJ
ap-1402	30	9	unit	unit	NOUN
ap-1402	30	10	j2	j2	NOUN
ap-1402	30	11	=	=	SYM
ap-1402	30	12	1	1	NUM
ap-1402	30	13	,	,	PUNCT
ap-1402	30	14	are	be	AUX
ap-1402	30	15	a	a	DET
ap-1402	30	16	natural	natural	ADJ
ap-1402	30	17	source	source	NOUN
ap-1402	30	18	of	of	ADP
ap-1402	30	19	hyperbolic	hyperbolic	ADJ
ap-1402	30	20	quantum	quantum	ADJ
ap-1402	30	21	mechanics	mechanic	NOUN
ap-1402	30	22	developed	develop	VERB
ap-1402	30	23	for	for	ADP
ap-1402	30	24	a	a	DET
ap-1402	30	25	while	while	NOUN
ap-1402	30	26	[	[	X
ap-1402	30	27	14,15,17	14,15,17	NUM
ap-1402	30	28	,	,	PUNCT
ap-1402	30	29	16	16	NUM
ap-1402	30	30	,	,	PUNCT
ap-1402	30	31	18	18	NUM
ap-1402	30	32	]	]	PUNCT
ap-1402	30	33	.	.	PUNCT
ap-1402	31	1	the	the	DET
ap-1402	31	2	representation	representation	NOUN
ap-1402	31	3	acts	act	VERB
ap-1402	31	4	on	on	ADP
ap-1402	31	5	a	a	DET
ap-1402	31	6	krein	krein	ADJ
ap-1402	31	7	space	space	NOUN
ap-1402	31	8	with	with	ADP
ap-1402	31	9	an	an	DET
ap-1402	31	10	indefinite	indefinite	ADJ
ap-1402	31	11	inner	inner	ADJ
ap-1402	31	12	product	product	NOUN
ap-1402	31	13	[	[	X
ap-1402	31	14	2	2	NUM
ap-1402	31	15	]	]	PUNCT
ap-1402	31	16	.	.	PUNCT
ap-1402	32	1	this	this	PRON
ap-1402	32	2	aroused	arouse	VERB
ap-1402	32	3	significant	significant	ADJ
ap-1402	32	4	recent	recent	ADJ
ap-1402	32	5	interest	interest	NOUN
ap-1402	32	6	in	in	ADP
ap-1402	32	7	connection	connection	NOUN
ap-1402	32	8	with	with	ADP
ap-1402	32	9	pt	pt	X
ap-1402	32	10	symmetric	symmetric	ADJ
ap-1402	32	11	quantum	quantum	ADJ
ap-1402	32	12	mechanics	mechanic	NOUN
ap-1402	32	13	[	[	X
ap-1402	32	14	10	10	NUM
ap-1402	32	15	]	]	PUNCT
ap-1402	32	16	.	.	PUNCT
ap-1402	33	1	however	however	ADV
ap-1402	33	2	,	,	PUNCT
ap-1402	33	3	our	our	PRON
ap-1402	33	4	approach	approach	NOUN
ap-1402	33	5	is	be	AUX
ap-1402	33	6	different	different	ADJ
ap-1402	33	7	from	from	ADP
ap-1402	33	8	the	the	DET
ap-1402	33	9	classical	classical	ADJ
ap-1402	33	10	treatment	treatment	NOUN
ap-1402	33	11	of	of	ADP
ap-1402	33	12	krein	krein	ADJ
ap-1402	33	13	spaces	space	NOUN
ap-1402	33	14	:	:	PUNCT
ap-1402	33	15	we	we	PRON
ap-1402	33	16	use	use	VERB
ap-1402	33	17	the	the	DET
ap-1402	33	18	hyperbolic	hyperbolic	ADJ
ap-1402	33	19	unit	unit	NOUN
ap-1402	33	20	j	j	PROPN
ap-1402	33	21	and	and	CCONJ
ap-1402	33	22	build	build	VERB
ap-1402	33	23	the	the	DET
ap-1402	33	24	hyperbolic	hyperbolic	ADJ
ap-1402	33	25	analytic	analytic	ADJ
ap-1402	33	26	function	function	NOUN
ap-1402	33	27	theory	theory	NOUN
ap-1402	33	28	on	on	ADP
ap-1402	33	29	its	its	PRON
ap-1402	33	30	own	own	ADJ
ap-1402	33	31	basis	basis	NOUN
ap-1402	33	32	[	[	X
ap-1402	33	33	21	21	NUM
ap-1402	33	34	,	,	PUNCT
ap-1402	33	35	27	27	NUM
ap-1402	33	36	]	]	PUNCT
ap-1402	33	37	.	.	PUNCT
ap-1402	34	1	in	in	ADP
ap-1402	34	2	the	the	DET
ap-1402	34	3	traditional	traditional	ADJ
ap-1402	34	4	approach	approach	NOUN
ap-1402	34	5	,	,	PUNCT
ap-1402	34	6	the	the	DET
ap-1402	34	7	indefinite	indefinite	ADJ
ap-1402	34	8	metric	metric	NOUN
ap-1402	34	9	is	be	AUX
ap-1402	34	10	mapped	map	VERB
ap-1402	34	11	to	to	ADP
ap-1402	34	12	a	a	DET
ap-1402	34	13	definite	definite	ADJ
ap-1402	34	14	inner	inner	ADJ
ap-1402	34	15	product	product	NOUN
ap-1402	34	16	through	through	ADP
ap-1402	34	17	auxiliary	auxiliary	ADJ
ap-1402	34	18	operators	operator	NOUN
ap-1402	34	19	.	.	PUNCT
ap-1402	35	1	44	44	NUM
ap-1402	35	2	acta	acta	PROPN
ap-1402	35	3	polytechnica	polytechnica	PROPN
ap-1402	35	4	vol	vol	NOUN
ap-1402	35	5	.	.	PUNCT
ap-1402	36	1	51	51	NUM
ap-1402	36	2	no	no	INTJ
ap-1402	36	3	.	.	PUNCT
ap-1402	37	1	4/2011	4/2011	NUM
ap-1402	38	1	the	the	DET
ap-1402	38	2	representation	representation	NOUN
ap-1402	38	3	with	with	ADP
ap-1402	38	4	values	value	NOUN
ap-1402	38	5	in	in	ADP
ap-1402	38	6	dual	dual	ADJ
ap-1402	38	7	numbers	number	NOUN
ap-1402	38	8	provides	provide	VERB
ap-1402	38	9	a	a	DET
ap-1402	38	10	convenient	convenient	ADJ
ap-1402	38	11	description	description	NOUN
ap-1402	38	12	of	of	ADP
ap-1402	38	13	the	the	DET
ap-1402	38	14	classical	classical	ADJ
ap-1402	38	15	mechanics	mechanic	NOUN
ap-1402	38	16	.	.	PUNCT
ap-1402	39	1	to	to	ADP
ap-1402	39	2	this	this	DET
ap-1402	39	3	end	end	NOUN
ap-1402	39	4	we	we	PRON
ap-1402	39	5	do	do	AUX
ap-1402	39	6	not	not	PART
ap-1402	39	7	take	take	VERB
ap-1402	39	8	any	any	DET
ap-1402	39	9	sort	sort	NOUN
ap-1402	39	10	of	of	ADP
ap-1402	39	11	semiclassical	semiclassical	ADJ
ap-1402	39	12	limit	limit	NOUN
ap-1402	39	13	,	,	PUNCT
ap-1402	39	14	rather	rather	ADV
ap-1402	39	15	the	the	DET
ap-1402	39	16	nilpotency	nilpotency	NOUN
ap-1402	39	17	of	of	ADP
ap-1402	39	18	the	the	DET
ap-1402	39	19	imaginary	imaginary	ADJ
ap-1402	39	20	unit	unit	NOUN
ap-1402	39	21	(	(	PUNCT
ap-1402	39	22	ε2	ε2	NOUN
ap-1402	39	23	=	=	SYM
ap-1402	39	24	0	0	NUM
ap-1402	39	25	)	)	PUNCT
ap-1402	39	26	performs	perform	VERB
ap-1402	39	27	the	the	DET
ap-1402	39	28	task	task	NOUN
ap-1402	39	29	.	.	PUNCT
ap-1402	40	1	this	this	PRON
ap-1402	40	2	removes	remove	VERB
ap-1402	40	3	the	the	DET
ap-1402	40	4	vicious	vicious	ADJ
ap-1402	40	5	necessity	necessity	NOUN
ap-1402	40	6	to	to	PART
ap-1402	40	7	consider	consider	VERB
ap-1402	40	8	the	the	DET
ap-1402	40	9	planck	planck	NOUN
ap-1402	40	10	constant	constant	ADJ
ap-1402	40	11	tending	tend	VERB
ap-1402	40	12	to	to	ADP
ap-1402	40	13	zero	zero	NUM
ap-1402	40	14	.	.	PUNCT
ap-1402	41	1	mixing	mix	VERB
ap-1402	41	2	this	this	PRON
ap-1402	41	3	with	with	ADP
ap-1402	41	4	complex	complex	ADJ
ap-1402	41	5	numbers	number	NOUN
ap-1402	41	6	we	we	PRON
ap-1402	41	7	get	get	VERB
ap-1402	41	8	a	a	DET
ap-1402	41	9	convenient	convenient	ADJ
ap-1402	41	10	tool	tool	NOUN
ap-1402	41	11	for	for	ADP
ap-1402	41	12	modelling	model	VERB
ap-1402	41	13	the	the	DET
ap-1402	41	14	interaction	interaction	NOUN
ap-1402	41	15	between	between	ADP
ap-1402	41	16	quantum	quantum	NOUN
ap-1402	41	17	and	and	CCONJ
ap-1402	41	18	classical	classical	ADJ
ap-1402	41	19	systems	system	NOUN
ap-1402	41	20	[	[	X
ap-1402	41	21	22	22	NUM
ap-1402	41	22	,	,	PUNCT
ap-1402	41	23	24	24	NUM
ap-1402	41	24	]	]	PUNCT
ap-1402	41	25	.	.	PUNCT
ap-1402	42	1	our	our	PRON
ap-1402	42	2	construction	construction	NOUN
ap-1402	42	3	[	[	X
ap-1402	42	4	25	25	NUM
ap-1402	42	5	]	]	PUNCT
ap-1402	42	6	provides	provide	VERB
ap-1402	42	7	three	three	NUM
ap-1402	42	8	different	different	ADJ
ap-1402	42	9	types	type	NOUN
ap-1402	42	10	of	of	ADP
ap-1402	42	11	dynamics	dynamic	NOUN
ap-1402	42	12	and	and	CCONJ
ap-1402	42	13	also	also	ADV
ap-1402	42	14	generates	generate	VERB
ap-1402	42	15	the	the	DET
ap-1402	42	16	respective	respective	ADJ
ap-1402	42	17	rules	rule	NOUN
ap-1402	42	18	for	for	ADP
ap-1402	42	19	addition	addition	NOUN
ap-1402	42	20	of	of	ADP
ap-1402	42	21	probabilities	probability	NOUN
ap-1402	42	22	.	.	PUNCT
ap-1402	43	1	in	in	ADP
ap-1402	43	2	this	this	DET
ap-1402	43	3	paper	paper	NOUN
ap-1402	43	4	we	we	PRON
ap-1402	43	5	analyse	analyse	VERB
ap-1402	43	6	the	the	DET
ap-1402	43	7	three	three	NUM
ap-1402	43	8	types	type	NOUN
ap-1402	43	9	of	of	ADP
ap-1402	43	10	dynamics	dynamic	NOUN
ap-1402	43	11	produced	produce	VERB
ap-1402	43	12	by	by	ADP
ap-1402	43	13	transformations	transformation	NOUN
ap-1402	43	14	(	(	PUNCT
ap-1402	43	15	1–3	1–3	NOUN
ap-1402	43	16	)	)	PUNCT
ap-1402	43	17	from	from	ADP
ap-1402	43	18	the	the	DET
ap-1402	43	19	symplectic	symplectic	ADJ
ap-1402	43	20	group	group	NOUN
ap-1402	43	21	sp(2	sp(2	NOUN
ap-1402	43	22	)	)	PUNCT
ap-1402	43	23	by	by	ADP
ap-1402	43	24	means	mean	NOUN
ap-1402	43	25	of	of	ADP
ap-1402	43	26	ladder	ladder	NOUN
ap-1402	43	27	operators	operator	NOUN
ap-1402	43	28	.	.	PUNCT
ap-1402	44	1	as	as	ADP
ap-1402	44	2	a	a	DET
ap-1402	44	3	result	result	NOUN
ap-1402	44	4	we	we	PRON
ap-1402	44	5	obtain	obtain	VERB
ap-1402	44	6	further	further	ADJ
ap-1402	44	7	illustrations	illustration	NOUN
ap-1402	44	8	to	to	ADP
ap-1402	44	9	the	the	DET
ap-1402	44	10	following	following	NOUN
ap-1402	44	11	:	:	PUNCT
ap-1402	44	12	principle	principle	NOUN
ap-1402	44	13	(	(	PUNCT
ap-1402	44	14	similarity	similarity	NOUN
ap-1402	44	15	and	and	CCONJ
ap-1402	44	16	correspondence	correspondence	NOUN
ap-1402	44	17	)	)	PUNCT
ap-1402	45	1	[	[	X
ap-1402	45	2	23	23	NUM
ap-1402	45	3	,	,	PUNCT
ap-1402	45	4	principle	principle	NOUN
ap-1402	45	5	29	29	NUM
ap-1402	45	6	]	]	SYM
ap-1402	45	7	1	1	NUM
ap-1402	45	8	.	.	PUNCT
ap-1402	45	9	subgroups	subgroup	NOUN
ap-1402	45	10	k	k	X
ap-1402	45	11	,	,	PUNCT
ap-1402	45	12	n	n	PROPN
ap-1402	45	13	and	and	CCONJ
ap-1402	45	14	a	a	DET
ap-1402	45	15	play	play	NOUN
ap-1402	45	16	a	a	DET
ap-1402	45	17	similar	similar	ADJ
ap-1402	45	18	role	role	NOUN
ap-1402	45	19	in	in	ADP
ap-1402	45	20	the	the	DET
ap-1402	45	21	structure	structure	NOUN
ap-1402	45	22	of	of	ADP
ap-1402	45	23	the	the	DET
ap-1402	45	24	group	group	NOUN
ap-1402	45	25	sp(2	sp(2	NOUN
ap-1402	45	26	)	)	PUNCT
ap-1402	45	27	and	and	CCONJ
ap-1402	45	28	its	its	PRON
ap-1402	45	29	representations	representation	NOUN
ap-1402	45	30	.	.	PUNCT
ap-1402	46	1	2	2	X
ap-1402	46	2	.	.	PUNCT
ap-1402	46	3	the	the	DET
ap-1402	46	4	subgroups	subgroup	NOUN
ap-1402	46	5	shall	shall	AUX
ap-1402	46	6	be	be	AUX
ap-1402	46	7	swapped	swap	VERB
ap-1402	46	8	simultaneously	simultaneously	ADV
ap-1402	46	9	with	with	ADP
ap-1402	46	10	the	the	DET
ap-1402	46	11	respective	respective	ADJ
ap-1402	46	12	replacement	replacement	NOUN
ap-1402	46	13	of	of	ADP
ap-1402	46	14	hypercomplex	hypercomplex	PROPN
ap-1402	46	15	unit	unit	NOUN
ap-1402	46	16	ι	ι	X
ap-1402	46	17	.	.	PUNCT
ap-1402	47	1	here	here	ADV
ap-1402	47	2	the	the	DET
ap-1402	47	3	two	two	NUM
ap-1402	47	4	parts	part	NOUN
ap-1402	47	5	are	be	AUX
ap-1402	47	6	interrelated	interrelated	ADJ
ap-1402	47	7	:	:	PUNCT
ap-1402	47	8	without	without	ADP
ap-1402	47	9	a	a	DET
ap-1402	47	10	swap	swap	NOUN
ap-1402	47	11	of	of	ADP
ap-1402	47	12	imaginary	imaginary	ADJ
ap-1402	47	13	units	unit	NOUN
ap-1402	47	14	there	there	PRON
ap-1402	47	15	can	can	AUX
ap-1402	47	16	be	be	AUX
ap-1402	47	17	no	no	DET
ap-1402	47	18	similarity	similarity	NOUN
ap-1402	47	19	between	between	ADP
ap-1402	47	20	different	different	ADJ
ap-1402	47	21	subgroups	subgroup	NOUN
ap-1402	47	22	.	.	PUNCT
ap-1402	48	1	in	in	ADP
ap-1402	48	2	this	this	DET
ap-1402	48	3	paper	paper	NOUN
ap-1402	48	4	we	we	PRON
ap-1402	48	5	work	work	VERB
ap-1402	48	6	with	with	ADP
ap-1402	48	7	the	the	DET
ap-1402	48	8	simplest	simple	ADJ
ap-1402	48	9	case	case	NOUN
ap-1402	48	10	of	of	ADP
ap-1402	48	11	a	a	DET
ap-1402	48	12	particle	particle	NOUN
ap-1402	48	13	with	with	ADP
ap-1402	48	14	only	only	ADV
ap-1402	48	15	one	one	NUM
ap-1402	48	16	degree	degree	NOUN
ap-1402	48	17	of	of	ADP
ap-1402	48	18	freedom	freedom	NOUN
ap-1402	48	19	.	.	PUNCT
ap-1402	49	1	higher	high	ADJ
ap-1402	49	2	dimensions	dimension	NOUN
ap-1402	49	3	and	and	CCONJ
ap-1402	49	4	the	the	DET
ap-1402	49	5	respective	respective	ADJ
ap-1402	49	6	group	group	NOUN
ap-1402	49	7	of	of	ADP
ap-1402	49	8	symplectomorphisms	symplectomorphism	NOUN
ap-1402	49	9	sp(2n	sp(2n	ADJ
ap-1402	49	10	)	)	PUNCT
ap-1402	49	11	may	may	AUX
ap-1402	49	12	require	require	VERB
ap-1402	49	13	consideration	consideration	NOUN
ap-1402	49	14	of	of	ADP
ap-1402	49	15	clifford	clifford	PROPN
ap-1402	49	16	algebras	algebras	PROPN
ap-1402	49	17	[	[	X
ap-1402	49	18	32	32	NUM
ap-1402	49	19	]	]	PUNCT
ap-1402	49	20	.	.	PUNCT
ap-1402	49	21	2	2	NUM
ap-1402	49	22	heisenberg	heisenberg	PROPN
ap-1402	49	23	group	group	NOUN
ap-1402	49	24	and	and	CCONJ
ap-1402	49	25	its	its	PRON
ap-1402	49	26	automorphisms	automorphism	NOUN
ap-1402	49	27	let	let	VERB
ap-1402	49	28	(	(	PUNCT
ap-1402	49	29	s	s	X
ap-1402	49	30	,	,	PUNCT
ap-1402	49	31	x	x	NOUN
ap-1402	49	32	,	,	PUNCT
ap-1402	49	33	y	y	PROPN
ap-1402	49	34	)	)	PUNCT
ap-1402	49	35	,	,	PUNCT
ap-1402	49	36	where	where	SCONJ
ap-1402	49	37	s	s	X
ap-1402	49	38	,	,	PUNCT
ap-1402	49	39	x	x	PRON
ap-1402	49	40	,	,	PUNCT
ap-1402	49	41	y	y	PROPN
ap-1402	49	42	∈	∈	PROPN
ap-1402	49	43	r	r	NOUN
ap-1402	49	44	,	,	PUNCT
ap-1402	49	45	be	be	AUX
ap-1402	49	46	an	an	DET
ap-1402	49	47	element	element	NOUN
ap-1402	49	48	of	of	ADP
ap-1402	49	49	the	the	DET
ap-1402	49	50	one	one	NUM
ap-1402	49	51	-	-	PUNCT
ap-1402	49	52	dimensional	dimensional	ADJ
ap-1402	49	53	heisenberg	heisenberg	PROPN
ap-1402	49	54	group	group	NOUN
ap-1402	49	55	h	h	NOUN
ap-1402	49	56	1	1	NUM
ap-1402	50	1	[	[	X
ap-1402	50	2	8	8	NUM
ap-1402	50	3	,	,	PUNCT
ap-1402	50	4	12	12	NUM
ap-1402	50	5	]	]	PUNCT
ap-1402	50	6	.	.	PUNCT
ap-1402	51	1	consideration	consideration	NOUN
ap-1402	51	2	of	of	ADP
ap-1402	51	3	the	the	DET
ap-1402	51	4	general	general	ADJ
ap-1402	51	5	case	case	NOUN
ap-1402	51	6	of	of	ADP
ap-1402	51	7	h	h	NOUN
ap-1402	51	8	n	n	NOUN
ap-1402	51	9	will	will	AUX
ap-1402	51	10	be	be	AUX
ap-1402	51	11	similar	similar	ADJ
ap-1402	51	12	,	,	PUNCT
ap-1402	51	13	but	but	CCONJ
ap-1402	51	14	is	be	AUX
ap-1402	51	15	beyond	beyond	ADP
ap-1402	51	16	the	the	DET
ap-1402	51	17	scope	scope	NOUN
ap-1402	51	18	of	of	ADP
ap-1402	51	19	present	present	ADJ
ap-1402	51	20	paper	paper	NOUN
ap-1402	51	21	.	.	PUNCT
ap-1402	52	1	the	the	DET
ap-1402	52	2	group	group	NOUN
ap-1402	52	3	law	law	NOUN
ap-1402	52	4	on	on	ADP
ap-1402	52	5	h	h	PROPN
ap-1402	52	6	1	1	NUM
ap-1402	52	7	is	be	AUX
ap-1402	52	8	given	give	VERB
ap-1402	52	9	as	as	SCONJ
ap-1402	52	10	follows	follow	VERB
ap-1402	52	11	:	:	PUNCT
ap-1402	52	12	(	(	PUNCT
ap-1402	52	13	s	s	X
ap-1402	52	14	,	,	PUNCT
ap-1402	52	15	x	x	NOUN
ap-1402	52	16	,	,	PUNCT
ap-1402	52	17	y	y	PROPN
ap-1402	52	18	)	)	PUNCT
ap-1402	52	19	·	·	PUNCT
ap-1402	53	1	(	(	PUNCT
ap-1402	53	2	s′	s′	X
ap-1402	53	3	,	,	PUNCT
ap-1402	53	4	x′	x′	NUM
ap-1402	53	5	,	,	PUNCT
ap-1402	53	6	y′	y′	NUM
ap-1402	53	7	)	)	PUNCT
ap-1402	53	8	=(	=(	PROPN
ap-1402	53	9	s	s	PART
ap-1402	53	10	+	+	NOUN
ap-1402	53	11	s′	s′	ADJ
ap-1402	53	12	+	+	NUM
ap-1402	53	13	1	1	NUM
ap-1402	53	14	2	2	NUM
ap-1402	53	15	ω(x	ω(x	NOUN
ap-1402	53	16	,	,	PUNCT
ap-1402	53	17	y	y	PROPN
ap-1402	53	18	;	;	PUNCT
ap-1402	53	19	x′	x′	NUM
ap-1402	53	20	,	,	PUNCT
ap-1402	53	21	y′	y′	NUM
ap-1402	53	22	)	)	PUNCT
ap-1402	53	23	,	,	PUNCT
ap-1402	53	24	x	x	X
ap-1402	54	1	+	+	NUM
ap-1402	54	2	x′	x′	NUM
ap-1402	54	3	,	,	PUNCT
ap-1402	54	4	y	y	PROPN
ap-1402	54	5	+	+	NOUN
ap-1402	54	6	y′	y′	ADV
ap-1402	54	7	)	)	PUNCT
ap-1402	54	8	,	,	PUNCT
ap-1402	54	9	(	(	PUNCT
ap-1402	54	10	4	4	X
ap-1402	54	11	)	)	PUNCT
ap-1402	54	12	where	where	SCONJ
ap-1402	54	13	the	the	DET
ap-1402	54	14	non	non	NOUN
ap-1402	54	15	-	-	NOUN
ap-1402	54	16	commutativity	commutativity	NOUN
ap-1402	54	17	is	be	AUX
ap-1402	54	18	due	due	ADJ
ap-1402	54	19	to	to	ADP
ap-1402	54	20	ω	ω	NUM
ap-1402	54	21	—	—	PUNCT
ap-1402	54	22	the	the	DET
ap-1402	54	23	symplectic	symplectic	ADJ
ap-1402	54	24	form	form	NOUN
ap-1402	54	25	on	on	ADP
ap-1402	54	26	r	r	NOUN
ap-1402	54	27	2n	2n	NUM
ap-1402	55	1	[	[	X
ap-1402	55	2	1	1	NUM
ap-1402	55	3	,	,	PUNCT
ap-1402	55	4	§	§	PROPN
ap-1402	55	5	37	37	NUM
ap-1402	55	6	]	]	SYM
ap-1402	55	7	:	:	PUNCT
ap-1402	55	8	ω(x	ω(x	X
ap-1402	55	9	,	,	PUNCT
ap-1402	55	10	y	y	PROPN
ap-1402	55	11	;	;	PUNCT
ap-1402	55	12	x′	x′	NUM
ap-1402	55	13	,	,	PUNCT
ap-1402	55	14	y′	y′	NUM
ap-1402	55	15	)	)	PUNCT
ap-1402	55	16	=	=	SYM
ap-1402	56	1	xy′	xy′	PROPN
ap-1402	57	1	−	−	PROPN
ap-1402	58	1	x′y	x′y	PROPN
ap-1402	58	2	.	.	PUNCT
ap-1402	59	1	(	(	PUNCT
ap-1402	59	2	5	5	X
ap-1402	59	3	)	)	PUNCT
ap-1402	59	4	the	the	DET
ap-1402	59	5	heisenberg	heisenberg	PROPN
ap-1402	59	6	group	group	NOUN
ap-1402	59	7	is	be	AUX
ap-1402	59	8	a	a	DET
ap-1402	59	9	non	non	ADJ
ap-1402	59	10	-	-	ADJ
ap-1402	59	11	commutative	commutative	ADJ
ap-1402	59	12	lie	lie	NOUN
ap-1402	59	13	group	group	NOUN
ap-1402	59	14	.	.	PUNCT
ap-1402	60	1	the	the	DET
ap-1402	60	2	left	left	ADJ
ap-1402	60	3	shifts	shift	NOUN
ap-1402	60	4	λ(g	λ(g	NOUN
ap-1402	60	5	)	)	PUNCT
ap-1402	60	6	:	:	PUNCT
ap-1402	60	7	f(g′	f(g′	X
ap-1402	60	8	)	)	PUNCT
ap-1402	60	9	�	�	PROPN
ap-1402	60	10	→	→	SYM
ap-1402	60	11	f(g−1g′	f(g−1g′	NUM
ap-1402	60	12	)	)	PUNCT
ap-1402	60	13	(	(	PUNCT
ap-1402	60	14	6	6	NUM
ap-1402	60	15	)	)	PUNCT
ap-1402	60	16	act	act	NOUN
ap-1402	60	17	as	as	ADP
ap-1402	60	18	a	a	DET
ap-1402	60	19	representation	representation	NOUN
ap-1402	60	20	of	of	ADP
ap-1402	60	21	h	h	NOUN
ap-1402	60	22	1	1	NUM
ap-1402	60	23	on	on	ADP
ap-1402	60	24	a	a	DET
ap-1402	60	25	certain	certain	ADJ
ap-1402	60	26	linear	linear	ADJ
ap-1402	60	27	space	space	NOUN
ap-1402	60	28	of	of	ADP
ap-1402	60	29	functions	function	NOUN
ap-1402	60	30	.	.	PUNCT
ap-1402	61	1	for	for	ADP
ap-1402	61	2	example	example	NOUN
ap-1402	61	3	,	,	PUNCT
ap-1402	61	4	an	an	DET
ap-1402	61	5	action	action	NOUN
ap-1402	61	6	on	on	ADP
ap-1402	61	7	l2(h	l2(h	PROPN
ap-1402	61	8	,	,	PUNCT
ap-1402	61	9	dg	dg	X
ap-1402	61	10	)	)	PUNCT
ap-1402	61	11	with	with	ADP
ap-1402	61	12	respect	respect	NOUN
ap-1402	61	13	to	to	ADP
ap-1402	61	14	the	the	DET
ap-1402	61	15	haar	haar	NOUN
ap-1402	61	16	measure	measure	NOUN
ap-1402	61	17	dg	dg	VERB
ap-1402	61	18	=	=	NOUN
ap-1402	61	19	ds	ds	PROPN
ap-1402	61	20	dx	dx	PROPN
ap-1402	61	21	dy	dy	PROPN
ap-1402	61	22	is	be	AUX
ap-1402	61	23	the	the	DET
ap-1402	61	24	left	left	ADJ
ap-1402	61	25	regular	regular	ADJ
ap-1402	61	26	representation	representation	NOUN
ap-1402	61	27	,	,	PUNCT
ap-1402	61	28	which	which	PRON
ap-1402	61	29	is	be	AUX
ap-1402	61	30	unitary	unitary	ADJ
ap-1402	61	31	.	.	PUNCT
ap-1402	62	1	the	the	DET
ap-1402	62	2	lie	lie	NOUN
ap-1402	62	3	algebra	algebra	NOUN
ap-1402	62	4	h	h	NOUN
ap-1402	62	5	n	n	PROPN
ap-1402	62	6	of	of	ADP
ap-1402	62	7	h1	h1	PROPN
ap-1402	62	8	is	be	AUX
ap-1402	62	9	spanned	span	VERB
ap-1402	62	10	by	by	ADP
ap-1402	62	11	left(right-)invariant	left(right-)invariant	ADJ
ap-1402	62	12	vector	vector	NOUN
ap-1402	62	13	fields	field	NOUN
ap-1402	62	14	sl(r	sl(r	PRON
ap-1402	62	15	)	)	PUNCT
ap-1402	63	1	=	=	SYM
ap-1402	63	2	±∂s	±∂s	NOUN
ap-1402	63	3	,	,	PUNCT
ap-1402	63	4	x	x	PUNCT
ap-1402	63	5	l(r	l(r	PROPN
ap-1402	63	6	)	)	PUNCT
ap-1402	63	7	=	=	SYM
ap-1402	63	8	±∂x	±∂x	NOUN
ap-1402	63	9	−	−	NOUN
ap-1402	63	10	1	1	NUM
ap-1402	63	11	2	2	NUM
ap-1402	63	12	y∂s	y∂s	NOUN
ap-1402	63	13	,	,	PUNCT
ap-1402	63	14	(	(	PUNCT
ap-1402	63	15	7	7	X
ap-1402	63	16	)	)	PUNCT
ap-1402	63	17	y	y	NOUN
ap-1402	63	18	l(r	l(r	PROPN
ap-1402	63	19	)	)	PUNCT
ap-1402	64	1	=	=	NUM
ap-1402	64	2	±∂y	±∂y	NOUN
ap-1402	64	3	+	+	CCONJ
ap-1402	64	4	1	1	NUM
ap-1402	64	5	2	2	NUM
ap-1402	64	6	x∂s	x∂s	X
ap-1402	64	7	on	on	ADP
ap-1402	64	8	h	h	PROPN
ap-1402	64	9	1	1	NUM
ap-1402	64	10	with	with	ADP
ap-1402	64	11	the	the	DET
ap-1402	64	12	heisenberg	heisenberg	PROPN
ap-1402	64	13	commutator	commutator	PROPN
ap-1402	64	14	relation	relation	PROPN
ap-1402	65	1	[	[	X
ap-1402	65	2	x	x	X
ap-1402	65	3	l(r	l(r	PROPN
ap-1402	65	4	)	)	PUNCT
ap-1402	65	5	,	,	PUNCT
ap-1402	65	6	y	y	PROPN
ap-1402	65	7	l(r	l(r	PROPN
ap-1402	65	8	)	)	PUNCT
ap-1402	65	9	]	]	PUNCT
ap-1402	66	1	=	=	SYM
ap-1402	66	2	sl(r	sl(r	X
ap-1402	66	3	)	)	PUNCT
ap-1402	66	4	(	(	PUNCT
ap-1402	66	5	8)	8)	NUM
ap-1402	66	6	and	and	CCONJ
ap-1402	66	7	all	all	DET
ap-1402	66	8	other	other	ADJ
ap-1402	66	9	commutators	commutator	NOUN
ap-1402	66	10	vanishing	vanish	VERB
ap-1402	66	11	.	.	PUNCT
ap-1402	67	1	we	we	PRON
ap-1402	67	2	will	will	AUX
ap-1402	67	3	sometime	sometime	ADV
ap-1402	67	4	omit	omit	VERB
ap-1402	67	5	the	the	DET
ap-1402	67	6	superscript	superscript	PROPN
ap-1402	67	7	l	l	NOUN
ap-1402	67	8	for	for	ADP
ap-1402	67	9	left	left	ADJ
ap-1402	67	10	-	-	PUNCT
ap-1402	67	11	invariant	invariant	ADJ
ap-1402	67	12	field	field	NOUN
ap-1402	67	13	.	.	PUNCT
ap-1402	68	1	the	the	DET
ap-1402	68	2	group	group	NOUN
ap-1402	68	3	of	of	ADP
ap-1402	68	4	outer	outer	ADJ
ap-1402	68	5	automorphisms	automorphism	NOUN
ap-1402	68	6	of	of	ADP
ap-1402	68	7	h1	h1	PROPN
ap-1402	68	8	,	,	PUNCT
ap-1402	68	9	which	which	PRON
ap-1402	68	10	trivially	trivially	ADV
ap-1402	68	11	acts	act	VERB
ap-1402	68	12	on	on	ADP
ap-1402	68	13	the	the	DET
ap-1402	68	14	centre	centre	NOUN
ap-1402	68	15	of	of	ADP
ap-1402	68	16	h	h	PROPN
ap-1402	68	17	1	1	NUM
ap-1402	68	18	,	,	PUNCT
ap-1402	68	19	is	be	AUX
ap-1402	68	20	the	the	DET
ap-1402	68	21	symplectic	symplectic	ADJ
ap-1402	68	22	group	group	NOUN
ap-1402	68	23	sp(2	sp(2	NOUN
ap-1402	68	24	)	)	PUNCT
ap-1402	68	25	defined	define	VERB
ap-1402	68	26	in	in	ADP
ap-1402	68	27	the	the	DET
ap-1402	68	28	previous	previous	ADJ
ap-1402	68	29	section	section	NOUN
ap-1402	68	30	.	.	PUNCT
ap-1402	69	1	it	it	PRON
ap-1402	69	2	is	be	AUX
ap-1402	69	3	the	the	DET
ap-1402	69	4	group	group	NOUN
ap-1402	69	5	of	of	ADP
ap-1402	69	6	symmetries	symmetry	NOUN
ap-1402	69	7	of	of	ADP
ap-1402	69	8	the	the	DET
ap-1402	69	9	symplectic	symplectic	ADJ
ap-1402	69	10	form	form	NOUN
ap-1402	69	11	ω	ω	NOUN
ap-1402	70	1	[	[	X
ap-1402	70	2	8	8	NUM
ap-1402	70	3	,	,	PUNCT
ap-1402	70	4	thm	thm	PROPN
ap-1402	70	5	.	.	PUNCT
ap-1402	71	1	1.22	1.22	NUM
ap-1402	71	2	]	]	PUNCT
ap-1402	71	3	,	,	PUNCT
ap-1402	71	4	[	[	X
ap-1402	71	5	11	11	NUM
ap-1402	71	6	,	,	PUNCT
ap-1402	71	7	p.	p.	NOUN
ap-1402	71	8	830	830	NUM
ap-1402	71	9	]	]	PUNCT
ap-1402	71	10	.	.	PUNCT
ap-1402	72	1	the	the	DET
ap-1402	72	2	symplectic	symplectic	ADJ
ap-1402	72	3	group	group	NOUN
ap-1402	72	4	is	be	AUX
ap-1402	72	5	isomorphic	isomorphic	ADJ
ap-1402	72	6	to	to	ADP
ap-1402	72	7	sl2(r	sl2(r	PROPN
ap-1402	72	8	)	)	PUNCT
ap-1402	73	1	[	[	X
ap-1402	73	2	28	28	NUM
ap-1402	73	3	]	]	PUNCT
ap-1402	73	4	,	,	PUNCT
ap-1402	73	5	[	[	X
ap-1402	73	6	34	34	NUM
ap-1402	73	7	,	,	PUNCT
ap-1402	73	8	ch	ch	NOUN
ap-1402	73	9	.	.	PROPN
ap-1402	73	10	8	8	NUM
ap-1402	73	11	]	]	PUNCT
ap-1402	73	12	.	.	PUNCT
ap-1402	74	1	the	the	DET
ap-1402	74	2	explicit	explicit	ADJ
ap-1402	74	3	action	action	NOUN
ap-1402	74	4	of	of	ADP
ap-1402	74	5	sp(2	sp(2	NOUN
ap-1402	74	6	)	)	PUNCT
ap-1402	74	7	on	on	ADP
ap-1402	74	8	the	the	DET
ap-1402	74	9	heisenberg	heisenberg	PROPN
ap-1402	74	10	group	group	NOUN
ap-1402	74	11	is	be	AUX
ap-1402	74	12	:	:	PUNCT
ap-1402	74	13	g	g	NOUN
ap-1402	74	14	:	:	PUNCT
ap-1402	74	15	h	h	NOUN
ap-1402	74	16	=	=	SYM
ap-1402	74	17	(	(	PUNCT
ap-1402	74	18	s	s	X
ap-1402	74	19	,	,	PUNCT
ap-1402	74	20	x	x	NOUN
ap-1402	74	21	,	,	PUNCT
ap-1402	74	22	y	y	PROPN
ap-1402	74	23	)	)	PUNCT
ap-1402	74	24	�	�	PROPN
ap-1402	74	25	→	→	SYM
ap-1402	74	26	g(h	g(h	PROPN
ap-1402	74	27	)	)	PUNCT
ap-1402	74	28	=	=	PUNCT
ap-1402	74	29	(	(	PUNCT
ap-1402	74	30	s	s	PROPN
ap-1402	74	31	,	,	PUNCT
ap-1402	74	32	x′	x′	NUM
ap-1402	74	33	,	,	PUNCT
ap-1402	74	34	y′	y′	NUM
ap-1402	74	35	)	)	PUNCT
ap-1402	74	36	,	,	PUNCT
ap-1402	74	37	(	(	PUNCT
ap-1402	74	38	9	9	X
ap-1402	74	39	)	)	PUNCT
ap-1402	74	40	where	where	SCONJ
ap-1402	74	41	g	g	NOUN
ap-1402	74	42	=	=	SYM
ap-1402	74	43	(	(	PUNCT
ap-1402	74	44	a	a	DET
ap-1402	74	45	b	b	NOUN
ap-1402	74	46	c	c	PROPN
ap-1402	74	47	d	d	NOUN
ap-1402	74	48	)	)	PUNCT
ap-1402	74	49	∈	∈	PROPN
ap-1402	74	50	sp(2	sp(2	NOUN
ap-1402	74	51	)	)	PUNCT
ap-1402	74	52	,	,	PUNCT
ap-1402	74	53	and	and	CCONJ
ap-1402	74	54	(	(	PUNCT
ap-1402	74	55	x′	x′	PROPN
ap-1402	74	56	y′	y′	ADV
ap-1402	74	57	)	)	PUNCT
ap-1402	75	1	=	=	PRON
ap-1402	75	2	(	(	PUNCT
ap-1402	75	3	a	a	DET
ap-1402	75	4	b	b	NOUN
ap-1402	75	5	c	c	NOUN
ap-1402	75	6	d	d	NOUN
ap-1402	75	7	)	)	PUNCT
ap-1402	75	8	(	(	PUNCT
ap-1402	75	9	x	x	SYM
ap-1402	75	10	y	y	PROPN
ap-1402	75	11	)	)	PUNCT
ap-1402	75	12	.	.	PUNCT
ap-1402	76	1	the	the	DET
ap-1402	76	2	shale	shale	PROPN
ap-1402	76	3	-	-	PUNCT
ap-1402	76	4	weil	weil	PROPN
ap-1402	76	5	theorem	theorem	VERB
ap-1402	76	6	[	[	X
ap-1402	76	7	8	8	NUM
ap-1402	76	8	,	,	PUNCT
ap-1402	76	9	§	§	NOUN
ap-1402	76	10	4.2	4.2	NUM
ap-1402	76	11	]	]	PUNCT
ap-1402	76	12	,	,	PUNCT
ap-1402	76	13	[	[	X
ap-1402	76	14	11	11	NUM
ap-1402	76	15	,	,	PUNCT
ap-1402	76	16	p.	p.	NOUN
ap-1402	76	17	830	830	NUM
ap-1402	76	18	]	]	PUNCT
ap-1402	76	19	states	state	VERB
ap-1402	76	20	that	that	SCONJ
ap-1402	76	21	any	any	DET
ap-1402	76	22	representation	representation	NOUN
ap-1402	76	23	ρh̄	ρh̄	NOUN
ap-1402	76	24	of	of	ADP
ap-1402	76	25	the	the	DET
ap-1402	76	26	heisenberg	heisenberg	PROPN
ap-1402	76	27	groups	group	NOUN
ap-1402	76	28	generates	generate	VERB
ap-1402	76	29	a	a	DET
ap-1402	76	30	unitary	unitary	ADJ
ap-1402	76	31	oscillator	oscillator	NOUN
ap-1402	76	32	(	(	PUNCT
ap-1402	76	33	or	or	CCONJ
ap-1402	76	34	metaplectic	metaplectic	ADJ
ap-1402	76	35	)	)	PUNCT
ap-1402	76	36	representation	representation	NOUN
ap-1402	76	37	ρswh̄	ρswh̄	PROPN
ap-1402	76	38	of	of	ADP
ap-1402	76	39	s̃p(2	s̃p(2	PROPN
ap-1402	76	40	)	)	PUNCT
ap-1402	76	41	,	,	PUNCT
ap-1402	76	42	the	the	DET
ap-1402	76	43	two	two	NUM
ap-1402	76	44	-	-	ADJ
ap-1402	76	45	fold	fold	ADJ
ap-1402	76	46	cover	cover	NOUN
ap-1402	76	47	of	of	ADP
ap-1402	76	48	the	the	DET
ap-1402	76	49	symplectic	symplectic	ADJ
ap-1402	76	50	group	group	NOUN
ap-1402	77	1	[	[	X
ap-1402	77	2	8	8	NUM
ap-1402	77	3	,	,	PUNCT
ap-1402	77	4	thm	thm	PROPN
ap-1402	77	5	.	.	PUNCT
ap-1402	78	1	4.58	4.58	NUM
ap-1402	78	2	]	]	PUNCT
ap-1402	78	3	.	.	PUNCT
ap-1402	79	1	we	we	PRON
ap-1402	79	2	can	can	AUX
ap-1402	79	3	consider	consider	VERB
ap-1402	79	4	the	the	DET
ap-1402	79	5	semidirect	semidirect	NOUN
ap-1402	79	6	product	product	NOUN
ap-1402	79	7	g	g	NOUN
ap-1402	79	8	=	=	PROPN
ap-1402	79	9	h	h	NOUN
ap-1402	79	10	1×|	1×|	NUM
ap-1402	79	11	s̃p(2	s̃p(2	NUM
ap-1402	79	12	)	)	PUNCT
ap-1402	79	13	with	with	ADP
ap-1402	79	14	the	the	DET
ap-1402	79	15	standard	standard	ADJ
ap-1402	79	16	group	group	NOUN
ap-1402	79	17	law	law	NOUN
ap-1402	79	18	:	:	PUNCT
ap-1402	79	19	(	(	PUNCT
ap-1402	79	20	h	h	NOUN
ap-1402	79	21	,	,	PUNCT
ap-1402	79	22	g	g	NOUN
ap-1402	79	23	)	)	PUNCT
ap-1402	79	24	∗	∗	NOUN
ap-1402	79	25	(	(	PUNCT
ap-1402	79	26	h′	h′	PROPN
ap-1402	79	27	,	,	PUNCT
