id	sid	tid	token	lemma	pos
ap-6650	1	1	acta	acta	PROPN
ap-6650	1	2	polytechnica	polytechnica	PROPN
ap-6650	1	3	https://doi.org/10.14311/ap.2021.61.0230	https://doi.org/10.14311/ap.2021.61.0230	PROPN
ap-6650	1	4	acta	acta	PROPN
ap-6650	1	5	polytechnica	polytechnica	PROPN
ap-6650	1	6	61(1):230–241	61(1):230–241	PROPN
ap-6650	1	7	,	,	PUNCT
ap-6650	1	8	2021	2021	NUM
ap-6650	1	9	©	©	ADP
ap-6650	1	10	2021	2021	NUM
ap-6650	1	11	the	the	DET
ap-6650	1	12	author(s	author(s	NOUN
ap-6650	1	13	)	)	PUNCT
ap-6650	1	14	.	.	PUNCT
ap-6650	2	1	licensed	license	VERB
ap-6650	2	2	under	under	ADP
ap-6650	2	3	a	a	DET
ap-6650	2	4	cc	cc	NOUN
ap-6650	2	5	-	-	PUNCT
ap-6650	2	6	by	by	ADP
ap-6650	2	7	4.0	4.0	NUM
ap-6650	2	8	licence	licence	NOUN
ap-6650	2	9	published	publish	VERB
ap-6650	2	10	by	by	ADP
ap-6650	2	11	the	the	DET
ap-6650	2	12	czech	czech	PROPN
ap-6650	2	13	technical	technical	PROPN
ap-6650	2	14	university	university	PROPN
ap-6650	2	15	in	in	ADP
ap-6650	2	16	prague	prague	PROPN
ap-6650	2	17	on	on	ADP
ap-6650	2	18	the	the	DET
ap-6650	2	19	three	three	NUM
ap-6650	2	20	-	-	PUNCT
ap-6650	2	21	dimensional	dimensional	ADJ
ap-6650	2	22	pauli	pauli	PROPN
ap-6650	2	23	equation	equation	NOUN
ap-6650	2	24	in	in	ADP
ap-6650	2	25	noncommutative	noncommutative	ADJ
ap-6650	2	26	phase	phase	NOUN
ap-6