ap-1402	79	28	g′	g′	NOUN
ap-1402	79	29	)	)	PUNCT
ap-1402	79	30	=	=	PUNCT
ap-1402	80	1	(	(	PUNCT
ap-1402	80	2	h	h	NOUN
ap-1402	80	3	∗	∗	PROPN
ap-1402	80	4	g(h′	g(h′	PROPN
ap-1402	80	5	)	)	PUNCT
ap-1402	80	6	,	,	PUNCT
ap-1402	80	7	g	g	PROPN
ap-1402	80	8	∗	∗	NOUN
ap-1402	80	9	g′	g′	NOUN
ap-1402	80	10	)	)	PUNCT
ap-1402	80	11	,	,	PUNCT
ap-1402	80	12	where	where	SCONJ
ap-1402	80	13	h	h	NOUN
ap-1402	80	14	,	,	PUNCT
ap-1402	80	15	h′	h′	PROPN
ap-1402	80	16	∈	∈	PROPN
ap-1402	80	17	h	h	NOUN
ap-1402	80	18	1	1	NUM
ap-1402	80	19	,	,	PUNCT
ap-1402	80	20	g	g	NOUN
ap-1402	80	21	,	,	PUNCT
ap-1402	80	22	g′	g′	NOUN
ap-1402	80	23	∈	∈	PROPN
ap-1402	80	24	s̃p(2	s̃p(2	NOUN
ap-1402	80	25	)	)	PUNCT
ap-1402	80	26	,	,	PUNCT
ap-1402	80	27	and	and	CCONJ
ap-1402	80	28	the	the	DET
ap-1402	80	29	stars	star	NOUN
ap-1402	80	30	denote	denote	VERB
ap-1402	80	31	the	the	DET
ap-1402	80	32	respective	respective	ADJ
ap-1402	80	33	group	group	NOUN
ap-1402	80	34	operations	operation	NOUN
ap-1402	80	35	while	while	SCONJ
ap-1402	80	36	the	the	DET
ap-1402	80	37	action	action	NOUN
ap-1402	80	38	g(h′	g(h′	NOUN
ap-1402	80	39	)	)	PUNCT
ap-1402	80	40	is	be	AUX
ap-1402	80	41	defined	define	VERB
ap-1402	80	42	as	as	ADP
ap-1402	80	43	the	the	DET
ap-1402	80	44	composition	composition	NOUN
ap-1402	80	45	of	of	ADP
ap-1402	80	46	the	the	DET
ap-1402	80	47	projection	projection	NOUN
ap-1402	80	48	map	map	NOUN
ap-1402	80	49	s̃p(2	s̃p(2	NOUN
ap-1402	80	50	)	)	PUNCT
ap-1402	80	51	→	→	SYM
ap-1402	80	52	sp(2	sp(2	NOUN
ap-1402	80	53	)	)	PUNCT
ap-1402	80	54	and	and	CCONJ
ap-1402	80	55	the	the	DET
ap-1402	80	56	action	action	NOUN
ap-1402	80	57	(	(	PUNCT
ap-1402	80	58	9	9	NUM
ap-1402	80	59	)	)	PUNCT
ap-1402	80	60	.	.	PUNCT
ap-1402	81	1	this	this	DET
ap-1402	81	2	group	group	NOUN
ap-1402	81	3	is	be	AUX
ap-1402	81	4	sometimes	sometimes	ADV
ap-1402	81	5	called	call	VERB
ap-1402	81	6	the	the	DET
ap-1402	81	7	schrödinger	schrödinger	NOUN
ap-1402	81	8	group	group	NOUN
ap-1402	81	9	,	,	PUNCT
ap-1402	81	10	and	and	CCONJ
ap-1402	81	11	it	it	PRON
ap-1402	81	12	is	be	AUX
ap-1402	81	13	known	know	VERB
ap-1402	81	14	as	as	ADP
ap-1402	81	15	the	the	DET
ap-1402	81	16	maximal	maximal	ADJ
ap-1402	81	17	kinematical	kinematical	ADJ
ap-1402	81	18	invariance	invariance	NOUN
ap-1402	81	19	group	group	NOUN
ap-1402	81	20	of	of	ADP
ap-1402	81	21	both	both	CCONJ
ap-1402	81	22	the	the	DET
ap-1402	81	23	free	free	ADJ
ap-1402	81	24	schrödinger	schrödinger	NOUN
ap-1402	81	25	equation	equation	NOUN
ap-1402	81	26	and	and	CCONJ
ap-1402	81	27	the	the	DET
ap-1402	81	28	quantum	quantum	ADJ
ap-1402	81	29	harmonic	harmonic	NOUN
ap-1402	81	30	oscillator	oscillator	NOUN
ap-1402	81	31	[	[	X
ap-1402	81	32	31	31	NUM
ap-1402	81	33	]	]	PUNCT
ap-1402	81	34	.	.	PUNCT
ap-1402	82	1	this	this	DET
ap-1402	82	2	group	group	NOUN
ap-1402	82	3	is	be	AUX
ap-1402	82	4	of	of	ADP
ap-1402	82	5	interest	interest	NOUN
ap-1402	82	6	not	not	PART
ap-1402	82	7	only	only	ADV
ap-1402	82	8	in	in	ADP
ap-1402	82	9	quantum	quantum	ADJ
ap-1402	82	10	mechanics	mechanic	NOUN
ap-1402	82	11	but	but	CCONJ
ap-1402	82	12	also	also	ADV
ap-1402	82	13	in	in	ADP
ap-1402	82	14	optics	optic	NOUN
ap-1402	82	15	[	[	X
ap-1402	82	16	36	36	NUM
ap-1402	82	17	,	,	PUNCT
ap-1402	82	18	35	35	NUM
ap-1402	82	19	]	]	PUNCT
ap-1402	82	20	.	.	PUNCT
ap-1402	83	1	45	45	NUM
ap-1402	83	2	acta	acta	PROPN
ap-1402	83	3	polytechnica	polytechnica	PROPN
ap-1402	83	4	vol	vol	NOUN
ap-1402	83	5	.	.	PUNCT
ap-1402	84	1	51	51	NUM
ap-1402	84	2	no	no	NOUN
ap-1402	84	3	.	.	PUNCT
ap-1402	85	1	4/2011	4/2011	PROPN
ap-1402	85	2	consider	consider	VERB
ap-1402	85	3	the	the	DET
ap-1402	85	4	lie	lie	NOUN
ap-1402	85	5	algebra	algebra	NOUN
ap-1402	85	6	sp2	sp2	NOUN
ap-1402	85	7	of	of	ADP
ap-1402	85	8	the	the	DET
ap-1402	85	9	group	group	NOUN
ap-1402	85	10	sp(2	sp(2	NOUN
ap-1402	85	11	)	)	PUNCT
ap-1402	85	12	.	.	PUNCT
ap-1402	86	1	pick	pick	VERB
ap-1402	86	2	up	up	ADP
ap-1402	86	3	the	the	DET
ap-1402	86	4	following	following	ADJ
ap-1402	86	5	basis	basis	NOUN
ap-1402	86	6	in	in	ADP
ap-1402	86	7	sp2	sp2	NOUN
ap-1402	86	8	[	[	X
ap-1402	86	9	34	34	NUM
ap-1402	86	10	,	,	PUNCT
ap-1402	86	11	§	§	PROPN
ap-1402	86	12	8.1	8.1	NUM
ap-1402	86	13	]	]	X
ap-1402	86	14	:	:	PUNCT
ap-1402	86	15	a	a	PRON
ap-1402	86	16	=	=	SYM
ap-1402	86	17	1	1	NUM
ap-1402	86	18	2	2	NUM
ap-1402	86	19	(	(	PUNCT
ap-1402	86	20	−1	−1	NOUN
ap-1402	86	21	0	0	SYM
ap-1402	86	22	0	0	NUM
ap-1402	86	23	1	1	NUM
ap-1402	86	24	)	)	PUNCT
ap-1402	86	25	,	,	PUNCT
ap-1402	86	26	b	b	X
ap-1402	86	27	=	=	SYM
ap-1402	86	28	1	1	NUM
ap-1402	86	29	2	2	NUM
ap-1402	86	30	(	(	PUNCT
ap-1402	86	31	0	0	NUM
ap-1402	86	32	1	1	NUM
ap-1402	86	33	1	1	NUM
ap-1402	86	34	0	0	NUM
ap-1402	86	35	)	)	PUNCT
ap-1402	86	36	,	,	PUNCT
ap-1402	86	37	z	z	NOUN
ap-1402	86	38	=	=	PUNCT
ap-1402	86	39	(	(	PUNCT
ap-1402	86	40	0	0	NUM
ap-1402	86	41	1	1	NUM
ap-1402	86	42	−1	−1	NOUN
ap-1402	86	43	0	0	NUM
ap-1402	86	44	)	)	PUNCT
ap-1402	86	45	.	.	PUNCT
ap-1402	87	1	the	the	DET
ap-1402	87	2	commutation	commutation	NOUN
ap-1402	87	3	relations	relation	NOUN
ap-1402	87	4	between	between	ADP
ap-1402	87	5	the	the	DET
ap-1402	87	6	elements	element	NOUN
ap-1402	87	7	are	be	AUX
ap-1402	87	8	:	:	PUNCT
ap-1402	88	1	[	[	X
ap-1402	88	2	z	z	X
ap-1402	88	3	,	,	PUNCT
ap-1402	88	4	a	a	PRON
ap-1402	88	5	]	]	X
ap-1402	88	6	=	=	SYM
ap-1402	88	7	2b	2b	NOUN
ap-1402	88	8	,	,	PUNCT
ap-1402	88	9	[	[	X
ap-1402	88	10	z	z	X
ap-1402	88	11	,	,	PUNCT
ap-1402	88	12	b	b	NOUN
ap-1402	88	13	]	]	X
ap-1402	88	14	=	=	SYM
ap-1402	88	15	−2a	−2a	PROPN
ap-1402	88	16	,	,	PUNCT
ap-1402	88	17	[	[	X
ap-1402	88	18	a	a	X
ap-1402	88	19	,	,	PUNCT
ap-1402	88	20	b	b	NOUN
ap-1402	88	21	]	]	X
ap-1402	88	22	=	=	SYM
ap-1402	88	23	−1	−1	NOUN
ap-1402	88	24	2	2	NUM
ap-1402	88	25	z.	z.	X
ap-1402	88	26	(	(	PUNCT
ap-1402	88	27	10	10	NUM
ap-1402	88	28	)	)	PUNCT
ap-1402	88	29	vectors	vector	NOUN
ap-1402	88	30	z	z	PROPN
ap-1402	88	31	,	,	PUNCT
ap-1402	88	32	b	b	PROPN
ap-1402	88	33	+	+	CCONJ
ap-1402	88	34	z/2	z/2	NUM
ap-1402	88	35	and	and	CCONJ
ap-1402	88	36	−a	−a	NOUN
ap-1402	88	37	are	be	AUX
ap-1402	88	38	generators	generator	NOUN
ap-1402	88	39	of	of	ADP
ap-1402	88	40	the	the	DET
ap-1402	88	41	one	one	NUM
ap-1402	88	42	-	-	PUNCT
ap-1402	88	43	parameter	parameter	NOUN
ap-1402	88	44	subgroups	subgroup	NOUN
ap-1402	88	45	k	k	X
ap-1402	88	46	,	,	PUNCT
ap-1402	88	47	n	n	PROPN
ap-1402	88	48	and	and	CCONJ
ap-1402	88	49	a	a	DET
ap-1402	88	50	(	(	PUNCT
ap-1402	88	51	1–3	1–3	NOUN
ap-1402	88	52	)	)	PUNCT
ap-1402	88	53	respectively	respectively	ADV
ap-1402	88	54	.	.	PUNCT
ap-1402	89	1	furthermore	furthermore	ADV
ap-1402	89	2	,	,	PUNCT
ap-1402	89	3	we	we	PRON
ap-1402	89	4	can	can	AUX
ap-1402	89	5	consider	consider	VERB
ap-1402	89	6	the	the	DET
ap-1402	89	7	basis	basis	NOUN
ap-1402	89	8	{	{	PUNCT
ap-1402	89	9	s	s	X
ap-1402	89	10	,	,	PUNCT
ap-1402	89	11	x	x	NOUN
ap-1402	89	12	,	,	PUNCT
ap-1402	89	13	y	y	PROPN
ap-1402	89	14	,	,	PUNCT
ap-1402	89	15	a	a	DET
ap-1402	89	16	,	,	PUNCT
ap-1402	89	17	b	b	NOUN
ap-1402	89	18	,	,	PUNCT
ap-1402	89	19	z	z	NOUN
ap-1402	89	20	}	}	PUNCT
ap-1402	89	21	of	of	ADP
ap-1402	89	22	the	the	DET
ap-1402	89	23	lie	lie	NOUN
ap-1402	89	24	algebra	algebra	VERB
ap-1402	89	25	g	g	PROPN
ap-1402	89	26	of	of	ADP
ap-1402	89	27	the	the	DET
ap-1402	89	28	lie	lie	NOUN
ap-1402	89	29	group	group	NOUN
ap-1402	89	30	g	g	PROPN
ap-1402	89	31	=	=	PROPN
ap-1402	89	32	h	h	PROPN
ap-1402	89	33	1×|	1×|	NUM
ap-1402	89	34	s̃p(2	s̃p(2	NUM
ap-1402	89	35	)	)	PUNCT
ap-1402	89	36	.	.	PUNCT
ap-1402	90	1	all	all	DET
ap-1402	90	2	non	non	ADJ
ap-1402	90	3	-	-	ADJ
ap-1402	90	4	zero	zero	ADJ
ap-1402	90	5	commutators	commutator	NOUN
ap-1402	90	6	besides	besides	SCONJ
ap-1402	90	7	those	those	PRON
ap-1402	90	8	already	already	ADV
ap-1402	90	9	listed	list	VERB
ap-1402	90	10	in	in	ADP
ap-1402	90	11	(	(	PUNCT
ap-1402	90	12	8)	8)	NUM
ap-1402	90	13	and	and	CCONJ
ap-1402	90	14	(	(	PUNCT
ap-1402	90	15	10	10	NUM
ap-1402	90	16	)	)	PUNCT
ap-1402	90	17	are	be	AUX
ap-1402	90	18	:	:	PUNCT
ap-1402	91	1	[	[	X
ap-1402	91	2	a	a	X
ap-1402	91	3	,	,	PUNCT
ap-1402	91	4	x	x	SYM
ap-1402	91	5	]	]	X
ap-1402	91	6	=	=	SYM
ap-1402	91	7	1	1	NUM
ap-1402	91	8	2	2	NUM
ap-1402	91	9	x	x	NOUN
ap-1402	91	10	,	,	PUNCT
ap-1402	91	11	[	[	X
ap-1402	91	12	b	b	X
ap-1402	91	13	,	,	PUNCT
ap-1402	91	14	x	x	X
ap-1402	91	15	]	]	PUNCT
ap-1402	91	16	=	=	SYM
ap-1402	91	17	−1	−1	NOUN
ap-1402	91	18	2	2	NUM
ap-1402	91	19	y	y	NOUN
ap-1402	91	20	,	,	PUNCT
ap-1402	91	21	[	[	X
ap-1402	91	22	z	z	X
ap-1402	91	23	,	,	PUNCT
ap-1402	91	24	x	x	X
ap-1402	91	25	]	]	PUNCT
ap-1402	91	26	=	=	PUNCT
ap-1402	91	27	y	y	PROPN
ap-1402	91	28	;	;	PUNCT
ap-1402	91	29	(	(	PUNCT
ap-1402	91	30	11	11	NUM
ap-1402	91	31	)	)	PUNCT
ap-1402	91	32	[	[	X
ap-1402	91	33	a	a	X
ap-1402	91	34	,	,	PUNCT
ap-1402	91	35	y	y	NOUN
ap-1402	91	36	]	]	PUNCT
ap-1402	91	37	=	=	PUNCT
ap-1402	91	38	−1	−1	NOUN
ap-1402	91	39	2	2	NUM
ap-1402	91	40	y	y	NOUN
ap-1402	91	41	,	,	PUNCT
ap-1402	91	42	[	[	X
ap-1402	91	43	b	b	X
ap-1402	91	44	,	,	PUNCT
ap-1402	91	45	y	y	NOUN
ap-1402	91	46	]	]	PUNCT
ap-1402	91	47	=	=	PUNCT
ap-1402	91	48	−1	−1	NOUN
ap-1402	91	49	2	2	NUM
ap-1402	91	50	x	x	NOUN
ap-1402	91	51	,	,	PUNCT
ap-1402	91	52	[	[	X
ap-1402	91	53	z	z	X
ap-1402	91	54	,	,	PUNCT
ap-1402	91	55	y	y	PROPN
ap-1402	91	56	]	]	PUNCT
ap-1402	91	57	=	=	PUNCT
ap-1402	91	58	−x	−x	NOUN
ap-1402	91	59	.	.	PUNCT
ap-1402	92	1	(	(	PUNCT
ap-1402	92	2	12	12	NUM
ap-1402	92	3	)	)	PUNCT
ap-1402	92	4	the	the	DET
ap-1402	92	5	shale	shale	NOUN
ap-1402	92	6	-	-	PUNCT
ap-1402	92	7	weil	weil	PROPN
ap-1402	92	8	theorem	theorem	NOUN
ap-1402	92	9	allows	allow	VERB
ap-1402	92	10	us	we	PRON
ap-1402	92	11	to	to	PART
ap-1402	92	12	expand	expand	VERB
ap-1402	92	13	any	any	DET
ap-1402	92	14	representation	representation	NOUN
ap-1402	92	15	ρh̄	ρh̄	NOUN
ap-1402	92	16	of	of	ADP
ap-1402	92	17	the	the	DET
ap-1402	92	18	heisenberg	heisenberg	PROPN
ap-1402	92	19	group	group	NOUN
ap-1402	92	20	to	to	ADP
ap-1402	92	21	the	the	DET
ap-1402	92	22	representation	representation	NOUN
ap-1402	92	23	ρ̃h̄	ρ̃h̄	NOUN
ap-1402	92	24	=	=	SYM
ap-1402	92	25	ρh̄	ρh̄	NOUN
ap-1402	92	26	⊕	⊕	PROPN
ap-1402	92	27	ρswh̄	ρswh̄	PROPN
ap-1402	92	28	of	of	ADP
ap-1402	92	29	group	group	PROPN
ap-1402	92	30	g.	g.	PROPN
ap-1402	92	31	example	example	NOUN
ap-1402	92	32	1	1	NUM
ap-1402	92	33	let	let	VERB
ap-1402	92	34	ρh̄	ρh̄	NOUN
ap-1402	92	35	be	be	AUX
ap-1402	92	36	the	the	DET
ap-1402	92	37	schrödinger	schrödinger	NOUN
ap-1402	92	38	representation	representation	NOUN
ap-1402	92	39	[	[	X
ap-1402	92	40	8	8	NUM
ap-1402	92	41	,	,	PUNCT
ap-1402	92	42	§	§	NOUN
ap-1402	92	43	1.3	1.3	NUM
ap-1402	92	44	]	]	PUNCT
ap-1402	92	45	of	of	ADP
ap-1402	92	46	h	h	NOUN
ap-1402	92	47	1	1	NUM
ap-1402	92	48	in	in	ADP
ap-1402	92	49	�	�	PROPN
ap-1402	92	50	l2(r	l2(r	NOUN
ap-1402	92	51	)	)	PUNCT
ap-1402	92	52	,	,	PUNCT
ap-1402	92	53	that	that	PRON
ap-1402	92	54	is	be	AUX
ap-1402	92	55	[	[	X
ap-1402	92	56	25	25	NUM
ap-1402	92	57	,	,	PUNCT
ap-1402	92	58	(	(	PUNCT
ap-1402	92	59	3.5	3.5	NUM
ap-1402	92	60	)	)	PUNCT
ap-1402	92	61	]	]	PUNCT
ap-1402	92	62	:	:	PUNCT
ap-1402	93	1	[	[	X
ap-1402	93	2	ρχ(s	ρχ(s	NUM
ap-1402	93	3	,	,	PUNCT
ap-1402	93	4	x	x	X
ap-1402	93	5	,	,	PUNCT
ap-1402	93	6	y)f	y)f	VERB
ap-1402	93	7	]	]	PUNCT
ap-1402	93	8	(	(	PUNCT
ap-1402	93	9	q	q	X
ap-1402	93	10	)	)	PUNCT
ap-1402	93	11	=	=	SYM
ap-1402	93	12	e2πih̄(s−xy/2)+2πixq	e2πih̄(s−xy/2)+2πixq	PROPN
ap-1402	93	13	·	·	PUNCT
ap-1402	93	14	f(q	f(q	PROPN
ap-1402	93	15	−	−	PROPN
ap-1402	93	16	h̄y	h̄y	PROPN
ap-1402	93	17	)	)	PUNCT
ap-1402	93	18	.	.	PUNCT
ap-1402	94	1	(	(	PUNCT
ap-1402	94	2	13	13	NUM
ap-1402	94	3	)	)	PUNCT
ap-1402	94	4	thus	thus	ADV
ap-1402	94	5	the	the	DET
ap-1402	94	6	action	action	NOUN
ap-1402	94	7	of	of	ADP
ap-1402	94	8	the	the	DET
ap-1402	94	9	derived	derive	VERB
ap-1402	94	10	representation	representation	NOUN
ap-1402	94	11	on	on	ADP
ap-1402	94	12	the	the	DET
ap-1402	94	13	lie	lie	NOUN
ap-1402	94	14	algebra	algebra	NOUN
ap-1402	94	15	h1	h1	NOUN
ap-1402	94	16	is	be	AUX
ap-1402	94	17	:	:	PUNCT
ap-1402	94	18	ρh̄(x	ρh̄(x	NUM
ap-1402	94	19	)	)	PUNCT
ap-1402	94	20	=	=	SYM
ap-1402	94	21	2πiq	2πiq	NUM
ap-1402	94	22	,	,	PUNCT
ap-1402	94	23	ρh̄(y	ρh̄(y	NOUN
ap-1402	94	24	)	)	PUNCT
ap-1402	94	25	=	=	PUNCT
ap-1402	95	1	−h̄	−h̄	NOUN
ap-1402	95	2	d	d	X
ap-1402	95	3	dq	dq	PROPN
ap-1402	95	4	,	,	PUNCT
ap-1402	95	5	ρh̄(s	ρh̄(s	NUM
ap-1402	95	6	)	)	PUNCT
ap-1402	95	7	=	=	SYM
ap-1402	95	8	2πih̄i	2πih̄i	NUM
ap-1402	95	9	.	.	PUNCT
ap-1402	96	1	(	(	PUNCT
ap-1402	96	2	14	14	NUM
ap-1402	96	3	)	)	PUNCT
ap-1402	96	4	then	then	ADV
ap-1402	96	5	the	the	DET
ap-1402	96	6	associated	associated	ADJ
ap-1402	96	7	shale	shale	PROPN
ap-1402	96	8	-	-	PUNCT
ap-1402	96	9	weil	weil	PROPN
ap-1402	96	10	representation	representation	NOUN
ap-1402	96	11	of	of	ADP
ap-1402	96	12	sp(2	sp(2	NOUN
ap-1402	96	13	)	)	PUNCT
ap-1402	96	14	in	in	ADP
ap-1402	96	15	l2(r	l2(r	NOUN
ap-1402	96	16	)	)	PUNCT
ap-1402	96	17	has	have	VERB
ap-1402	96	18	the	the	DET
ap-1402	96	19	derived	derive	VERB
ap-1402	96	20	action	action	NOUN
ap-1402	96	21	,	,	PUNCT
ap-1402	96	22	cf	cf	NOUN
ap-1402	96	23	.	.	PUNCT
ap-1402	97	1	[	[	X
ap-1402	97	2	35	35	NUM
ap-1402	97	3	,	,	PUNCT
ap-1402	97	4	(	(	PUNCT
ap-1402	97	5	2.2	2.2	NUM
ap-1402	97	6	)	)	PUNCT
ap-1402	97	7	]	]	PUNCT
ap-1402	97	8	,	,	PUNCT
ap-1402	98	1	[	[	X
ap-1402	98	2	8	8	NUM
ap-1402	98	3	,	,	PUNCT
ap-1402	98	4	§	§	PROPN
ap-1402	98	5	4.3	4.3	NUM
ap-1402	98	6	]	]	PUNCT
ap-1402	98	7	:	:	PUNCT
ap-1402	98	8	ρswh̄	ρswh̄	PROPN
ap-1402	98	9	(	(	PUNCT
ap-1402	98	10	a	a	NOUN
ap-1402	98	11	)	)	PUNCT
ap-1402	98	12	=	=	SYM
ap-1402	99	1	−	−	PROPN
ap-1402	99	2	q	q	NOUN
ap-1402	99	3	2	2	NUM
ap-1402	99	4	d	d	NOUN
ap-1402	99	5	dq	dq	NOUN
ap-1402	99	6	−	−	NUM
ap-1402	99	7	1	1	NUM
ap-1402	99	8	4	4	NUM
ap-1402	99	9	,	,	PUNCT
ap-1402	99	10	ρswh̄	ρswh̄	PROPN
ap-1402	99	11	(	(	PUNCT
ap-1402	99	12	b	b	NOUN
ap-1402	99	13	)	)	PUNCT
ap-1402	99	14	=	=	PUNCT
ap-1402	100	1	−	−	PROPN
ap-1402	100	2	h̄i	h̄i	PROPN
ap-1402	100	3	8π	8π	NUM
ap-1402	100	4	d2	d2	PROPN
ap-1402	100	5	dq2	dq2	PROPN
ap-1402	100	6	−	−	PROPN
ap-1402	100	7	πiq2	πiq2	PROPN
ap-1402	100	8	2h̄	2h̄	NUM
ap-1402	100	9	,	,	PUNCT
ap-1402	100	10	(	(	PUNCT
ap-1402	100	11	15	15	NUM
ap-1402	100	12	)	)	PUNCT
ap-1402	100	13	ρswh̄	ρswh̄	PROPN
ap-1402	100	14	(	(	PUNCT
ap-1402	100	15	z	z	NOUN
ap-1402	100	16	)	)	PUNCT
ap-1402	100	17	=	=	SYM
ap-1402	100	18	h̄i	h̄i	PROPN
ap-1402	100	19	4π	4π	PROPN
ap-1402	100	20	d2	d2	PROPN
ap-1402	100	21	dq2	dq2	PROPN
ap-1402	100	22	−	−	PROPN
ap-1402	100	23	πiq2	πiq2	PROPN
ap-1402	100	24	h̄	h̄	X
ap-1402	100	25	.	.	PUNCT
ap-1402	101	1	we	we	PRON
ap-1402	101	2	can	can	AUX
ap-1402	101	3	verify	verify	VERB
ap-1402	101	4	commutators	commutator	NOUN
ap-1402	101	5	(	(	PUNCT
ap-1402	101	6	8)	8)	NUM
ap-1402	101	7	and	and	CCONJ
ap-1402	101	8	(	(	PUNCT
ap-1402	101	9	10–12	10–12	NUM
ap-1402	101	10	)	)	PUNCT
ap-1402	101	11	for	for	ADP
ap-1402	101	12	operators	operator	NOUN
ap-1402	101	13	(	(	PUNCT
ap-1402	101	14	14–15	14–15	NUM
ap-1402	101	15	)	)	PUNCT
ap-1402	101	16	.	.	PUNCT
ap-1402	102	1	it	it	PRON
ap-1402	102	2	is	be	AUX
ap-1402	102	3	also	also	ADV
ap-1402	102	4	obvious	obvious	ADJ
ap-1402	102	5	that	that	SCONJ
ap-1402	102	6	in	in	ADP
ap-1402	102	7	this	this	DET
ap-1402	102	8	representation	representation	NOUN
ap-1402	102	9	the	the	DET
ap-1402	102	10	following	follow	VERB
ap-1402	102	11	algebraic	algebraic	ADJ
ap-1402	102	12	relations	relation	NOUN
ap-1402	102	13	hold	hold	VERB
ap-1402	102	14	:	:	PUNCT
ap-1402	102	15	ρswh̄	ρswh̄	PROPN
ap-1402	102	16	(	(	PUNCT
ap-1402	102	17	a	a	X
ap-1402	102	18	)	)	PUNCT
ap-1402	103	1	=	=	SYM
ap-1402	103	2	i	i	PRON
ap-1402	103	3	4πh̄	4πh̄	VERB
ap-1402	103	4	(	(	PUNCT
ap-1402	103	5	ρh̄(x)ρh̄(y	ρh̄(x)ρh̄(y	NOUN
ap-1402	103	6	)	)	PUNCT
ap-1402	104	1	−	−	PROPN
ap-1402	104	2	1	1	NUM
ap-1402	104	3	2	2	NUM
ap-1402	104	4	ρh̄(s	ρh̄(s	NUM
ap-1402	104	5	)	)	PUNCT
ap-1402	104	6	)	)	PUNCT
ap-1402	105	1	=	=	PUNCT
ap-1402	105	2	(	(	PUNCT
ap-1402	105	3	16	16	NUM
ap-1402	105	4	)	)	PUNCT
ap-1402	106	1	i	i	PRON
ap-1402	106	2	8πh̄	8πh̄	PROPN
ap-1402	106	3	(	(	PUNCT
ap-1402	106	4	ρh̄(x)ρh̄(y	ρh̄(x)ρh̄(y	PROPN
ap-1402	106	5	)	)	PUNCT
ap-1402	107	1	+	+	CCONJ
ap-1402	107	2	ρh̄(y	ρh̄(y	X
ap-1402	107	3	)	)	PUNCT
ap-1402	107	4	ρh̄(x	ρh̄(x	NUM
ap-1402	107	5	)	)	PUNCT
ap-1402	107	6	)	)	PUNCT
ap-1402	107	7	,	,	PUNCT
ap-1402	107	8	ρswh̄	ρswh̄	PROPN
ap-1402	107	9	(	(	PUNCT
ap-1402	107	10	b	b	NOUN
ap-1402	107	11	)	)	PUNCT
ap-1402	107	12	=	=	SYM
ap-1402	108	1	i	i	PRON
ap-1402	108	2	8πh̄	8πh̄	PROPN
ap-1402	108	3	(	(	PUNCT
ap-1402	108	4	ρh̄(x)2	ρh̄(x)2	VERB
ap-1402	108	5	−	−	PROPN
ap-1402	108	6	ρh̄(y	ρh̄(y	NOUN
ap-1402	108	7	)	)	PUNCT
ap-1402	108	8	2	2	NUM
ap-1402	108	9	)	)	PUNCT
ap-1402	108	10	,	,	PUNCT
ap-1402	108	11	(	(	PUNCT
ap-1402	108	12	17	17	NUM
ap-1402	108	13	)	)	PUNCT
ap-1402	108	14	ρswh̄	ρswh̄	PROPN
ap-1402	108	15	(	(	PUNCT
ap-1402	108	16	z	z	NOUN
ap-1402	108	17	)	)	PUNCT
ap-1402	109	1	=	=	NOUN
ap-1402	109	2	i	i	PRON
ap-1402	109	3	4πh̄	4πh̄	VERB
ap-1402	109	4	(	(	PUNCT
ap-1402	109	5	ρh̄(x)2	ρh̄(x)2	VERB
ap-1402	109	6	+	+	CCONJ
ap-1402	109	7	ρh̄(y	ρh̄(y	NOUN
ap-1402	109	8	)	)	PUNCT
ap-1402	109	9	2	2	NUM
ap-1402	109	10	)	)	PUNCT
ap-1402	109	11	.	.	PUNCT
ap-1402	110	1	(	(	PUNCT
ap-1402	110	2	18	18	NUM
ap-1402	110	3	)	)	PUNCT
ap-1402	110	4	thus	thus	ADV
ap-1402	110	5	it	it	PRON
ap-1402	110	6	is	be	AUX
ap-1402	110	7	common	common	ADJ
ap-1402	110	8	in	in	ADP
ap-1402	110	9	quantum	quantum	ADJ
ap-1402	110	10	optics	optic	NOUN
ap-1402	110	11	to	to	PART
ap-1402	110	12	name	name	VERB
ap-1402	110	13	g	g	NOUN
ap-1402	110	14	as	as	ADP
ap-1402	110	15	a	a	DET
ap-1402	110	16	lie	lie	NOUN
ap-1402	110	17	algebra	algebra	NOUN
ap-1402	110	18	with	with	ADP
ap-1402	110	19	quadratic	quadratic	ADJ
ap-1402	110	20	generators	generator	NOUN
ap-1402	110	21	,	,	PUNCT
ap-1402	110	22	see	see	VERB
ap-1402	110	23	[	[	X
ap-1402	110	24	9	9	NUM
ap-1402	110	25	,	,	PUNCT
ap-1402	110	26	§	§	NOUN
ap-1402	110	27	2.2.4	2.2.4	NUM
ap-1402	110	28	]	]	X
ap-1402	110	29	.	.	PUNCT
ap-1402	111	1	note	note	VERB
ap-1402	111	2	that	that	SCONJ
ap-1402	111	3	ρswh̄	ρswh̄	PROPN
ap-1402	111	4	(	(	PUNCT
ap-1402	111	5	z	z	NOUN
ap-1402	111	6	)	)	PUNCT
ap-1402	111	7	is	be	AUX
ap-1402	111	8	the	the	DET
ap-1402	111	9	hamiltonian	hamiltonian	NOUN
ap-1402	111	10	of	of	ADP
ap-1402	111	11	the	the	DET
ap-1402	111	12	harmonic	harmonic	ADJ
ap-1402	111	13	oscillator	oscillator	NOUN
ap-1402	111	14	(	(	PUNCT
ap-1402	111	15	up	up	ADP
ap-1402	111	16	to	to	ADP
ap-1402	111	17	a	a	DET
ap-1402	111	18	factor	factor	NOUN
ap-1402	111	19	)	)	PUNCT
ap-1402	111	20	.	.	PUNCT
ap-1402	112	1	then	then	ADV
ap-1402	112	2	we	we	PRON
ap-1402	112	3	can	can	AUX
ap-1402	112	4	consider	consider	VERB
ap-1402	112	5	ρswh̄	ρswh̄	PROPN
ap-1402	112	6	(	(	PUNCT
ap-1402	112	7	b	b	NOUN
ap-1402	112	8	)	)	PUNCT
ap-1402	112	9	as	as	ADP
ap-1402	112	10	the	the	DET
ap-1402	112	11	hamiltonian	hamiltonian	NOUN
ap-1402	112	12	of	of	ADP
ap-1402	112	13	a	a	DET
ap-1402	112	14	repulsive	repulsive	ADJ
ap-1402	112	15	(	(	PUNCT
ap-1402	112	16	hyperbolic	hyperbolic	ADJ
ap-1402	112	17	)	)	PUNCT
ap-1402	112	18	oscillator	oscillator	NOUN
ap-1402	112	19	.	.	PUNCT
ap-1402	113	1	the	the	DET
ap-1402	113	2	operator	operator	NOUN
ap-1402	113	3	ρswh̄	ρswh̄	PROPN
ap-1402	113	4	(	(	PUNCT
ap-1402	113	5	b	b	NOUN
ap-1402	113	6	−	−	PROPN
ap-1402	113	7	z/2	z/2	NUM
ap-1402	113	8	)	)	PUNCT
ap-1402	114	1	=	=	PRON
ap-1402	114	2	h̄i	h̄i	PROPN
ap-1402	114	3	4π	4π	NUM
ap-1402	114	4	d2	d2	PROPN
ap-1402	114	5	dq2	dq2	PROPN
ap-1402	114	6	is	be	AUX
ap-1402	114	7	the	the	DET
ap-1402	114	8	parabolic	parabolic	ADJ
ap-1402	114	9	analog	analog	NOUN
ap-1402	114	10	.	.	PUNCT
ap-1402	115	1	a	a	DET
ap-1402	115	2	graphical	graphical	ADJ
ap-1402	115	3	representation	representation	NOUN
ap-1402	115	4	of	of	ADP
ap-1402	115	5	all	all	DET
ap-1402	115	6	three	three	NUM
ap-1402	115	7	transformations	transformation	NOUN
ap-1402	115	8	is	be	AUX
ap-1402	115	9	given	give	VERB
ap-1402	115	10	in	in	ADP
ap-1402	115	11	figure	figure	NOUN
ap-1402	115	12	1	1	NUM
ap-1402	115	13	,	,	PUNCT
ap-1402	115	14	and	and	CCONJ
ap-1402	115	15	a	a	DET
ap-1402	115	16	further	further	ADJ
ap-1402	115	17	discussion	discussion	NOUN
ap-1402	115	18	of	of	ADP
ap-1402	115	19	these	these	DET
ap-1402	115	20	hamiltonians	hamiltonian	NOUN
ap-1402	115	21	can	can	AUX
ap-1402	115	22	be	be	AUX
ap-1402	115	23	found	find	VERB
ap-1402	115	24	in	in	ADP
ap-1402	115	25	[	[	X
ap-1402	115	26	37	37	NUM
ap-1402	115	27	,	,	PUNCT
ap-1402	115	28	§	§	PROPN
ap-1402	115	29	3.8	3.8	NUM
ap-1402	115	30	]	]	PUNCT
ap-1402	115	31	.	.	PUNCT
ap-1402	116	1	an	an	DET
ap-1402	116	2	important	important	ADJ
ap-1402	116	3	observation	observation	NOUN
ap-1402	116	4	,	,	PUNCT
ap-1402	116	5	which	which	PRON
ap-1402	116	6	is	be	AUX
ap-1402	116	7	often	often	ADV
ap-1402	116	8	missed	miss	VERB
ap-1402	116	9	,	,	PUNCT
ap-1402	116	10	is	be	AUX
ap-1402	116	11	that	that	SCONJ
ap-1402	116	12	the	the	DET
ap-1402	116	13	three	three	NUM
ap-1402	116	14	linear	linear	ADJ
ap-1402	116	15	symplectic	symplectic	ADJ
ap-1402	116	16	transformations	transformation	NOUN
ap-1402	116	17	are	be	AUX
ap-1402	116	18	unitary	unitary	ADJ
ap-1402	116	19	rotations	rotation	NOUN
ap-1402	116	20	in	in	ADP
ap-1402	116	21	the	the	DET
ap-1402	116	22	corresponding	corresponding	ADJ
ap-1402	116	23	hypercomplex	hypercomplex	NOUN
ap-1402	116	24	algebra	algebra	NOUN
ap-1402	116	25	.	.	PUNCT
ap-1402	117	1	this	this	PRON
ap-1402	117	2	means	mean	VERB
ap-1402	117	3	that	that	SCONJ
ap-1402	117	4	the	the	DET
ap-1402	117	5	symplectomorphisms	symplectomorphism	NOUN
ap-1402	117	6	generated	generate	VERB
ap-1402	117	7	by	by	ADP
ap-1402	117	8	operators	operator	NOUN
ap-1402	117	9	z	z	PROPN
ap-1402	117	10	,	,	PUNCT
ap-1402	117	11	b	b	PROPN
ap-1402	117	12	−z/2	−z/2	NOUN
ap-1402	117	13	,	,	PUNCT
ap-1402	117	14	b	b	NOUN
ap-1402	117	15	within	within	ADP
ap-1402	117	16	time	time	NOUN
ap-1402	117	17	t	t	PROPN
ap-1402	117	18	coincide	coincide	NOUN
ap-1402	117	19	with	with	ADP
ap-1402	117	20	the	the	DET
ap-1402	117	21	multiplication	multiplication	NOUN
ap-1402	117	22	of	of	ADP
ap-1402	117	23	hypercomplex	hypercomplex	ADJ
ap-1402	117	24	number	number	NOUN
ap-1402	117	25	q	q	PROPN
ap-1402	118	1	+	+	CCONJ
ap-1402	118	2	ιp	ιp	VERB
ap-1402	118	3	by	by	ADP
ap-1402	118	4	eιt	eιt	PROPN
ap-1402	119	1	[	[	X
ap-1402	119	2	23	23	NUM
ap-1402	119	3	,	,	PUNCT
ap-1402	119	4	§	§	PROPN
ap-1402	119	5	3	3	NUM
ap-1402	119	6	]	]	PUNCT
ap-1402	119	7	,	,	PUNCT
ap-1402	119	8	which	which	PRON
ap-1402	119	9	is	be	AUX
ap-1402	119	10	just	just	ADV
ap-1402	119	11	another	another	DET
ap-1402	119	12	illustration	illustration	NOUN
ap-1402	119	13	of	of	ADP
ap-1402	119	14	the	the	DET
ap-1402	119	15	similarity	similarity	NOUN
ap-1402	119	16	and	and	CCONJ
ap-1402	119	17	correspondence	correspondence	NOUN
ap-1402	119	18	principle	principle	NOUN
ap-1402	119	19	.	.	PUNCT
ap-1402	120	1	q	q	PUNCT
ap-1402	121	1	p	p	X
ap-1402	121	2	q	q	X
ap-1402	121	3	p	p	X
ap-1402	121	4	q	q	X
ap-1402	121	5	p	p	X
ap-1402	121	6	fig	fig	NOUN
ap-1402	121	7	.	.	PUNCT
ap-1402	122	1	1	1	NUM
ap-1402	122	2	:	:	SYM
ap-1402	122	3	three	three	NUM
ap-1402	122	4	types	type	NOUN
ap-1402	122	5	(	(	PUNCT
ap-1402	122	6	elliptic	elliptic	ADJ
ap-1402	122	7	,	,	PUNCT
ap-1402	122	8	parabolic	parabolic	ADJ
ap-1402	122	9	and	and	CCONJ
ap-1402	122	10	hyperbolic	hyperbolic	ADJ
ap-1402	122	11	)	)	PUNCT
ap-1402	122	12	of	of	ADP
ap-1402	122	13	linear	linear	ADJ
ap-1402	122	14	symplectic	symplectic	ADJ
ap-1402	122	15	transformations	transformation	NOUN
ap-1402	122	16	on	on	ADP
ap-1402	122	17	the	the	DET
ap-1402	122	18	plane	plane	NOUN
ap-1402	122	19	46	46	NUM
ap-1402	122	20	acta	acta	PROPN
ap-1402	122	21	polytechnica	polytechnica	PROPN
ap-1402	122	22	vol	vol	NOUN
ap-1402	122	23	.	.	PUNCT
ap-1402	123	1	51	51	NUM
ap-1402	123	2	no	no	INTJ
ap-1402	123	3	.	.	PUNCT
ap-1402	124	1	4/2011	4/2011	NUM
ap-1402	124	2	example	example	NOUN
ap-1402	124	3	2	2	NUM
ap-1402	124	4	there	there	PRON
ap-1402	124	5	are	be	VERB
ap-1402	124	6	many	many	ADJ
ap-1402	124	7	advantages	advantage	NOUN
ap-1402	124	8	of	of	ADP
ap-1402	124	9	considering	consider	VERB
ap-1402	124	10	representations	representation	NOUN
ap-1402	124	11	of	of	ADP
ap-1402	124	12	the	the	DET
ap-1402	124	13	heisenberg	heisenberg	PROPN
ap-1402	124	14	group	group	NOUN
ap-1402	124	15	on	on	ADP
ap-1402	124	16	the	the	DET
ap-1402	124	17	phase	phase	NOUN
ap-1402	124	18	space	space	NOUN
ap-1402	124	19	[	[	X
ap-1402	124	20	12	12	NUM
ap-1402	124	21	,	,	PUNCT
ap-1402	124	22	§	§	PROPN
ap-1402	124	23	1.7	1.7	NUM
ap-1402	124	24	]	]	PUNCT
ap-1402	124	25	,	,	PUNCT
ap-1402	124	26	[	[	X
ap-1402	124	27	8	8	NUM
ap-1402	124	28	,	,	PUNCT
ap-1402	124	29	§	§	PROPN
ap-1402	124	30	1.6	1.6	NUM
ap-1402	124	31	]	]	PUNCT
ap-1402	124	32	,	,	PUNCT
ap-1402	124	33	[	[	X
ap-1402	124	34	6	6	NUM
ap-1402	124	35	]	]	PUNCT
ap-1402	124	36	.	.	PUNCT
ap-1402	125	1	a	a	DET
ap-1402	125	2	convenient	convenient	ADJ
ap-1402	125	3	expression	expression	NOUN
ap-1402	125	4	for	for	ADP
ap-1402	125	5	fock	fock	ADJ
ap-1402	125	6	-	-	PUNCT
ap-1402	125	7	segal	segal	NOUN
ap-1402	125	8	-	-	PUNCT
ap-1402	125	9	bargmann	bargmann	PROPN
ap-1402	125	10	(	(	PUNCT
ap-1402	125	11	fsb	fsb	NOUN
ap-1402	125	12	)	)	PUNCT
ap-1402	125	13	representation	representation	NOUN
ap-1402	125	14	on	on	ADP
ap-1402	125	15	the	the	DET
ap-1402	125	16	phase	phase	NOUN
ap-1402	125	17	space	space	NOUN
ap-1402	125	18	is	be	AUX
ap-1402	125	19	[	[	X
ap-1402	125	20	25	25	NUM
ap-1402	125	21	,	,	PUNCT
ap-1402	125	22	(	(	PUNCT
ap-1402	125	23	3.2	3.2	NUM
ap-1402	125	24	)	)	PUNCT
ap-1402	125	25	]	]	PUNCT
ap-1402	125	26	:	:	PUNCT
ap-1402	126	1	[	[	X
ap-1402	126	2	ρf	ρf	X
ap-1402	126	3	(	(	PUNCT
ap-1402	126	4	s	s	PROPN
ap-1402	126	5	,	,	PUNCT
ap-1402	126	6	x	x	X
ap-1402	126	7	,	,	PUNCT
ap-1402	126	8	y)f	y)f	VERB
ap-1402	126	9	]	]	PUNCT
ap-1402	126	10	(	(	PUNCT
ap-1402	126	11	q	q	ADJ
ap-1402	126	12	,	,	PUNCT
ap-1402	126	13	p	p	NOUN
ap-1402	126	14	)	)	PUNCT
ap-1402	126	15	=	=	SYM
ap-1402	126	16	e−2πi(h̄s+qx+py	e−2πi(h̄s+qx+py	NOUN
ap-1402	126	17	)	)	PUNCT
ap-1402	126	18	·	·	PUNCT
ap-1402	126	19	(	(	PUNCT
ap-1402	126	20	19	19	NUM
ap-1402	126	21	)	)	PUNCT
ap-1402	126	22	f	f	NOUN
ap-1402	126	23	(	(	PUNCT
ap-1402	126	24	q	q	PROPN
ap-1402	126	25	−	−	PROPN
ap-1402	126	26	h̄	h̄	NUM
ap-1402	126	27	2	2	NUM
ap-1402	126	28	y	y	PROPN
ap-1402	126	29	,	,	PUNCT
ap-1402	126	30	p	p	X
ap-1402	126	31	+	+	X
ap-1402	126	32	h̄	h̄	NUM
ap-1402	126	33	2	2	NUM
ap-1402	126	34	x	x	NOUN
ap-1402	126	35	)	)	PUNCT
ap-1402	126	36	.	.	PUNCT
ap-1402	127	1	then	then	ADV
ap-1402	127	2	the	the	DET
ap-1402	127	3	derived	derived	ADJ
ap-1402	127	4	representation	representation	NOUN
ap-1402	127	5	of	of	ADP
ap-1402	127	6	h1	h1	PROPN
ap-1402	127	7	is	be	AUX
ap-1402	127	8	:	:	PUNCT
ap-1402	127	9	ρf	ρf	X
ap-1402	127	10	(	(	PUNCT
ap-1402	127	11	x	x	X
ap-1402	127	12	)	)	PUNCT
ap-1402	127	13	=	=	SYM
ap-1402	127	14	−2πiq	−2πiq	NOUN
ap-1402	127	15	+	+	CCONJ
ap-1402	127	16	h̄	h̄	NOUN
ap-1402	127	17	2	2	NUM
ap-1402	127	18	∂p	∂p	PROPN
ap-1402	127	19	,	,	PUNCT
ap-1402	127	20	ρf	ρf	X
ap-1402	127	21	(	(	PUNCT
ap-1402	127	22	y	y	PROPN
ap-1402	127	23	)	)	PUNCT
ap-1402	127	24	=	=	SYM
ap-1402	128	1	−2πip	−2πip	PROPN
ap-1402	129	1	−	−	PROPN
ap-1402	129	2	h̄	h̄	NOUN
ap-1402	129	3	2	2	NUM
ap-1402	129	4	∂q	∂q	PROPN
ap-1402	129	5	,	,	PUNCT
ap-1402	129	6	(	(	PUNCT
ap-1402	129	7	20	20	NUM
ap-1402	129	8	)	)	PUNCT
ap-1402	129	9	ρf	ρf	NOUN
ap-1402	129	10	(	(	PUNCT
ap-1402	129	11	s	s	X
ap-1402	129	12	)	)	PUNCT
ap-1402	129	13	=	=	PUNCT
ap-1402	129	14	−2πih̄i	−2πih̄i	NOUN
ap-1402	129	15	.	.	PUNCT
ap-1402	130	1	this	this	PRON
ap-1402	130	2	produces	produce	VERB
ap-1402	130	3	the	the	DET
ap-1402	130	4	derived	derived	ADJ
ap-1402	130	5	form	form	NOUN
ap-1402	130	6	of	of	ADP
ap-1402	130	7	the	the	DET
ap-1402	130	8	shale	shale	NOUN
ap-1402	130	9	-	-	PUNCT
ap-1402	130	10	weil	weil	PROPN
ap-1402	130	11	representation	representation	NOUN
ap-1402	130	12	:	:	PUNCT
ap-1402	130	13	ρswf	ρswf	NOUN
ap-1402	130	14	(	(	PUNCT
ap-1402	130	15	a	a	X
ap-1402	130	16	)	)	PUNCT
ap-1402	130	17	=	=	SYM
ap-1402	130	18	1	1	NUM
ap-1402	130	19	2	2	NUM
ap-1402	130	20	(	(	PUNCT
ap-1402	130	21	q∂q	q∂q	NOUN
ap-1402	130	22	−	−	PROPN
ap-1402	130	23	p∂p	p∂p	NOUN
ap-1402	130	24	)	)	PUNCT
ap-1402	130	25	,	,	PUNCT
ap-1402	130	26	ρswf	ρswf	X
ap-1402	130	27	(	(	PUNCT
ap-1402	130	28	b	b	NOUN
ap-1402	130	29	)	)	PUNCT
ap-1402	130	30	=	=	SYM
ap-1402	130	31	−1	−1	NOUN
ap-1402	130	32	2	2	NUM
ap-1402	130	33	(	(	PUNCT
ap-1402	130	34	p∂q	p∂q	NOUN
ap-1402	130	35	+	+	X
ap-1402	130	36	q∂p	q∂p	NOUN
ap-1402	130	37	)	)	PUNCT
ap-1402	130	38	,	,	PUNCT
ap-1402	130	39	(	(	PUNCT
ap-1402	130	40	21	21	NUM
ap-1402	130	41	)	)	PUNCT
ap-1402	130	42	ρswf	ρswf	NOUN
ap-1402	130	43	(	(	PUNCT
ap-1402	130	44	z	z	NOUN
ap-1402	130	45	)	)	PUNCT
ap-1402	130	46	=	=	PUNCT
ap-1402	130	47	p∂q	p∂q	NOUN
ap-1402	131	1	−	−	NOUN
ap-1402	131	2	q∂p	q∂p	NOUN
ap-1402	131	3	.	.	PUNCT
ap-1402	132	1	note	note	VERB
ap-1402	132	2	that	that	SCONJ
ap-1402	132	3	this	this	DET
ap-1402	132	4	representation	representation	NOUN
ap-1402	132	5	does	do	AUX
ap-1402	132	6	not	not	PART
ap-1402	132	7	contain	contain	VERB
ap-1402	132	8	the	the	DET
ap-1402	132	9	parameter	parameter	NOUN
ap-1402	132	10	h̄	h̄	NOUN
ap-1402	132	11	,	,	PUNCT
ap-1402	132	12	unlike	unlike	ADP
ap-1402	132	13	the	the	DET
ap-1402	132	14	equivalent	equivalent	ADJ
ap-1402	132	15	representation	representation	NOUN
ap-1402	132	16	(	(	PUNCT
ap-1402	132	17	15	15	NUM
ap-1402	132	18	)	)	PUNCT
ap-1402	132	19	.	.	PUNCT
ap-1402	133	1	thus	thus	ADV
ap-1402	133	2	the	the	DET
ap-1402	133	3	fsb	fsb	ADJ
ap-1402	133	4	model	model	NOUN
ap-1402	133	5	explicitly	explicitly	ADV
ap-1402	133	6	shows	show	VERB
ap-1402	133	7	the	the	DET
ap-1402	133	8	equivalence	equivalence	NOUN
ap-1402	133	9	of	of	ADP
ap-1402	133	10	ρswh̄1	ρswh̄1	NOUN
ap-1402	133	11	and	and	CCONJ
ap-1402	133	12	ρswh̄2	ρswh̄2	NOUN
ap-1402	133	13	if	if	SCONJ
ap-1402	133	14	h̄1h̄2	h̄1h̄2	NOUN
ap-1402	133	15	>	>	X
ap-1402	133	16	0	0	PUNCT
ap-1402	134	1	[	[	X
ap-1402	134	2	8	8	NUM
ap-1402	134	3	,	,	PUNCT
ap-1402	134	4	thm	thm	PROPN
ap-1402	134	5	.	.	PUNCT
ap-1402	135	1	4.57	4.57	NUM
ap-1402	135	2	]	]	PUNCT
ap-1402	135	3	.	.	PUNCT
ap-1402	136	1	as	as	SCONJ
ap-1402	136	2	we	we	PRON
ap-1402	136	3	will	will	AUX
ap-1402	136	4	also	also	ADV
ap-1402	136	5	see	see	VERB
ap-1402	136	6	below	below	ADV
ap-1402	136	7	,	,	PUNCT
ap-1402	136	8	the	the	DET
ap-1402	136	9	fsb	fsb	ADJ
ap-1402	136	10	-	-	PUNCT
ap-1402	136	11	type	type	NOUN
ap-1402	136	12	representations	representation	NOUN
ap-1402	136	13	in	in	ADP
ap-1402	136	14	hypercomplex	hypercomplex	ADJ
ap-1402	136	15	numbers	number	NOUN
ap-1402	136	16	produce	produce	VERB
ap-1402	136	17	almost	almost	ADV
ap-1402	136	18	the	the	DET
ap-1402	136	19	same	same	ADJ
ap-1402	136	20	shale	shale	NOUN
ap-1402	136	21	-	-	PUNCT
ap-1402	136	22	weil	weil	NOUN
ap-1402	136	23	representations	representation	NOUN
ap-1402	136	24	.	.	PUNCT
ap-1402	137	1	3	3	NUM
ap-1402	137	2	ladder	ladder	NOUN
ap-1402	137	3	operators	operator	NOUN
ap-1402	137	4	in	in	ADP
ap-1402	137	5	quantum	quantum	ADJ
ap-1402	137	6	mechanics	mechanic	NOUN
ap-1402	137	7	let	let	VERB
ap-1402	137	8	ρ	ρ	NOUN
ap-1402	137	9	be	be	AUX
ap-1402	137	10	a	a	DET
ap-1402	137	11	representation	representation	NOUN
ap-1402	137	12	of	of	ADP
ap-1402	137	13	the	the	DET
ap-1402	137	14	group	group	NOUN
ap-1402	137	15	g	g	NOUN
ap-1402	137	16	=	=	PROPN
ap-1402	137	17	h	h	PROPN
ap-1402	137	18	1×|	1×|	NUM
ap-1402	137	19	s̃p(2	s̃p(2	NUM
ap-1402	137	20	)	)	PUNCT
ap-1402	137	21	in	in	ADP
ap-1402	137	22	a	a	DET
ap-1402	137	23	space	space	NOUN
ap-1402	137	24	v	v	NOUN
ap-1402	137	25	.	.	PUNCT
ap-1402	138	1	consider	consider	VERB
ap-1402	138	2	the	the	DET
ap-1402	138	3	derived	derive	VERB
ap-1402	138	4	representation	representation	NOUN
ap-1402	138	5	of	of	ADP
ap-1402	138	6	the	the	DET
ap-1402	138	7	lie	lie	NOUN
ap-1402	138	8	algebra	algebra	NOUN
ap-1402	138	9	g	g	PROPN
ap-1402	138	10	[	[	X
ap-1402	138	11	28	28	NUM
ap-1402	138	12	,	,	PUNCT
ap-1402	138	13	§	§	PROPN
ap-1402	138	14	vi.1	vi.1	PROPN
ap-1402	138	15	]	]	PUNCT
ap-1402	138	16	and	and	CCONJ
ap-1402	138	17	denote	denote	VERB
ap-1402	138	18	x̃	x̃	PROPN
ap-1402	138	19	=	=	SYM
ap-1402	138	20	ρ(x	ρ(x	PROPN
ap-1402	138	21	)	)	PUNCT
ap-1402	138	22	for	for	ADP
ap-1402	138	23	x	x	PROPN
ap-1402	138	24	∈	∈	PROPN
ap-1402	138	25	g.	g.	NOUN
ap-1402	138	26	to	to	PART
ap-1402	138	27	see	see	VERB
ap-1402	138	28	the	the	DET
ap-1402	138	29	structure	structure	NOUN
ap-1402	138	30	of	of	ADP
ap-1402	138	31	the	the	DET
ap-1402	138	32	representation	representation	NOUN
ap-1402	138	33	ρ	ρ	NOUN
ap-1402	138	34	we	we	PRON
ap-1402	138	35	can	can	AUX
ap-1402	138	36	decompose	decompose	VERB
ap-1402	138	37	the	the	DET
ap-1402	138	38	space	space	NOUN
ap-1402	138	39	v	v	NOUN
ap-1402	138	40	into	into	ADP
ap-1402	138	41	eigenspaces	eigenspace	NOUN
ap-1402	138	42	of	of	ADP
ap-1402	138	43	the	the	DET
ap-1402	138	44	operator	operator	NOUN
ap-1402	138	45	x̃	x̃	PROPN
ap-1402	138	46	for	for	ADP
ap-1402	138	47	some	some	DET
ap-1402	138	48	x	x	SYM
ap-1402	138	49	∈	∈	PROPN
ap-1402	138	50	g.	g.	NOUN
ap-1402	138	51	the	the	DET
ap-1402	138	52	canonical	canonical	ADJ
ap-1402	138	53	example	example	NOUN
ap-1402	138	54	is	be	AUX
ap-1402	138	55	the	the	DET
ap-1402	138	56	taylor	taylor	PROPN
ap-1402	138	57	series	series	PROPN
ap-1402	138	58	in	in	ADP
ap-1402	138	59	complex	complex	ADJ
ap-1402	138	60	analysis	analysis	NOUN
ap-1402	138	61	.	.	PUNCT
ap-1402	139	1	we	we	PRON
ap-1402	139	2	are	be	AUX
ap-1402	139	3	going	go	VERB
ap-1402	139	4	to	to	PART
ap-1402	139	5	consider	consider	VERB
ap-1402	139	6	three	three	NUM
ap-1402	139	7	cases	case	NOUN
ap-1402	139	8	corresponding	correspond	VERB
ap-1402	139	9	to	to	ADP
ap-1402	139	10	three	three	NUM
ap-1402	139	11	non	non	ADJ
ap-1402	139	12	-	-	ADJ
ap-1402	139	13	isomorphic	isomorphic	ADJ
ap-1402	139	14	subgroups	subgroup	NOUN
ap-1402	139	15	(	(	PUNCT
ap-1402	139	16	1–3	1–3	NOUN
ap-1402	139	17	)	)	PUNCT
ap-1402	139	18	of	of	ADP
ap-1402	139	19	sp(2	sp(2	NOUN
ap-1402	139	20	)	)	PUNCT
ap-1402	139	21	starting	start	VERB
ap-1402	139	22	from	from	ADP
ap-1402	139	23	the	the	DET
ap-1402	139	24	compact	compact	ADJ
ap-1402	139	25	case	case	NOUN
ap-1402	139	26	.	.	PUNCT
ap-1402	140	1	let	let	VERB
ap-1402	140	2	h	h	NOUN
ap-1402	141	1	=	=	PUNCT
ap-1402	141	2	z	z	AUX
ap-1402	141	3	be	be	AUX
ap-1402	141	4	a	a	DET
ap-1402	141	5	generator	generator	NOUN
ap-1402	141	6	of	of	ADP
ap-1402	141	7	the	the	DET
ap-1402	141	8	compact	compact	ADJ
ap-1402	141	9	subgroup	subgroup	PROPN
ap-1402	141	10	k.	k.	PROPN
ap-1402	142	1	corresponding	corresponding	PROPN
ap-1402	142	2	symplectomorphisms	symplectomorphism	NOUN
ap-1402	142	3	(	(	PUNCT
ap-1402	142	4	9	9	NUM
ap-1402	142	5	)	)	PUNCT
ap-1402	142	6	of	of	ADP
ap-1402	142	7	the	the	DET
ap-1402	142	8	phase	phase	NOUN
ap-1402	142	9	space	space	NOUN
ap-1402	142	10	are	be	AUX
ap-1402	142	11	given	give	VERB
ap-1402	142	12	by	by	ADP
ap-1402	142	13	orthogonal	orthogonal	ADJ
ap-1402	142	14	rotations	rotation	NOUN
ap-1402	142	15	with	with	ADP
ap-1402	142	16	matrices	matrix	NOUN
ap-1402	142	17	(	(	PUNCT
ap-1402	142	18	cos	cos	ADP
ap-1402	142	19	t	t	PROPN
ap-1402	142	20	sin	sin	NOUN
ap-1402	142	21	t	t	PROPN
ap-1402	142	22	−	−	PROPN
ap-1402	142	23	sin	sin	PROPN
ap-1402	142	24	t	t	PROPN
ap-1402	142	25	cos	cos	PROPN
ap-1402	142	26	t	t	PROPN
ap-1402	142	27	)	)	PUNCT
ap-1402	142	28	.	.	PUNCT
ap-1402	143	1	the	the	DET
ap-1402	143	2	shale	shale	PROPN
ap-1402	143	3	-	-	PUNCT
ap-1402	143	4	weil	weil	PROPN
ap-1402	143	5	representation	representation	NOUN
ap-1402	143	6	(	(	PUNCT
ap-1402	143	7	15	15	NUM
ap-1402	143	8	)	)	PUNCT
ap-1402	143	9	coincides	coincide	VERB
ap-1402	143	10	with	with	ADP
ap-1402	143	11	the	the	DET
ap-1402	143	12	hamiltonian	hamiltonian	NOUN
ap-1402	143	13	of	of	ADP
ap-1402	143	14	the	the	DET
ap-1402	143	15	harmonic	harmonic	ADJ
ap-1402	143	16	oscillator	oscillator	NOUN
ap-1402	143	17	.	.	PUNCT
ap-1402	144	1	since	since	SCONJ
ap-1402	144	2	this	this	PRON
ap-1402	144	3	is	be	AUX
ap-1402	144	4	a	a	DET
ap-1402	144	5	double	double	ADJ
ap-1402	144	6	cover	cover	NOUN
ap-1402	144	7	of	of	ADP
ap-1402	144	8	a	a	DET
ap-1402	144	9	compact	compact	ADJ
ap-1402	144	10	group	group	NOUN
ap-1402	144	11	,	,	PUNCT
ap-1402	144	12	the	the	DET
ap-1402	144	13	corresponding	correspond	VERB
ap-1402	144	14	eigenspaces	eigenspace	NOUN
ap-1402	144	15	z̃vk	z̃vk	PROPN
ap-1402	144	16	=	=	SYM
ap-1402	144	17	ikvk	ikvk	NOUN
ap-1402	144	18	are	be	AUX
ap-1402	144	19	parametrised	parametrise	VERB
ap-1402	144	20	by	by	ADP
ap-1402	144	21	a	a	DET
ap-1402	144	22	half	half	ADJ
ap-1402	144	23	-	-	PUNCT
ap-1402	144	24	integer	integer	NOUN
ap-1402	144	25	k	k	PROPN
ap-1402	144	26	∈	∈	PROPN
ap-1402	144	27	z/2	z/2	PROPN
ap-1402	144	28	.	.	PUNCT
ap-1402	145	1	explicitly	explicitly	ADV
ap-1402	145	2	for	for	ADP
ap-1402	145	3	a	a	DET
ap-1402	145	4	half	half	ADJ
ap-1402	145	5	-	-	PUNCT
ap-1402	145	6	integer	integer	NOUN
ap-1402	145	7	k	k	NOUN
ap-1402	145	8	:	:	PUNCT
ap-1402	145	9	vk(q	vk(q	NUM
ap-1402	145	10	)	)	PUNCT
ap-1402	145	11	=	=	SYM
ap-1402	145	12	hk+	hk+	NOUN
ap-1402	145	13	12	12	NUM
ap-1402	145	14	(	(	PUNCT
ap-1402	145	15	√	√	NUM
ap-1402	145	16	2π	2π	PROPN
ap-1402	145	17	h̄	h̄	NOUN
ap-1402	145	18	q	q	NOUN
ap-1402	145	19	)	)	PUNCT
ap-1402	145	20	e−	e−	PROPN
ap-1402	145	21	π	π	PROPN
ap-1402	145	22	h̄	h̄	X
ap-1402	145	23	q2	q2	NOUN
ap-1402	145	24	,	,	PUNCT
ap-1402	145	25	(	(	PUNCT
ap-1402	145	26	22	22	NUM
ap-1402	145	27	)	)	PUNCT
ap-1402	145	28	where	where	SCONJ
ap-1402	145	29	hk	hk	PROPN
ap-1402	145	30	is	be	AUX
ap-1402	145	31	the	the	DET
ap-1402	145	32	hermite	hermite	ADJ
ap-1402	145	33	polynomial	polynomial	NOUN
ap-1402	145	34	[	[	X
ap-1402	145	35	8	8	NUM
ap-1402	145	36	,	,	PUNCT
ap-1402	145	37	§	§	PROPN
ap-1402	145	38	1.7	1.7	NUM
ap-1402	145	39	]	]	PUNCT
ap-1402	145	40	,	,	PUNCT
ap-1402	145	41	[	[	X
ap-1402	145	42	7	7	NUM
ap-1402	145	43	,	,	PUNCT
ap-1402	145	44	8.2(9	8.2(9	NUM
ap-1402	145	45	)	)	PUNCT
ap-1402	145	46	]	]	PUNCT
ap-1402	145	47	.	.	PUNCT
ap-1402	146	1	from	from	ADP
ap-1402	146	2	the	the	DET
ap-1402	146	3	point	point	NOUN
ap-1402	146	4	of	of	ADP
ap-1402	146	5	view	view	NOUN
ap-1402	146	6	of	of	ADP
ap-1402	146	7	quantum	quantum	ADJ
ap-1402	146	8	mechanics	mechanic	NOUN
ap-1402	146	9	and	and	CCONJ
ap-1402	146	10	representation	representation	NOUN
ap-1402	146	11	theory	theory	NOUN
ap-1402	146	12	(	(	PUNCT
ap-1402	146	13	which	which	PRON
ap-1402	146	14	may	may	AUX
ap-1402	146	15	be	be	AUX
ap-1402	146	16	the	the	DET
ap-1402	146	17	same	same	ADJ
ap-1402	146	18	)	)	PUNCT
ap-1402	146	19	,	,	PUNCT
ap-1402	146	20	it	it	PRON
ap-1402	146	21	is	be	AUX
ap-1402	146	22	beneficial	beneficial	ADJ
ap-1402	146	23	to	to	PART
ap-1402	146	24	introduce	introduce	VERB
ap-1402	146	25	the	the	DET
ap-1402	146	26	ladder	ladder	NOUN
ap-1402	146	27	operators	operator	NOUN
ap-1402	146	28	l±	l±	VERB
ap-1402	146	29	,	,	PUNCT
ap-1402	146	30	known	know	VERB
ap-1402	146	31	as	as	ADP
ap-1402	146	32	creation	creation	NOUN
ap-1402	146	33	/	/	SYM
ap-1402	146	34	annihilation	annihilation	NOUN
ap-1402	146	35	in	in	ADP
ap-1402	146	36	quantum	quantum	ADJ
ap-1402	146	37	mechanics	mechanic	NOUN
ap-1402	146	38	[	[	X
ap-1402	146	39	8	8	NUM
ap-1402	146	40	,	,	PUNCT
ap-1402	146	41	p.	p.	NOUN
ap-1402	146	42	49	49	NUM
ap-1402	146	43	]	]	PUNCT
ap-1402	146	44	or	or	CCONJ
ap-1402	146	45	raising	raise	VERB
ap-1402	146	46	/	/	SYM
ap-1402	146	47	lowering	lower	VERB
ap-1402	146	48	in	in	ADP
ap-1402	146	49	representation	representation	NOUN
ap-1402	146	50	theory	theory	NOUN
ap-1402	146	51	[	[	X
ap-1402	146	52	28	28	NUM
ap-1402	146	53	,	,	PUNCT
ap-1402	146	54	§	§	PROPN
ap-1402	146	55	vi.2	vi.2	PROPN
ap-1402	146	56	]	]	PUNCT
ap-1402	146	57	,	,	PUNCT
ap-1402	147	1	[	[	X
ap-1402	147	2	34	34	NUM
ap-1402	147	3	,	,	PUNCT
ap-1402	147	4	§	§	PROPN
ap-1402	147	5	8.2	8.2	NUM
ap-1402	147	6	]	]	PUNCT
ap-1402	147	7	,	,	PUNCT
ap-1402	148	1	[	[	X
ap-1402	148	2	3	3	NUM
ap-1402	148	3	]	]	PUNCT
ap-1402	148	4	.	.	PUNCT
ap-1402	149	1	they	they	PRON
ap-1402	149	2	are	be	AUX
ap-1402	149	3	defined	define	VERB
ap-1402	149	4	by	by	ADP
ap-1402	149	5	the	the	DET
ap-1402	149	6	following	follow	VERB
ap-1402	149	7	commutation	commutation	NOUN
ap-1402	149	8	relations	relation	NOUN
ap-1402	149	9	:	:	PUNCT
ap-1402	150	1	[	[	X
ap-1402	150	2	z̃	z̃	PROPN
ap-1402	150	3	,	,	PUNCT
ap-1402	150	4	l±	l±	X
ap-1402	150	5	]	]	X
ap-1402	150	6	=	=	PUNCT
ap-1402	151	1	λ±l±.	λ±l±.	X
ap-1402	151	2	(	(	PUNCT
ap-1402	151	3	23	23	NUM
ap-1402	151	4	)	)	PUNCT
ap-1402	151	5	in	in	ADP
ap-1402	151	6	other	other	ADJ
ap-1402	151	7	words	word	NOUN
ap-1402	151	8	,	,	PUNCT
ap-1402	151	9	l±	l±	PROPN
ap-1402	151	10	are	be	AUX
ap-1402	151	11	eigenvectors	eigenvector	NOUN
ap-1402	151	12	for	for	ADP
ap-1402	151	13	operators	operator	NOUN
ap-1402	151	14	ad	ad	NOUN
ap-1402	151	15	z	z	PROPN
ap-1402	151	16	of	of	ADP
ap-1402	151	17	the	the	DET
ap-1402	151	18	adjoint	adjoint	PROPN
ap-1402	151	19	representation	representation	NOUN
ap-1402	151	20	of	of	ADP
ap-1402	151	21	g	g	PROPN
ap-1402	151	22	[	[	X
ap-1402	151	23	28	28	NUM
ap-1402	151	24	,	,	PUNCT
ap-1402	151	25	§	§	PROPN
ap-1402	151	26	vi.2	vi.2	PROPN
ap-1402	151	27	]	]	PUNCT
ap-1402	151	28	.	.	PUNCT
ap-1402	152	1	remark	remark	PROPN
ap-1402	152	2	1	1	NUM
ap-1402	152	3	the	the	DET
ap-1402	152	4	existence	existence	NOUN
ap-1402	152	5	of	of	ADP
ap-1402	152	6	such	such	ADJ
ap-1402	152	7	ladder	ladder	NOUN
ap-1402	152	8	operators	operator	NOUN
ap-1402	152	9	follows	follow	VERB
ap-1402	152	10	from	from	ADP
ap-1402	152	11	the	the	DET
ap-1402	152	12	general	general	ADJ
ap-1402	152	13	properties	property	NOUN
ap-1402	152	14	of	of	ADP
ap-1402	152	15	lie	lie	NOUN
ap-1402	152	16	algebras	algebras	PROPN
ap-1402	152	17	if	if	SCONJ
ap-1402	152	18	the	the	DET
ap-1402	152	19	hamiltonian	hamiltonian	NOUN
ap-1402	152	20	belongs	belong	VERB
ap-1402	152	21	to	to	ADP
ap-1402	152	22	a	a	DET
ap-1402	152	23	cartan	cartan	ADJ
ap-1402	152	24	subalgebra	subalgebra	NOUN
ap-1402	152	25	.	.	PUNCT
ap-1402	153	1	this	this	PRON
ap-1402	153	2	is	be	AUX
ap-1402	153	3	the	the	DET
ap-1402	153	4	case	case	NOUN
ap-1402	153	5	for	for	ADP
ap-1402	153	6	vectors	vector	NOUN
ap-1402	153	7	z	z	PROPN
ap-1402	153	8	and	and	CCONJ
ap-1402	153	9	b	b	NOUN
ap-1402	153	10	,	,	PUNCT
ap-1402	153	11	which	which	PRON
ap-1402	153	12	are	be	AUX
ap-1402	153	13	the	the	DET
ap-1402	153	14	only	only	ADJ
ap-1402	153	15	two	two	NUM
ap-1402	153	16	non	non	ADJ
ap-1402	153	17	-	-	ADJ
ap-1402	153	18	isomorphic	isomorphic	ADJ
ap-1402	153	19	types	type	NOUN
ap-1402	153	20	of	of	ADP
ap-1402	153	21	cartan	cartan	PROPN
ap-1402	153	22	subalgebras	subalgebras	PROPN
ap-1402	153	23	in	in	ADP
ap-1402	153	24	sl2	sl2	PROPN
ap-1402	153	25	.	.	PUNCT
ap-1402	154	1	however	however	ADV
ap-1402	154	2	,	,	PUNCT
ap-1402	154	3	the	the	DET
ap-1402	154	4	third	third	ADJ
ap-1402	154	5	case	case	NOUN
ap-1402	154	6	considered	consider	VERB
ap-1402	154	7	in	in	ADP
ap-1402	154	8	this	this	DET
ap-1402	154	9	paper	paper	NOUN
ap-1402	154	10	,	,	PUNCT
ap-1402	154	11	the	the	DET
ap-1402	154	12	parabolic	parabolic	ADJ
ap-1402	154	13	vector	vector	PROPN
ap-1402	154	14	b	b	PROPN
ap-1402	154	15	+	+	NOUN
ap-1402	154	16	z/2	z/2	NUM
ap-1402	154	17	,	,	PUNCT
ap-1402	154	18	does	do	AUX
ap-1402	154	19	not	not	PART
ap-1402	154	20	belong	belong	VERB
ap-1402	154	21	to	to	ADP
ap-1402	154	22	a	a	DET
ap-1402	154	23	cartan	cartan	ADJ
ap-1402	154	24	subalgebra	subalgebra	NOUN
ap-1402	154	25	,	,	PUNCT
ap-1402	154	26	yet	yet	CCONJ
ap-1402	154	27	a	a	DET
ap-1402	154	28	sort	sort	NOUN
ap-1402	154	29	of	of	ADP
ap-1402	154	30	ladder	ladder	NOUN
ap-1402	154	31	operators	operator	NOUN
ap-1402	154	32	is	be	AUX
ap-1402	154	33	still	still	ADV
ap-1402	154	34	possible	possible	ADJ
ap-1402	154	35	with	with	ADP
ap-1402	154	36	dual	dual	ADJ
ap-1402	154	37	number	number	NOUN
ap-1402	154	38	coefficients	coefficient	NOUN
ap-1402	154	39	.	.	PUNCT
ap-1402	155	1	moreover	moreover	ADV
ap-1402	155	2	,	,	PUNCT
ap-1402	155	3	for	for	ADP
ap-1402	155	4	the	the	DET
ap-1402	155	5	hyperbolic	hyperbolic	ADJ
ap-1402	155	6	vector	vector	NOUN
ap-1402	155	7	b	b	PROPN
ap-1402	155	8	,	,	PUNCT
ap-1402	155	9	besides	besides	SCONJ
ap-1402	155	10	the	the	DET
ap-1402	155	11	standard	standard	ADJ
ap-1402	155	12	ladder	ladder	NOUN
ap-1402	155	13	operators	operator	NOUN
ap-1402	155	14	an	an	DET
ap-1402	155	15	additional	additional	ADJ
ap-1402	155	16	pair	pair	NOUN
ap-1402	155	17	with	with	ADP
ap-1402	155	18	double	double	ADJ
ap-1402	155	19	number	number	NOUN
ap-1402	155	20	coefficients	coefficient	NOUN
ap-1402	155	21	will	will	AUX
ap-1402	155	22	also	also	ADV
ap-1402	155	23	be	be	AUX
ap-1402	155	24	described	describe	VERB
ap-1402	155	25	.	.	PUNCT
ap-1402	156	1	from	from	ADP
ap-1402	156	2	the	the	DET
ap-1402	156	3	commutators	commutator	NOUN
ap-1402	156	4	(	(	PUNCT
ap-1402	156	5	23	23	NUM
ap-1402	156	6	)	)	PUNCT
ap-1402	156	7	we	we	PRON
ap-1402	156	8	deduce	deduce	VERB
ap-1402	156	9	that	that	SCONJ
ap-1402	156	10	if	if	SCONJ
ap-1402	156	11	vk	vk	NOUN
ap-1402	156	12	is	be	AUX
ap-1402	156	13	an	an	DET
ap-1402	156	14	eigenvector	eigenvector	NOUN
ap-1402	156	15	of	of	ADP
ap-1402	156	16	z̃	z̃	PROPN
ap-1402	156	17	then	then	ADV
ap-1402	156	18	l+vk	l+vk	NOUN
ap-1402	156	19	is	be	AUX
ap-1402	156	20	an	an	DET
ap-1402	156	21	eigenvector	eigenvector	NOUN
ap-1402	156	22	as	as	ADV
ap-1402	156	23	well	well	ADV
ap-1402	156	24	:	:	PUNCT
ap-1402	156	25	z̃(l+vk	z̃(l+vk	ADJ
ap-1402	156	26	)	)	PUNCT
ap-1402	156	27	=	=	PUNCT
ap-1402	156	28	(	(	PUNCT
ap-1402	156	29	l+z̃	l+z̃	ADJ
ap-1402	156	30	+	+	PUNCT
ap-1402	156	31	λ+l+)vk	λ+l+)vk	PROPN
ap-1402	156	32	=	=	SYM
ap-1402	156	33	l+(z̃vk	l+(z̃vk	PROPN
ap-1402	156	34	)	)	PUNCT
ap-1402	157	1	+	+	NUM
ap-1402	157	2	λ+l+vk	λ+l+vk	NOUN
ap-1402	157	3	=	=	SYM
ap-1402	157	4	ikl+vk	ikl+vk	PROPN
ap-1402	157	5	+	+	NUM
ap-1402	157	6	λ+l+vk	λ+l+vk	PROPN
ap-1402	157	7	=	=	SYM
ap-1402	157	8	(	(	PUNCT
ap-1402	157	9	ik	ik	X
ap-1402	157	10	+	+	PROPN
ap-1402	157	11	λ+)l+vk	λ+)l+vk	PROPN
ap-1402	157	12	.	.	PUNCT
ap-1402	158	1	(	(	PUNCT
ap-1402	158	2	24	24	NUM
ap-1402	158	3	)	)	PUNCT
ap-1402	158	4	thus	thus	ADV
ap-1402	158	5	the	the	DET
ap-1402	158	6	action	action	NOUN
ap-1402	158	7	of	of	ADP
ap-1402	158	8	ladder	ladder	NOUN
ap-1402	158	9	operators	operator	NOUN
ap-1402	158	10	on	on	ADP
ap-1402	158	11	the	the	DET
ap-1402	158	12	respective	respective	ADJ
ap-1402	158	13	eigenspaces	eigenspace	NOUN
ap-1402	158	14	vk	vk	NOUN
ap-1402	158	15	can	can	AUX
ap-1402	158	16	be	be	AUX
ap-1402	158	17	visualised	visualise	VERB
ap-1402	158	18	by	by	ADP
ap-1402	158	19	the	the	DET
ap-1402	158	20	diagram	diagram	NOUN
ap-1402	158	21	:	:	PUNCT
ap-1402	158	22	(	(	PUNCT
ap-1402	158	23	25	25	NUM
ap-1402	158	24	)	)	PUNCT
ap-1402	158	25	there	there	PRON
ap-1402	158	26	are	be	VERB
ap-1402	158	27	two	two	NUM
ap-1402	158	28	ways	way	NOUN
ap-1402	158	29	to	to	PART
ap-1402	158	30	search	search	VERB
ap-1402	158	31	for	for	ADP
ap-1402	158	32	ladder	ladder	NOUN
ap-1402	158	33	operators	operator	NOUN
ap-1402	158	34	:	:	PUNCT
ap-1402	158	35	in	in	ADP
ap-1402	158	36	(	(	PUNCT
ap-1402	158	37	complexified	complexified	ADJ
ap-1402	158	38	)	)	PUNCT
ap-1402	158	39	lie	lie	NOUN
ap-1402	158	40	algebras	algebras	PROPN
ap-1402	158	41	h1	h1	PROPN
ap-1402	158	42	and	and	CCONJ
ap-1402	158	43	sp2	sp2	NOUN
ap-1402	158	44	.	.	PUNCT
ap-1402	159	1	we	we	PRON
ap-1402	159	2	will	will	AUX
ap-1402	159	3	consider	consider	VERB
ap-1402	159	4	them	they	PRON
ap-1402	159	5	in	in	ADP
ap-1402	159	6	sequence	sequence	NOUN
ap-1402	159	7	.	.	PUNCT
ap-1402	160	1	3.1	3.1	NUM
ap-1402	160	2	ladder	ladder	NOUN
ap-1402	160	3	operators	operator	NOUN
ap-1402	160	4	from	from	ADP
ap-1402	160	5	the	the	DET
ap-1402	160	6	heisenberg	heisenberg	PROPN
ap-1402	160	7	group	group	PROPN
ap-1402	160	8	assuming	assume	VERB
ap-1402	160	9	l+	l+	X
ap-1402	160	10	=	=	PUNCT
ap-1402	160	11	ax̃	ax̃	PROPN
ap-1402	161	1	+	+	CCONJ
ap-1402	161	2	bỹ	bỹ	NOUN
ap-1402	161	3	we	we	PRON
ap-1402	161	4	obtain	obtain	VERB
ap-1402	161	5	from	from	ADP
ap-1402	161	6	the	the	DET
ap-1402	161	7	relations	relation	NOUN
ap-1402	161	8	(	(	PUNCT
ap-1402	161	9	11–12	11–12	NUM
ap-1402	161	10	)	)	PUNCT
ap-1402	161	11	and	and	CCONJ
ap-1402	161	12	(	(	PUNCT
ap-1402	161	13	23	23	NUM
ap-1402	161	14	)	)	PUNCT
ap-1402	161	15	the	the	DET
ap-1402	161	16	linear	linear	ADJ
ap-1402	161	17	equations	equation	NOUN
ap-1402	161	18	with	with	ADP
ap-1402	161	19	unknown	unknown	ADJ
ap-1402	161	20	a	a	PRON
ap-1402	161	21	and	and	CCONJ
ap-1402	161	22	b	b	NOUN
ap-1402	161	23	:	:	PUNCT
ap-1402	161	24	47	47	NUM
ap-1402	161	25	acta	acta	PROPN
ap-1402	161	26	polytechnica	polytechnica	PROPN
ap-1402	161	27	vol	vol	NOUN
ap-1402	161	28	.	.	PUNCT
ap-1402	162	1	51	51	NUM
ap-1402	162	2	no	no	INTJ
ap-1402	162	3	.	.	PUNCT
ap-1402	163	1	4/2011	4/2011	NUM
ap-1402	163	2	a	a	DET
ap-1402	163	3	=	=	SYM
ap-1402	163	4	λ+b	λ+b	NOUN
ap-1402	163	5	,	,	PUNCT
ap-1402	163	6	−b	−b	NOUN
ap-1402	163	7	=	=	PUNCT
ap-1402	163	8	λ+a	λ+a	X
ap-1402	163	9	.	.	PUNCT
ap-1402	164	1	the	the	DET
ap-1402	164	2	equations	equation	NOUN
ap-1402	164	3	have	have	VERB
ap-1402	164	4	a	a	DET
ap-1402	164	5	solution	solution	NOUN
ap-1402	164	6	if	if	SCONJ
ap-1402	165	1	and	and	CCONJ
ap-1402	165	2	only	only	ADV
ap-1402	165	3	if	if	SCONJ
ap-1402	165	4	λ2++1	λ2++1	PROPN
ap-1402	165	5	=	=	SYM
ap-1402	165	6	0	0	NUM
ap-1402	165	7	,	,	PUNCT
ap-1402	165	8	and	and	CCONJ
ap-1402	165	9	the	the	DET
ap-1402	165	10	raising	raising	NOUN
ap-1402	165	11	/	/	SYM
ap-1402	165	12	lowering	lower	VERB
ap-1402	165	13	operators	operator	NOUN
ap-1402	165	14	are	be	AUX
ap-1402	165	15	l±	l±	X
ap-1402	165	16	=	=	PUNCT
ap-1402	165	17	x̃	x̃	PROPN
ap-1402	165	18	∓	∓	PROPN
ap-1402	165	19	iỹ	iỹ	NOUN
ap-1402	165	20	.	.	PUNCT
ap-1402	166	1	remark	remark	NOUN
ap-1402	166	2	2	2	NUM
ap-1402	166	3	here	here	ADV
ap-1402	166	4	we	we	PRON
ap-1402	166	5	have	have	VERB
ap-1402	166	6	an	an	DET
ap-1402	166	7	interesting	interesting	ADJ
ap-1402	166	8	asymmetric	asymmetric	ADJ
ap-1402	166	9	response	response	NOUN
ap-1402	166	10	:	:	PUNCT
ap-1402	166	11	due	due	ADP
ap-1402	166	12	to	to	ADP
ap-1402	166	13	the	the	DET
ap-1402	166	14	structure	structure	NOUN
ap-1402	166	15	of	of	ADP
ap-1402	166	16	the	the	DET
ap-1402	166	17	semidirect	semidirect	NOUN
ap-1402	166	18	product	product	NOUN
ap-1402	166	19	h	h	NOUN
ap-1402	166	20	1×|	1×|	NUM
ap-1402	167	1	s̃p(2	s̃p(2	NUM
ap-1402	167	2	)	)	PUNCT
ap-1402	167	3	it	it	PRON
ap-1402	167	4	is	be	AUX
ap-1402	167	5	the	the	DET
ap-1402	167	6	symplectic	symplectic	ADJ
ap-1402	167	7	group	group	NOUN
ap-1402	167	8	which	which	PRON
ap-1402	167	9	acts	act	VERB
ap-1402	167	10	on	on	ADP
ap-1402	167	11	h	h	PROPN
ap-1402	167	12	1	1	NUM
ap-1402	167	13	,	,	PUNCT
ap-1402	167	14	not	not	PART
ap-1402	167	15	vise	vise	VERB
ap-1402	167	16	versa	versa	ADV
ap-1402	167	17	.	.	PUNCT
ap-1402	168	1	however	however	ADV
ap-1402	168	2	,	,	PUNCT
ap-1402	168	3	the	the	DET
ap-1402	168	4	heisenberg	heisenberg	PROPN
ap-1402	168	5	group	group	PROPN
ap-1402	168	6	has	have	VERB
ap-1402	168	7	a	a	DET
ap-1402	168	8	weak	weak	ADJ
ap-1402	168	9	action	action	NOUN
ap-1402	168	10	in	in	ADP
ap-1402	168	11	the	the	DET
ap-1402	168	12	opposite	opposite	ADJ
ap-1402	168	13	direction	direction	NOUN
ap-1402	168	14	:	:	PUNCT
ap-1402	168	15	it	it	PRON
ap-1402	168	16	shifts	shift	VERB
ap-1402	168	17	eigenfunctions	eigenfunction	NOUN
ap-1402	168	18	of	of	ADP
ap-1402	168	19	sp(2	sp(2	NOUN
ap-1402	168	20	)	)	PUNCT
ap-1402	168	21	.	.	PUNCT
ap-1402	169	1	in	in	ADP
ap-1402	169	2	the	the	DET
ap-1402	169	3	schrödinger	schrödinger	NOUN
ap-1402	169	4	representation	representation	NOUN
ap-1402	169	5	(	(	PUNCT
ap-1402	169	6	14	14	NUM
ap-1402	169	7	)	)	PUNCT
ap-1402	169	8	the	the	DET
ap-1402	169	9	ladder	ladder	NOUN
ap-1402	169	10	operators	operator	NOUN
ap-1402	169	11	are	be	AUX
ap-1402	169	12	ρh̄(l±	ρh̄(l±	NUM
ap-1402	169	13	)	)	PUNCT
ap-1402	170	1	=	=	SYM
ap-1402	170	2	2πiq	2πiq	NUM
ap-1402	170	3	±	±	NUM
ap-1402	170	4	ih̄	ih̄	NOUN
ap-1402	170	5	d	d	X
ap-1402	170	6	dq	dq	PROPN
ap-1402	170	7	.	.	PUNCT
ap-1402	171	1	(	(	PUNCT
ap-1402	171	2	26	26	NUM
ap-1402	171	3	)	)	PUNCT
ap-1402	171	4	the	the	DET
ap-1402	171	5	standard	standard	ADJ
ap-1402	171	6	treatment	treatment	NOUN
ap-1402	171	7	of	of	ADP
ap-1402	171	8	the	the	DET
ap-1402	171	9	harmonic	harmonic	ADJ
ap-1402	171	10	oscillator	oscillator	NOUN
ap-1402	171	11	in	in	ADP
ap-1402	171	12	quantum	quantum	ADJ
ap-1402	171	13	mechanics	mechanic	NOUN
ap-1402	171	14	,	,	PUNCT
ap-1402	171	15	which	which	PRON
ap-1402	171	16	can	can	AUX
ap-1402	171	17	be	be	AUX
ap-1402	171	18	found	find	VERB
ap-1402	171	19	in	in	ADP
ap-1402	171	20	many	many	ADJ
ap-1402	171	21	textbooks	textbook	NOUN
ap-1402	171	22	,	,	PUNCT
ap-1402	171	23	e.g.	e.g.	ADV
ap-1402	171	24	[	[	X
ap-1402	171	25	8	8	NUM
ap-1402	171	26	,	,	PUNCT
ap-1402	171	27	§	§	PROPN
ap-1402	171	28	1.7	1.7	NUM
ap-1402	171	29	]	]	PUNCT
ap-1402	171	30	,	,	PUNCT
ap-1402	172	1	[	[	X
ap-1402	172	2	9	9	NUM
ap-1402	172	3	,	,	PUNCT
ap-1402	172	4	§	§	PROPN
ap-1402	172	5	2.2.3	2.2.3	NUM
ap-1402	172	6	]	]	PUNCT
ap-1402	172	7	,	,	PUNCT
ap-1402	172	8	is	be	AUX
ap-1402	172	9	as	as	SCONJ
ap-1402	172	10	follows	follow	VERB
ap-1402	172	11	.	.	PUNCT
ap-1402	173	1	the	the	DET
ap-1402	173	2	vector	vector	NOUN
ap-1402	173	3	v−1/2(q	v−1/2(q	PROPN
ap-1402	173	4	)	)	PUNCT
ap-1402	173	5	=	=	SYM
ap-1402	173	6	e−πq2	e−πq2	NOUN
ap-1402	173	7	/	/	SYM
ap-1402	173	8	h̄	h̄	NOUN
ap-1402	173	9	is	be	AUX
ap-1402	173	10	an	an	DET
ap-1402	173	11	eigenvector	eigenvector	NOUN
ap-1402	173	12	of	of	ADP
ap-1402	173	13	z̃	z̃	PROPN
ap-1402	173	14	with	with	ADP
ap-1402	173	15	the	the	DET
ap-1402	173	16	eigenvalue	eigenvalue	PROPN
ap-1402	173	17	−	−	NOUN
ap-1402	173	18	i	i	NOUN
ap-1402	173	19	2	2	NUM
ap-1402	173	20	.	.	PUNCT
ap-1402	174	1	in	in	ADP
ap-1402	174	2	addition	addition	NOUN
ap-1402	174	3	v−1/2	v−1/2	PROPN
ap-1402	174	4	is	be	AUX
ap-1402	174	5	annihilated	annihilate	VERB
ap-1402	174	6	by	by	ADP
ap-1402	174	7	l+	l+	PROPN
ap-1402	174	8	.	.	PUNCT
ap-1402	175	1	thus	thus	ADV
ap-1402	175	2	the	the	DET
ap-1402	175	3	chain	chain	NOUN
ap-1402	175	4	(	(	PUNCT
ap-1402	175	5	25	25	NUM
ap-1402	175	6	)	)	PUNCT
ap-1402	175	7	terminates	terminate	VERB
ap-1402	175	8	to	to	ADP
ap-1402	175	9	the	the	DET
ap-1402	175	10	right	right	NOUN
ap-1402	175	11	and	and	CCONJ
ap-1402	175	12	the	the	DET
ap-1402	175	13	complete	complete	ADJ
ap-1402	175	14	set	set	NOUN
ap-1402	175	15	of	of	ADP
ap-1402	175	16	eigenvectors	eigenvector	NOUN
ap-1402	175	17	of	of	ADP
ap-1402	175	18	the	the	DET
ap-1402	175	19	harmonic	harmonic	ADJ
ap-1402	175	20	oscillator	oscillator	NOUN
ap-1402	175	21	hamiltonian	hamiltonian	NOUN
ap-1402	175	22	is	be	AUX
ap-1402	175	23	presented	present	VERB
ap-1402	175	24	by	by	ADP
ap-1402	175	25	(	(	PUNCT
ap-1402	175	26	l−)kv−1/2	l−)kv−1/2	PROPN
ap-1402	175	27	with	with	ADP
ap-1402	175	28	k	k	PROPN
ap-1402	175	29	=	=	SYM
ap-1402	175	30	0	0	NUM
ap-1402	175	31	,	,	PUNCT
ap-1402	175	32	1	1	NUM
ap-1402	175	33	,	,	PUNCT
ap-1402	175	34	2	2	NUM
ap-1402	175	35	,	,	PUNCT
ap-1402	175	36	.	.	PUNCT
ap-1402	175	37	.	.	PUNCT
ap-1402	176	1	.	.	PUNCT
ap-1402	177	1	we	we	PRON
ap-1402	177	2	can	can	AUX
ap-1402	177	3	make	make	VERB
ap-1402	177	4	a	a	DET
ap-1402	177	5	wavelet	wavelet	NOUN
ap-1402	177	6	transform	transform	NOUN
ap-1402	177	7	generated	generate	VERB
ap-1402	177	8	by	by	ADP
ap-1402	177	9	the	the	DET
ap-1402	177	10	heisenberg	heisenberg	PROPN
ap-1402	177	11	group	group	NOUN
ap-1402	177	12	with	with	ADP
ap-1402	177	13	the	the	DET
ap-1402	177	14	mother	mother	NOUN
ap-1402	177	15	wavelet	wavelet	PROPN
ap-1402	177	16	v−1/2	v−1/2	PROPN
ap-1402	177	17	,	,	PUNCT
ap-1402	177	18	and	and	CCONJ
ap-1402	177	19	the	the	DET
ap-1402	177	20	image	image	NOUN
ap-1402	177	21	will	will	AUX
ap-1402	177	22	be	be	AUX
ap-1402	177	23	the	the	DET
ap-1402	177	24	fock	fock	ADJ
ap-1402	177	25	-	-	PUNCT
ap-1402	177	26	segal	segal	NOUN
ap-1402	177	27	-	-	PUNCT
ap-1402	177	28	bargmann	bargmann	PROPN
ap-1402	177	29	(	(	PUNCT
ap-1402	177	30	fsb	fsb	NOUN
ap-1402	177	31	)	)	PUNCT
ap-1402	177	32	space	space	NOUN
ap-1402	178	1	[	[	X
ap-1402	178	2	12	12	NUM
ap-1402	178	3	]	]	PUNCT
ap-1402	178	4	,	,	PUNCT
ap-1402	178	5	[	[	X
ap-1402	178	6	8	8	NUM
ap-1402	178	7	,	,	PUNCT
ap-1402	178	8	§	§	PROPN
ap-1402	178	9	1.6	1.6	NUM
ap-1402	178	10	]	]	PUNCT
ap-1402	178	11	.	.	PUNCT
ap-1402	179	1	since	since	SCONJ
ap-1402	179	2	v−1/2	v−1/2	PROPN
ap-1402	179	3	is	be	AUX
ap-1402	179	4	the	the	DET
ap-1402	179	5	null	null	ADJ
ap-1402	179	6	solution	solution	NOUN
ap-1402	179	7	of	of	ADP
ap-1402	179	8	l+	l+	NOUN
ap-1402	179	9	=	=	PUNCT
ap-1402	179	10	x̃	x̃	PROPN
ap-1402	179	11	−	−	PROPN
ap-1402	179	12	iỹ	iỹ	NOUN
ap-1402	179	13	,	,	PUNCT
ap-1402	179	14	then	then	ADV
ap-1402	179	15	by	by	ADP
ap-1402	179	16	the	the	DET
ap-1402	179	17	general	general	ADJ
ap-1402	179	18	result	result	NOUN
ap-1402	179	19	[	[	X
ap-1402	179	20	26	26	NUM
ap-1402	179	21	,	,	PUNCT
ap-1402	179	22	cor	cor	PROPN
ap-1402	179	23	.	.	PROPN
ap-1402	179	24	24	24	NUM
ap-1402	179	25	]	]	PUNCT
ap-1402	179	26	the	the	DET
ap-1402	179	27	image	image	NOUN
ap-1402	179	28	of	of	ADP
ap-1402	179	29	the	the	DET
ap-1402	179	30	wavelet	wavelet	NOUN
ap-1402	179	31	transform	transform	NOUN
ap-1402	179	32	will	will	AUX
ap-1402	179	33	be	be	AUX
ap-1402	179	34	null	null	ADJ
ap-1402	179	35	-	-	PUNCT
ap-1402	179	36	solutions	solution	NOUN
ap-1402	179	37	of	of	ADP
ap-1402	179	38	the	the	DET
ap-1402	179	39	corresponding	corresponding	ADJ
ap-1402	179	40	linear	linear	ADJ
ap-1402	179	41	combination	combination	NOUN
ap-1402	179	42	of	of	ADP
ap-1402	179	43	the	the	DET
ap-1402	179	44	lie	lie	NOUN
ap-1402	179	45	derivatives	derivative	NOUN
ap-1402	179	46	(	(	PUNCT
ap-1402	179	47	7	7	NUM
ap-1402	179	48	):	):	PUNCT
ap-1402	180	1	d	d	NOUN
ap-1402	180	2	=	=	SYM
ap-1402	180	3	xr	xr	PROPN
ap-1402	180	4	−	−	PROPN
ap-1402	181	1	iy	iy	INTJ
ap-1402	181	2	r	r	NOUN
ap-1402	181	3	=	=	PUNCT
ap-1402	181	4	(	(	PUNCT
ap-1402	181	5	∂x	∂x	PROPN
ap-1402	181	6	+	+	NUM
ap-1402	181	7	i∂y	i∂y	NOUN
ap-1402	181	8	)	)	PUNCT
ap-1402	181	9	−	−	PROPN
ap-1402	182	1	πh̄(x	πh̄(x	PROPN
ap-1402	182	2	−	−	PROPN
ap-1402	182	3	iy	iy	PROPN
ap-1402	182	4	)	)	PUNCT
ap-1402	182	5	,	,	PUNCT
ap-1402	182	6	(	(	PUNCT
ap-1402	182	7	27	27	NUM
ap-1402	182	8	)	)	PUNCT
ap-1402	182	9	which	which	PRON
ap-1402	182	10	turns	turn	VERB
ap-1402	182	11	out	out	ADP
ap-1402	182	12	to	to	PART
ap-1402	182	13	be	be	AUX
ap-1402	182	14	the	the	DET
ap-1402	182	15	cauchy	cauchy	PROPN
ap-1402	182	16	-	-	PUNCT
ap-1402	182	17	riemann	riemann	PROPN
ap-1402	182	18	equation	equation	NOUN
ap-1402	182	19	on	on	ADP
ap-1402	182	20	a	a	DET
ap-1402	182	21	weighted	weight	VERB
ap-1402	182	22	fsb	fsb	ADJ
ap-1402	182	23	-	-	PUNCT
ap-1402	182	24	type	type	NOUN
ap-1402	182	25	space	space	NOUN
ap-1402	182	26	.	.	PUNCT
ap-1402	183	1	3.2	3.2	NUM
ap-1402	183	2	symplectic	symplectic	ADJ
ap-1402	183	3	ladder	ladder	NOUN
ap-1402	183	4	operators	operator	NOUN
ap-1402	183	5	we	we	PRON
ap-1402	183	6	can	can	AUX
ap-1402	183	7	also	also	ADV
ap-1402	183	8	look	look	VERB
ap-1402	183	9	for	for	ADP
ap-1402	183	10	ladder	ladder	NOUN
ap-1402	183	11	operators	operator	NOUN
ap-1402	183	12	within	within	ADP
ap-1402	183	13	the	the	DET
ap-1402	183	14	lie	lie	NOUN
ap-1402	183	15	algebra	algebra	NOUN
ap-1402	183	16	sp2	sp2	NOUN
ap-1402	183	17	,	,	PUNCT
ap-1402	183	18	see	see	VERB
ap-1402	183	19	[	[	X
ap-1402	183	20	23	23	NUM
ap-1402	183	21	,	,	PUNCT
ap-1402	183	22	§	§	PROPN
ap-1402	183	23	8	8	NUM
ap-1402	183	24	]	]	PUNCT
ap-1402	183	25	.	.	PUNCT
ap-1402	184	1	assuming	assume	VERB
ap-1402	184	2	l+2	l+2	NOUN
ap-1402	184	3	=	=	SYM
ap-1402	184	4	aã	aã	PROPN
ap-1402	185	1	+	+	CCONJ
ap-1402	185	2	bb̃	bb̃	PRON
ap-1402	185	3	+	+	NUM
ap-1402	185	4	cz̃	cz̃	NOUN
ap-1402	185	5	from	from	ADP
ap-1402	185	6	the	the	DET
ap-1402	185	7	relations	relation	NOUN
ap-1402	185	8	(	(	PUNCT
ap-1402	185	9	10	10	NUM
ap-1402	185	10	)	)	PUNCT
ap-1402	185	11	and	and	CCONJ
ap-1402	185	12	defining	define	VERB
ap-1402	185	13	condition	condition	NOUN
ap-1402	185	14	(	(	PUNCT
ap-1402	185	15	23	23	NUM
ap-1402	185	16	)	)	PUNCT
ap-1402	185	17	we	we	PRON
ap-1402	185	18	obtain	obtain	VERB
ap-1402	185	19	the	the	DET
ap-1402	185	20	linear	linear	ADJ
ap-1402	185	21	equations	equation	NOUN
ap-1402	185	22	with	with	ADP
ap-1402	185	23	unknown	unknown	ADJ
ap-1402	185	24	a	a	DET
ap-1402	185	25	,	,	PUNCT
ap-1402	185	26	b	b	PROPN
ap-1402	185	27	and	and	CCONJ
ap-1402	185	28	c	c	NOUN
ap-1402	185	29	:	:	PUNCT
ap-1402	185	30	c	c	NOUN
ap-1402	185	31	=	=	SYM
ap-1402	185	32	0	0	NUM
ap-1402	185	33	,	,	PUNCT
ap-1402	185	34	2a	2a	NUM
ap-1402	185	35	=	=	SYM
ap-1402	185	36	λ+b	λ+b	NOUN
ap-1402	185	37	,	,	PUNCT
ap-1402	185	38	−2b	−2b	NOUN
ap-1402	185	39	=	=	PUNCT
ap-1402	185	40	λ+a	λ+a	X
ap-1402	185	41	.	.	PUNCT
ap-1402	186	1	the	the	DET
ap-1402	186	2	equations	equation	NOUN
ap-1402	186	3	have	have	VERB
ap-1402	186	4	a	a	DET
ap-1402	186	5	solution	solution	NOUN
ap-1402	186	6	if	if	SCONJ
ap-1402	186	7	and	and	CCONJ
ap-1402	186	8	only	only	ADV
ap-1402	186	9	if	if	SCONJ
ap-1402	186	10	λ2	λ2	NOUN
ap-1402	186	11	+	+	X
ap-1402	186	12	+	+	NUM
ap-1402	186	13	4	4	NUM
ap-1402	186	14	=	=	SYM
ap-1402	186	15	0	0	NUM
ap-1402	186	16	,	,	PUNCT
ap-1402	186	17	and	and	CCONJ
ap-1402	186	18	the	the	DET
ap-1402	186	19	raising	raising	NOUN
ap-1402	186	20	/	/	SYM
ap-1402	186	21	lowering	lower	VERB
ap-1402	186	22	operators	operator	NOUN
ap-1402	186	23	are	be	AUX
ap-1402	186	24	l±	l±	X
ap-1402	186	25	2	2	NUM
ap-1402	186	26	=	=	SYM
ap-1402	186	27	±iã	±iã	PROPN
ap-1402	186	28	+	+	CCONJ
ap-1402	186	29	b̃.	b̃.	NOUN
ap-1402	186	30	in	in	ADP
ap-1402	186	31	the	the	DET
ap-1402	186	32	shale	shale	NOUN
ap-1402	186	33	-	-	PUNCT
ap-1402	186	34	weil	weil	PROPN
ap-1402	186	35	representation	representation	NOUN
ap-1402	186	36	(	(	PUNCT
ap-1402	186	37	15	15	NUM
ap-1402	186	38	)	)	PUNCT
ap-1402	186	39	they	they	PRON
ap-1402	186	40	turn	turn	VERB
ap-1402	186	41	out	out	ADP
ap-1402	186	42	to	to	PART
ap-1402	186	43	be	be	AUX
ap-1402	186	44	:	:	PUNCT
ap-1402	186	45	l±	l±	VERB
ap-1402	186	46	2	2	NUM
ap-1402	186	47	=	=	SYM
ap-1402	186	48	±i	±i	PROPN
ap-1402	186	49	(	(	PUNCT
ap-1402	186	50	q	q	PROPN
ap-1402	186	51	2	2	NUM
ap-1402	186	52	d	d	NOUN
ap-1402	186	53	dq	dq	NOUN
ap-1402	186	54	+	+	CCONJ
ap-1402	186	55	1	1	NUM
ap-1402	186	56	4	4	NUM
ap-1402	186	57	)	)	PUNCT
ap-1402	186	58	−	−	PROPN
ap-1402	187	1	h̄i	h̄i	PROPN
ap-1402	187	2	8π	8π	NUM
ap-1402	187	3	d2	d2	PROPN
ap-1402	187	4	dq2	dq2	PROPN
ap-1402	187	5	−	−	PROPN
ap-1402	187	6	πiq2	πiq2	PROPN
ap-1402	187	7	2h̄	2h̄	NUM
ap-1402	188	1	=	=	PUNCT
ap-1402	189	1	−	−	NOUN
ap-1402	190	1	i	i	PRON
ap-1402	190	2	8πh̄	8πh̄	PROPN
ap-1402	190	3	(	(	PUNCT
ap-1402	190	4	∓2πq	∓2πq	ADJ
ap-1402	190	5	+	+	NUM
ap-1402	190	6	h̄	h̄	X
ap-1402	190	7	d	d	X
ap-1402	190	8	dq	dq	PROPN
ap-1402	190	9	)	)	PUNCT
ap-1402	190	10	2	2	NUM
ap-1402	190	11	.	.	PUNCT
ap-1402	191	1	(	(	PUNCT
ap-1402	191	2	28	28	NUM
ap-1402	191	3	)	)	PUNCT
ap-1402	191	4	since	since	SCONJ
ap-1402	191	5	this	this	DET
ap-1402	191	6	time	time	NOUN
ap-1402	191	7	λ+	λ+	PUNCT
ap-1402	191	8	=	=	NOUN
ap-1402	191	9	2i	2i	NUM
ap-1402	191	10	the	the	DET
ap-1402	191	11	ladder	ladder	NOUN
ap-1402	191	12	operators	operator	NOUN
ap-1402	191	13	l±	l±	VERB
ap-1402	191	14	2	2	NUM
ap-1402	191	15	produce	produce	VERB
ap-1402	191	16	a	a	DET
ap-1402	191	17	shift	shift	NOUN
ap-1402	191	18	on	on	ADP
ap-1402	191	19	the	the	DET
ap-1402	191	20	diagram	diagram	NOUN
ap-1402	191	21	(	(	PUNCT
ap-1402	191	22	25	25	NUM
ap-1402	191	23	)	)	PUNCT
ap-1402	191	24	twice	twice	ADV
ap-1402	191	25	bigger	big	ADJ
ap-1402	191	26	than	than	ADP
ap-1402	191	27	the	the	DET
ap-1402	191	28	operators	operator	NOUN
ap-1402	191	29	l±	l±	VERB
ap-1402	191	30	from	from	ADP
ap-1402	191	31	the	the	DET
ap-1402	191	32	heisenberg	heisenberg	PROPN
ap-1402	191	33	group	group	NOUN
ap-1402	191	34	.	.	PUNCT
ap-1402	192	1	after	after	ADV
ap-1402	192	2	all	all	ADV
ap-1402	192	3	,	,	PUNCT
ap-1402	192	4	this	this	PRON
ap-1402	192	5	is	be	AUX
ap-1402	192	6	not	not	PART
ap-1402	192	7	surprising	surprising	ADJ
ap-1402	192	8	since	since	SCONJ
ap-1402	192	9	from	from	ADP
ap-1402	192	10	the	the	DET
ap-1402	192	11	explicit	explicit	ADJ
ap-1402	192	12	representations	representation	NOUN
ap-1402	192	13	(	(	PUNCT
ap-1402	192	14	26	26	NUM
ap-1402	192	15	)	)	PUNCT
ap-1402	192	16	and	and	CCONJ
ap-1402	192	17	(	(	PUNCT
ap-1402	192	18	28	28	NUM
ap-1402	192	19	)	)	PUNCT
ap-1402	192	20	we	we	PRON
ap-1402	192	21	get	get	VERB
ap-1402	192	22	:	:	PUNCT
ap-1402	192	23	l±	l±	PROPN
ap-1402	192	24	2	2	NUM
ap-1402	192	25	=	=	SYM
ap-1402	192	26	−	−	NOUN
ap-1402	193	1	i	i	PRON
ap-1402	193	2	8πh̄	8πh̄	INTJ
ap-1402	193	3	(	(	PUNCT
ap-1402	193	4	l±)2	l±)2	NOUN
ap-1402	193	5	.	.	NOUN
ap-1402	193	6	4	4	NUM
ap-1402	193	7	ladder	ladder	NOUN
ap-1402	193	8	operators	operator	NOUN
ap-1402	193	9	for	for	ADP
ap-1402	193	10	the	the	DET
ap-1402	193	11	hyperbolic	hyperbolic	ADJ
ap-1402	193	12	subgroup	subgroup	NOUN
ap-1402	193	13	consider	consider	VERB
ap-1402	193	14	the	the	DET
ap-1402	193	15	case	case	NOUN
ap-1402	193	16	of	of	ADP
ap-1402	193	17	the	the	DET
ap-1402	193	18	hamiltonian	hamiltonian	ADJ
ap-1402	193	19	h	h	NOUN
ap-1402	193	20	=	=	SYM
ap-1402	193	21	2b	2b	NOUN
ap-1402	193	22	,	,	PUNCT
ap-1402	193	23	which	which	PRON
ap-1402	193	24	is	be	AUX
ap-1402	193	25	a	a	DET
ap-1402	193	26	repulsive	repulsive	ADJ
ap-1402	193	27	(	(	PUNCT
ap-1402	193	28	hyperbolic	hyperbolic	ADJ
ap-1402	193	29	)	)	PUNCT
ap-1402	193	30	harmonic	harmonic	ADJ
ap-1402	193	31	oscillator	oscillator	NOUN
ap-1402	193	32	[	[	X
ap-1402	193	33	37	37	NUM
ap-1402	193	34	,	,	PUNCT
ap-1402	193	35	§	§	PROPN
ap-1402	193	36	3.8	3.8	NUM
ap-1402	193	37	]	]	PUNCT
ap-1402	193	38	.	.	PUNCT
ap-1402	194	1	the	the	DET
ap-1402	194	2	corresponding	correspond	VERB
ap-1402	194	3	one	one	NUM
ap-1402	194	4	-	-	PUNCT
ap-1402	194	5	dimensional	dimensional	ADJ
ap-1402	194	6	subgroup	subgroup	NOUN
ap-1402	194	7	of	of	ADP
ap-1402	194	8	symplectomorphisms	symplectomorphism	NOUN
ap-1402	194	9	produces	produce	VERB
ap-1402	194	10	hyperbolic	hyperbolic	ADJ
ap-1402	194	11	rotations	rotation	NOUN
ap-1402	194	12	of	of	ADP
ap-1402	194	13	the	the	DET
ap-1402	194	14	phase	phase	NOUN
ap-1402	194	15	space	space	NOUN
ap-1402	194	16	.	.	PUNCT
ap-1402	195	1	the	the	DET
ap-1402	195	2	eigenvectors	eigenvector	NOUN
ap-1402	195	3	vμ	vμ	INTJ
ap-1402	195	4	of	of	ADP
ap-1402	195	5	the	the	DET
ap-1402	195	6	operator	operator	NOUN
ap-1402	195	7	ρswh̄	ρswh̄	PROPN
ap-1402	195	8	(	(	PUNCT
ap-1402	195	9	2b)vν	2b)vν	NUM
ap-1402	195	10	=	=	SYM
ap-1402	195	11	−i	−i	PROPN
ap-1402	195	12	(	(	PUNCT
ap-1402	195	13	h̄	h̄	NUM
ap-1402	195	14	4π	4π	NUM
ap-1402	195	15	d2	d2	PROPN
ap-1402	195	16	dq2	dq2	PROPN
ap-1402	195	17	+	+	CCONJ
ap-1402	195	18	πq2	πq2	PROPN
ap-1402	195	19	h̄	h̄	NOUN
ap-1402	195	20	)	)	PUNCT
ap-1402	195	21	vν	vν	ADV
ap-1402	195	22	=	=	NUM
ap-1402	195	23	iνvν	iνvν	PROPN
ap-1402	195	24	,	,	PUNCT
ap-1402	195	25	are	be	AUX
ap-1402	195	26	weber	weber	NOUN
ap-1402	195	27	-	-	PUNCT
ap-1402	195	28	hermite	hermite	ADJ
ap-1402	195	29	(	(	PUNCT
ap-1402	195	30	or	or	CCONJ
ap-1402	195	31	parabolic	parabolic	ADJ
ap-1402	195	32	cylinder	cylinder	NOUN
ap-1402	195	33	)	)	PUNCT
ap-1402	195	34	functions	function	NOUN
ap-1402	195	35	vν	vν	NOUN
ap-1402	195	36	=	=	PUNCT
ap-1402	195	37	dν−	dν−	NUM
ap-1402	195	38	1	1	NUM
ap-1402	195	39	2	2	NUM
ap-1402	195	40	(	(	PUNCT
ap-1402	195	41	±2ei	±2ei	X
ap-1402	195	42	π	π	PROPN
ap-1402	195	43	4	4	NUM
ap-1402	195	44	√	√	PROPN
ap-1402	195	45	π	π	PROPN
ap-1402	195	46	h̄	h̄	PUNCT
ap-1402	195	47	q	q	PROPN
ap-1402	195	48	)	)	PUNCT
ap-1402	195	49	,	,	PUNCT
ap-1402	195	50	see	see	VERB
ap-1402	195	51	[	[	X
ap-1402	195	52	7	7	NUM
ap-1402	195	53	,	,	PUNCT
ap-1402	195	54	§	§	NOUN
ap-1402	195	55	8.2	8.2	NUM
ap-1402	195	56	]	]	PUNCT
ap-1402	195	57	,	,	PUNCT
ap-1402	195	58	[	[	X
ap-1402	195	59	33	33	NUM
ap-1402	195	60	]	]	PUNCT
ap-1402	195	61	for	for	ADP
ap-1402	195	62	fundamentals	fundamental	NOUN
ap-1402	195	63	of	of	ADP
ap-1402	195	64	weber	weber	PROPN
ap-1402	195	65	-	-	PUNCT
ap-1402	195	66	hermite	hermite	ADJ
ap-1402	195	67	functions	function	NOUN
ap-1402	195	68	and	and	CCONJ
ap-1402	195	69	[	[	X
ap-1402	195	70	35	35	NUM
ap-1402	195	71	]	]	PUNCT
ap-1402	195	72	for	for	ADP
ap-1402	195	73	further	further	ADJ
ap-1402	195	74	illustrations	illustration	NOUN
ap-1402	195	75	and	and	CCONJ
ap-1402	195	76	applications	application	NOUN
ap-1402	195	77	in	in	ADP
ap-1402	195	78	optics	optic	NOUN
ap-1402	195	79	.	.	PUNCT
ap-1402	196	1	the	the	DET
ap-1402	196	2	corresponding	correspond	VERB
ap-1402	196	3	one	one	NUM
ap-1402	196	4	-	-	PUNCT
ap-1402	196	5	parameter	parameter	NOUN
ap-1402	196	6	group	group	NOUN
ap-1402	196	7	is	be	AUX
ap-1402	196	8	not	not	PART
ap-1402	196	9	compact	compact	ADJ
ap-1402	196	10	and	and	CCONJ
ap-1402	196	11	the	the	DET
ap-1402	196	12	eigenvalues	eigenvalue	NOUN
ap-1402	196	13	of	of	ADP
ap-1402	196	14	the	the	DET
ap-1402	196	15	operator	operator	NOUN
ap-1402	196	16	2b̃	2b̃	NUM
ap-1402	196	17	are	be	AUX
ap-1402	196	18	not	not	PART
ap-1402	196	19	restricted	restrict	VERB
ap-1402	196	20	by	by	ADP
ap-1402	196	21	any	any	DET
ap-1402	196	22	integrality	integrality	NOUN
ap-1402	196	23	condition	condition	NOUN
ap-1402	196	24	,	,	PUNCT
ap-1402	196	25	but	but	CCONJ
ap-1402	196	26	the	the	DET
ap-1402	196	27	raising	raising	NOUN
ap-1402	196	28	/	/	SYM
ap-1402	196	29	lowering	lower	VERB
ap-1402	196	30	operators	operator	NOUN
ap-1402	196	31	are	be	AUX
ap-1402	196	32	still	still	ADV
ap-1402	196	33	important	important	ADJ
ap-1402	196	34	[	[	X
ap-1402	196	35	13	13	NUM
ap-1402	196	36	,	,	PUNCT
ap-1402	196	37	§	§	PROPN
ap-1402	196	38	ii.1	ii.1	PROPN
ap-1402	196	39	]	]	PUNCT
ap-1402	196	40	,	,	PUNCT
ap-1402	196	41	[	[	X
ap-1402	196	42	30	30	NUM
ap-1402	196	43	,	,	PUNCT
ap-1402	196	44	§	§	PROPN
ap-1402	196	45	1.1	1.1	NUM
ap-1402	196	46	]	]	PUNCT
ap-1402	196	47	.	.	PUNCT
ap-1402	197	1	we	we	PRON
ap-1402	197	2	again	again	ADV
ap-1402	197	3	seek	seek	VERB
ap-1402	197	4	solutions	solution	NOUN
ap-1402	197	5	in	in	ADP
ap-1402	197	6	two	two	NUM
ap-1402	197	7	subalgebras	subalgebras	PROPN
ap-1402	197	8	h1	h1	PROPN
ap-1402	197	9	and	and	CCONJ
ap-1402	197	10	sp2	sp2	VERB
ap-1402	197	11	separately	separately	ADV
ap-1402	197	12	.	.	PUNCT
ap-1402	198	1	however	however	ADV
ap-1402	198	2	,	,	PUNCT
ap-1402	198	3	the	the	DET
ap-1402	198	4	additional	additional	ADJ
ap-1402	198	5	options	option	NOUN
ap-1402	198	6	will	will	AUX
ap-1402	198	7	be	be	AUX
ap-1402	198	8	provided	provide	VERB
ap-1402	198	9	by	by	ADP
ap-1402	198	10	a	a	DET
ap-1402	198	11	choice	choice	NOUN
ap-1402	198	12	of	of	ADP
ap-1402	198	13	the	the	DET
ap-1402	198	14	number	number	NOUN
ap-1402	198	15	system	system	NOUN
ap-1402	198	16	:	:	PUNCT
ap-1402	198	17	either	either	CCONJ
ap-1402	198	18	complex	complex	ADJ
ap-1402	198	19	or	or	CCONJ
ap-1402	198	20	double	double	ADJ
ap-1402	198	21	.	.	PUNCT
ap-1402	198	22	4.1	4.1	NUM
ap-1402	198	23	complex	complex	ADJ
ap-1402	198	24	ladder	ladder	NOUN
ap-1402	198	25	operators	operator	NOUN
ap-1402	198	26	assuming	assume	VERB
ap-1402	198	27	l+h	l+h	NOUN
ap-1402	198	28	=	=	PUNCT
ap-1402	198	29	ax̃	ax̃	NOUN
ap-1402	199	1	+	+	CCONJ
ap-1402	199	2	bỹ	bỹ	NOUN
ap-1402	199	3	from	from	ADP
ap-1402	199	4	the	the	DET
ap-1402	199	5	commutators	commutator	NOUN
ap-1402	199	6	(	(	PUNCT
ap-1402	199	7	11–12	11–12	NUM
ap-1402	199	8	)	)	PUNCT
ap-1402	199	9	,	,	PUNCT
ap-1402	199	10	we	we	PRON
ap-1402	199	11	obtain	obtain	VERB
ap-1402	199	12	the	the	DET
ap-1402	199	13	linear	linear	ADJ
ap-1402	199	14	equations	equation	NOUN
ap-1402	199	15	:	:	PUNCT
ap-1402	199	16	−	−	PROPN
ap-1402	199	17	a	a	DET
ap-1402	199	18	=	=	SYM
ap-1402	199	19	λ+b	λ+b	NOUN
ap-1402	199	20	,	,	PUNCT
ap-1402	199	21	−b	−b	NOUN
ap-1402	199	22	=	=	PUNCT
ap-1402	200	1	λ+a	λ+a	X
ap-1402	200	2	.	.	PUNCT
ap-1402	201	1	(	(	PUNCT
ap-1402	201	2	29	29	NUM
ap-1402	201	3	)	)	PUNCT
ap-1402	201	4	the	the	DET
ap-1402	201	5	equations	equation	NOUN
ap-1402	201	6	have	have	VERB
ap-1402	201	7	a	a	DET
ap-1402	201	8	solution	solution	NOUN
ap-1402	201	9	if	if	SCONJ
ap-1402	201	10	and	and	CCONJ
ap-1402	201	11	only	only	ADV
ap-1402	201	12	if	if	SCONJ
ap-1402	201	13	λ2+−1	λ2+−1	PROPN
ap-1402	201	14	=	=	SYM
ap-1402	201	15	0	0	X
ap-1402	201	16	.	.	PUNCT
ap-1402	202	1	taking	take	VERB
ap-1402	202	2	the	the	DET
ap-1402	202	3	real	real	ADJ
ap-1402	202	4	roots	root	NOUN
ap-1402	202	5	λ	λ	X
ap-1402	202	6	=	=	SYM
ap-1402	202	7	±1	±1	VERB
ap-1402	202	8	we	we	PRON
ap-1402	202	9	obtain	obtain	VERB
ap-1402	202	10	that	that	SCONJ
ap-1402	202	11	the	the	DET
ap-1402	202	12	raising	raising	NOUN
ap-1402	202	13	/	/	SYM
ap-1402	202	14	lowering	lower	VERB
ap-1402	202	15	operators	operator	NOUN
ap-1402	202	16	are	be	AUX
ap-1402	202	17	l±	l±	NOUN
ap-1402	202	18	h	h	PROPN
ap-1402	203	1	=	=	PUNCT
ap-1402	203	2	x̃	x̃	PROPN
ap-1402	203	3	∓	∓	PROPN
ap-1402	203	4	ỹ	ỹ	PROPN
ap-1402	203	5	.	.	PUNCT
ap-1402	204	1	in	in	ADP
ap-1402	204	2	the	the	DET
ap-1402	204	3	schrödinger	schrödinger	NOUN
ap-1402	204	4	representation	representation	NOUN
ap-1402	204	5	(	(	PUNCT
ap-1402	204	6	14	14	NUM
ap-1402	204	7	)	)	PUNCT
ap-1402	204	8	the	the	DET
ap-1402	204	9	ladder	ladder	NOUN
ap-1402	204	10	operators	operator	NOUN
ap-1402	204	11	are	be	AUX
ap-1402	204	12	l±	l±	NOUN
ap-1402	204	13	h	h	NOUN
ap-1402	204	14	=	=	SYM
ap-1402	204	15	2πiq	2πiq	NUM
ap-1402	204	16	±	±	NUM
ap-1402	204	17	h̄	h̄	NOUN
ap-1402	204	18	d	d	X
ap-1402	204	19	dq	dq	PROPN
ap-1402	204	20	.	.	PUNCT
ap-1402	205	1	(	(	PUNCT
ap-1402	205	2	30	30	NUM
ap-1402	205	3	)	)	PUNCT
ap-1402	205	4	the	the	DET
ap-1402	205	5	null	null	ADJ
ap-1402	205	6	solutions	solution	NOUN
ap-1402	205	7	v±	v±	PROPN
ap-1402	205	8	1	1	NUM
ap-1402	205	9	2	2	NUM
ap-1402	205	10	(	(	PUNCT
ap-1402	205	11	q	q	NOUN
ap-1402	205	12	)	)	PUNCT
ap-1402	205	13	=	=	SYM
ap-1402	205	14	e±	e±	PROPN
ap-1402	205	15	πi	πi	CCONJ
ap-1402	205	16	h̄	h̄	PROPN
ap-1402	205	17	q2	q2	PROPN
ap-1402	205	18	to	to	ADP
ap-1402	205	19	operators	operator	NOUN
ap-1402	205	20	ρh̄(l±	ρh̄(l±	PROPN
ap-1402	205	21	)	)	PUNCT
ap-1402	205	22	are	be	AUX
ap-1402	205	23	also	also	ADV
ap-1402	205	24	eigenvectors	eigenvector	NOUN
ap-1402	205	25	of	of	ADP
ap-1402	205	26	the	the	DET
ap-1402	205	27	hamiltonian	hamiltonian	NOUN
ap-1402	205	28	48	48	NUM
ap-1402	205	29	acta	acta	PROPN
ap-1402	205	30	polytechnica	polytechnica	PROPN
ap-1402	205	31	vol	vol	NOUN
ap-1402	205	32	.	.	PUNCT
ap-1402	206	1	51	51	NUM
ap-1402	206	2	no	no	INTJ
ap-1402	206	3	.	.	PUNCT
ap-1402	207	1	4/2011	4/2011	NUM
ap-1402	207	2	ρswh̄	ρswh̄	PROPN
ap-1402	207	3	(	(	PUNCT
ap-1402	207	4	2b	2b	NUM
ap-1402	207	5	)	)	PUNCT
ap-1402	207	6	with	with	ADP
ap-1402	207	7	the	the	DET
ap-1402	207	8	eigenvalue	eigenvalue	NOUN
ap-1402	207	9	±1	±1	ADJ
ap-1402	207	10	2	2	NUM
ap-1402	207	11	.	.	PUNCT
ap-1402	208	1	however	however	ADV
ap-1402	208	2	the	the	DET
ap-1402	208	3	important	important	ADJ
ap-1402	208	4	distinction	distinction	NOUN
ap-1402	208	5	from	from	ADP
ap-1402	208	6	the	the	DET
ap-1402	208	7	elliptic	elliptic	ADJ
ap-1402	208	8	case	case	NOUN
ap-1402	208	9	is	be	AUX
ap-1402	208	10	that	that	SCONJ
ap-1402	208	11	they	they	PRON
ap-1402	208	12	are	be	AUX
ap-1402	208	13	not	not	PART
ap-1402	208	14	square	square	ADJ
ap-1402	208	15	-	-	PUNCT
ap-1402	208	16	integrable	integrable	ADJ
ap-1402	208	17	on	on	ADP
ap-1402	208	18	the	the	DET
ap-1402	208	19	real	real	ADJ
ap-1402	208	20	line	line	NOUN
ap-1402	208	21	anymore	anymore	ADV
ap-1402	208	22	.	.	PUNCT
ap-1402	209	1	we	we	PRON
ap-1402	209	2	can	can	AUX
ap-1402	209	3	also	also	ADV
ap-1402	209	4	look	look	VERB
ap-1402	209	5	for	for	ADP
ap-1402	209	6	ladder	ladder	NOUN
ap-1402	209	7	operators	operator	NOUN
ap-1402	209	8	within	within	ADP
ap-1402	209	9	the	the	DET
ap-1402	209	10	sp2	sp2	NOUN
ap-1402	209	11	,	,	PUNCT
ap-1402	209	12	that	that	PRON
ap-1402	209	13	is	be	AUX
ap-1402	209	14	in	in	ADP
ap-1402	209	15	the	the	DET
ap-1402	209	16	form	form	NOUN
ap-1402	210	1	l+2h	l+2h	PROPN
ap-1402	210	2	=	=	SYM
ap-1402	210	3	aã	aã	PROPN
ap-1402	210	4	+	+	CCONJ
ap-1402	210	5	bb̃	bb̃	PRON
ap-1402	210	6	+	+	NUM
ap-1402	210	7	cz̃	cz̃	NOUN
ap-1402	210	8	for	for	ADP
ap-1402	210	9	the	the	DET
ap-1402	210	10	commutator	commutator	NOUN
ap-1402	210	11	[	[	X
ap-1402	210	12	2b̃	2b̃	NUM
ap-1402	210	13	,	,	PUNCT
ap-1402	210	14	l+h	l+h	X
ap-1402	210	15	]	]	PUNCT
ap-1402	210	16	=	=	PUNCT
ap-1402	210	17	λl+h	λl+h	X
ap-1402	210	18	.	.	PUNCT
ap-1402	211	1	we	we	PRON
ap-1402	211	2	will	will	AUX
ap-1402	211	3	get	get	VERB
ap-1402	211	4	the	the	DET
ap-1402	211	5	system	system	NOUN
ap-1402	211	6	:	:	PUNCT
ap-1402	211	7	4c	4c	NUM
ap-1402	211	8	=	=	SYM
ap-1402	211	9	λa	λa	PROPN
ap-1402	211	10	,	,	PUNCT
ap-1402	211	11	b	b	PROPN
ap-1402	211	12	=	=	SYM
ap-1402	211	13	0	0	PROPN
ap-1402	211	14	,	,	PUNCT
ap-1402	211	15	a	a	DET
ap-1402	211	16	=	=	X
ap-1402	211	17	λc	λc	NOUN
ap-1402	211	18	.	.	PUNCT
ap-1402	212	1	a	a	DET
ap-1402	212	2	solution	solution	NOUN
ap-1402	212	3	again	again	ADV
ap-1402	212	4	exists	exist	VERB
ap-1402	212	5	if	if	SCONJ
ap-1402	212	6	and	and	CCONJ
ap-1402	212	7	only	only	ADV
ap-1402	212	8	if	if	SCONJ
ap-1402	212	9	λ2	λ2	NOUN
ap-1402	212	10	=	=	SYM
ap-1402	212	11	4	4	NUM
ap-1402	212	12	.	.	PUNCT
ap-1402	213	1	within	within	ADP
ap-1402	213	2	complex	complex	ADJ
ap-1402	213	3	numbers	number	NOUN
ap-1402	213	4	we	we	PRON
ap-1402	213	5	get	get	VERB
ap-1402	213	6	only	only	ADV
ap-1402	213	7	the	the	DET
ap-1402	213	8	values	value	NOUN
ap-1402	213	9	λ	λ	NOUN
ap-1402	213	10	=	=	SYM
ap-1402	213	11	±2	±2	NOUN
ap-1402	213	12	with	with	ADP
ap-1402	213	13	the	the	DET
ap-1402	213	14	ladder	ladder	NOUN
ap-1402	213	15	operators	operator	NOUN
ap-1402	213	16	l±	l±	VERB
ap-1402	213	17	2h	2h	NUM
ap-1402	213	18	=	=	SYM
ap-1402	213	19	±2ã+	±2ã+	ADJ
ap-1402	213	20	z̃/2	z̃/2	PROPN
ap-1402	213	21	,	,	PUNCT
ap-1402	213	22	see	see	VERB
ap-1402	213	23	[	[	X
ap-1402	213	24	13	13	NUM
ap-1402	213	25	,	,	PUNCT
ap-1402	213	26	§	§	PROPN
ap-1402	213	27	ii.1	ii.1	PROPN
ap-1402	213	28	]	]	PUNCT
ap-1402	213	29	,	,	PUNCT
ap-1402	214	1	[	[	X
ap-1402	214	2	30	30	NUM
ap-1402	214	3	,	,	PUNCT
ap-1402	214	4	§	§	PROPN
ap-1402	214	5	1.1	1.1	NUM
ap-1402	214	6	]	]	PUNCT
ap-1402	214	7	.	.	PUNCT
ap-1402	215	1	each	each	PRON
ap-1402	215	2	indecomposable	indecomposable	ADJ
ap-1402	215	3	h1or	h1or	PUNCT
ap-1402	215	4	sp2	sp2	NOUN
ap-1402	215	5	-	-	PUNCT
ap-1402	215	6	module	module	NOUN
ap-1402	215	7	is	be	AUX
ap-1402	215	8	formed	form	VERB
ap-1402	215	9	by	by	ADP
ap-1402	215	10	a	a	DET
ap-1402	215	11	one	one	NUM
ap-1402	215	12	-	-	PUNCT
ap-1402	215	13	dimensional	dimensional	ADJ
ap-1402	215	14	chain	chain	NOUN
ap-1402	215	15	of	of	ADP
ap-1402	215	16	eigenvalues	eigenvalue	NOUN
ap-1402	215	17	with	with	ADP
ap-1402	215	18	a	a	DET
ap-1402	215	19	transitive	transitive	ADJ
ap-1402	215	20	action	action	NOUN
ap-1402	215	21	of	of	ADP
ap-1402	215	22	ladder	ladder	NOUN
ap-1402	215	23	operators	operator	NOUN
ap-1402	215	24	l±	l±	VERB
ap-1402	215	25	h	h	PROPN
ap-1402	215	26	or	or	CCONJ
ap-1402	215	27	l±	l±	VERB
ap-1402	215	28	2h	2h	NUM
ap-1402	215	29	respectively	respectively	ADV
ap-1402	215	30	.	.	PUNCT
ap-1402	216	1	and	and	CCONJ
ap-1402	216	2	we	we	PRON
ap-1402	216	3	again	again	ADV
ap-1402	216	4	have	have	VERB
ap-1402	216	5	a	a	DET
ap-1402	216	6	quadratic	quadratic	ADJ
ap-1402	216	7	relation	relation	NOUN
ap-1402	216	8	between	between	ADP
ap-1402	216	9	the	the	DET
ap-1402	216	10	ladder	ladder	NOUN
ap-1402	216	11	operators	operator	NOUN
ap-1402	216	12	:	:	PUNCT
ap-1402	216	13	l±	l±	X
ap-1402	216	14	2h	2h	NUM
ap-1402	217	1	=	=	PUNCT
ap-1402	217	2	i	i	PRON
ap-1402	217	3	4πh̄	4πh̄	VERB
ap-1402	217	4	(	(	PUNCT
ap-1402	217	5	l±	l±	PROPN
ap-1402	217	6	h	h	NOUN
ap-1402	217	7	)	)	PUNCT
ap-1402	217	8	2	2	X
ap-1402	217	9	.	.	NOUN
ap-1402	217	10	4.2	4.2	NUM
ap-1402	217	11	double	double	ADJ
ap-1402	217	12	ladder	ladder	NOUN
ap-1402	217	13	operators	operator	NOUN
ap-1402	217	14	there	there	PRON
ap-1402	217	15	are	be	VERB
ap-1402	217	16	extra	extra	ADJ
ap-1402	217	17	possibilities	possibility	NOUN
ap-1402	217	18	in	in	ADP
ap-1402	217	19	the	the	DET
ap-1402	217	20	context	context	NOUN
ap-1402	217	21	of	of	ADP
ap-1402	217	22	hyperbolic	hyperbolic	ADJ
ap-1402	217	23	quantum	quantum	ADJ
ap-1402	217	24	mechanics	mechanic	NOUN
ap-1402	217	25	[	[	X
ap-1402	217	26	17,16,18	17,16,18	NUM
ap-1402	217	27	]	]	PUNCT
ap-1402	217	28	.	.	PUNCT
ap-1402	218	1	here	here	ADV
ap-1402	218	2	we	we	PRON
ap-1402	218	3	use	use	VERB
ap-1402	218	4	the	the	DET
ap-1402	218	5	representation	representation	NOUN
ap-1402	218	6	of	of	ADP
ap-1402	218	7	h	h	NOUN
ap-1402	218	8	1	1	NUM
ap-1402	218	9	induced	induce	VERB
ap-1402	218	10	by	by	ADP
ap-1402	218	11	a	a	DET
ap-1402	218	12	hyperbolic	hyperbolic	ADJ
ap-1402	218	13	character	character	NOUN
ap-1402	218	14	ejht	ejht	NOUN
ap-1402	218	15	=	=	SYM
ap-1402	218	16	cosh(ht	cosh(ht	PROPN
ap-1402	218	17	)	)	PUNCT
ap-1402	218	18	+	+	NUM
ap-1402	218	19	j	j	PROPN
ap-1402	218	20	sinh(ht	sinh(ht	NOUN
ap-1402	218	21	)	)	PUNCT
ap-1402	218	22	,	,	PUNCT
ap-1402	218	23	see	see	VERB
ap-1402	218	24	[	[	X
ap-1402	218	25	25	25	NUM
ap-1402	218	26	,	,	PUNCT
ap-1402	218	27	(	(	PUNCT
ap-1402	218	28	4.5	4.5	NUM
ap-1402	218	29	)	)	PUNCT
ap-1402	218	30	]	]	PUNCT
ap-1402	218	31	,	,	PUNCT
ap-1402	218	32	and	and	CCONJ
ap-1402	218	33	obtain	obtain	VERB
ap-1402	218	34	the	the	DET
ap-1402	218	35	hyperbolic	hyperbolic	ADJ
ap-1402	218	36	representation	representation	NOUN
ap-1402	218	37	of	of	ADP
ap-1402	218	38	h1	h1	PROPN
ap-1402	218	39	,	,	PUNCT
ap-1402	218	40	cf	cf	INTJ
ap-1402	218	41	.	.	PUNCT
ap-1402	219	1	(	(	PUNCT
ap-1402	219	2	13	13	NUM
ap-1402	219	3	):	):	PUNCT
ap-1402	219	4	[	[	X
ap-1402	219	5	ρjh(s′	ρjh(s′	ADJ
ap-1402	219	6	,	,	PUNCT
ap-1402	219	7	x′	x′	NUM
ap-1402	219	8	,	,	PUNCT
ap-1402	219	9	y′)f̂	y′)f̂	NOUN
ap-1402	219	10	]	]	X
ap-1402	219	11	(	(	PUNCT
ap-1402	219	12	q	q	X
ap-1402	219	13	)	)	PUNCT
ap-1402	219	14	=	=	SYM
ap-1402	219	15	ejh(s	ejh(s	PROPN
ap-1402	219	16	′−x′y′/2)+jx′q	′−x′y′/2)+jx′q	NOUN
ap-1402	219	17	·	·	PUNCT
ap-1402	219	18	f̂(q	f̂(q	NOUN
ap-1402	219	19	−	−	NOUN
ap-1402	219	20	hy′	hy′	PROPN
ap-1402	219	21	)	)	PUNCT
ap-1402	219	22	.	.	PUNCT
ap-1402	220	1	(	(	PUNCT
ap-1402	220	2	31	31	NUM
ap-1402	220	3	)	)	PUNCT
ap-1402	220	4	the	the	DET
ap-1402	220	5	corresponding	corresponding	ADJ
ap-1402	220	6	derived	derive	VERB
ap-1402	220	7	representation	representation	NOUN
ap-1402	220	8	is	be	AUX
ap-1402	220	9	ρjh(x	ρjh(x	PROPN
ap-1402	220	10	)	)	PUNCT
ap-1402	220	11	=	=	SYM
ap-1402	220	12	jq	jq	PROPN
ap-1402	220	13	,	,	PUNCT
ap-1402	220	14	ρjh(y	ρjh(y	PROPN
ap-1402	220	15	)	)	PUNCT
ap-1402	221	1	=	=	PUNCT
ap-1402	221	2	−h	−h	ADV
ap-1402	221	3	d	d	X
ap-1402	221	4	dq	dq	INTJ
ap-1402	221	5	,	,	PUNCT
ap-1402	221	6	(	(	PUNCT
ap-1402	221	7	32	32	NUM
ap-1402	221	8	)	)	PUNCT
ap-1402	221	9	ρjh(s	ρjh(s	NUM
ap-1402	221	10	)	)	PUNCT
ap-1402	222	1	=	=	SYM
ap-1402	222	2	jhi	jhi	PROPN
ap-1402	222	3	.	.	PUNCT
ap-1402	223	1	then	then	ADV
ap-1402	223	2	the	the	DET
ap-1402	223	3	associated	associated	ADJ
ap-1402	223	4	shale	shale	PROPN
ap-1402	223	5	–	–	PUNCT
ap-1402	223	6	weil	weil	NOUN
ap-1402	223	7	derived	derive	VERB
ap-1402	223	8	representation	representation	NOUN
ap-1402	223	9	of	of	ADP
ap-1402	223	10	sp2	sp2	NOUN
ap-1402	223	11	in	in	ADP
ap-1402	223	12	the	the	DET
ap-1402	223	13	schwartz	schwartz	PROPN
ap-1402	223	14	space	space	PROPN
ap-1402	223	15	s(r	s(r	PROPN
ap-1402	223	16	)	)	PUNCT
ap-1402	223	17	is	be	AUX
ap-1402	223	18	,	,	PUNCT
ap-1402	223	19	cf	cf	INTJ
ap-1402	223	20	.	.	PUNCT
ap-1402	224	1	(	(	PUNCT
ap-1402	224	2	15	15	NUM
ap-1402	224	3	):	):	PUNCT
ap-1402	224	4	ρswh	ρswh	NOUN
ap-1402	224	5	(	(	PUNCT
ap-1402	224	6	a	a	NOUN
ap-1402	224	7	)	)	PUNCT
ap-1402	224	8	=	=	SYM
ap-1402	225	1	−	−	PROPN
ap-1402	225	2	q	q	NOUN
ap-1402	225	3	2	2	NUM
ap-1402	225	4	d	d	NOUN
ap-1402	225	5	dq	dq	NOUN
ap-1402	225	6	−	−	NUM
ap-1402	225	7	1	1	NUM
ap-1402	225	8	4	4	NUM
ap-1402	225	9	,	,	PUNCT
ap-1402	225	10	ρswh	ρswh	NOUN
ap-1402	225	11	(	(	PUNCT
ap-1402	225	12	b	b	NOUN
ap-1402	225	13	)	)	PUNCT
ap-1402	225	14	=	=	SYM
ap-1402	225	15	jh	jh	PROPN
ap-1402	225	16	4	4	NUM
ap-1402	225	17	d2	d2	PROPN
ap-1402	225	18	dq2	dq2	PROPN
ap-1402	225	19	−	−	PROPN
ap-1402	225	20	jq2	jq2	PROPN
ap-1402	225	21	4h	4h	NOUN
ap-1402	225	22	,	,	PUNCT
ap-1402	225	23	(	(	PUNCT
ap-1402	225	24	33	33	NUM
ap-1402	225	25	)	)	PUNCT
ap-1402	225	26	ρswh	ρswh	NOUN
ap-1402	225	27	(	(	PUNCT
ap-1402	225	28	z	z	NOUN
ap-1402	225	29	)	)	PUNCT
ap-1402	225	30	=	=	SYM
ap-1402	225	31	−	−	PROPN
ap-1402	225	32	jh	jh	PROPN
ap-1402	225	33	2	2	NUM
ap-1402	225	34	d2	d2	PROPN
ap-1402	225	35	dq2	dq2	PROPN
ap-1402	225	36	−	−	PROPN
ap-1402	225	37	jq2	jq2	PROPN
ap-1402	225	38	2h	2h	NUM
ap-1402	225	39	.	.	PUNCT
ap-1402	226	1	note	note	VERB
ap-1402	226	2	that	that	SCONJ
ap-1402	226	3	ρswh	ρswh	NOUN
ap-1402	226	4	(	(	PUNCT
ap-1402	226	5	b	b	NOUN
ap-1402	226	6	)	)	PUNCT
ap-1402	226	7	now	now	ADV
ap-1402	226	8	generates	generate	VERB
ap-1402	226	9	a	a	DET
ap-1402	226	10	usual	usual	ADJ
ap-1402	226	11	harmonic	harmonic	ADJ
ap-1402	226	12	oscillator	oscillator	NOUN
ap-1402	226	13	,	,	PUNCT
ap-1402	226	14	not	not	PART
ap-1402	226	15	the	the	DET
ap-1402	226	16	repulsive	repulsive	ADJ
ap-1402	226	17	one	one	NOUN
ap-1402	226	18	like	like	ADP
ap-1402	226	19	ρswh̄	ρswh̄	PROPN
ap-1402	226	20	(	(	PUNCT
ap-1402	226	21	b	b	NOUN
ap-1402	226	22	)	)	PUNCT
ap-1402	226	23	in	in	ADP
ap-1402	226	24	(	(	PUNCT
ap-1402	226	25	15	15	NUM
ap-1402	226	26	)	)	PUNCT
ap-1402	226	27	.	.	PUNCT
ap-1402	227	1	however	however	ADV
ap-1402	227	2	,	,	PUNCT
ap-1402	227	3	the	the	DET
ap-1402	227	4	expressions	expression	NOUN
ap-1402	227	5	in	in	ADP
ap-1402	227	6	the	the	DET
ap-1402	227	7	quadratic	quadratic	ADJ
ap-1402	227	8	algebra	algebra	NOUN
ap-1402	227	9	are	be	AUX
ap-1402	227	10	still	still	ADV
ap-1402	227	11	the	the	DET
ap-1402	227	12	same	same	ADJ
ap-1402	227	13	(	(	PUNCT
ap-1402	227	14	up	up	ADP
ap-1402	227	15	to	to	ADP
ap-1402	227	16	a	a	DET
ap-1402	227	17	factor	factor	NOUN
ap-1402	227	18	)	)	PUNCT
ap-1402	227	19	,	,	PUNCT
ap-1402	227	20	cf	cf	NOUN
ap-1402	227	21	.	.	PUNCT
ap-1402	228	1	(	(	PUNCT
ap-1402	228	2	16–18	16–18	NUM
ap-1402	228	3	):	):	PUNCT
ap-1402	228	4	ρswh	ρswh	NOUN
ap-1402	228	5	(	(	PUNCT
ap-1402	228	6	a	a	X
ap-1402	228	7	)	)	PUNCT
ap-1402	228	8	=	=	SYM
ap-1402	229	1	−	−	PROPN
ap-1402	229	2	j	j	NOUN
ap-1402	229	3	2h	2h	NUM
ap-1402	229	4	(	(	PUNCT
ap-1402	229	5	ρjh(x)ρjh(y	ρjh(x)ρjh(y	PROPN
ap-1402	229	6	)	)	PUNCT
ap-1402	229	7	−	−	PROPN
ap-1402	230	1	1	1	NUM
ap-1402	230	2	2ρ	2ρ	NOUN
ap-1402	230	3	j	j	PROPN
ap-1402	230	4	h(s	h(s	PROPN
ap-1402	230	5	)	)	PUNCT
ap-1402	230	6	)	)	PUNCT
ap-1402	231	1	=	=	PUNCT
ap-1402	231	2	(	(	PUNCT
ap-1402	231	3	34	34	NUM
ap-1402	231	4	)	)	PUNCT
ap-1402	231	5	−	−	PROPN
ap-1402	232	1	j	j	PROPN
ap-1402	232	2	4h	4h	NOUN
ap-1402	232	3	(	(	PUNCT
ap-1402	232	4	ρjh(x)ρjh(y	ρjh(x)ρjh(y	PROPN
ap-1402	232	5	)	)	PUNCT
ap-1402	233	1	+	+	CCONJ
ap-1402	233	2	ρjh(y	ρjh(y	X
ap-1402	233	3	)	)	PUNCT
ap-1402	233	4	ρjh(x	ρjh(x	PROPN
ap-1402	233	5	)	)	PUNCT
ap-1402	233	6	)	)	PUNCT
ap-1402	233	7	,	,	PUNCT
ap-1402	233	8	ρswh	ρswh	NOUN
ap-1402	233	9	(	(	PUNCT
ap-1402	233	10	b	b	NOUN
ap-1402	233	11	)	)	PUNCT
ap-1402	233	12	=	=	SYM
ap-1402	233	13	j	j	X
ap-1402	233	14	4h	4h	NOUN
ap-1402	233	15	(	(	PUNCT
ap-1402	233	16	ρjh(x)2	ρjh(x)2	VERB
ap-1402	233	17	−	−	NUM
ap-1402	233	18	ρjh(y	ρjh(y	NUM
ap-1402	233	19	)	)	PUNCT
ap-1402	233	20	2	2	NUM
ap-1402	233	21	)	)	PUNCT
ap-1402	233	22	,	,	PUNCT
ap-1402	233	23	(	(	PUNCT
ap-1402	233	24	35	35	NUM
ap-1402	233	25	)	)	PUNCT
ap-1402	233	26	ρswh	ρswh	NOUN
ap-1402	233	27	(	(	PUNCT
ap-1402	233	28	z	z	NOUN
ap-1402	233	29	)	)	PUNCT
ap-1402	233	30	=	=	SYM
ap-1402	234	1	−	−	PROPN
ap-1402	234	2	j	j	NOUN
ap-1402	234	3	2h	2h	NUM
ap-1402	234	4	(	(	PUNCT
ap-1402	234	5	ρjh(x)2	ρjh(x)2	NOUN
ap-1402	234	6	+	+	CCONJ
ap-1402	234	7	ρjh(y	ρjh(y	NUM
ap-1402	234	8	)	)	PUNCT
ap-1402	234	9	2	2	NUM
ap-1402	234	10	)	)	PUNCT
ap-1402	234	11	.	.	PUNCT
ap-1402	235	1	(	(	PUNCT
ap-1402	235	2	36	36	NUM
ap-1402	235	3	)	)	PUNCT
ap-1402	235	4	this	this	PRON
ap-1402	235	5	is	be	AUX
ap-1402	235	6	due	due	ADJ
ap-1402	235	7	to	to	ADP
ap-1402	235	8	the	the	DET
ap-1402	235	9	principle	principle	NOUN
ap-1402	235	10	of	of	ADP
ap-1402	235	11	similarity	similarity	NOUN
ap-1402	235	12	and	and	CCONJ
ap-1402	235	13	correspondence	correspondence	NOUN
ap-1402	235	14	:	:	PUNCT
ap-1402	235	15	we	we	PRON
ap-1402	235	16	can	can	AUX
ap-1402	235	17	swap	swap	VERB
ap-1402	235	18	operators	operator	NOUN
ap-1402	235	19	z	z	PROPN
ap-1402	235	20	and	and	CCONJ
ap-1402	235	21	b	b	NOUN
ap-1402	235	22	with	with	ADP
ap-1402	235	23	simultaneous	simultaneous	ADJ
ap-1402	235	24	replacement	replacement	NOUN
ap-1402	235	25	of	of	ADP
ap-1402	235	26	hypercomplex	hypercomplex	ADJ
ap-1402	235	27	units	unit	NOUN
ap-1402	235	28	i	i	PRON
ap-1402	235	29	and	and	CCONJ
ap-1402	235	30	j.	j.	PROPN
ap-1402	236	1	the	the	DET
ap-1402	236	2	eigenspace	eigenspace	NOUN
ap-1402	236	3	of	of	ADP
ap-1402	236	4	the	the	DET
ap-1402	236	5	operator	operator	NOUN
ap-1402	236	6	2ρswh	2ρswh	NUM
ap-1402	236	7	(	(	PUNCT
ap-1402	236	8	b	b	NOUN
ap-1402	236	9	)	)	PUNCT
ap-1402	236	10	with	with	ADP
ap-1402	236	11	an	an	DET
ap-1402	236	12	eigenvalue	eigenvalue	NOUN
ap-1402	236	13	jν	jν	NOUN
ap-1402	236	14	are	be	AUX
ap-1402	236	15	spanned	span	VERB
ap-1402	236	16	by	by	ADP
ap-1402	236	17	the	the	DET
ap-1402	236	18	weber	weber	PROPN
ap-1402	236	19	-	-	PUNCT
ap-1402	236	20	hermite	hermite	ADJ
ap-1402	236	21	functions	function	NOUN
ap-1402	236	22	d−ν−	d−ν−	ADP
ap-1402	236	23	1	1	NUM
ap-1402	236	24	2	2	NUM
ap-1402	236	25	(	(	PUNCT
ap-1402	236	26	±	±	NOUN
ap-1402	236	27	√	√	ADV
ap-1402	236	28	2	2	NUM
ap-1402	236	29	h	h	NOUN
ap-1402	236	30	x	x	NOUN
ap-1402	236	31	)	)	PUNCT
ap-1402	236	32	,	,	PUNCT
ap-1402	236	33	see	see	VERB
ap-1402	236	34	[	[	X
ap-1402	236	35	7	7	NUM
ap-1402	236	36	,	,	PUNCT
ap-1402	236	37	§	§	PROPN
ap-1402	236	38	8.2	8.2	NUM
ap-1402	236	39	]	]	PUNCT
ap-1402	236	40	.	.	PUNCT
ap-1402	237	1	functions	function	NOUN
ap-1402	237	2	dν	dν	VERB
ap-1402	237	3	are	be	AUX
ap-1402	237	4	generalisations	generalisation	NOUN
ap-1402	237	5	of	of	ADP
ap-1402	237	6	the	the	DET
ap-1402	237	7	hermit	hermit	NOUN
ap-1402	237	8	functions	function	NOUN
ap-1402	237	9	(	(	PUNCT
ap-1402	237	10	22	22	NUM
ap-1402	237	11	)	)	PUNCT
ap-1402	237	12	.	.	PUNCT
ap-1402	238	1	the	the	DET
ap-1402	238	2	compatibility	compatibility	NOUN
ap-1402	238	3	condition	condition	NOUN
ap-1402	238	4	for	for	ADP
ap-1402	238	5	a	a	DET
ap-1402	238	6	ladder	ladder	NOUN
ap-1402	238	7	operator	operator	NOUN
ap-1402	238	8	within	within	ADP
ap-1402	238	9	the	the	DET
ap-1402	238	10	lie	lie	NOUN
ap-1402	238	11	algebra	algebra	NOUN
ap-1402	238	12	h1	h1	NOUN
ap-1402	238	13	will	will	AUX
ap-1402	238	14	be	be	AUX
ap-1402	238	15	(	(	PUNCT
ap-1402	238	16	29	29	NUM
ap-1402	238	17	)	)	PUNCT
ap-1402	238	18	as	as	ADP
ap-1402	238	19	before	before	ADV
ap-1402	238	20	,	,	PUNCT
ap-1402	238	21	since	since	SCONJ
ap-1402	238	22	it	it	PRON
ap-1402	238	23	depends	depend	VERB
ap-1402	238	24	only	only	ADV
ap-1402	238	25	on	on	ADP
ap-1402	238	26	the	the	DET
ap-1402	238	27	commutators	commutator	NOUN
ap-1402	238	28	(	(	PUNCT
ap-1402	238	29	11–12	11–12	NUM
ap-1402	238	30	)	)	PUNCT
ap-1402	238	31	.	.	PUNCT
ap-1402	239	1	thus	thus	ADV
ap-1402	239	2	we	we	PRON
ap-1402	239	3	still	still	ADV
ap-1402	239	4	have	have	VERB
ap-1402	239	5	the	the	DET
ap-1402	239	6	set	set	NOUN
ap-1402	239	7	of	of	ADP
ap-1402	239	8	ladder	ladder	NOUN
ap-1402	239	9	operators	operator	NOUN
ap-1402	239	10	corresponding	correspond	VERB
ap-1402	239	11	to	to	ADP
ap-1402	239	12	values	value	NOUN
ap-1402	239	13	λ	λ	X
ap-1402	239	14	=	=	SYM
ap-1402	239	15	±1	±1	PROPN
ap-1402	239	16	:	:	PUNCT
ap-1402	239	17	l±	l±	VERB
ap-1402	239	18	h	h	NOUN
ap-1402	240	1	=	=	PUNCT
ap-1402	241	1	x̃	x̃	PROPN
ap-1402	241	2	∓	∓	PROPN
ap-1402	241	3	ỹ	ỹ	PROPN
ap-1402	241	4	=	=	SYM
ap-1402	241	5	jq	jq	PROPN
ap-1402	241	6	±	±	NUM
ap-1402	241	7	h	h	NOUN
ap-1402	241	8	d	d	NOUN
ap-1402	241	9	dq	dq	PROPN
ap-1402	241	10	.	.	PUNCT
ap-1402	242	1	admitting	admit	VERB
ap-1402	242	2	double	double	ADJ
ap-1402	242	3	numbers	number	NOUN
ap-1402	242	4	,	,	PUNCT
ap-1402	242	5	we	we	PRON
ap-1402	242	6	have	have	VERB
ap-1402	242	7	an	an	DET
ap-1402	242	8	extra	extra	ADJ
ap-1402	242	9	way	way	NOUN
ap-1402	242	10	to	to	PART
ap-1402	242	11	satisfy	satisfy	VERB
ap-1402	242	12	λ2	λ2	NOUN
ap-1402	242	13	=	=	SYM
ap-1402	242	14	1	1	NUM
ap-1402	242	15	in	in	ADP
ap-1402	242	16	(	(	PUNCT
ap-1402	242	17	29	29	NUM
ap-1402	242	18	)	)	PUNCT
ap-1402	242	19	with	with	ADP
ap-1402	242	20	values	value	NOUN
ap-1402	242	21	λ	λ	X
ap-1402	242	22	=	=	SYM
ap-1402	242	23	±j	±j	PROPN
ap-1402	242	24	.	.	PUNCT
ap-1402	243	1	then	then	ADV
ap-1402	243	2	there	there	PRON
ap-1402	243	3	is	be	VERB
ap-1402	243	4	an	an	DET
ap-1402	243	5	additional	additional	ADJ
ap-1402	243	6	pair	pair	NOUN
ap-1402	243	7	of	of	ADP
ap-1402	243	8	hyperbolic	hyperbolic	ADJ
ap-1402	243	9	ladder	ladder	NOUN
ap-1402	243	10	operators	operator	NOUN
ap-1402	243	11	,	,	PUNCT
ap-1402	243	12	which	which	PRON
ap-1402	243	13	are	be	AUX
ap-1402	243	14	identical	identical	ADJ
ap-1402	243	15	(	(	PUNCT
ap-1402	243	16	up	up	ADP
ap-1402	243	17	to	to	ADP
ap-1402	243	18	factors	factor	NOUN
ap-1402	243	19	)	)	PUNCT
ap-1402	243	20	to	to	ADP
ap-1402	243	21	(	(	PUNCT
ap-1402	243	22	26	26	NUM
ap-1402	243	23	):	):	PUNCT
ap-1402	243	24	l±	l±	PROPN
ap-1402	243	25	j	j	PROPN
ap-1402	243	26	=	=	PUNCT
ap-1402	243	27	x̃	x̃	PROPN
ap-1402	243	28	∓	∓	PROPN
ap-1402	243	29	jỹ	jỹ	PROPN
ap-1402	244	1	=	=	SYM
ap-1402	244	2	jq	jq	PROPN
ap-1402	244	3	±	±	NUM
ap-1402	245	1	jh	jh	PROPN
ap-1402	245	2	d	d	NOUN
ap-1402	245	3	dq	dq	PROPN
ap-1402	245	4	.	.	PUNCT
ap-1402	246	1	pairs	pair	NOUN
ap-1402	246	2	l±	l±	VERB
ap-1402	246	3	h	h	PROPN
ap-1402	246	4	and	and	CCONJ
ap-1402	246	5	l±	l±	PROPN
ap-1402	246	6	j	j	PROPN
ap-1402	246	7	shift	shift	NOUN
ap-1402	246	8	eigenvectors	eigenvector	NOUN
ap-1402	246	9	in	in	ADP
ap-1402	246	10	the	the	DET
ap-1402	246	11	“	"	PUNCT
ap-1402	246	12	orthogonal	orthogonal	ADJ
ap-1402	246	13	”	"	PUNCT
ap-1402	246	14	directions	direction	NOUN
ap-1402	246	15	changing	change	VERB
ap-1402	246	16	their	their	PRON
ap-1402	246	17	eigenvalues	eigenvalue	NOUN
ap-1402	246	18	by	by	ADP
ap-1402	246	19	±1	±1	ADJ
ap-1402	246	20	and	and	CCONJ
ap-1402	246	21	±j	±j	PROPN
ap-1402	246	22	.	.	PUNCT
ap-1402	247	1	therefore	therefore	ADV
ap-1402	247	2	an	an	DET
ap-1402	247	3	indecomposable	indecomposable	ADJ
ap-1402	247	4	sp2	sp2	NOUN
ap-1402	247	5	-	-	PUNCT
ap-1402	247	6	module	module	NOUN
ap-1402	247	7	can	can	AUX
ap-1402	247	8	be	be	AUX
ap-1402	247	9	parametrised	parametrise	VERB
ap-1402	247	10	by	by	ADP
ap-1402	247	11	a	a	DET
ap-1402	247	12	two	two	NUM
ap-1402	247	13	-	-	PUNCT
ap-1402	247	14	dimensional	dimensional	ADJ
ap-1402	247	15	lattice	lattice	NOUN
ap-1402	247	16	of	of	ADP
ap-1402	247	17	eigenvalues	eigenvalue	NOUN
ap-1402	247	18	in	in	ADP
ap-1402	247	19	double	double	ADJ
ap-1402	247	20	numbers	number	NOUN
ap-1402	247	21	,	,	PUNCT
ap-1402	247	22	see	see	VERB
ap-1402	247	23	table	table	NOUN
ap-1402	247	24	1	1	NUM
ap-1402	247	25	.	.	PUNCT
ap-1402	248	1	the	the	DET
ap-1402	248	2	following	follow	VERB
ap-1402	248	3	functions	function	NOUN
ap-1402	248	4	v±h	v±h	ADP
ap-1402	248	5	1	1	NUM
ap-1402	248	6	2	2	NUM
ap-1402	248	7	(	(	PUNCT
ap-1402	248	8	q	q	X
ap-1402	248	9	)	)	PUNCT
ap-1402	248	10	=	=	VERB
ap-1402	248	11	e∓jq	e∓jq	VERB
ap-1402	248	12	2/(2h	2/(2h	X
ap-1402	248	13	)	)	PUNCT
ap-1402	248	14	=	=	VERB
ap-1402	248	15	cosh	cosh	PROPN
ap-1402	248	16	q2	q2	NOUN
ap-1402	248	17	2h	2h	NUM
ap-1402	248	18	∓	∓	PROPN
ap-1402	248	19	j	j	PROPN
ap-1402	248	20	sinh	sinh	PROPN
ap-1402	248	21	q2	q2	PROPN
ap-1402	248	22	2h	2h	NUM
ap-1402	248	23	,	,	PUNCT
ap-1402	248	24	v±j1	v±j1	NOUN
ap-1402	248	25	2	2	NUM
ap-1402	248	26	(	(	PUNCT
ap-1402	248	27	q	q	NOUN
ap-1402	248	28	)	)	PUNCT
ap-1402	248	29	=	=	SYM
ap-1402	248	30	e∓q2/(2h	e∓q2/(2h	NOUN
ap-1402	248	31	)	)	PUNCT
ap-1402	248	32	are	be	AUX
ap-1402	248	33	null	null	ADJ
ap-1402	248	34	solutions	solution	NOUN
ap-1402	248	35	to	to	ADP
ap-1402	248	36	the	the	DET
ap-1402	248	37	operators	operator	NOUN
ap-1402	248	38	l±	l±	VERB
ap-1402	248	39	h	h	PROPN
ap-1402	248	40	and	and	CCONJ
ap-1402	248	41	l±	l±	PROPN
ap-1402	248	42	j	j	PROPN
ap-1402	248	43	,	,	PUNCT
ap-1402	248	44	respectively	respectively	ADV
ap-1402	248	45	.	.	PUNCT
ap-1402	249	1	they	they	PRON
ap-1402	249	2	are	be	AUX
ap-1402	249	3	also	also	ADV
ap-1402	249	4	eigenvectors	eigenvector	NOUN
ap-1402	249	5	of	of	ADP
ap-1402	249	6	2ρswh	2ρswh	NUM
ap-1402	249	7	(	(	PUNCT
ap-1402	249	8	b	b	NOUN
ap-1402	249	9	)	)	PUNCT
ap-1402	249	10	with	with	ADP
ap-1402	249	11	eigenvalues	eigenvalue	NOUN
ap-1402	249	12	∓	∓	PROPN
ap-1402	249	13	j	j	NOUN
ap-1402	249	14	2	2	NUM
ap-1402	249	15	and	and	CCONJ
ap-1402	249	16	∓1	∓1	NUM
ap-1402	249	17	2	2	NUM
ap-1402	249	18	,	,	PUNCT
ap-1402	249	19	respectively	respectively	ADV
ap-1402	249	20	.	.	PUNCT
ap-1402	250	1	if	if	SCONJ
ap-1402	250	2	these	these	DET
ap-1402	250	3	functions	function	NOUN
ap-1402	250	4	are	be	AUX
ap-1402	250	5	used	use	VERB
ap-1402	250	6	as	as	ADP
ap-1402	250	7	mother	mother	NOUN
ap-1402	250	8	wavelets	wavelet	NOUN
ap-1402	250	9	for	for	ADP
ap-1402	250	10	the	the	DET
ap-1402	250	11	wavelet	wavelet	NOUN
ap-1402	250	12	transforms	transform	VERB
ap-1402	250	13	generated	generate	VERB
ap-1402	250	14	by	by	ADP
ap-1402	250	15	the	the	DET
ap-1402	250	16	heisenberg	heisenberg	PROPN
ap-1402	250	17	group	group	NOUN
ap-1402	250	18	,	,	PUNCT
ap-1402	250	19	then	then	ADV
ap-1402	250	20	the	the	DET
ap-1402	250	21	image	image	NOUN
ap-1402	250	22	space	space	NOUN
ap-1402	250	23	will	will	AUX
ap-1402	250	24	consist	consist	VERB
ap-1402	250	25	of	of	ADP
ap-1402	250	26	the	the	DET
ap-1402	250	27	null	null	ADJ
ap-1402	250	28	-	-	PUNCT
ap-1402	250	29	solutions	solution	NOUN
ap-1402	250	30	of	of	ADP
ap-1402	250	31	the	the	DET
ap-1402	250	32	following	follow	VERB
ap-1402	250	33	differential	differential	NOUN
ap-1402	250	34	operators	operator	NOUN
ap-1402	250	35	,	,	PUNCT
ap-1402	250	36	see	see	VERB
ap-1402	250	37	[	[	X
ap-1402	250	38	26	26	NUM
ap-1402	250	39	,	,	PUNCT
ap-1402	250	40	cor	cor	PROPN
ap-1402	250	41	.	.	PROPN
ap-1402	250	42	24	24	NUM
ap-1402	250	43	]	]	PUNCT
ap-1402	250	44	:	:	PUNCT
ap-1402	251	1	dh	dh	NOUN
ap-1402	251	2	=	=	PUNCT
ap-1402	251	3	xr	xr	PROPN
ap-1402	251	4	−	−	PROPN
ap-1402	252	1	y	y	PROPN
ap-1402	252	2	r	r	NOUN
ap-1402	252	3	=	=	PUNCT
ap-1402	252	4	(	(	PUNCT
ap-1402	252	5	∂x	∂x	PROPN
ap-1402	252	6	−	−	PROPN
ap-1402	252	7	∂y	∂y	PROPN
ap-1402	252	8	)	)	PUNCT
ap-1402	253	1	+	+	NUM
ap-1402	253	2	h	h	NOUN
ap-1402	253	3	2	2	NUM
ap-1402	253	4	(	(	PUNCT
ap-1402	253	5	x	x	PROPN
ap-1402	253	6	+	+	NUM
ap-1402	253	7	y	y	NOUN
ap-1402	253	8	)	)	PUNCT
ap-1402	253	9	,	,	PUNCT
ap-1402	253	10	dj	dj	NOUN
ap-1402	253	11	=	=	PUNCT
ap-1402	253	12	xr	xr	PROPN
ap-1402	253	13	−	−	PROPN
ap-1402	254	1	jy	jy	PROPN
ap-1402	254	2	r	r	NOUN
ap-1402	254	3	=	=	PUNCT
ap-1402	254	4	(	(	PUNCT
ap-1402	254	5	∂x	∂x	PROPN
ap-1402	254	6	+	+	CCONJ
ap-1402	254	7	j∂y	j∂y	NOUN
ap-1402	254	8	)	)	PUNCT
ap-1402	255	1	−	−	NOUN
ap-1402	255	2	h	h	NOUN
ap-1402	255	3	2	2	NUM
ap-1402	255	4	(	(	PUNCT
ap-1402	255	5	x	x	NOUN
ap-1402	255	6	−	−	PROPN
ap-1402	255	7	jy	jy	PROPN
ap-1402	255	8	)	)	PUNCT
ap-1402	255	9	,	,	PUNCT
ap-1402	255	10	49	49	NUM
ap-1402	255	11	acta	acta	PROPN
ap-1402	255	12	polytechnica	polytechnica	PROPN
ap-1402	255	13	vol	vol	NOUN
ap-1402	255	14	.	.	PUNCT
ap-1402	256	1	51	51	NUM
ap-1402	256	2	no	no	INTJ
ap-1402	256	3	.	.	PUNCT
ap-1402	257	1	4/2011	4/2011	NUM
ap-1402	257	2	table	table	NOUN
ap-1402	257	3	1	1	NUM
ap-1402	257	4	:	:	PUNCT
ap-1402	257	5	the	the	DET
ap-1402	257	6	action	action	NOUN
ap-1402	257	7	of	of	ADP
ap-1402	257	8	hyperbolic	hyperbolic	ADJ
ap-1402	257	9	ladder	ladder	NOUN
ap-1402	257	10	operators	operator	NOUN
ap-1402	257	11	on	on	ADP
ap-1402	257	12	a	a	DET
ap-1402	257	13	2d	2d	NUM
ap-1402	257	14	lattice	lattice	NOUN
ap-1402	257	15	of	of	ADP
ap-1402	257	16	eigenspaces	eigenspace	NOUN
ap-1402	257	17	.	.	PUNCT
ap-1402	258	1	operators	operator	NOUN
ap-1402	258	2	l±	l±	AUX
ap-1402	258	3	h	h	NOUN
ap-1402	258	4	move	move	VERB
ap-1402	258	5	the	the	DET
ap-1402	258	6	eigenvalues	eigenvalue	NOUN
ap-1402	258	7	by	by	ADP
ap-1402	258	8	1	1	NUM
ap-1402	258	9	,	,	PUNCT
ap-1402	258	10	making	make	VERB
ap-1402	258	11	shifts	shift	NOUN
ap-1402	258	12	in	in	ADP
ap-1402	258	13	the	the	DET
ap-1402	258	14	horizontal	horizontal	ADJ
ap-1402	258	15	direction	direction	NOUN
ap-1402	258	16	.	.	PUNCT
ap-1402	259	1	operators	operator	NOUN
ap-1402	259	2	l±	l±	VERB
ap-1402	259	3	j	j	PROPN
ap-1402	259	4	change	change	VERB
ap-1402	259	5	the	the	DET
ap-1402	259	6	eigenvalues	eigenvalue	NOUN
ap-1402	259	7	by	by	ADP
ap-1402	259	8	j	j	PROPN
ap-1402	259	9	,	,	PUNCT
ap-1402	259	10	shown	show	VERB
ap-1402	259	11	as	as	ADP
ap-1402	259	12	vertical	vertical	ADJ
ap-1402	259	13	shifts	shift	NOUN
ap-1402	259	14	for	for	ADP
ap-1402	259	15	v±h	v±h	PROPN
ap-1402	259	16	1	1	NUM
ap-1402	259	17	2	2	NUM
ap-1402	259	18	and	and	CCONJ
ap-1402	259	19	v±j1	v±j1	NOUN
ap-1402	259	20	2	2	NUM
ap-1402	259	21	,	,	PUNCT
ap-1402	259	22	respectively	respectively	ADV
ap-1402	259	23	.	.	PUNCT
ap-1402	260	1	this	this	PRON
ap-1402	260	2	is	be	AUX
ap-1402	260	3	again	again	ADV
ap-1402	260	4	in	in	ADP
ap-1402	260	5	line	line	NOUN
ap-1402	260	6	with	with	ADP
ap-1402	260	7	the	the	DET
ap-1402	260	8	classical	classical	ADJ
ap-1402	260	9	result	result	NOUN
ap-1402	260	10	(	(	PUNCT
ap-1402	260	11	27	27	NUM
ap-1402	260	12	)	)	PUNCT
ap-1402	260	13	.	.	PUNCT
ap-1402	261	1	however	however	ADV
ap-1402	261	2	annihilation	annihilation	NOUN
ap-1402	261	3	of	of	ADP
ap-1402	261	4	the	the	DET
ap-1402	261	5	eigenvector	eigenvector	NOUN
ap-1402	261	6	by	by	ADP
ap-1402	261	7	a	a	DET
ap-1402	261	8	ladder	ladder	NOUN
ap-1402	261	9	operator	operator	NOUN
ap-1402	261	10	does	do	AUX
ap-1402	261	11	not	not	PART
ap-1402	261	12	mean	mean	VERB
ap-1402	261	13	that	that	SCONJ
ap-1402	261	14	the	the	DET
ap-1402	261	15	part	part	NOUN
ap-1402	261	16	of	of	ADP
ap-1402	261	17	the	the	DET
ap-1402	261	18	2d	2d	NOUN
ap-1402	261	19	-	-	PUNCT
ap-1402	261	20	lattice	lattice	NOUN
ap-1402	261	21	becomes	become	VERB
ap-1402	261	22	void	void	ADJ
ap-1402	261	23	,	,	PUNCT
ap-1402	261	24	since	since	SCONJ
ap-1402	261	25	it	it	PRON
ap-1402	261	26	can	can	AUX
ap-1402	261	27	be	be	AUX
ap-1402	261	28	reached	reach	VERB
ap-1402	261	29	via	via	ADP
ap-1402	261	30	alternative	alternative	ADJ
ap-1402	261	31	routes	route	NOUN
ap-1402	261	32	.	.	PUNCT
ap-1402	262	1	instead	instead	ADV
ap-1402	262	2	of	of	ADP
ap-1402	262	3	multiplication	multiplication	NOUN
ap-1402	262	4	by	by	ADP
ap-1402	262	5	a	a	DET
ap-1402	262	6	zero	zero	NUM
ap-1402	262	7	,	,	PUNCT
ap-1402	262	8	as	as	SCONJ
ap-1402	262	9	happens	happen	VERB
ap-1402	262	10	in	in	ADP
ap-1402	262	11	the	the	DET
ap-1402	262	12	elliptic	elliptic	ADJ
ap-1402	262	13	case	case	NOUN
ap-1402	262	14	,	,	PUNCT
ap-1402	262	15	a	a	DET
ap-1402	262	16	half	half	ADJ
ap-1402	262	17	-	-	PUNCT
ap-1402	262	18	plane	plane	NOUN
ap-1402	262	19	of	of	ADP
ap-1402	262	20	eigenvalues	eigenvalue	NOUN
ap-1402	262	21	will	will	AUX
ap-1402	262	22	be	be	AUX
ap-1402	262	23	multiplied	multiply	VERB
ap-1402	262	24	by	by	ADP
ap-1402	262	25	the	the	DET
ap-1402	262	26	divisors	divisor	NOUN
ap-1402	262	27	of	of	ADP
ap-1402	262	28	zero	zero	NUM
ap-1402	262	29	1	1	NUM
ap-1402	262	30	±	±	NOUN
ap-1402	262	31	j.	j.	NOUN
ap-1402	262	32	we	we	PRON
ap-1402	262	33	can	can	AUX
ap-1402	262	34	also	also	ADV
ap-1402	262	35	search	search	VERB
ap-1402	262	36	ladder	ladder	NOUN
ap-1402	262	37	operators	operator	NOUN
ap-1402	262	38	within	within	ADP
ap-1402	262	39	the	the	DET
ap-1402	262	40	algebra	algebra	NOUN
ap-1402	262	41	sp2	sp2	NOUN
ap-1402	262	42	and	and	CCONJ
ap-1402	262	43	admitting	admit	VERB
ap-1402	262	44	double	double	ADJ
ap-1402	262	45	numbers	number	NOUN
ap-1402	262	46	we	we	PRON
ap-1402	262	47	will	will	AUX
ap-1402	262	48	again	again	ADV
ap-1402	262	49	find	find	VERB
ap-1402	262	50	two	two	NUM
ap-1402	262	51	sets	set	NOUN
ap-1402	262	52	of	of	ADP
ap-1402	262	53	them	they	PRON
ap-1402	263	1	[	[	X
ap-1402	263	2	23	23	NUM
ap-1402	263	3	,	,	PUNCT
ap-1402	263	4	§	§	PROPN
ap-1402	263	5	3	3	NUM
ap-1402	263	6	]	]	PUNCT
ap-1402	263	7	:	:	PUNCT
ap-1402	263	8	l±	l±	X
ap-1402	263	9	2h	2h	X
ap-1402	263	10	=	=	SYM
ap-1402	263	11	±ã	±ã	ADJ
ap-1402	263	12	+	+	CCONJ
ap-1402	263	13	z̃/2	z̃/2	PUNCT
ap-1402	263	14	=	=	SYM
ap-1402	263	15	∓	∓	NOUN
ap-1402	263	16	q	q	NOUN
ap-1402	263	17	2	2	NUM
ap-1402	263	18	d	d	NOUN
ap-1402	263	19	dq	dq	NOUN
ap-1402	263	20	∓	∓	NOUN
ap-1402	263	21	1	1	NUM
ap-1402	263	22	4	4	NUM
ap-1402	263	23	−	−	PROPN
ap-1402	263	24	jh	jh	PROPN
ap-1402	263	25	4	4	NUM
ap-1402	263	26	d2	d2	PROPN
ap-1402	263	27	dq2	dq2	PROPN
ap-1402	263	28	−	−	PROPN
ap-1402	263	29	jq2	jq2	PROPN
ap-1402	263	30	4h	4h	NUM
ap-1402	263	31	=	=	SYM
ap-1402	264	1	−	−	PROPN
ap-1402	264	2	j	j	PROPN
ap-1402	264	3	4h	4h	NOUN
ap-1402	264	4	(	(	PUNCT
ap-1402	264	5	l±	l±	PROPN
ap-1402	264	6	h	h	PROPN
ap-1402	264	7	)	)	PUNCT
ap-1402	264	8	2	2	NUM
ap-1402	264	9	,	,	PUNCT
ap-1402	264	10	l±	l±	X
ap-1402	264	11	2j	2j	X
ap-1402	264	12	=	=	SYM
ap-1402	264	13	±jã	±jã	PROPN
ap-1402	264	14	+	+	CCONJ
ap-1402	264	15	z̃/2	z̃/2	PROPN
ap-1402	264	16	=	=	SYM
ap-1402	265	1	∓	∓	PROPN
ap-1402	265	2	jq	jq	PROPN
ap-1402	265	3	2	2	NUM
ap-1402	265	4	d	d	NOUN
ap-1402	265	5	dq	dq	NOUN
ap-1402	265	6	∓	∓	PROPN
ap-1402	265	7	j	j	NOUN
ap-1402	265	8	4	4	NUM
ap-1402	265	9	−	−	PROPN
ap-1402	265	10	jh	jh	PROPN
ap-1402	265	11	4	4	NUM
ap-1402	265	12	d2	d2	PROPN
ap-1402	265	13	dq2	dq2	PROPN
ap-1402	266	1	−	−	PROPN
ap-1402	266	2	jq2	jq2	PROPN
ap-1402	266	3	4h	4h	NUM
ap-1402	266	4	=	=	SYM
ap-1402	267	1	−	−	PROPN
ap-1402	267	2	j	j	PROPN
ap-1402	267	3	4h	4h	NOUN
ap-1402	267	4	(	(	PUNCT
ap-1402	267	5	l±	l±	PROPN
ap-1402	267	6	j	j	PROPN
ap-1402	267	7	)	)	PUNCT
ap-1402	267	8	2	2	X
ap-1402	267	9	.	.	X
ap-1402	267	10	again	again	ADV
ap-1402	267	11	these	these	DET
ap-1402	267	12	operators	operator	NOUN
ap-1402	267	13	l±	l±	VERB
ap-1402	267	14	2h	2h	NUM
ap-1402	267	15	and	and	CCONJ
ap-1402	267	16	l±	l±	X
ap-1402	267	17	2h	2h	NUM
ap-1402	267	18	produce	produce	VERB
ap-1402	267	19	double	double	ADJ
ap-1402	267	20	shifts	shift	NOUN
ap-1402	267	21	in	in	ADP
ap-1402	267	22	the	the	DET
ap-1402	267	23	orthogonal	orthogonal	ADJ
ap-1402	267	24	directions	direction	NOUN
ap-1402	267	25	on	on	ADP
ap-1402	267	26	the	the	DET
ap-1402	267	27	same	same	ADJ
ap-1402	267	28	twodimensional	twodimensional	ADJ
ap-1402	267	29	lattice	lattice	NOUN
ap-1402	267	30	in	in	ADP
ap-1402	267	31	tabular	tabular	NOUN
ap-1402	267	32	1	1	NUM
ap-1402	267	33	.	.	SYM
ap-1402	267	34	5	5	NUM
ap-1402	267	35	ladder	ladder	NOUN
ap-1402	267	36	operator	operator	NOUN
ap-1402	267	37	for	for	ADP
ap-1402	267	38	the	the	DET
ap-1402	267	39	nilpotent	nilpotent	ADJ
ap-1402	267	40	subgroup	subgroup	NOUN
ap-1402	267	41	finally	finally	ADV
ap-1402	267	42	,	,	PUNCT
ap-1402	267	43	we	we	PRON
ap-1402	267	44	look	look	VERB
ap-1402	267	45	for	for	ADP
ap-1402	267	46	ladder	ladder	NOUN
ap-1402	267	47	operators	operator	NOUN
ap-1402	267	48	for	for	ADP
ap-1402	267	49	the	the	DET
ap-1402	267	50	hamiltonian	hamiltonian	ADJ
ap-1402	267	51	b̃	b̃	PROPN
ap-1402	267	52	+	+	CCONJ
ap-1402	267	53	z̃/2	z̃/2	PROPN
ap-1402	267	54	or	or	CCONJ
ap-1402	267	55	,	,	PUNCT
ap-1402	267	56	equivalently	equivalently	ADV
ap-1402	267	57	,	,	PUNCT
ap-1402	267	58	−b̃	−b̃	PUNCT
ap-1402	267	59	+	+	CCONJ
ap-1402	267	60	z̃/2	z̃/2	PROPN
ap-1402	267	61	.	.	PUNCT
ap-1402	268	1	it	it	PRON
ap-1402	268	2	can	can	AUX
ap-1402	268	3	be	be	AUX
ap-1402	268	4	identified	identify	VERB
ap-1402	268	5	with	with	ADP
ap-1402	268	6	a	a	DET
ap-1402	268	7	free	free	ADJ
ap-1402	268	8	particle	particle	NOUN
ap-1402	268	9	[	[	X
ap-1402	268	10	37	37	NUM
ap-1402	268	11	,	,	PUNCT
ap-1402	268	12	§	§	PROPN
ap-1402	268	13	3.8	3.8	NUM
ap-1402	268	14	]	]	PUNCT
ap-1402	268	15	.	.	PUNCT
ap-1402	269	1	we	we	PRON
ap-1402	269	2	can	can	AUX
ap-1402	269	3	look	look	VERB
ap-1402	269	4	for	for	ADP
ap-1402	269	5	ladder	ladder	NOUN
ap-1402	269	6	operators	operator	NOUN
ap-1402	269	7	in	in	ADP
ap-1402	269	8	the	the	DET
ap-1402	269	9	representation	representation	NOUN
ap-1402	269	10	(	(	PUNCT
ap-1402	269	11	14–15	14–15	NUM
ap-1402	269	12	)	)	PUNCT
ap-1402	269	13	within	within	ADP
ap-1402	269	14	the	the	DET
ap-1402	269	15	lie	lie	NOUN
ap-1402	269	16	algebra	algebra	NOUN
ap-1402	269	17	h1	h1	NOUN
ap-1402	269	18	in	in	ADP
ap-1402	269	19	the	the	DET
ap-1402	269	20	form	form	NOUN
ap-1402	269	21	l±	l±	X
ap-1402	269	22	ε	ε	PROPN
ap-1402	269	23	=	=	PUNCT
ap-1402	269	24	ax̃	ax̃	PROPN
ap-1402	270	1	+	+	CCONJ
ap-1402	270	2	bỹ	bỹ	NOUN
ap-1402	270	3	.	.	PUNCT
ap-1402	271	1	this	this	PRON
ap-1402	271	2	is	be	AUX
ap-1402	271	3	possible	possible	ADJ
ap-1402	271	4	if	if	SCONJ
ap-1402	271	5	and	and	CCONJ
ap-1402	271	6	only	only	ADV
ap-1402	271	7	if	if	SCONJ
ap-1402	271	8	−	−	PROPN
ap-1402	271	9	b	b	X
ap-1402	271	10	=	=	SYM
ap-1402	271	11	λa	λa	PROPN
ap-1402	271	12	,	,	PUNCT
ap-1402	271	13	0	0	PUNCT
ap-1402	271	14	=	=	SYM
ap-1402	271	15	λb	λb	PROPN
ap-1402	271	16	.	.	PUNCT
ap-1402	272	1	(	(	PUNCT
ap-1402	272	2	37	37	NUM
ap-1402	272	3	)	)	PUNCT
ap-1402	272	4	the	the	DET
ap-1402	272	5	compatibility	compatibility	NOUN
ap-1402	272	6	condition	condition	NOUN
ap-1402	272	7	λ2	λ2	NOUN
ap-1402	272	8	=	=	SYM
ap-1402	272	9	0	0	NUM
ap-1402	272	10	implies	imply	VERB
ap-1402	272	11	λ	λ	X
ap-1402	272	12	=	=	SYM
ap-1402	272	13	0	0	NUM
ap-1402	272	14	within	within	ADP
ap-1402	272	15	complex	complex	ADJ
ap-1402	272	16	numbers	number	NOUN
ap-1402	272	17	.	.	PUNCT
ap-1402	273	1	however	however	ADV
ap-1402	273	2	,	,	PUNCT
ap-1402	273	3	such	such	DET
ap-1402	273	4	a	a	DET
ap-1402	273	5	“	"	PUNCT
ap-1402	273	6	ladder	ladder	NOUN
ap-1402	273	7	”	"	PUNCT
ap-1402	273	8	operator	operator	NOUN
ap-1402	273	9	produces	produce	VERB
ap-1402	273	10	only	only	ADV
ap-1402	273	11	the	the	DET
ap-1402	273	12	zero	zero	NUM
ap-1402	273	13	shift	shift	NOUN
ap-1402	273	14	on	on	ADP
ap-1402	273	15	the	the	DET
ap-1402	273	16	eigenvectors	eigenvector	NOUN
ap-1402	273	17	,	,	PUNCT
ap-1402	273	18	cf	cf	INTJ
ap-1402	273	19	.	.	PUNCT
ap-1402	274	1	(	(	PUNCT
ap-1402	274	2	24	24	NUM
ap-1402	274	3	)	)	PUNCT
ap-1402	274	4	.	.	PUNCT
ap-1402	275	1	another	another	DET
ap-1402	275	2	possibility	possibility	NOUN
ap-1402	275	3	appears	appear	VERB
ap-1402	275	4	if	if	SCONJ
ap-1402	275	5	we	we	PRON
ap-1402	275	6	consider	consider	VERB
ap-1402	275	7	the	the	DET
ap-1402	275	8	representation	representation	NOUN
ap-1402	275	9	of	of	ADP
ap-1402	275	10	the	the	DET
ap-1402	275	11	heisenberg	heisenberg	PROPN
ap-1402	275	12	group	group	NOUN
ap-1402	275	13	induced	induce	VERB
ap-1402	275	14	by	by	ADP
ap-1402	275	15	dualvalued	dualvalue	VERB
ap-1402	275	16	characters	character	NOUN
ap-1402	275	17	.	.	PUNCT
ap-1402	276	1	on	on	ADP
ap-1402	276	2	the	the	DET
ap-1402	276	3	configurational	configurational	ADJ
ap-1402	276	4	space	space	NOUN
ap-1402	276	5	such	such	DET
ap-1402	276	6	a	a	DET
ap-1402	276	7	representation	representation	NOUN
ap-1402	276	8	is	be	AUX
ap-1402	276	9	[	[	X
ap-1402	276	10	25	25	NUM
ap-1402	276	11	,	,	PUNCT
ap-1402	276	12	(	(	PUNCT
ap-1402	276	13	4.11	4.11	NUM
ap-1402	276	14	)	)	PUNCT
ap-1402	276	15	]	]	PUNCT
ap-1402	276	16	:	:	PUNCT
ap-1402	277	1	[	[	X
ap-1402	277	2	ρε	ρε	PROPN
ap-1402	277	3	χ(s	χ(s	PROPN
ap-1402	277	4	,	,	PUNCT
ap-1402	277	5	x	x	X
ap-1402	277	6	,	,	PUNCT
ap-1402	277	7	y)f	y)f	VERB
ap-1402	277	8	]	]	PUNCT
ap-1402	277	9	(	(	PUNCT
ap-1402	277	10	q	q	X
ap-1402	277	11	)	)	PUNCT
ap-1402	277	12	=	=	SYM
ap-1402	277	13	e2πixq	e2πixq	ADV
ap-1402	277	14	(	(	PUNCT
ap-1402	277	15	(	(	PUNCT
ap-1402	277	16	1	1	NUM
ap-1402	277	17	−	−	NOUN
ap-1402	277	18	εh	εh	ADP
ap-1402	277	19	(	(	PUNCT
ap-1402	277	20	s	s	NOUN
ap-1402	277	21	−	−	PROPN
ap-1402	277	22	1	1	NUM
ap-1402	277	23	2	2	NUM
ap-1402	277	24	xy	xy	NOUN
ap-1402	277	25	)	)	PUNCT
ap-1402	277	26	)	)	PUNCT
ap-1402	277	27	·	·	PUNCT
ap-1402	277	28	f(q	f(q	NOUN
ap-1402	277	29	)	)	PUNCT
ap-1402	278	1	+	+	CCONJ
ap-1402	278	2	εhy	εhy	PROPN
ap-1402	278	3	2πi	2πi	PROPN
ap-1402	278	4	f	f	PROPN
ap-1402	278	5	′(q	′(q	PROPN
ap-1402	278	6	)	)	PUNCT
ap-1402	278	7	)	)	PUNCT
ap-1402	278	8	.	.	PUNCT
ap-1402	279	1	(	(	PUNCT
ap-1402	279	2	38	38	NUM
ap-1402	279	3	)	)	PUNCT
ap-1402	279	4	the	the	DET
ap-1402	279	5	corresponding	corresponding	ADJ
ap-1402	279	6	derived	derive	VERB
ap-1402	279	7	representation	representation	NOUN
ap-1402	279	8	of	of	ADP
ap-1402	279	9	h1	h1	PROPN
ap-1402	279	10	is	be	AUX
ap-1402	279	11	ρp	ρp	ADP
ap-1402	279	12	h(x	h(x	PROPN
ap-1402	279	13	)	)	PUNCT
ap-1402	280	1	=	=	SYM
ap-1402	280	2	2πiq	2πiq	NUM
ap-1402	280	3	,	,	PUNCT
ap-1402	280	4	ρp	ρp	DET
ap-1402	280	5	h(y	h(y	ADV
ap-1402	280	6	)	)	PUNCT
ap-1402	280	7	=	=	PUNCT
ap-1402	280	8	εh	εh	ADP
ap-1402	280	9	2πi	2πi	NOUN
ap-1402	281	1	d	d	ADP
ap-1402	281	2	dq	dq	INTJ
ap-1402	281	3	,	,	PUNCT
ap-1402	281	4	(	(	PUNCT
ap-1402	281	5	39	39	NUM
ap-1402	281	6	)	)	PUNCT
ap-1402	281	7	ρp	ρp	DET
ap-1402	281	8	h(s	h(	NOUN
ap-1402	281	9	)	)	PUNCT
ap-1402	281	10	=	=	PUNCT
ap-1402	281	11	−εhi	−εhi	NOUN
ap-1402	281	12	.	.	PUNCT
ap-1402	282	1	however	however	ADV
ap-1402	282	2	the	the	DET
ap-1402	282	3	shale	shale	PROPN
ap-1402	282	4	-	-	PUNCT
ap-1402	282	5	weil	weil	PROPN
ap-1402	282	6	extension	extension	NOUN
ap-1402	282	7	generated	generate	VERB
ap-1402	282	8	by	by	ADP
ap-1402	282	9	this	this	DET
ap-1402	282	10	representation	representation	NOUN
ap-1402	282	11	is	be	AUX
ap-1402	282	12	inconvenient	inconvenient	ADJ
ap-1402	282	13	.	.	PUNCT
ap-1402	283	1	it	it	PRON
ap-1402	283	2	is	be	AUX
ap-1402	283	3	better	well	ADJ
ap-1402	283	4	to	to	PART
ap-1402	283	5	consider	consider	VERB
ap-1402	283	6	the	the	DET
ap-1402	283	7	fsb	fsb	ADJ
ap-1402	283	8	-	-	PUNCT
ap-1402	283	9	type	type	NOUN
ap-1402	283	10	parabolic	parabolic	NOUN
ap-1402	283	11	representation	representation	NOUN
ap-1402	283	12	[	[	X
ap-1402	283	13	25	25	NUM
ap-1402	283	14	,	,	PUNCT
ap-1402	283	15	(	(	PUNCT
ap-1402	283	16	4.9	4.9	NUM
ap-1402	283	17	)	)	PUNCT
ap-1402	283	18	]	]	PUNCT
ap-1402	283	19	on	on	ADP
ap-1402	283	20	the	the	DET
ap-1402	283	21	phase	phase	NOUN
ap-1402	283	22	space	space	NOUN
ap-1402	283	23	induced	induce	VERB
ap-1402	283	24	by	by	ADP
ap-1402	283	25	the	the	DET
ap-1402	283	26	same	same	ADJ
ap-1402	283	27	dual	dual	ADV
ap-1402	283	28	-	-	PUNCT
ap-1402	283	29	valued	value	VERB
ap-1402	283	30	character	character	NOUN
ap-1402	283	31	,	,	PUNCT
ap-1402	283	32	cf	cf	NOUN
ap-1402	283	33	.	.	PUNCT
ap-1402	284	1	(	(	PUNCT
ap-1402	284	2	19	19	NUM
ap-1402	284	3	):	):	PUNCT
ap-1402	284	4	[	[	X
ap-1402	284	5	ρε	ρε	ADJ
ap-1402	284	6	h(s	h(s	PROPN
ap-1402	284	7	,	,	PUNCT
ap-1402	284	8	x	x	X
ap-1402	284	9	,	,	PUNCT
ap-1402	284	10	y)f	y)f	VERB
ap-1402	284	11	]	]	PUNCT
ap-1402	284	12	(	(	PUNCT
ap-1402	284	13	q	q	ADJ
ap-1402	284	14	,	,	PUNCT
ap-1402	284	15	p	p	NOUN
ap-1402	284	16	)	)	PUNCT
ap-1402	284	17	=	=	SYM
ap-1402	284	18	e−2πi(xq+yp	e−2πi(xq+yp	NOUN
ap-1402	284	19	)	)	PUNCT
ap-1402	284	20	·	·	PUNCT
ap-1402	285	1	(	(	PUNCT
ap-1402	285	2	40	40	NUM
ap-1402	285	3	)	)	PUNCT
ap-1402	285	4	(	(	PUNCT
ap-1402	285	5	f(q	f(q	PROPN
ap-1402	285	6	,	,	PUNCT
ap-1402	285	7	p	p	NOUN
ap-1402	285	8	)	)	PUNCT
ap-1402	285	9	+	+	CCONJ
ap-1402	285	10	εh(sf(q	εh(sf(q	PROPN
ap-1402	285	11	,	,	PUNCT
ap-1402	285	12	p	p	NOUN
ap-1402	285	13	)	)	PUNCT
ap-1402	286	1	+	+	CCONJ
ap-1402	286	2	y	y	PROPN
ap-1402	286	3	4πi	4πi	NOUN
ap-1402	287	1	f	f	PROPN
ap-1402	287	2	′	′	NUM
ap-1402	287	3	q(q	q(q	PROPN
ap-1402	287	4	,	,	PUNCT
ap-1402	287	5	p	p	NOUN
ap-1402	287	6	)	)	PUNCT
ap-1402	287	7	−	−	NOUN
ap-1402	288	1	x	x	SYM
ap-1402	288	2	4πi	4πi	NOUN
ap-1402	288	3	f	f	PROPN
ap-1402	288	4	′	′	NUM
ap-1402	289	1	p(q	p(q	NOUN
ap-1402	289	2	,	,	PUNCT
ap-1402	289	3	p	p	NOUN
ap-1402	289	4	)	)	PUNCT
ap-1402	289	5	)	)	PUNCT
ap-1402	289	6	)	)	PUNCT
ap-1402	289	7	.	.	PUNCT
ap-1402	290	1	then	then	ADV
ap-1402	290	2	the	the	DET
ap-1402	290	3	derived	derived	ADJ
ap-1402	290	4	representation	representation	NOUN
ap-1402	290	5	of	of	ADP
ap-1402	290	6	h1	h1	PROPN
ap-1402	290	7	is	be	AUX
ap-1402	290	8	:	:	PUNCT
ap-1402	290	9	ρp	ρp	DET
ap-1402	290	10	h(x	h(x	PROPN
ap-1402	290	11	)	)	PUNCT
ap-1402	291	1	=	=	PRON
ap-1402	291	2	−2πiq	−2πiq	NOUN
ap-1402	291	3	−	−	ADP
ap-1402	292	1	εh	εh	ADP
ap-1402	292	2	4πi	4πi	NOUN
ap-1402	292	3	∂p	∂p	PROPN
ap-1402	292	4	,	,	PUNCT
ap-1402	292	5	ρp	ρp	DET
ap-1402	292	6	h(y	h(y	ADV
ap-1402	292	7	)	)	PUNCT
ap-1402	292	8	=	=	SYM
ap-1402	292	9	−2πip	−2πip	NOUN
ap-1402	293	1	+	+	CCONJ
ap-1402	293	2	εh	εh	ADP
ap-1402	293	3	4πi	4πi	NOUN
ap-1402	293	4	∂q	∂q	PROPN
ap-1402	293	5	,	,	PUNCT
ap-1402	293	6	(	(	PUNCT
ap-1402	293	7	41	41	NUM
ap-1402	293	8	)	)	PUNCT
ap-1402	293	9	ρp	ρp	PRON
ap-1402	293	10	h(s	h(	NOUN
ap-1402	293	11	)	)	PUNCT
ap-1402	294	1	=	=	SYM
ap-1402	294	2	εhi	εhi	NOUN
ap-1402	294	3	.	.	PUNCT
ap-1402	295	1	50	50	NUM
ap-1402	295	2	acta	acta	PROPN
ap-1402	295	3	polytechnica	polytechnica	PROPN
ap-1402	295	4	vol	vol	NOUN
ap-1402	295	5	.	.	PUNCT
ap-1402	295	6	51	51	NUM
ap-1402	295	7	no	no	INTJ
ap-1402	295	8	.	.	PUNCT
ap-1402	296	1	4/2011	4/2011	NUM
ap-1402	296	2	an	an	DET
ap-1402	296	3	advantage	advantage	NOUN
ap-1402	296	4	of	of	ADP
ap-1402	296	5	the	the	DET
ap-1402	296	6	fsb	fsb	ADJ
ap-1402	296	7	representation	representation	NOUN
ap-1402	296	8	is	be	AUX
ap-1402	296	9	that	that	SCONJ
ap-1402	296	10	the	the	DET
ap-1402	296	11	derived	derived	ADJ
ap-1402	296	12	form	form	NOUN
ap-1402	296	13	of	of	ADP
ap-1402	296	14	the	the	DET
ap-1402	296	15	parabolic	parabolic	ADJ
ap-1402	296	16	shale	shale	PROPN
ap-1402	296	17	–	–	PUNCT
ap-1402	296	18	weil	weil	PROPN
ap-1402	296	19	representation	representation	NOUN
ap-1402	296	20	coincides	coincide	VERB
ap-1402	296	21	with	with	ADP
ap-1402	296	22	the	the	DET
ap-1402	296	23	elliptic	elliptic	ADJ
ap-1402	296	24	one	one	NUM
ap-1402	296	25	(	(	PUNCT
ap-1402	296	26	21	21	NUM
ap-1402	296	27	)	)	PUNCT
ap-1402	296	28	.	.	PUNCT
ap-1402	297	1	eigenfunctions	eigenfunction	NOUN
ap-1402	297	2	with	with	ADP
ap-1402	297	3	the	the	DET
ap-1402	297	4	eigenvalue	eigenvalue	PROPN
ap-1402	297	5	μ	μ	PROPN
ap-1402	297	6	of	of	ADP
ap-1402	297	7	the	the	DET
ap-1402	297	8	parabolic	parabolic	ADJ
ap-1402	297	9	hamiltonian	hamiltonian	NOUN
ap-1402	297	10	b̃	b̃	PROPN
ap-1402	297	11	+	+	CCONJ
ap-1402	297	12	z̃/2	z̃/2	PROPN
ap-1402	297	13	=	=	PUNCT
ap-1402	297	14	q∂p	q∂p	CCONJ
ap-1402	297	15	have	have	VERB
ap-1402	297	16	the	the	DET
ap-1402	297	17	form	form	NOUN
ap-1402	297	18	vμ(q	vμ(q	NOUN
ap-1402	297	19	,	,	PUNCT
ap-1402	297	20	p	p	NOUN
ap-1402	297	21	)	)	PUNCT
ap-1402	297	22	=	=	VERB
ap-1402	297	23	eμp	eμp	ADJ
ap-1402	297	24	/	/	SYM
ap-1402	297	25	qf(q	qf(q	NUM
ap-1402	297	26	)	)	PUNCT
ap-1402	297	27	,	,	PUNCT
ap-1402	297	28	(	(	PUNCT
ap-1402	297	29	42	42	NUM
ap-1402	297	30	)	)	PUNCT
ap-1402	297	31	with	with	ADP
ap-1402	297	32	an	an	DET
ap-1402	297	33	arbitrary	arbitrary	ADJ
ap-1402	297	34	function	function	NOUN
ap-1402	297	35	f(q	f(q	NOUN
ap-1402	297	36	)	)	PUNCT
ap-1402	297	37	.	.	PUNCT
ap-1402	298	1	the	the	DET
ap-1402	298	2	linear	linear	ADJ
ap-1402	298	3	equations	equation	NOUN
ap-1402	298	4	defining	define	VERB
ap-1402	298	5	the	the	DET
ap-1402	298	6	corresponding	corresponding	ADJ
ap-1402	298	7	ladder	ladder	NOUN
ap-1402	298	8	operator	operator	NOUN
ap-1402	298	9	l±	l±	X
ap-1402	298	10	ε	ε	PROPN
ap-1402	298	11	=	=	PUNCT
ap-1402	298	12	ax̃	ax̃	PROPN
ap-1402	299	1	+	+	CCONJ
ap-1402	299	2	bỹ	bỹ	NOUN
ap-1402	299	3	in	in	ADP
ap-1402	299	4	the	the	DET
ap-1402	299	5	algebra	algebra	NOUN
ap-1402	299	6	h1	h1	NOUN
ap-1402	299	7	are	be	AUX
ap-1402	299	8	(	(	PUNCT
ap-1402	299	9	37	37	NUM
ap-1402	299	10	)	)	PUNCT
ap-1402	299	11	.	.	PUNCT
ap-1402	300	1	the	the	DET
ap-1402	300	2	compatibility	compatibility	NOUN
ap-1402	300	3	condition	condition	NOUN
ap-1402	300	4	λ2	λ2	NOUN
ap-1402	300	5	=	=	SYM
ap-1402	300	6	0	0	NUM
ap-1402	300	7	implies	imply	VERB
ap-1402	300	8	λ	λ	X
ap-1402	300	9	=	=	SYM
ap-1402	300	10	0	0	NUM
ap-1402	300	11	within	within	ADP
ap-1402	300	12	complex	complex	ADJ
ap-1402	300	13	numbers	number	NOUN
ap-1402	300	14	again	again	ADV
ap-1402	300	15	.	.	PUNCT
ap-1402	301	1	admitting	admit	VERB
ap-1402	301	2	dual	dual	ADJ
ap-1402	301	3	numbers	number	NOUN
ap-1402	301	4	,	,	PUNCT
ap-1402	301	5	we	we	PRON
ap-1402	301	6	have	have	VERB
ap-1402	301	7	additional	additional	ADJ
ap-1402	301	8	values	value	NOUN
ap-1402	301	9	λ	λ	NOUN
ap-1402	301	10	=	=	PUNCT
ap-1402	301	11	±ελ1	±ελ1	NOUN
ap-1402	301	12	with	with	ADP
ap-1402	301	13	λ1	λ1	PROPN
ap-1402	301	14	∈	∈	PROPN
ap-1402	301	15	c	c	NOUN
ap-1402	301	16	with	with	ADP
ap-1402	301	17	the	the	DET
ap-1402	301	18	corresponding	corresponding	ADJ
ap-1402	301	19	ladder	ladder	NOUN
ap-1402	301	20	operators	operator	NOUN
ap-1402	301	21	l±	l±	VERB
ap-1402	301	22	ε	ε	PROPN
ap-1402	301	23	=	=	SYM
ap-1402	301	24	x̃	x̃	PROPN
ap-1402	301	25	∓	∓	PROPN
ap-1402	301	26	ελ1ỹ	ελ1ỹ	NOUN
ap-1402	302	1	=	=	PUNCT
ap-1402	302	2	−2πiq	−2πiq	NOUN
ap-1402	302	3	−	−	ADP
ap-1402	302	4	εh	εh	ADP
ap-1402	302	5	4πi	4πi	NOUN
ap-1402	302	6	∂p	∂p	PROPN
ap-1402	302	7	±	±	PROPN
ap-1402	302	8	2πελ1ip	2πελ1ip	NOUN
ap-1402	302	9	=	=	PUNCT
ap-1402	302	10	−2πiq	−2πiq	PROPN
ap-1402	302	11	+	+	CCONJ
ap-1402	302	12	εi	εi	INTJ
ap-1402	302	13	(	(	PUNCT
ap-1402	302	14	±2πλ1p	±2πλ1p	ADP
ap-1402	302	15	+	+	CCONJ
ap-1402	302	16	h	h	NOUN
ap-1402	302	17	4π	4π	NUM
ap-1402	302	18	∂p	∂p	NUM
ap-1402	302	19	)	)	PUNCT
ap-1402	302	20	.	.	PUNCT
ap-1402	303	1	for	for	ADP
ap-1402	303	2	the	the	DET
ap-1402	303	3	eigenvalue	eigenvalue	PROPN
ap-1402	303	4	μ	μ	PROPN
ap-1402	303	5	=	=	PROPN
ap-1402	303	6	μ0	μ0	PROPN
ap-1402	303	7	+	+	CCONJ
ap-1402	303	8	εμ1	εμ1	NOUN
ap-1402	303	9	with	with	ADP
ap-1402	303	10	μ0	μ0	PROPN
ap-1402	303	11	,	,	PUNCT
ap-1402	303	12	μ1	μ1	PROPN
ap-1402	303	13	∈	∈	PROPN
ap-1402	303	14	c	c	VERB
ap-1402	303	15	the	the	DET
ap-1402	303	16	eigenfunction	eigenfunction	NOUN
ap-1402	303	17	(	(	PUNCT
ap-1402	303	18	42	42	NUM
ap-1402	303	19	)	)	PUNCT
ap-1402	303	20	can	can	AUX
ap-1402	303	21	be	be	AUX
ap-1402	303	22	rewritten	rewrite	VERB
ap-1402	303	23	as	as	ADP
ap-1402	303	24	:	:	PUNCT
ap-1402	303	25	vμ(q	vμ(q	ADV
ap-1402	303	26	,	,	PUNCT
ap-1402	303	27	p	p	NOUN
ap-1402	303	28	)	)	PUNCT
ap-1402	304	1	=	=	VERB
ap-1402	304	2	eμp	eμp	ADJ
ap-1402	304	3	/	/	SYM
ap-1402	304	4	qf(q	qf(q	NUM
ap-1402	304	5	)	)	PUNCT
ap-1402	305	1	=	=	SYM
ap-1402	305	2	eμ0p	eμ0p	PROPN
ap-1402	305	3	/	/	SYM
ap-1402	305	4	q	q	PROPN
ap-1402	305	5	(	(	PUNCT
ap-1402	305	6	1	1	NUM
ap-1402	306	1	+	+	CCONJ
ap-1402	306	2	εμ1	εμ1	NOUN
ap-1402	306	3	p	p	X
ap-1402	306	4	q	q	PROPN
ap-1402	306	5	)	)	PUNCT
ap-1402	306	6	f(q	f(q	PROPN
ap-1402	306	7	)	)	PUNCT
ap-1402	306	8	(	(	PUNCT
ap-1402	306	9	43	43	NUM
ap-1402	306	10	)	)	PUNCT
ap-1402	306	11	due	due	ADP
ap-1402	306	12	to	to	ADP
ap-1402	306	13	the	the	DET
ap-1402	306	14	nilpotency	nilpotency	NOUN
ap-1402	306	15	of	of	ADP
ap-1402	306	16	ε	ε	PROPN
ap-1402	306	17	.	.	PUNCT
ap-1402	307	1	then	then	ADV
ap-1402	307	2	the	the	DET
ap-1402	307	3	ladder	ladder	NOUN
ap-1402	307	4	action	action	NOUN
ap-1402	307	5	of	of	ADP
ap-1402	307	6	l±	l±	PROPN
ap-1402	307	7	ε	ε	PROPN
ap-1402	307	8	is	be	AUX
ap-1402	307	9	μ0	μ0	PROPN
ap-1402	307	10	+	+	CCONJ
ap-1402	307	11	εμ1	εμ1	NOUN
ap-1402	307	12	�	�	PROPN
ap-1402	307	13	→	→	SYM
ap-1402	307	14	μ0	μ0	PROPN
ap-1402	307	15	+	+	CCONJ
ap-1402	307	16	ε(μ1	ε(μ1	X
ap-1402	307	17	±	±	NUM
ap-1402	307	18	λ1	λ1	PROPN
ap-1402	307	19	)	)	PUNCT
ap-1402	307	20	.	.	PUNCT
ap-1402	308	1	therefore	therefore	ADV
ap-1402	308	2	,	,	PUNCT
ap-1402	308	3	these	these	DET
ap-1402	308	4	operators	operator	NOUN
ap-1402	308	5	are	be	AUX
ap-1402	308	6	suitable	suitable	ADJ
ap-1402	308	7	for	for	ADP
ap-1402	308	8	building	build	VERB
ap-1402	308	9	sp2	sp2	NOUN
ap-1402	308	10	-	-	PUNCT
ap-1402	308	11	modules	module	NOUN
ap-1402	308	12	with	with	ADP
ap-1402	308	13	a	a	DET
ap-1402	308	14	one	one	NUM
ap-1402	308	15	-	-	PUNCT
ap-1402	308	16	dimensional	dimensional	ADJ
ap-1402	308	17	chain	chain	NOUN
ap-1402	308	18	of	of	ADP
ap-1402	308	19	eigenvalues	eigenvalue	NOUN
ap-1402	308	20	.	.	PUNCT
ap-1402	309	1	finally	finally	ADV
ap-1402	309	2	,	,	PUNCT
ap-1402	309	3	consider	consider	VERB
ap-1402	309	4	the	the	DET
ap-1402	309	5	ladder	ladder	NOUN
ap-1402	309	6	operator	operator	NOUN
ap-1402	309	7	for	for	ADP
ap-1402	309	8	the	the	DET
ap-1402	309	9	same	same	ADJ
ap-1402	309	10	element	element	NOUN
ap-1402	309	11	b	b	PROPN
ap-1402	309	12	+	+	NOUN
ap-1402	309	13	z/2	z/2	NUM
ap-1402	309	14	within	within	ADP
ap-1402	309	15	the	the	DET
ap-1402	309	16	lie	lie	NOUN
ap-1402	309	17	algebra	algebra	NOUN
ap-1402	309	18	sp2	sp2	NOUN
ap-1402	309	19	.	.	PUNCT
ap-1402	310	1	according	accord	VERB
ap-1402	310	2	to	to	ADP
ap-1402	310	3	the	the	DET
ap-1402	310	4	above	above	ADJ
ap-1402	310	5	procedure	procedure	NOUN
ap-1402	310	6	we	we	PRON
ap-1402	310	7	get	get	VERB
ap-1402	310	8	the	the	DET
ap-1402	310	9	equations	equation	NOUN
ap-1402	310	10	:	:	PUNCT
ap-1402	310	11	−b	−b	X
ap-1402	310	12	+	+	NOUN
ap-1402	310	13	2c	2c	NUM
ap-1402	310	14	=	=	SYM
ap-1402	310	15	λa	λa	NOUN
ap-1402	310	16	,	,	PUNCT
ap-1402	310	17	a	a	DET
ap-1402	310	18	=	=	SYM
ap-1402	310	19	λb	λb	PROPN
ap-1402	310	20	,	,	PUNCT
ap-1402	310	21	a	a	DET
ap-1402	310	22	2	2	NUM
ap-1402	310	23	=	=	SYM
ap-1402	310	24	λc	λc	NOUN
ap-1402	310	25	,	,	PUNCT
ap-1402	310	26	which	which	PRON
ap-1402	310	27	can	can	AUX
ap-1402	310	28	again	again	ADV
ap-1402	310	29	be	be	AUX
ap-1402	310	30	resolved	resolve	VERB
ap-1402	310	31	if	if	SCONJ
ap-1402	310	32	and	and	CCONJ
ap-1402	310	33	only	only	ADV
ap-1402	310	34	if	if	SCONJ
ap-1402	310	35	λ2	λ2	NOUN
ap-1402	310	36	=	=	SYM
ap-1402	310	37	0	0	X
ap-1402	310	38	.	.	PUNCT
ap-1402	311	1	there	there	PRON
ap-1402	311	2	is	be	VERB
ap-1402	311	3	the	the	DET
ap-1402	311	4	only	only	ADJ
ap-1402	311	5	complex	complex	ADJ
ap-1402	311	6	root	root	NOUN
ap-1402	311	7	λ	λ	NOUN
ap-1402	311	8	=	=	NOUN
ap-1402	311	9	0	0	NUM
ap-1402	311	10	with	with	SCONJ
ap-1402	311	11	the	the	DET
ap-1402	311	12	corresponding	correspond	VERB
ap-1402	311	13	operators	operator	NOUN
ap-1402	311	14	l±	l±	VERB
ap-1402	311	15	p	p	PROPN
ap-1402	311	16	=	=	PROPN
ap-1402	311	17	b̃+z̃/2	b̃+z̃/2	NOUN
ap-1402	311	18	,	,	PUNCT
ap-1402	311	19	which	which	PRON
ap-1402	311	20	does	do	AUX
ap-1402	311	21	not	not	PART
ap-1402	311	22	affect	affect	VERB
ap-1402	311	23	the	the	DET
ap-1402	311	24	eigenvalues	eigenvalue	NOUN
ap-1402	311	25	.	.	PUNCT
ap-1402	312	1	however	however	ADV
ap-1402	312	2	the	the	DET
ap-1402	312	3	dual	dual	ADJ
ap-1402	312	4	number	number	NOUN
ap-1402	312	5	roots	root	NOUN
ap-1402	312	6	λ	λ	NOUN
ap-1402	312	7	=	=	SYM
ap-1402	312	8	±ελ2	±ελ2	VERB
ap-1402	312	9	with	with	ADP
ap-1402	312	10	λ2	λ2	PROPN
ap-1402	312	11	∈	∈	PROPN
ap-1402	312	12	c	c	NOUN
ap-1402	312	13	lead	lead	NOUN
ap-1402	312	14	to	to	ADP
ap-1402	312	15	the	the	DET
ap-1402	312	16	operators	operator	NOUN
ap-1402	312	17	l±	l±	VERB
ap-1402	312	18	ε	ε	PROPN
ap-1402	312	19	=	=	SYM
ap-1402	312	20	±ελ2ã	±ελ2ã	PROPN
ap-1402	313	1	+	+	CCONJ
ap-1402	313	2	b̃	b̃	PROPN
ap-1402	313	3	+	+	CCONJ
ap-1402	313	4	z̃/2	z̃/2	PROPN
ap-1402	313	5	=	=	SYM
ap-1402	313	6	±ελ2	±ελ2	X
ap-1402	313	7	2	2	NUM
ap-1402	313	8	(	(	PUNCT
ap-1402	313	9	q∂q	q∂q	NOUN
ap-1402	313	10	−	−	PROPN
ap-1402	313	11	p∂p	p∂p	NOUN
ap-1402	313	12	)	)	PUNCT
ap-1402	314	1	+	+	CCONJ
ap-1402	314	2	q∂p	q∂p	NOUN
ap-1402	314	3	.	.	PUNCT
ap-1402	314	4	6	6	NUM
ap-1402	314	5	conclusions	conclusion	NOUN
ap-1402	314	6	:	:	PUNCT
ap-1402	314	7	similarity	similarity	NOUN
ap-1402	314	8	and	and	CCONJ
ap-1402	314	9	correspondence	correspondence	NOUN
ap-1402	314	10	we	we	PRON
ap-1402	314	11	wish	wish	VERB
ap-1402	314	12	to	to	PART
ap-1402	314	13	summarise	summarise	VERB
ap-1402	314	14	our	our	PRON
ap-1402	314	15	findings	finding	NOUN
ap-1402	314	16	.	.	PUNCT
ap-1402	315	1	firstly	firstly	ADV
ap-1402	315	2	,	,	PUNCT
ap-1402	315	3	the	the	DET
ap-1402	315	4	appearance	appearance	NOUN
ap-1402	315	5	of	of	ADP
ap-1402	315	6	hypercomplex	hypercomplex	ADJ
ap-1402	315	7	numbers	number	NOUN
ap-1402	315	8	in	in	ADP
ap-1402	315	9	ladder	ladder	NOUN
ap-1402	315	10	operators	operator	NOUN
ap-1402	315	11	for	for	ADP
ap-1402	315	12	h1	h1	PROPN
ap-1402	315	13	follows	follow	VERB
ap-1402	315	14	exactly	exactly	ADV
ap-1402	315	15	the	the	DET
ap-1402	315	16	same	same	ADJ
ap-1402	315	17	pattern	pattern	NOUN
ap-1402	315	18	as	as	SCONJ
ap-1402	315	19	was	be	AUX
ap-1402	315	20	already	already	ADV
ap-1402	315	21	noted	note	VERB
ap-1402	315	22	for	for	ADP
ap-1402	315	23	sp2	sp2	NOUN
ap-1402	315	24	[	[	X
ap-1402	315	25	23	23	NUM
ap-1402	315	26	,	,	PUNCT
ap-1402	315	27	rem	rem	X
ap-1402	315	28	.	.	NOUN
ap-1402	315	29	32	32	NUM
ap-1402	315	30	]	]	PUNCT
ap-1402	315	31	:	:	PUNCT
ap-1402	315	32	•	•	ADP
ap-1402	315	33	the	the	DET
ap-1402	315	34	introduction	introduction	NOUN
ap-1402	315	35	of	of	ADP
ap-1402	315	36	complex	complex	ADJ
ap-1402	315	37	numbers	number	NOUN
ap-1402	315	38	is	be	AUX
ap-1402	315	39	a	a	DET
ap-1402	315	40	necessity	necessity	NOUN
ap-1402	315	41	for	for	ADP
ap-1402	315	42	the	the	DET
ap-1402	315	43	existence	existence	NOUN
ap-1402	315	44	of	of	ADP
ap-1402	315	45	ladder	ladder	NOUN
ap-1402	315	46	operators	operator	NOUN
ap-1402	315	47	in	in	ADP
ap-1402	315	48	the	the	DET
ap-1402	315	49	elliptic	elliptic	ADJ
ap-1402	315	50	case	case	NOUN
ap-1402	315	51	;	;	PUNCT
ap-1402	315	52	•	•	X
ap-1402	315	53	in	in	ADP
ap-1402	315	54	the	the	DET
ap-1402	315	55	parabolic	parabolic	NOUN
ap-1402	315	56	case	case	NOUN
ap-1402	315	57	,	,	PUNCT
ap-1402	315	58	we	we	PRON
ap-1402	315	59	need	need	VERB
ap-1402	315	60	dual	dual	ADJ
ap-1402	315	61	numbers	number	NOUN
ap-1402	315	62	to	to	PART
ap-1402	315	63	make	make	VERB
ap-1402	315	64	ladder	ladder	NOUN
ap-1402	315	65	operators	operator	NOUN
ap-1402	315	66	useful	useful	ADJ
ap-1402	315	67	;	;	PUNCT
ap-1402	315	68	•	•	ADP
ap-1402	315	69	in	in	ADP
ap-1402	315	70	the	the	DET
ap-1402	315	71	hyperbolic	hyperbolic	ADJ
ap-1402	315	72	case	case	NOUN
ap-1402	315	73	,	,	PUNCT
ap-1402	315	74	double	double	ADJ
ap-1402	315	75	numbers	number	NOUN
ap-1402	315	76	are	be	AUX
ap-1402	315	77	not	not	PART
ap-1402	315	78	required	require	VERB
ap-1402	315	79	neither	neither	CCONJ
ap-1402	315	80	for	for	ADP
ap-1402	315	81	the	the	DET
ap-1402	315	82	existence	existence	NOUN
ap-1402	315	83	or	or	CCONJ
ap-1402	315	84	for	for	ADP
ap-1402	315	85	the	the	DET
ap-1402	315	86	usability	usability	NOUN
ap-1402	315	87	of	of	ADP
ap-1402	315	88	ladder	ladder	NOUN
ap-1402	315	89	operators	operator	NOUN
ap-1402	315	90	,	,	PUNCT
ap-1402	315	91	but	but	CCONJ
ap-1402	315	92	they	they	PRON
ap-1402	315	93	do	do	AUX
ap-1402	315	94	provide	provide	VERB
ap-1402	315	95	an	an	DET
ap-1402	315	96	enhancement	enhancement	NOUN
ap-1402	315	97	.	.	PUNCT
ap-1402	316	1	in	in	ADP
ap-1402	316	2	the	the	DET
ap-1402	316	3	spirit	spirit	NOUN
ap-1402	316	4	of	of	ADP
ap-1402	316	5	the	the	DET
ap-1402	316	6	similarity	similarity	NOUN
ap-1402	316	7	and	and	CCONJ
ap-1402	316	8	correspondence	correspondence	NOUN
ap-1402	316	9	principle	principle	NOUN
ap-1402	316	10	we	we	PRON
ap-1402	316	11	have	have	VERB
ap-1402	316	12	the	the	DET
ap-1402	316	13	following	following	ADJ
ap-1402	316	14	extension	extension	NOUN
ap-1402	316	15	of	of	ADP
ap-1402	316	16	prop	prop	NOUN
ap-1402	316	17	.	.	PUNCT
ap-1402	317	1	33	33	NUM
ap-1402	317	2	from	from	ADP
ap-1402	317	3	[	[	X
ap-1402	317	4	23	23	NUM
ap-1402	317	5	]	]	PUNCT
ap-1402	317	6	:	:	PUNCT
ap-1402	317	7	proposition	proposition	NOUN
ap-1402	317	8	let	let	VERB
ap-1402	317	9	a	a	DET
ap-1402	317	10	vector	vector	NOUN
ap-1402	317	11	h	h	NOUN
ap-1402	317	12	∈	∈	NOUN
ap-1402	317	13	sp2	sp2	NOUN
ap-1402	317	14	generate	generate	VERB
ap-1402	317	15	the	the	DET
ap-1402	317	16	subgroup	subgroup	NOUN
ap-1402	317	17	k	k	PROPN
ap-1402	317	18	,	,	PUNCT
ap-1402	317	19	n	n	PRON
ap-1402	317	20	′	′	NUM
ap-1402	317	21	or	or	CCONJ
ap-1402	317	22	a′	a′	PROPN
ap-1402	317	23	,	,	PUNCT
ap-1402	317	24	that	that	PRON
ap-1402	317	25	is	be	AUX
ap-1402	317	26	h	h	NOUN
ap-1402	317	27	=	=	SYM
ap-1402	317	28	z	z	PROPN
ap-1402	317	29	,	,	PUNCT
ap-1402	317	30	b	b	PROPN
ap-1402	317	31	+	+	NOUN
ap-1402	317	32	z/2	z/2	NUM
ap-1402	317	33	,	,	PUNCT
ap-1402	317	34	or	or	CCONJ
ap-1402	317	35	2b	2b	NOUN
ap-1402	317	36	,	,	PUNCT
ap-1402	317	37	respectively	respectively	ADV
ap-1402	317	38	.	.	PUNCT
ap-1402	318	1	let	let	VERB
ap-1402	318	2	ι	ι	PRON
ap-1402	318	3	be	be	AUX
ap-1402	318	4	the	the	DET
ap-1402	318	5	respective	respective	ADJ
ap-1402	318	6	hypercomplex	hypercomplex	NOUN
ap-1402	318	7	unit	unit	NOUN
ap-1402	318	8	.	.	PUNCT
ap-1402	319	1	then	then	ADV
ap-1402	319	2	the	the	DET
ap-1402	319	3	ladder	ladder	NOUN
ap-1402	319	4	operators	operator	NOUN
ap-1402	319	5	l±	l±	AUX
ap-1402	319	6	satisfying	satisfy	VERB
ap-1402	319	7	the	the	DET
ap-1402	319	8	commutation	commutation	NOUN
ap-1402	319	9	relation	relation	NOUN
ap-1402	319	10	:	:	PUNCT
ap-1402	320	1	[	[	X
ap-1402	320	2	h	h	NOUN
ap-1402	320	3	,	,	PUNCT
ap-1402	320	4	l±	l±	X
ap-1402	320	5	2	2	NUM
ap-1402	320	6	]	]	PUNCT
ap-1402	320	7	=	=	X
ap-1402	320	8	±ιl±	±ιl±	NOUN
ap-1402	320	9	are	be	AUX
ap-1402	320	10	given	give	VERB
ap-1402	320	11	by	by	ADP
ap-1402	320	12	:	:	PUNCT
ap-1402	320	13	1	1	NUM
ap-1402	320	14	.	.	X
ap-1402	321	1	within	within	ADP
ap-1402	321	2	the	the	DET
ap-1402	321	3	lie	lie	NOUN
ap-1402	321	4	algebra	algebra	PROPN
ap-1402	321	5	h1	h1	PROPN
ap-1402	321	6	:	:	PUNCT
ap-1402	321	7	l±	l±	PROPN
ap-1402	321	8	=	=	PUNCT
ap-1402	322	1	x̃	x̃	PROPN
ap-1402	322	2	∓	∓	PROPN
ap-1402	322	3	ιỹ	ιỹ	PUNCT
ap-1402	322	4	.	.	PUNCT
ap-1402	323	1	2	2	X
ap-1402	323	2	.	.	X
ap-1402	323	3	within	within	ADP
ap-1402	323	4	the	the	DET
ap-1402	323	5	lie	lie	NOUN
ap-1402	323	6	algebra	algebra	NOUN
ap-1402	323	7	sp2	sp2	NOUN
ap-1402	323	8	:	:	PUNCT
ap-1402	323	9	l±	l±	NOUN
ap-1402	323	10	2	2	NUM
ap-1402	323	11	=	=	SYM
ap-1402	323	12	±ιã+ẽ.	±ιã+ẽ.	PUNCT
ap-1402	323	13	here	here	ADV
ap-1402	323	14	e	e	X
ap-1402	323	15	∈	∈	PROPN
ap-1402	323	16	sp2	sp2	NOUN
ap-1402	323	17	is	be	AUX
ap-1402	323	18	a	a	DET
ap-1402	323	19	linear	linear	ADJ
ap-1402	323	20	combination	combination	NOUN
ap-1402	323	21	of	of	ADP
ap-1402	323	22	b	b	NOUN
ap-1402	323	23	and	and	CCONJ
ap-1402	323	24	z	z	NOUN
ap-1402	323	25	with	with	ADP
ap-1402	323	26	the	the	DET
ap-1402	323	27	properties	property	NOUN
ap-1402	323	28	:	:	PUNCT
ap-1402	323	29	•	•	NUM
ap-1402	323	30	e	e	X
ap-1402	323	31	=	=	PUNCT
ap-1402	324	1	[	[	X
ap-1402	324	2	a	a	X
ap-1402	324	3	,	,	PUNCT
ap-1402	324	4	h	h	NOUN
ap-1402	324	5	]	]	X
ap-1402	324	6	.	.	PUNCT
ap-1402	325	1	•	•	NUM
ap-1402	325	2	h	h	NOUN
ap-1402	326	1	=	=	PUNCT
ap-1402	327	1	[	[	X
ap-1402	327	2	a	a	X
ap-1402	327	3	,	,	PUNCT
ap-1402	327	4	e	e	NOUN
ap-1402	327	5	]	]	X
ap-1402	327	6	.	.	PUNCT
ap-1402	328	1	•	•	NUM
ap-1402	328	2	killings	killing	NOUN
ap-1402	328	3	form	form	VERB
ap-1402	328	4	k(h	k(h	PROPN
ap-1402	328	5	,	,	PUNCT
ap-1402	328	6	e	e	NOUN
ap-1402	328	7	)	)	PUNCT
ap-1402	329	1	[	[	X
ap-1402	329	2	19	19	NUM
ap-1402	329	3	,	,	PUNCT
ap-1402	329	4	§	§	PROPN
ap-1402	329	5	6.2	6.2	NUM
ap-1402	329	6	]	]	PUNCT
ap-1402	329	7	vanishes	vanish	VERB
ap-1402	329	8	.	.	PUNCT
ap-1402	330	1	any	any	PRON
ap-1402	330	2	of	of	ADP
ap-1402	330	3	the	the	DET
ap-1402	330	4	above	above	ADJ
ap-1402	330	5	properties	property	NOUN
ap-1402	330	6	defines	define	VERB
ap-1402	330	7	the	the	DET
ap-1402	330	8	vector	vector	NOUN
ap-1402	330	9	e	e	PROPN
ap-1402	330	10	∈	∈	PROPN
ap-1402	330	11	span	span	NOUN
ap-1402	330	12	{	{	PUNCT
ap-1402	330	13	b	b	PROPN
ap-1402	330	14	,	,	PUNCT
ap-1402	330	15	z	z	NOUN
ap-1402	330	16	}	}	PUNCT
ap-1402	330	17	up	up	ADP
ap-1402	330	18	to	to	ADP
ap-1402	330	19	a	a	DET
ap-1402	330	20	real	real	ADJ
ap-1402	330	21	constant	constant	ADJ
ap-1402	330	22	factor	factor	NOUN
ap-1402	330	23	.	.	PUNCT
ap-1402	331	1	it	it	PRON
ap-1402	331	2	is	be	AUX
ap-1402	331	3	worth	worth	ADJ
ap-1402	331	4	continuing	continue	VERB
ap-1402	331	5	this	this	DET
ap-1402	331	6	investigation	investigation	NOUN
ap-1402	331	7	and	and	CCONJ
ap-1402	331	8	describing	describe	VERB
ap-1402	331	9	in	in	ADP
ap-1402	331	10	detail	detail	NOUN
ap-1402	331	11	hyperbolic	hyperbolic	ADJ
ap-1402	331	12	and	and	CCONJ
ap-1402	331	13	parabolic	parabolic	ADJ
ap-1402	331	14	versions	version	NOUN
ap-1402	331	15	of	of	ADP
ap-1402	331	16	fsb	fsb	ADJ
ap-1402	331	17	spaces	space	NOUN
ap-1402	331	18	.	.	PUNCT
ap-1402	332	1	acknowledgement	acknowledgement	NOUN
ap-1402	332	2	i	i	PRON
ap-1402	332	3	am	be	AUX
ap-1402	332	4	grateful	grateful	ADJ
ap-1402	332	5	to	to	ADP
ap-1402	332	6	the	the	DET
ap-1402	332	7	anonymous	anonymous	ADJ
ap-1402	332	8	referees	referee	NOUN
ap-1402	332	9	for	for	ADP
ap-1402	332	10	their	their	PRON
ap-1402	332	11	helpful	helpful	ADJ
ap-1402	332	12	remarks	remark	NOUN
ap-1402	332	13	.	.	PUNCT
ap-1402	333	1	references	reference	NOUN
ap-1402	333	2	[	[	X
ap-1402	333	3	1	1	NUM
ap-1402	333	4	]	]	PUNCT
ap-1402	333	5	arnol’d	arnol’d	NOUN
ap-1402	333	6	,	,	PUNCT
ap-1402	333	7	v.	v.	PROPN
ap-1402	333	8	i.	i.	PROPN
ap-1402	333	9	:	:	PUNCT
ap-1402	333	10	mathematical	mathematical	ADJ
ap-1402	333	11	methods	method	NOUN
ap-1402	333	12	of	of	ADP
ap-1402	333	13	classical	classical	ADJ
ap-1402	333	14	mechanics	mechanic	NOUN
ap-1402	333	15	.	.	PUNCT
ap-1402	334	1	graduate	graduate	NOUN
ap-1402	334	2	texts	text	NOUN
ap-1402	334	3	in	in	ADP
ap-1402	334	4	mathematics	mathematic	NOUN
ap-1402	334	5	,	,	PUNCT
ap-1402	334	6	vol	vol	NOUN
ap-1402	334	7	.	.	PROPN
ap-1402	334	8	60	60	NUM
ap-1402	334	9	,	,	PUNCT
ap-1402	334	10	new	new	PROPN
ap-1402	334	11	york	york	PROPN
ap-1402	334	12	:	:	PUNCT
ap-1402	334	13	springer	springer	NOUN
ap-1402	334	14	-	-	PUNCT
ap-1402	334	15	verlag	verlag	PROPN
ap-1402	334	16	,	,	PUNCT
ap-1402	334	17	1991	1991	NUM
ap-1402	334	18	.	.	PUNCT
ap-1402	335	1	translated	translate	VERB
ap-1402	335	2	from	from	ADP
ap-1402	335	3	the	the	DET
ap-1402	335	4	1974	1974	NUM
ap-1402	335	5	russian	russian	ADJ
ap-1402	335	6	original	original	NOUN
ap-1402	335	7	by	by	ADP
ap-1402	335	8	k.	k.	PROPN
ap-1402	335	9	vogtmann	vogtmann	PROPN
ap-1402	335	10	,	,	PUNCT
ap-1402	335	11	a.	a.	PROPN
ap-1402	335	12	weinstein	weinstein	PROPN
ap-1402	335	13	,	,	PUNCT
ap-1402	335	14	corrected	correct	VERB
ap-1402	335	15	reprint	reprint	NOUN
ap-1402	335	16	of	of	ADP
ap-1402	335	17	the	the	DET
ap-1402	335	18	second	second	ADJ
ap-1402	335	19	(	(	PUNCT
ap-1402	335	20	1989	1989	NUM
ap-1402	335	21	)	)	PUNCT
ap-1402	335	22	edition	edition	NOUN
ap-1402	335	23	.	.	PUNCT
ap-1402	336	1	[	[	X
ap-1402	336	2	2	2	NUM
ap-1402	336	3	]	]	PUNCT
ap-1402	336	4	azizov	azizov	PROPN
ap-1402	336	5	,	,	PUNCT
ap-1402	336	6	t.	t.	PROPN
ap-1402	336	7	ja	ja	PROPN
ap-1402	336	8	.	.	PROPN
ap-1402	336	9	,	,	PUNCT
ap-1402	336	10	iohvidov	iohvidov	PROPN
ap-1402	336	11	,	,	PUNCT
ap-1402	336	12	i.	i.	PROPN
ap-1402	336	13	s.	s.	PROPN
ap-1402	336	14	:	:	PUNCT
ap-1402	337	1	linear	linear	PROPN
ap-1402	337	2	operators	operator	NOUN
ap-1402	337	3	in	in	ADP
ap-1402	337	4	hilbert	hilbert	PROPN
ap-1402	337	5	spaces	space	NOUN
ap-1402	337	6	with	with	ADP
ap-1402	337	7	g	g	NOUN
ap-1402	337	8	-	-	PUNCT
ap-1402	337	9	metric	metric	ADJ
ap-1402	337	10	,	,	PUNCT
ap-1402	337	11	uspehi	uspehi	NOUN
ap-1402	337	12	mat	mat	NOUN
ap-1402	337	13	.	.	PUNCT
ap-1402	338	1	nauk	nauk	PROPN
ap-1402	338	2	26	26	NUM
ap-1402	338	3	(	(	PUNCT
ap-1402	338	4	1971	1971	NUM
ap-1402	338	5	)	)	PUNCT
ap-1402	338	6	,	,	PUNCT
ap-1402	338	7	no	no	INTJ
ap-1402	338	8	.	.	NOUN
ap-1402	338	9	4	4	NUM
ap-1402	338	10	(	(	PUNCT
ap-1402	338	11	160	160	NUM
ap-1402	338	12	)	)	PUNCT
ap-1402	338	13	,	,	PUNCT
ap-1402	338	14	43–92	43–92	NUM
ap-1402	338	15	.	.	PUNCT
ap-1402	339	1	[	[	X
ap-1402	339	2	3	3	NUM
ap-1402	339	3	]	]	X
ap-1402	339	4	boyer	boyer	PROPN
ap-1402	339	5	,	,	PUNCT
ap-1402	339	6	ch	ch	NOUN
ap-1402	339	7	.	.	PUNCT
ap-1402	340	1	p.	p.	PROPN
ap-1402	340	2	,	,	PUNCT
ap-1402	340	3	miller	miller	PROPN
ap-1402	340	4	,	,	PUNCT
ap-1402	340	5	w.	w.	PROPN
ap-1402	340	6	,	,	PUNCT
ap-1402	340	7	jr	jr	PROPN
ap-1402	340	8	.	.	PROPN
ap-1402	340	9	:	:	PUNCT
ap-1402	340	10	a	a	DET
ap-1402	340	11	classification	classification	NOUN
ap-1402	340	12	of	of	ADP
ap-1402	340	13	second	second	ADJ
ap-1402	340	14	-	-	PUNCT
ap-1402	340	15	order	order	NOUN
ap-1402	340	16	raising	raise	VERB
ap-1402	340	17	operators	operator	NOUN
ap-1402	340	18	for	for	ADP
ap-1402	340	19	hamiltonians	hamiltonian	NOUN
ap-1402	340	20	in	in	ADP
ap-1402	340	21	two	two	NUM
ap-1402	340	22	variables	variable	NOUN
ap-1402	340	23	,	,	PUNCT
ap-1402	340	24	j.	j.	PROPN
ap-1402	340	25	mathematical	mathematical	PROPN
ap-1402	340	26	phys	phys	PROPN
ap-1402	340	27	.	.	PUNCT
ap-1402	341	1	15	15	NUM
ap-1402	341	2	(	(	PUNCT
ap-1402	341	3	1974	1974	NUM
ap-1402	341	4	)	)	PUNCT
ap-1402	341	5	,	,	PUNCT
ap-1402	341	6	1	1	NUM
ap-1402	341	7	484–1489	484–1489	NUM
ap-1402	341	8	.	.	PUNCT
ap-1402	342	1	[	[	X
ap-1402	342	2	4	4	NUM
ap-1402	342	3	]	]	X
ap-1402	342	4	cnops	cnop	NOUN
ap-1402	342	5	,	,	PUNCT
ap-1402	342	6	j.	j.	PROPN
ap-1402	342	7	,	,	PUNCT
ap-1402	342	8	kisil	kisil	PROPN
ap-1402	342	9	,	,	PUNCT
ap-1402	342	10	v.	v.	PROPN
ap-1402	343	1	v.	v.	ADJ
ap-1402	343	2	:	:	PUNCT
ap-1402	343	3	monogenic	monogenic	ADJ
ap-1402	343	4	functions	function	NOUN
ap-1402	343	5	and	and	CCONJ
ap-1402	343	6	representations	representation	NOUN
ap-1402	343	7	of	of	ADP
ap-1402	343	8	nilpotent	nilpotent	ADJ
ap-1402	343	9	lie	lie	NOUN
ap-1402	343	10	groups	group	NOUN
ap-1402	343	11	in	in	ADP
ap-1402	343	12	quantum	quantum	ADJ
ap-1402	343	13	mechanics	mechanic	NOUN
ap-1402	343	14	,	,	PUNCT
ap-1402	343	15	math	math	NOUN
ap-1402	343	16	.	.	PUNCT
ap-1402	344	1	methods	method	NOUN
ap-1402	344	2	appl	appl	PROPN
ap-1402	344	3	.	.	PUNCT
ap-1402	345	1	sci	sci	PROPN
ap-1402	345	2	.	.	PROPN
ap-1402	346	1	22	22	NUM
ap-1402	346	2	(	(	PUNCT
ap-1402	346	3	1999	1999	NUM
ap-1402	346	4	)	)	PUNCT
ap-1402	346	5	,	,	PUNCT
ap-1402	347	1	no	no	INTJ
ap-1402	347	2	.	.	NOUN
ap-1402	347	3	4	4	NUM
ap-1402	347	4	,	,	PUNCT
ap-1402	347	5	353–373	353–373	NUM
ap-1402	347	6	.	.	PUNCT
ap-1402	348	1	51	51	NUM
ap-1402	348	2	acta	acta	PROPN
ap-1402	348	3	polytechnica	polytechnica	PROPN
ap-1402	348	4	vol	vol	NOUN
ap-1402	348	5	.	.	PUNCT
ap-1402	348	6	51	51	NUM
ap-1402	348	7	no	no	INTJ
ap-1402	348	8	.	.	PUNCT
ap-1402	349	1	4/2011	4/2011	NUM
ap-1402	350	1	[	[	X
ap-1402	350	2	5	5	NUM
ap-1402	350	3	]	]	PUNCT
ap-1402	350	4	constales	constale	NOUN
ap-1402	350	5	,	,	PUNCT
ap-1402	350	6	d.	d.	PROPN
ap-1402	350	7	,	,	PUNCT
ap-1402	350	8	faustino	faustino	PROPN
ap-1402	350	9	,	,	PUNCT
ap-1402	350	10	n.	n.	NOUN
ap-1402	350	11	,	,	PUNCT
ap-1402	350	12	kraußhar	kraußhar	NOUN
ap-1402	350	13	,	,	PUNCT
ap-1402	350	14	r.	r.	PROPN
ap-1402	350	15	:	:	PUNCT
ap-1402	350	16	fock	fock	ADJ
ap-1402	350	17	spaces	space	NOUN
ap-1402	350	18	,	,	PUNCT
ap-1402	350	19	landau	landau	NOUN
ap-1402	350	20	operators	operator	NOUN
ap-1402	350	21	and	and	CCONJ
ap-1402	350	22	the	the	DET
ap-1402	350	23	time	time	NOUN
ap-1402	350	24	-	-	PUNCT
ap-1402	350	25	harmonic	harmonic	ADJ
ap-1402	350	26	maxwell	maxwell	PROPN
ap-1402	350	27	equations	equation	NOUN
ap-1402	350	28	,	,	PUNCT
ap-1402	350	29	journal	journal	NOUN
ap-1402	350	30	of	of	ADP
ap-1402	350	31	physics	physics	PROPN
ap-1402	350	32	a	a	PRON
ap-1402	350	33	:	:	PUNCT
ap-1402	350	34	mathematical	mathematical	ADJ
ap-1402	350	35	and	and	CCONJ
ap-1402	350	36	theoretical	theoretical	ADJ
ap-1402	350	37	44	44	NUM
ap-1402	350	38	(	(	PUNCT
ap-1402	350	39	2011	2011	NUM
ap-1402	350	40	)	)	PUNCT
ap-1402	350	41	,	,	PUNCT
ap-1402	350	42	no	no	INTJ
ap-1402	350	43	.	.	NOUN
ap-1402	350	44	13	13	NUM
ap-1402	350	45	,	,	PUNCT
ap-1402	350	46	135	135	NUM
ap-1402	350	47	303	303	NUM
ap-1402	350	48	.	.	PUNCT
ap-1402	351	1	[	[	X
ap-1402	351	2	6	6	NUM
ap-1402	351	3	]	]	SYM
ap-1402	351	4	de	de	PROPN
ap-1402	351	5	gosson	gosson	PROPN
ap-1402	351	6	,	,	PUNCT
ap-1402	351	7	maurice	maurice	PROPN
ap-1402	351	8	a.	a.	PROPN
ap-1402	351	9	:	:	PUNCT
ap-1402	351	10	spectral	spectral	ADJ
ap-1402	351	11	properties	property	NOUN
ap-1402	351	12	of	of	ADP
ap-1402	351	13	a	a	DET
ap-1402	351	14	class	class	NOUN
ap-1402	351	15	of	of	ADP
ap-1402	351	16	generalized	generalized	ADJ
ap-1402	351	17	landau	landau	NOUN
ap-1402	351	18	operators	operator	NOUN
ap-1402	351	19	,	,	PUNCT
ap-1402	351	20	comm	comm	NOUN
ap-1402	351	21	.	.	PUNCT
ap-1402	352	1	partial	partial	ADJ
ap-1402	352	2	differential	differential	ADJ
ap-1402	352	3	equations	equation	NOUN
ap-1402	352	4	33	33	NUM
ap-1402	352	5	(	(	PUNCT
ap-1402	352	6	2008	2008	NUM
ap-1402	352	7	)	)	PUNCT
ap-1402	352	8	,	,	PUNCT
ap-1402	352	9	no	no	INTJ
ap-1402	352	10	.	.	PUNCT
ap-1402	352	11	10–12	10–12	NUM
ap-1402	352	12	,	,	PUNCT
ap-1402	352	13	2	2	NUM
ap-1402	352	14	096–2	096–2	PRON
ap-1402	352	15	104	104	NUM
ap-1402	352	16	.	.	PUNCT
ap-1402	353	1	[	[	X
ap-1402	353	2	7	7	X
ap-1402	353	3	]	]	SYM
ap-1402	353	4	erdélyi	erdélyi	PROPN
ap-1402	353	5	,	,	PUNCT
ap-1402	353	6	a.	a.	NOUN
ap-1402	353	7	,	,	PUNCT
ap-1402	353	8	magnus	magnus	PROPN
ap-1402	353	9	,	,	PUNCT
ap-1402	353	10	w.	w.	PROPN
ap-1402	353	11	,	,	PUNCT
ap-1402	353	12	oberhettinger	oberhettinger	PROPN
ap-1402	353	13	,	,	PUNCT
ap-1402	353	14	f.	f.	PROPN
ap-1402	353	15	,	,	PUNCT
ap-1402	353	16	tricomi	tricomi	NOUN
ap-1402	353	17	,	,	PUNCT
ap-1402	353	18	f.	f.	PROPN
ap-1402	353	19	g.	g.	PROPN
ap-1402	353	20	:	:	PUNCT
ap-1402	353	21	higher	high	ADJ
ap-1402	353	22	transcendental	transcendental	ADJ
ap-1402	353	23	functions	function	NOUN
ap-1402	353	24	.	.	PUNCT
ap-1402	354	1	vol	vol	NOUN
ap-1402	354	2	.	.	PUNCT
ap-1402	354	3	ii	ii	PROPN
ap-1402	354	4	.	.	PUNCT
ap-1402	355	1	melbourne	melbourne	PROPN
ap-1402	355	2	:	:	PUNCT
ap-1402	355	3	robert	robert	PROPN
ap-1402	355	4	e.	e.	PROPN
ap-1402	355	5	krieger	krieger	PROPN
ap-1402	355	6	publishing	publishing	PROPN
ap-1402	355	7	co.	co.	PROPN
ap-1402	355	8	inc	inc	PROPN
ap-1402	355	9	.	.	PROPN
ap-1402	355	10	,	,	PUNCT
ap-1402	355	11	fla	fla	PROPN
ap-1402	355	12	.	.	PROPN
ap-1402	355	13	,	,	PUNCT
ap-1402	355	14	1981	1981	NUM
ap-1402	355	15	.	.	PUNCT
ap-1402	356	1	based	base	VERB
ap-1402	356	2	on	on	ADP
ap-1402	356	3	notes	note	NOUN
ap-1402	356	4	left	leave	VERB
ap-1402	356	5	by	by	ADP
ap-1402	356	6	harry	harry	PROPN
ap-1402	356	7	bateman	bateman	PROPN
ap-1402	356	8	,	,	PUNCT
ap-1402	356	9	reprint	reprint	NOUN
ap-1402	356	10	of	of	ADP
ap-1402	356	11	the	the	DET
ap-1402	356	12	1953	1953	NUM
ap-1402	356	13	original	original	NOUN
ap-1402	356	14	.	.	PUNCT
ap-1402	357	1	[	[	X
ap-1402	357	2	8	8	NUM
ap-1402	357	3	]	]	X
ap-1402	357	4	folland	folland	NOUN
ap-1402	357	5	,	,	PUNCT
ap-1402	357	6	g.	g.	PROPN
ap-1402	357	7	b.	b.	PROPN
ap-1402	357	8	:	:	PUNCT
ap-1402	357	9	harmonic	harmonic	VERB
ap-1402	357	10	analysis	analysis	NOUN
ap-1402	357	11	in	in	ADP
ap-1402	357	12	phase	phase	NOUN
ap-1402	357	13	space	space	NOUN
ap-1402	357	14	.	.	PUNCT
ap-1402	358	1	annals	annal	VERB
ap-1402	358	2	ofmathematics	ofmathematic	NOUN
ap-1402	358	3	studies	study	NOUN
ap-1402	358	4	,	,	PUNCT
ap-1402	358	5	vol	vol	NOUN
ap-1402	358	6	.	.	PROPN
ap-1402	358	7	122	122	NUM
ap-1402	358	8	,	,	PUNCT
ap-1402	358	9	princeton	princeton	PROPN
ap-1402	358	10	:	:	PUNCT
ap-1402	358	11	princeton	princeton	PROPN
ap-1402	358	12	university	university	PROPN
ap-1402	358	13	press	press	PROPN
ap-1402	358	14	,	,	PUNCT
ap-1402	358	15	nj	nj	PROPN
ap-1402	358	16	,	,	PUNCT
ap-1402	358	17	1989	1989	NUM
ap-1402	358	18	.	.	PUNCT
ap-1402	359	1	[	[	X
ap-1402	359	2	9	9	NUM
ap-1402	359	3	]	]	X
ap-1402	359	4	gazeau	gazeau	NOUN
ap-1402	359	5	,	,	PUNCT
ap-1402	359	6	j.-p	j.-p	PROPN
ap-1402	359	7	.	.	PUNCT
ap-1402	359	8	:	:	PUNCT
ap-1402	360	1	coherent	coherent	ADJ
ap-1402	360	2	states	state	NOUN
ap-1402	360	3	in	in	ADP
ap-1402	360	4	quantum	quantum	ADJ
ap-1402	360	5	physics	physics	NOUN
ap-1402	360	6	.	.	PUNCT
ap-1402	361	1	wiley	wiley	PROPN
ap-1402	361	2	-	-	PUNCT
ap-1402	361	3	vch	vch	PROPN
ap-1402	361	4	verlag	verlag	PROPN
ap-1402	361	5	,	,	PUNCT
ap-1402	361	6	2009	2009	NUM
ap-1402	361	7	.	.	PUNCT
ap-1402	362	1	[	[	X
ap-1402	362	2	10	10	NUM
ap-1402	362	3	]	]	X
ap-1402	362	4	günther	günther	PROPN
ap-1402	362	5	,	,	PUNCT
ap-1402	362	6	u.	u.	PROPN
ap-1402	362	7	,	,	PUNCT
ap-1402	362	8	kuzhel	kuzhel	PROPN
ap-1402	362	9	,	,	PUNCT
ap-1402	362	10	s.	s.	PROPN
ap-1402	362	11	:	:	PUNCT
ap-1402	362	12	pt	pt	PROPN
ap-1402	362	13	-symmetry	-symmetry	PROPN
ap-1402	362	14	,	,	PUNCT
ap-1402	362	15	cartan	cartan	ADJ
ap-1402	362	16	decompositions	decomposition	NOUN
ap-1402	362	17	,	,	PUNCT
ap-1402	362	18	lie	lie	VERB
ap-1402	362	19	triple	triple	ADJ
ap-1402	362	20	systems	system	NOUN
ap-1402	362	21	and	and	CCONJ
ap-1402	362	22	krein	krein	ADJ
ap-1402	362	23	space	space	NOUN
ap-1402	362	24	-	-	PUNCT
ap-1402	362	25	related	relate	VERB
ap-1402	362	26	clifford	clifford	PROPN
ap-1402	362	27	algebras	algebras	PROPN
ap-1402	362	28	,	,	PUNCT
ap-1402	362	29	journal	journal	NOUN
ap-1402	362	30	of	of	ADP
ap-1402	362	31	physics	physics	PROPN
ap-1402	362	32	a	a	PRON
ap-1402	362	33	:	:	PUNCT
ap-1402	362	34	mathematical	mathematical	ADJ
ap-1402	362	35	and	and	CCONJ
ap-1402	362	36	theoretical	theoretical	ADJ
ap-1402	362	37	43	43	NUM
ap-1402	362	38	(	(	PUNCT
ap-1402	362	39	2010	2010	NUM
ap-1402	362	40	)	)	PUNCT
ap-1402	362	41	,	,	PUNCT
ap-1402	362	42	no	no	INTJ
ap-1402	362	43	.	.	NOUN
ap-1402	362	44	39	39	NUM
ap-1402	362	45	,	,	PUNCT
ap-1402	362	46	392	392	NUM
ap-1402	362	47	002	002	NUM
ap-1402	362	48	.	.	PUNCT
ap-1402	363	1	[	[	X
ap-1402	363	2	11	11	NUM
ap-1402	363	3	]	]	PUNCT
ap-1402	363	4	howe	howe	NOUN
ap-1402	363	5	,	,	PUNCT
ap-1402	363	6	r.	r.	PROPN
ap-1402	363	7	:	:	PUNCT
ap-1402	363	8	roger	roger	PROPN
ap-1402	363	9	howe	howe	PROPN
ap-1402	363	10	,	,	PUNCT
ap-1402	363	11	on	on	ADP
ap-1402	363	12	the	the	DET
ap-1402	363	13	role	role	NOUN
ap-1402	363	14	of	of	ADP
ap-1402	363	15	the	the	DET
ap-1402	363	16	heisenberg	heisenberg	PROPN
ap-1402	363	17	group	group	NOUN
ap-1402	363	18	in	in	ADP
ap-1402	363	19	harmonic	harmonic	ADJ
ap-1402	363	20	analysis	analysis	NOUN
ap-1402	363	21	,	,	PUNCT
ap-1402	363	22	bull	bull	NOUN
ap-1402	363	23	.	.	PUNCT
ap-1402	363	24	amer.math	amer.math	PROPN
ap-1402	363	25	.	.	PUNCT
ap-1402	363	26	soc	soc	PROPN
ap-1402	363	27	.	.	PUNCT
ap-1402	364	1	(	(	PUNCT
ap-1402	364	2	n.s	n.s	PROPN
ap-1402	364	3	.	.	PROPN
ap-1402	364	4	)	)	PUNCT
ap-1402	364	5	3	3	NUM
ap-1402	364	6	(	(	PUNCT
ap-1402	364	7	1980	1980	NUM
ap-1402	364	8	)	)	PUNCT
ap-1402	364	9	,	,	PUNCT
ap-1402	364	10	no	no	INTJ
ap-1402	364	11	.	.	NOUN
ap-1402	364	12	2	2	NUM
ap-1402	364	13	,	,	PUNCT
ap-1402	364	14	821–843	821–843	NUM
ap-1402	364	15	.	.	PUNCT
ap-1402	365	1	[	[	X
ap-1402	365	2	12	12	NUM
ap-1402	365	3	]	]	PUNCT
ap-1402	365	4	howe	howe	NOUN
ap-1402	365	5	,	,	PUNCT
ap-1402	365	6	r.	r.	PROPN
ap-1402	365	7	:	:	PUNCT
ap-1402	365	8	quantum	quantum	ADJ
ap-1402	365	9	mechanics	mechanic	NOUN
ap-1402	365	10	and	and	CCONJ
ap-1402	365	11	partial	partial	ADJ
ap-1402	365	12	differential	differential	NOUN
ap-1402	365	13	equations	equation	NOUN
ap-1402	365	14	,	,	PUNCT
ap-1402	365	15	j.	j.	PROPN
ap-1402	365	16	funct	funct	PROPN
ap-1402	365	17	.	.	PUNCT
ap-1402	366	1	anal	anal	PROPN
ap-1402	366	2	.	.	PUNCT
ap-1402	367	1	38	38	NUM
ap-1402	367	2	(	(	PUNCT
ap-1402	367	3	1980	1980	NUM
ap-1402	367	4	)	)	PUNCT
ap-1402	367	5	,	,	PUNCT
ap-1402	367	6	no	no	INTJ
ap-1402	367	7	.	.	NOUN
ap-1402	367	8	2	2	NUM
ap-1402	367	9	,	,	PUNCT
ap-1402	367	10	188–254	188–254	NUM
ap-1402	367	11	.	.	PUNCT
ap-1402	368	1	[	[	X
ap-1402	368	2	13	13	NUM
ap-1402	368	3	]	]	PUNCT
ap-1402	368	4	howe	howe	NOUN
ap-1402	368	5	,	,	PUNCT
ap-1402	368	6	r.	r.	PROPN
ap-1402	368	7	,	,	PUNCT
ap-1402	368	8	tan	tan	PROPN
ap-1402	368	9	,	,	PUNCT
ap-1402	368	10	e.	e.	PROPN
ap-1402	368	11	ch	ch	PROPN
ap-1402	368	12	.	.	PUNCT
ap-1402	368	13	:	:	PUNCT
ap-1402	368	14	non	non	ADJ
ap-1402	368	15	-	-	ADJ
ap-1402	368	16	abelian	abelian	ADJ
ap-1402	368	17	harmonic	harmonic	ADJ
ap-1402	368	18	analysis	analysis	NOUN
ap-1402	368	19	:	:	PUNCT
ap-1402	368	20	applications	application	NOUN
ap-1402	368	21	of	of	ADP
ap-1402	368	22	sl(2,r	sl(2,r	NOUN
ap-1402	368	23	)	)	PUNCT
ap-1402	368	24	.	.	PUNCT
ap-1402	369	1	new	new	PROPN
ap-1402	369	2	york	york	PROPN
ap-1402	369	3	:	:	PUNCT
ap-1402	369	4	universitext	universitext	PROPN
ap-1402	369	5	,	,	PUNCT
ap-1402	369	6	springer	springer	NOUN
ap-1402	369	7	-	-	PUNCT
ap-1402	369	8	verlag	verlag	PROPN
ap-1402	369	9	,	,	PUNCT
ap-1402	369	10	1992	1992	NUM
ap-1402	369	11	.	.	PUNCT
ap-1402	370	1	[	[	X
ap-1402	370	2	14	14	NUM
ap-1402	370	3	]	]	X
ap-1402	370	4	hudson	hudson	PROPN
ap-1402	370	5	,	,	PUNCT
ap-1402	370	6	r.	r.	PROPN
ap-1402	370	7	:	:	PUNCT
ap-1402	370	8	generalised	generalise	VERB
ap-1402	370	9	translation	translation	NOUN
ap-1402	370	10	-	-	PUNCT
ap-1402	370	11	invariant	invariant	ADJ
ap-1402	370	12	mechanics	mechanic	NOUN
ap-1402	370	13	.	.	PUNCT
ap-1402	370	14	d.	d.	PROPN
ap-1402	370	15	phil	phil	PROPN
ap-1402	370	16	.	.	PUNCT
ap-1402	371	1	thesis	thesis	NOUN
ap-1402	371	2	,	,	PUNCT
ap-1402	371	3	oxford	oxford	PROPN
ap-1402	371	4	:	:	PUNCT
ap-1402	371	5	bodleian	bodleian	ADJ
ap-1402	371	6	library	library	NOUN
ap-1402	371	7	,	,	PUNCT
ap-1402	371	8	1966	1966	NUM
ap-1402	371	9	.	.	PUNCT
ap-1402	372	1	[	[	X
ap-1402	372	2	15	15	NUM
ap-1402	372	3	]	]	X
ap-1402	372	4	hudson	hudson	PROPN
ap-1402	372	5	,	,	PUNCT
ap-1402	372	6	r.	r.	PROPN
ap-1402	372	7	:	:	PUNCT
ap-1402	372	8	translation	translation	NOUN
ap-1402	372	9	invariant	invariant	ADJ
ap-1402	372	10	phase	phase	NOUN
ap-1402	372	11	space	space	NOUN
ap-1402	372	12	mechanics	mechanic	NOUN
ap-1402	372	13	,	,	PUNCT
ap-1402	372	14	quantum	quantum	ADJ
ap-1402	372	15	theory	theory	NOUN
ap-1402	372	16	:	:	PUNCT
ap-1402	372	17	reconsideration	reconsideration	NOUN
ap-1402	372	18	of	of	ADP
ap-1402	372	19	foundations	foundation	NOUN
ap-1402	372	20	–	–	PUNCT
ap-1402	372	21	2	2	NUM
ap-1402	372	22	,	,	PUNCT
ap-1402	372	23	2004	2004	NUM
ap-1402	372	24	,	,	PUNCT
ap-1402	372	25	pp	pp	ADP
ap-1402	372	26	.	.	PUNCT
ap-1402	373	1	301–314	301–314	NUM
ap-1402	373	2	.	.	PUNCT
ap-1402	374	1	[	[	X
ap-1402	374	2	16	16	NUM
ap-1402	374	3	]	]	X
ap-1402	374	4	khrennikov	khrennikov	PROPN
ap-1402	374	5	,	,	PUNCT
ap-1402	374	6	a.	a.	PROPN
ap-1402	374	7	yu	yu	PROPN
ap-1402	374	8	.	.	PUNCT
ap-1402	374	9	:	:	PUNCT
ap-1402	374	10	hyperbolic	hyperbolic	ADJ
ap-1402	374	11	quantum	quantum	NOUN
ap-1402	374	12	mechanics	mechanic	NOUN
ap-1402	374	13	,	,	PUNCT
ap-1402	374	14	dokl	dokl	NOUN
ap-1402	374	15	.	.	PUNCT
ap-1402	375	1	akad	akad	PROPN
ap-1402	375	2	.	.	PUNCT
ap-1402	376	1	nauk	nauk	VERB
ap-1402	376	2	402	402	NUM
ap-1402	376	3	(	(	PUNCT
ap-1402	376	4	2005	2005	NUM
ap-1402	376	5	)	)	PUNCT
ap-1402	376	6	,	,	PUNCT
ap-1402	376	7	no	no	INTJ
ap-1402	376	8	.	.	NOUN
ap-1402	376	9	2	2	NUM
ap-1402	376	10	,	,	PUNCT
ap-1402	376	11	170–172	170–172	NUM
ap-1402	376	12	.	.	PUNCT
ap-1402	377	1	[	[	X
ap-1402	377	2	17	17	NUM
ap-1402	377	3	]	]	X
ap-1402	377	4	khrennikov	khrennikov	PROPN
ap-1402	377	5	,	,	PUNCT
ap-1402	377	6	a.	a.	NOUN
ap-1402	377	7	:	:	PUNCT
ap-1402	377	8	hyperbolic	hyperbolic	ADJ
ap-1402	377	9	quantum	quantum	NOUN
ap-1402	377	10	mechanics	mechanic	NOUN
ap-1402	377	11	,	,	PUNCT
ap-1402	377	12	adv	adv	PROPN
ap-1402	377	13	.	.	PUNCT
ap-1402	377	14	appl	appl	PROPN
ap-1402	377	15	.	.	PUNCT
ap-1402	378	1	clifford	clifford	PROPN
ap-1402	378	2	algebr	algebr	PROPN
ap-1402	378	3	.	.	PUNCT
ap-1402	379	1	13	13	NUM
ap-1402	379	2	(	(	PUNCT
ap-1402	379	3	2003	2003	NUM
ap-1402	379	4	)	)	PUNCT
ap-1402	379	5	,	,	PUNCT
ap-1402	379	6	no	no	INTJ
ap-1402	379	7	.	.	NOUN
ap-1402	379	8	1	1	NUM
ap-1402	379	9	,	,	PUNCT
ap-1402	379	10	1–9	1–9	NUM
ap-1402	379	11	(	(	PUNCT
ap-1402	379	12	english	english	PROPN
ap-1402	379	13	)	)	PUNCT
ap-1402	379	14	.	.	PUNCT
ap-1402	380	1	[	[	X
ap-1402	380	2	18	18	NUM
ap-1402	380	3	]	]	X
ap-1402	380	4	khrennikov	khrennikov	PROPN
ap-1402	380	5	,	,	PUNCT
ap-1402	380	6	a.	a.	NOUN
ap-1402	380	7	:	:	PUNCT
ap-1402	380	8	hyperbolic	hyperbolic	ADJ
ap-1402	380	9	quantization	quantization	NOUN
ap-1402	380	10	,	,	PUNCT
ap-1402	380	11	adv	adv	PROPN
ap-1402	380	12	.	.	PUNCT
ap-1402	380	13	appl	appl	PROPN
ap-1402	380	14	.	.	PUNCT
ap-1402	381	1	clifford	clifford	PROPN
ap-1402	381	2	algebr	algebr	PROPN
ap-1402	381	3	.	.	PUNCT
ap-1402	382	1	18	18	NUM
ap-1402	382	2	(	(	PUNCT
ap-1402	382	3	2008	2008	NUM
ap-1402	382	4	)	)	PUNCT
ap-1402	382	5	,	,	PUNCT
ap-1402	382	6	no	no	INTJ
ap-1402	382	7	.	.	PUNCT
ap-1402	383	1	3–4	3–4	NUM
ap-1402	383	2	,	,	PUNCT
ap-1402	383	3	843–852	843–852	NUM
ap-1402	383	4	.	.	PUNCT
ap-1402	384	1	[	[	X
ap-1402	384	2	19	19	NUM
ap-1402	384	3	]	]	PUNCT
ap-1402	384	4	kirillov	kirillov	NOUN
ap-1402	384	5	,	,	PUNCT
ap-1402	384	6	a.	a.	NOUN
ap-1402	384	7	a.	a.	NOUN
ap-1402	384	8	:	:	PUNCT
ap-1402	384	9	elements	element	NOUN
ap-1402	384	10	of	of	ADP
ap-1402	384	11	the	the	DET
ap-1402	384	12	theory	theory	NOUN
ap-1402	384	13	of	of	ADP
ap-1402	384	14	representations	representation	NOUN
ap-1402	384	15	.	.	PUNCT
ap-1402	385	1	berlin	berlin	PROPN
ap-1402	385	2	:	:	PUNCT
ap-1402	385	3	springer	springer	NOUN
ap-1402	385	4	-	-	PUNCT
ap-1402	385	5	verlag	verlag	PROPN
ap-1402	385	6	,	,	PUNCT
ap-1402	385	7	1976	1976	NUM
ap-1402	385	8	.	.	PUNCT
ap-1402	386	1	translated	translate	VERB
ap-1402	386	2	from	from	ADP
ap-1402	386	3	the	the	DET
ap-1402	386	4	russian	russian	NOUN
ap-1402	386	5	by	by	ADP
ap-1402	386	6	edwin	edwin	PROPN
ap-1402	386	7	hewitt	hewitt	PROPN
ap-1402	386	8	,	,	PUNCT
ap-1402	386	9	grundlehren	grundlehren	PROPN
ap-1402	386	10	der	der	PROPN
ap-1402	386	11	mathematischenwissenschaften	mathematischenwissenschaften	VERB
ap-1402	386	12	,	,	PUNCT
ap-1402	386	13	band	band	NOUN
ap-1402	386	14	220	220	NUM
ap-1402	386	15	.	.	PUNCT
ap-1402	387	1	[	[	X
ap-1402	387	2	20	20	NUM
ap-1402	387	3	]	]	X
ap-1402	387	4	kisil	kisil	NOUN
ap-1402	387	5	,	,	PUNCT
ap-1402	387	6	v.	v.	PROPN
ap-1402	388	1	v.	v.	ADP
ap-1402	388	2	:	:	PUNCT
ap-1402	389	1	clifford	clifford	PROPN
ap-1402	389	2	valued	value	VERB
ap-1402	389	3	convolution	convolution	NOUN
ap-1402	389	4	operator	operator	NOUN
ap-1402	389	5	algebras	algebra	NOUN
ap-1402	389	6	on	on	ADP
ap-1402	389	7	the	the	DET
ap-1402	389	8	heisenberg	heisenberg	PROPN
ap-1402	389	9	group	group	NOUN
ap-1402	389	10	.	.	PUNCT
ap-1402	390	1	a	a	DET
ap-1402	390	2	quantum	quantum	ADJ
ap-1402	390	3	field	field	NOUN
ap-1402	390	4	theory	theory	NOUN
ap-1402	390	5	model	model	NOUN
ap-1402	390	6	.	.	PUNCT
ap-1402	391	1	clifford	clifford	PROPN
ap-1402	391	2	algebras	algebras	PROPN
ap-1402	391	3	and	and	CCONJ
ap-1402	391	4	their	their	PRON
ap-1402	391	5	applications	application	NOUN
ap-1402	391	6	in	in	ADP
ap-1402	391	7	mathematical	mathematical	ADJ
ap-1402	391	8	physics	physics	NOUN
ap-1402	391	9	,	,	PUNCT
ap-1402	391	10	proceedings	proceeding	NOUN
ap-1402	391	11	of	of	ADP
ap-1402	391	12	the	the	DET
ap-1402	391	13	third	third	ADJ
ap-1402	391	14	international	international	ADJ
ap-1402	391	15	conference	conference	NOUN
ap-1402	391	16	held	hold	VERB
ap-1402	391	17	in	in	ADP
ap-1402	391	18	deinze	deinze	NOUN
ap-1402	391	19	,	,	PUNCT
ap-1402	391	20	1993	1993	NUM
ap-1402	391	21	,	,	PUNCT
ap-1402	391	22	pp	pp	ADJ
ap-1402	391	23	.	.	PUNCT
ap-1402	392	1	287–294	287–294	NUM
ap-1402	392	2	.	.	PUNCT
ap-1402	393	1	[	[	X
ap-1402	393	2	21	21	NUM
ap-1402	393	3	]	]	X
ap-1402	393	4	kisil	kisil	NOUN
ap-1402	393	5	,	,	PUNCT
ap-1402	393	6	v.	v.	PROPN
ap-1402	394	1	v.	v.	NOUN
ap-1402	394	2	:	:	PUNCT
ap-1402	394	3	analysis	analysis	NOUN
ap-1402	394	4	in	in	ADP
ap-1402	394	5	r1,1	r1,1	NOUN
ap-1402	394	6	or	or	CCONJ
ap-1402	394	7	the	the	DET
ap-1402	394	8	principal	principal	ADJ
ap-1402	394	9	function	function	NOUN
ap-1402	394	10	theory	theory	NOUN
ap-1402	394	11	,	,	PUNCT
ap-1402	394	12	complex	complex	ADJ
ap-1402	394	13	variables	variable	NOUN
ap-1402	394	14	theory	theory	NOUN
ap-1402	394	15	appl	appl	NOUN
ap-1402	394	16	.	.	PUNCT
ap-1402	395	1	40	40	NUM
ap-1402	395	2	(	(	PUNCT
ap-1402	395	3	1999	1999	NUM
ap-1402	395	4	)	)	PUNCT
ap-1402	395	5	,	,	PUNCT
ap-1402	395	6	no	no	INTJ
ap-1402	395	7	.	.	NOUN
ap-1402	395	8	2	2	NUM
ap-1402	395	9	,	,	PUNCT
ap-1402	395	10	93–118	93–118	NUM
ap-1402	395	11	.	.	PUNCT
ap-1402	396	1	[	[	X
ap-1402	396	2	22	22	NUM
ap-1402	396	3	]	]	X
ap-1402	396	4	kisil	kisil	NOUN
ap-1402	396	5	,	,	PUNCT
ap-1402	396	6	v.	v.	PROPN
ap-1402	397	1	v.	v.	ADP
ap-1402	397	2	:	:	PUNCT
ap-1402	397	3	a	a	DET
ap-1402	397	4	quantum	quantum	ADJ
ap-1402	397	5	-	-	ADJ
ap-1402	397	6	classical	classical	ADJ
ap-1402	397	7	bracket	bracket	NOUN
ap-1402	397	8	from	from	ADP
ap-1402	397	9	p	p	NOUN
ap-1402	397	10	-	-	PUNCT
ap-1402	397	11	mechanics	mechanic	NOUN
ap-1402	397	12	,	,	PUNCT
ap-1402	397	13	europhys	europhy	NOUN
ap-1402	397	14	.	.	PUNCT
ap-1402	398	1	lett	lett	PROPN
ap-1402	398	2	.	.	PUNCT
ap-1402	399	1	72	72	NUM
ap-1402	399	2	(	(	PUNCT
ap-1402	399	3	2005	2005	NUM
ap-1402	399	4	)	)	PUNCT
ap-1402	399	5	,	,	PUNCT
ap-1402	399	6	no	no	INTJ
ap-1402	399	7	.	.	NOUN
ap-1402	399	8	6	6	NUM
ap-1402	399	9	,	,	PUNCT
ap-1402	399	10	873–879	873–879	NUM
ap-1402	399	11	.	.	PUNCT
ap-1402	400	1	[	[	X
ap-1402	400	2	23	23	NUM
ap-1402	400	3	]	]	X
ap-1402	400	4	kisil	kisil	NOUN
ap-1402	400	5	,	,	PUNCT
ap-1402	400	6	v.	v.	PROPN
ap-1402	401	1	v.	v.	ADJ
ap-1402	401	2	:	:	PUNCT
ap-1402	401	3	erlangen	erlangen	PROPN
ap-1402	401	4	program	program	PROPN
ap-1402	401	5	at	at	ADP
ap-1402	401	6	large	large	ADJ
ap-1402	401	7	–	–	PUNCT
ap-1402	401	8	2	2	NUM
ap-1402	401	9	1/2	1/2	NUM
ap-1402	401	10	:	:	PUNCT
ap-1402	401	11	induced	induce	VERB
ap-1402	401	12	representations	representation	NOUN
ap-1402	401	13	and	and	CCONJ
ap-1402	401	14	hypercomplex	hypercomplex	NOUN
ap-1402	401	15	numbers	number	NOUN
ap-1402	401	16	,	,	PUNCT
ap-1402	401	17	submitted	submit	VERB
ap-1402	401	18	(	(	PUNCT
ap-1402	401	19	2009	2009	NUM
ap-1402	401	20	)	)	PUNCT
ap-1402	401	21	.	.	PUNCT
ap-1402	402	1	[	[	X
ap-1402	402	2	24	24	NUM
ap-1402	402	3	]	]	PUNCT
ap-1402	402	4	kisil	kisil	NOUN
ap-1402	402	5	,	,	PUNCT
ap-1402	402	6	v.	v.	PROPN
ap-1402	402	7	v.	v.	NOUN
ap-1402	402	8	:	:	PUNCT
ap-1402	402	9	computation	computation	NOUN
ap-1402	402	10	and	and	CCONJ
ap-1402	402	11	dynamics	dynamic	NOUN
ap-1402	402	12	:	:	PUNCT
ap-1402	402	13	classical	classical	ADJ
ap-1402	402	14	and	and	CCONJ
ap-1402	402	15	quantum	quantum	NOUN
ap-1402	402	16	,	,	PUNCT
ap-1402	402	17	aip	aip	PROPN
ap-1402	402	18	conference	conference	NOUN
ap-1402	402	19	proceedings	proceeding	NOUN
ap-1402	402	20	1	1	NUM
ap-1402	402	21	232	232	NUM
ap-1402	402	22	(	(	PUNCT
ap-1402	402	23	2010	2010	NUM
ap-1402	402	24	)	)	PUNCT
ap-1402	402	25	,	,	PUNCT
ap-1402	402	26	no	no	INTJ
ap-1402	402	27	.	.	NOUN
ap-1402	402	28	1	1	NUM
ap-1402	402	29	,	,	PUNCT
ap-1402	402	30	306–312	306–312	NUM
ap-1402	402	31	.	.	PUNCT
ap-1402	403	1	[	[	X
ap-1402	403	2	25	25	NUM
ap-1402	403	3	]	]	PUNCT
ap-1402	403	4	kisil	kisil	NOUN
ap-1402	403	5	,	,	PUNCT
ap-1402	403	6	v.	v.	PROPN
ap-1402	404	1	v.	v.	ADJ
ap-1402	404	2	:	:	PUNCT
ap-1402	404	3	erlangen	erlangen	PROPN
ap-1402	404	4	programme	programme	PROPN
ap-1402	404	5	at	at	ADP
ap-1402	404	6	large	large	ADJ
ap-1402	404	7	3.1	3.1	NUM
ap-1402	404	8	:	:	PUNCT
ap-1402	404	9	hypercomplex	hypercomplex	ADJ
ap-1402	404	10	representations	representation	NOUN
ap-1402	404	11	of	of	ADP
ap-1402	404	12	the	the	DET
ap-1402	404	13	heisenberg	heisenberg	PROPN
ap-1402	404	14	group	group	NOUN
ap-1402	404	15	and	and	CCONJ
ap-1402	404	16	mechanics	mechanic	NOUN
ap-1402	404	17	,	,	PUNCT
ap-1402	404	18	submitted	submit	VERB
ap-1402	404	19	(	(	PUNCT
ap-1402	404	20	2010	2010	NUM
ap-1402	404	21	)	)	PUNCT
ap-1402	404	22	.	.	PUNCT
ap-1402	405	1	[	[	X
ap-1402	405	2	26	26	NUM
ap-1402	405	3	]	]	X
ap-1402	405	4	kisil	kisil	NOUN
ap-1402	405	5	,	,	PUNCT
ap-1402	405	6	v.	v.	PROPN
ap-1402	406	1	v.	v.	ADJ
ap-1402	406	2	:	:	PUNCT
ap-1402	406	3	covariant	covariant	ADJ
ap-1402	406	4	transform	transform	NOUN
ap-1402	406	5	,	,	PUNCT
ap-1402	406	6	journal	journal	NOUN
ap-1402	406	7	of	of	ADP
ap-1402	406	8	physics	physics	PROPN
ap-1402	406	9	:	:	PUNCT
ap-1402	406	10	conference	conference	NOUN
ap-1402	406	11	series	series	NOUN
ap-1402	406	12	,	,	PUNCT
ap-1402	406	13	284	284	NUM
ap-1402	406	14	(	(	PUNCT
ap-1402	406	15	2011	2011	NUM
ap-1402	406	16	)	)	PUNCT
ap-1402	406	17	,	,	PUNCT
ap-1402	406	18	no	no	INTJ
ap-1402	406	19	.	.	NOUN
ap-1402	406	20	1	1	NUM
ap-1402	406	21	,	,	PUNCT
ap-1402	406	22	pp	pp	ADJ
ap-1402	406	23	.	.	PUNCT
ap-1402	407	1	9	9	X
ap-1402	407	2	.	.	PUNCT
ap-1402	408	1	[	[	X
ap-1402	408	2	27	27	NUM
ap-1402	408	3	]	]	X
ap-1402	408	4	kisil	kisil	NOUN
ap-1402	408	5	,	,	PUNCT
ap-1402	408	6	v.	v.	NOUN
ap-1402	408	7	v.	v.	CCONJ
ap-1402	408	8	erlangen	erlangen	PROPN
ap-1402	408	9	programme	programme	PROPN
ap-1402	408	10	at	at	ADP
ap-1402	408	11	large	large	ADJ
ap-1402	408	12	:	:	PUNCT
ap-1402	408	13	an	an	DET
ap-1402	408	14	overview	overview	NOUN
ap-1402	408	15	,	,	PUNCT
ap-1402	408	16	rogosin	rogosin	PROPN
ap-1402	408	17	,	,	PUNCT
ap-1402	408	18	s.	s.	PROPN
ap-1402	408	19	v.	v.	PROPN
ap-1402	408	20	,	,	PUNCT
ap-1402	408	21	koroleva	koroleva	PROPN
ap-1402	408	22	,	,	PUNCT
ap-1402	408	23	a.	a.	NOUN
ap-1402	408	24	a.	a.	NOUN
ap-1402	408	25	(	(	PUNCT
ap-1402	408	26	eds	eds	PROPN
ap-1402	408	27	.	.	PROPN
ap-1402	408	28	):	):	PUNCT
ap-1402	408	29	advances	advance	NOUN
ap-1402	408	30	in	in	ADP
ap-1402	408	31	applied	apply	VERB
ap-1402	408	32	analysis	analysis	NOUN
ap-1402	408	33	.	.	PUNCT
ap-1402	409	1	imperial	imperial	ADJ
ap-1402	409	2	college	college	NOUN
ap-1402	409	3	press	press	NOUN
ap-1402	409	4	,	,	PUNCT
ap-1402	409	5	2011	2011	NUM
ap-1402	409	6	,	,	PUNCT
ap-1402	409	7	p.	p.	NOUN
ap-1402	409	8	1–65	1–65	PROPN
ap-1402	409	9	.	.	PUNCT
ap-1402	410	1	[	[	X
ap-1402	410	2	28	28	NUM
ap-1402	410	3	]	]	X
ap-1402	410	4	lang	lang	PROPN
ap-1402	410	5	,	,	PUNCT
ap-1402	410	6	s.	s.	PROPN
ap-1402	410	7	:	:	PUNCT
ap-1402	410	8	sl2(r	sl2(r	PROPN
ap-1402	410	9	)	)	PUNCT
ap-1402	410	10	,	,	PUNCT
ap-1402	410	11	graduate	graduate	NOUN
ap-1402	410	12	texts	text	NOUN
ap-1402	410	13	in	in	ADP
ap-1402	410	14	mathematics	mathematic	NOUN
ap-1402	410	15	.	.	PUNCT
ap-1402	411	1	vol	vol	NOUN
ap-1402	411	2	.	.	PROPN
ap-1402	412	1	105	105	NUM
ap-1402	412	2	,	,	PUNCT
ap-1402	413	1	new	new	PROPN
ap-1402	413	2	york	york	PROPN
ap-1402	413	3	:	:	PUNCT
ap-1402	413	4	springer	springer	NOUN
ap-1402	413	5	-	-	PUNCT
ap-1402	413	6	verlag	verlag	PROPN
ap-1402	413	7	,	,	PUNCT
ap-1402	413	8	1985	1985	NUM
ap-1402	413	9	.	.	PUNCT
ap-1402	414	1	[	[	X
ap-1402	414	2	29	29	NUM
ap-1402	414	3	]	]	PUNCT
ap-1402	414	4	lavrent’ev	lavrent’ev	PROPN
ap-1402	414	5	,	,	PUNCT
ap-1402	414	6	m.	m.	NOUN
ap-1402	414	7	a.	a.	PROPN
ap-1402	414	8	,	,	PUNCT
ap-1402	414	9	shabat	shabat	PROPN
ap-1402	414	10	,	,	PUNCT
ap-1402	414	11	b.	b.	PROPN
ap-1402	415	1	v.	v.	PROPN
ap-1402	415	2	:	:	PUNCT
ap-1402	415	3	problemy	problemy	PROPN
ap-1402	415	4	gidrodinamiki	gidrodinamiki	PROPN
ap-1402	416	1	i	i	PROPN
ap-1402	416	2	ih	ih	PROPN
ap-1402	416	3	matematiqeskie	matematiqeskie	PROPN
ap-1402	416	4	modeli	modeli	PROPN
ap-1402	416	5	.	.	PUNCT
ap-1402	417	1	(	(	PUNCT
ap-1402	417	2	russian	russian	PROPN
ap-1402	417	3	)	)	PUNCT
ap-1402	418	1	[	[	X
ap-1402	418	2	problems	problem	NOUN
ap-1402	418	3	of	of	ADP
ap-1402	418	4	hydrodynamics	hydrodynamic	NOUN
ap-1402	418	5	and	and	CCONJ
ap-1402	418	6	their	their	PRON
ap-1402	418	7	mathematical	mathematical	ADJ
ap-1402	418	8	models	model	NOUN
ap-1402	418	9	]	]	PUNCT
ap-1402	418	10	,	,	PUNCT
ap-1402	418	11	moscow	moscow	PROPN
ap-1402	418	12	:	:	PUNCT
ap-1402	418	13	second	second	ADJ
ap-1402	418	14	,	,	PUNCT
ap-1402	418	15	izdat	izdat	NOUN
ap-1402	418	16	.	.	PUNCT
ap-1402	419	1	“	"	PUNCT
ap-1402	419	2	nauka	nauka	PROPN
ap-1402	419	3	”	"	PUNCT
ap-1402	419	4	,	,	PUNCT
ap-1402	419	5	1977	1977	NUM
ap-1402	419	6	.	.	PUNCT
ap-1402	420	1	[	[	X
ap-1402	420	2	30	30	NUM
ap-1402	420	3	]	]	X
ap-1402	420	4	mazorchuk	mazorchuk	NOUN
ap-1402	420	5	,	,	PUNCT
ap-1402	420	6	v.	v.	CCONJ
ap-1402	420	7	:	:	PUNCT
ap-1402	420	8	lectures	lecture	NOUN
ap-1402	420	9	on	on	ADP
ap-1402	420	10	sl2	sl2	PROPN
ap-1402	420	11	-	-	PUNCT
ap-1402	420	12	modules	module	NOUN
ap-1402	420	13	.	.	PUNCT
ap-1402	421	1	world	world	NOUN
ap-1402	421	2	scientific	scientific	PROPN
ap-1402	421	3	,	,	PUNCT
ap-1402	421	4	2009	2009	NUM
ap-1402	421	5	.	.	PUNCT
ap-1402	422	1	[	[	X
ap-1402	422	2	31	31	NUM
ap-1402	422	3	]	]	PUNCT
ap-1402	422	4	niederer	niederer	NOUN
ap-1402	422	5	,	,	PUNCT
ap-1402	422	6	u.	u.	PROPN
ap-1402	422	7	:	:	PUNCT
ap-1402	422	8	the	the	DET
ap-1402	422	9	maximal	maximal	ADJ
ap-1402	422	10	kinematical	kinematical	ADJ
ap-1402	422	11	invariance	invariance	NOUN
ap-1402	422	12	group	group	NOUN
ap-1402	422	13	of	of	ADP
ap-1402	422	14	the	the	DET
ap-1402	422	15	free	free	ADJ
ap-1402	422	16	schrödinger	schrödinger	NOUN
ap-1402	422	17	equation	equation	NOUN
ap-1402	422	18	,	,	PUNCT
ap-1402	422	19	helv	helv	PROPN
ap-1402	422	20	.	.	PUNCT
ap-1402	423	1	phys	phy	NOUN
ap-1402	423	2	.	.	PUNCT
ap-1402	424	1	acta	acta	PROPN
ap-1402	424	2	,	,	PUNCT
ap-1402	424	3	vol	vol	NOUN
ap-1402	424	4	.	.	PROPN
ap-1402	425	1	45	45	NUM
ap-1402	425	2	,	,	PUNCT
ap-1402	425	3	1972/1973	1972/1973	NUM
ap-1402	425	4	,	,	PUNCT
ap-1402	425	5	no	no	INTJ
ap-1402	425	6	.	.	NOUN
ap-1402	425	7	5	5	NUM
ap-1402	425	8	,	,	PUNCT
ap-1402	425	9	p.	p.	NOUN
ap-1402	425	10	802–810	802–810	NUM
ap-1402	425	11	.	.	PUNCT
ap-1402	426	1	52	52	NUM
ap-1402	426	2	acta	acta	PROPN
ap-1402	426	3	polytechnica	polytechnica	PROPN
ap-1402	426	4	vol	vol	NOUN
ap-1402	426	5	.	.	PUNCT
ap-1402	426	6	51	51	NUM
ap-1402	426	7	no	no	INTJ
ap-1402	426	8	.	.	PUNCT
ap-1402	426	9	4/2011	4/2011	NUM
ap-1402	427	1	[	[	X
ap-1402	427	2	32	32	NUM
ap-1402	427	3	]	]	PUNCT
ap-1402	427	4	porteous	porteous	NOUN
ap-1402	427	5	,	,	PUNCT
ap-1402	427	6	i.	i.	PROPN
ap-1402	427	7	r.	r.	PROPN
ap-1402	427	8	:	:	PUNCT
ap-1402	427	9	clifford	clifford	PROPN
ap-1402	427	10	algebras	algebras	PROPN
ap-1402	427	11	and	and	CCONJ
ap-1402	427	12	the	the	DET
ap-1402	427	13	classical	classical	ADJ
ap-1402	427	14	groups	group	NOUN
ap-1402	427	15	,	,	PUNCT
ap-1402	427	16	cambridge	cambridge	PROPN
ap-1402	427	17	studies	study	NOUN
ap-1402	427	18	in	in	ADP
ap-1402	427	19	advanced	advanced	ADJ
ap-1402	427	20	mathematics	mathematic	NOUN
ap-1402	427	21	,	,	PUNCT
ap-1402	427	22	cambridge	cambridge	PROPN
ap-1402	427	23	:	:	PUNCT
ap-1402	427	24	cambridge	cambridge	PROPN
ap-1402	427	25	university	university	PROPN
ap-1402	427	26	press	press	NOUN
ap-1402	427	27	,	,	PUNCT
ap-1402	427	28	1995	1995	NUM
ap-1402	427	29	,	,	PUNCT
ap-1402	427	30	vol	vol	NOUN
ap-1402	427	31	.	.	PROPN
ap-1402	427	32	50	50	NUM
ap-1402	427	33	.	.	PUNCT
ap-1402	428	1	[	[	X
ap-1402	428	2	33	33	NUM
ap-1402	428	3	]	]	X
ap-1402	428	4	srivastava	srivastava	PROPN
ap-1402	428	5	,	,	PUNCT
ap-1402	428	6	h.	h.	PROPN
ap-1402	428	7	m.	m.	PROPN
ap-1402	428	8	,	,	PUNCT
ap-1402	428	9	tuan	tuan	PROPN
ap-1402	428	10	,	,	PUNCT
ap-1402	428	11	v.	v.	PROPN
ap-1402	428	12	k.	k.	PROPN
ap-1402	428	13	,	,	PUNCT
ap-1402	428	14	yakubovich	yakubovich	PROPN
ap-1402	428	15	,	,	PUNCT
ap-1402	428	16	s.	s.	PROPN
ap-1402	428	17	b.	b.	PROPN
ap-1402	428	18	:	:	PUNCT
ap-1402	428	19	the	the	DET
ap-1402	428	20	cherry	cherry	NOUN
ap-1402	428	21	transform	transform	NOUN
ap-1402	428	22	and	and	CCONJ
ap-1402	428	23	its	its	PRON
ap-1402	428	24	relationship	relationship	NOUN
ap-1402	428	25	with	with	ADP
ap-1402	428	26	a	a	DET
ap-1402	428	27	singular	singular	ADJ
ap-1402	428	28	sturm	sturm	NOUN
ap-1402	428	29	-	-	PUNCT
ap-1402	428	30	liouville	liouville	NOUN
ap-1402	428	31	problem	problem	NOUN
ap-1402	428	32	,	,	PUNCT
ap-1402	428	33	q.	q.	PROPN
ap-1402	428	34	j.	j.	PROPN
ap-1402	428	35	math	math	PROPN
ap-1402	428	36	.	.	PUNCT
ap-1402	429	1	51	51	NUM
ap-1402	429	2	(	(	PUNCT
ap-1402	429	3	2000	2000	NUM
ap-1402	429	4	)	)	PUNCT
ap-1402	429	5	,	,	PUNCT
ap-1402	429	6	no	no	INTJ
ap-1402	429	7	.	.	NOUN
ap-1402	429	8	3	3	NUM
ap-1402	429	9	,	,	PUNCT
ap-1402	429	10	371–383	371–383	NUM
ap-1402	429	11	.	.	PUNCT
ap-1402	430	1	[	[	X
ap-1402	430	2	34	34	NUM
ap-1402	430	3	]	]	X
ap-1402	430	4	taylor	taylor	PROPN
ap-1402	430	5	,	,	PUNCT
ap-1402	430	6	m.	m.	PROPN
ap-1402	430	7	e.	e.	PROPN
ap-1402	430	8	:	:	PUNCT
ap-1402	430	9	noncommutative	noncommutative	ADJ
ap-1402	430	10	harmonic	harmonic	ADJ
ap-1402	430	11	analysis	analysis	NOUN
ap-1402	430	12	,	,	PUNCT
ap-1402	430	13	mathematical	mathematical	ADJ
ap-1402	430	14	surveys	survey	NOUN
ap-1402	430	15	and	and	CCONJ
ap-1402	430	16	monographs	monograph	NOUN
ap-1402	430	17	.	.	PUNCT
ap-1402	431	1	vol	vol	NOUN
ap-1402	431	2	.	.	PROPN
ap-1402	432	1	22	22	NUM
ap-1402	432	2	,	,	PUNCT
ap-1402	432	3	providence	providence	NOUN
ap-1402	432	4	:	:	PUNCT
ap-1402	432	5	american	american	PROPN
ap-1402	432	6	mathematical	mathematical	PROPN
ap-1402	432	7	society	society	PROPN
ap-1402	432	8	,	,	PUNCT
ap-1402	432	9	ri	ri	PROPN
ap-1402	432	10	,	,	PUNCT
ap-1402	432	11	1986	1986	NUM
ap-1402	432	12	.	.	PUNCT
ap-1402	433	1	[	[	X
ap-1402	433	2	35	35	NUM
ap-1402	433	3	]	]	X
ap-1402	433	4	torre	torre	PROPN
ap-1402	433	5	,	,	PUNCT
ap-1402	433	6	a.	a.	NOUN
ap-1402	433	7	:	:	PUNCT
ap-1402	433	8	a	a	DET
ap-1402	433	9	note	note	NOUN
ap-1402	433	10	on	on	ADP
ap-1402	433	11	the	the	DET
ap-1402	433	12	general	general	ADJ
ap-1402	433	13	solution	solution	NOUN
ap-1402	433	14	of	of	ADP
ap-1402	433	15	the	the	DET
ap-1402	433	16	paraxial	paraxial	ADJ
ap-1402	433	17	wave	wave	NOUN
ap-1402	433	18	equation	equation	NOUN
ap-1402	433	19	:	:	PUNCT
ap-1402	433	20	a	a	DET
ap-1402	433	21	lie	lie	NOUN
ap-1402	433	22	algebra	algebra	NOUN
ap-1402	433	23	view	view	NOUN
ap-1402	433	24	,	,	PUNCT
ap-1402	433	25	journal	journal	NOUN
ap-1402	433	26	of	of	ADP
ap-1402	433	27	optics	optic	NOUN
ap-1402	433	28	a	a	PRON
ap-1402	433	29	:	:	PUNCT
ap-1402	433	30	pure	pure	ADJ
ap-1402	433	31	and	and	CCONJ
ap-1402	433	32	applied	applied	ADJ
ap-1402	433	33	optics	optic	NOUN
ap-1402	433	34	10	10	NUM
ap-1402	433	35	(	(	PUNCT
ap-1402	433	36	2008	2008	NUM
ap-1402	433	37	)	)	PUNCT
ap-1402	433	38	,	,	PUNCT
ap-1402	433	39	no	no	INTJ
ap-1402	433	40	.	.	NOUN
ap-1402	433	41	5	5	NUM
ap-1402	433	42	,	,	PUNCT
ap-1402	433	43	055	055	NUM
ap-1402	433	44	006	006	NUM
ap-1402	433	45	(	(	PUNCT
ap-1402	433	46	14	14	NUM
ap-1402	433	47	pp	pp	NUM
ap-1402	433	48	)	)	PUNCT
ap-1402	433	49	.	.	PUNCT
ap-1402	434	1	[	[	X
ap-1402	434	2	36	36	NUM
ap-1402	434	3	]	]	X
ap-1402	434	4	torre	torre	PROPN
ap-1402	434	5	,	,	PUNCT
ap-1402	434	6	a.	a.	NOUN
ap-1402	434	7	:	:	PUNCT
ap-1402	434	8	linear	linear	ADJ
ap-1402	434	9	and	and	CCONJ
ap-1402	434	10	quadratic	quadratic	ADJ
ap-1402	434	11	exponential	exponential	ADJ
ap-1402	434	12	modulation	modulation	NOUN
ap-1402	434	13	of	of	ADP
ap-1402	434	14	the	the	DET
ap-1402	434	15	solutions	solution	NOUN
ap-1402	434	16	of	of	ADP
ap-1402	434	17	the	the	DET
ap-1402	434	18	paraxial	paraxial	ADJ
ap-1402	434	19	wave	wave	NOUN
ap-1402	434	20	equation	equation	NOUN
ap-1402	434	21	,	,	PUNCT
ap-1402	434	22	journal	journal	NOUN
ap-1402	434	23	of	of	ADP
ap-1402	434	24	optics	optic	NOUN
ap-1402	434	25	a	a	PRON
ap-1402	434	26	:	:	PUNCT
ap-1402	434	27	pure	pure	ADJ
ap-1402	434	28	and	and	CCONJ
ap-1402	434	29	applied	applied	ADJ
ap-1402	434	30	optics	optic	NOUN
ap-1402	434	31	12	12	NUM
ap-1402	434	32	(	(	PUNCT
ap-1402	434	33	2010	2010	NUM
ap-1402	434	34	)	)	PUNCT
ap-1402	434	35	,	,	PUNCT
ap-1402	434	36	no	no	INTJ
ap-1402	434	37	.	.	NOUN
ap-1402	434	38	3	3	NUM
ap-1402	434	39	,	,	PUNCT
ap-1402	434	40	035	035	NUM
ap-1402	434	41	701	701	NUM
ap-1402	434	42	(	(	PUNCT
ap-1402	434	43	11	11	NUM
ap-1402	434	44	pp	pp	NUM
ap-1402	434	45	)	)	PUNCT
ap-1402	434	46	.	.	PUNCT
ap-1402	435	1	[	[	X
ap-1402	435	2	37	37	NUM
ap-1402	435	3	]	]	SYM
ap-1402	435	4	wulfman	wulfman	PROPN
ap-1402	435	5	,	,	PUNCT
ap-1402	435	6	c.	c.	PROPN
ap-1402	435	7	e.	e.	PROPN
ap-1402	435	8	:	:	PUNCT
ap-1402	435	9	dynamical	dynamical	ADJ
ap-1402	435	10	symmetry	symmetry	NOUN
ap-1402	435	11	.	.	PUNCT
ap-1402	436	1	world	world	PROPN
ap-1402	436	2	scientific	scientific	PROPN
ap-1402	436	3	,	,	PUNCT
ap-1402	436	4	2010	2010	NUM
ap-1402	436	5	.	.	PUNCT
ap-1402	437	1	[	[	X
ap-1402	437	2	38	38	NUM
ap-1402	437	3	]	]	PUNCT
ap-1402	437	4	yaglom	yaglom	NOUN
ap-1402	437	5	,	,	PUNCT
ap-1402	437	6	i.	i.	NOUN
ap-1402	437	7	m.	m.	PROPN
ap-1402	437	8	:	:	PUNCT
ap-1402	437	9	a	a	DET
ap-1402	437	10	simple	simple	ADJ
ap-1402	437	11	non	non	ADJ
ap-1402	437	12	-	-	ADJ
ap-1402	437	13	euclidean	euclidean	ADJ
ap-1402	437	14	geometry	geometry	NOUN
ap-1402	437	15	and	and	CCONJ
ap-1402	437	16	its	its	PRON
ap-1402	437	17	physical	physical	ADJ
ap-1402	437	18	basis	basis	NOUN
ap-1402	437	19	.	.	PUNCT
ap-1402	438	1	new	new	PROPN
ap-1402	438	2	york	york	PROPN
ap-1402	438	3	:	:	PUNCT
ap-1402	438	4	springerverlag	springerverlag	PROPN
ap-1402	438	5	,	,	PUNCT
ap-1402	438	6	1979	1979	NUM
ap-1402	438	7	.	.	PUNCT
ap-1402	439	1	an	an	DET
ap-1402	439	2	elementary	elementary	ADJ
ap-1402	439	3	account	account	NOUN
ap-1402	439	4	of	of	ADP
ap-1402	439	5	galilean	galilean	PROPN
ap-1402	439	6	geometry	geometry	NOUN
ap-1402	439	7	and	and	CCONJ
ap-1402	439	8	the	the	DET
ap-1402	439	9	galilean	galilean	PROPN
ap-1402	439	10	principle	principle	NOUN
ap-1402	439	11	of	of	ADP
ap-1402	439	12	relativity	relativity	NOUN
ap-1402	439	13	,	,	PUNCT
ap-1402	439	14	heidelberg	heidelberg	PROPN
ap-1402	439	15	science	science	NOUN
ap-1402	439	16	library	library	NOUN
ap-1402	439	17	,	,	PUNCT
ap-1402	439	18	translated	translate	VERB
ap-1402	439	19	from	from	ADP
ap-1402	439	20	the	the	DET
ap-1402	439	21	russian	russian	NOUN
ap-1402	439	22	by	by	ADP
ap-1402	439	23	abe	abe	PROPN
ap-1402	439	24	shenitzer	shenitzer	PROPN
ap-1402	439	25	,	,	PUNCT
ap-1402	439	26	with	with	ADP
ap-1402	439	27	the	the	DET
ap-1402	439	28	editorial	editorial	ADJ
ap-1402	439	29	assistance	assistance	NOUN
ap-1402	439	30	of	of	ADP
ap-1402	439	31	basil	basil	PROPN
ap-1402	439	32	gordon	gordon	PROPN
ap-1402	439	33	.	.	PUNCT
ap-1402	440	1	vladimir	vladimir	PROPN
ap-1402	440	2	v.	v.	ADP
ap-1402	440	3	kisil	kisil	PROPN
ap-1402	440	4	e	e	NOUN
ap-1402	440	5	-	-	NOUN
ap-1402	440	6	mail	mail	NOUN
ap-1402	440	7	:	:	PUNCT
ap-1402	440	8	kisilv@maths.leeds.ac.uk	kisilv@maths.leeds.ac.uk	PROPN
ap-1402	440	9	http://www.maths.leeds.ac.uk/∼kisilv/	http://www.maths.leeds.ac.uk/∼kisilv/	X
ap-1402	440	10	school	school	NOUN
ap-1402	440	11	of	of	ADP
ap-1402	440	12	mathematics	mathematics	PROPN
ap-1402	440	13	university	university	PROPN
ap-1402	440	14	of	of	ADP
ap-1402	440	15	leeds	leeds	PROPN
ap-1402	440	16	leeds	leeds	PROPN
ap-1402	440	17	ls2	ls2	PROPN
ap-1402	440	18	9jt	9jt	PROPN
ap-1402	440	19	,	,	PUNCT
ap-1402	440	20	uk	uk	PROPN
ap-1402	440	21	53	53	NUM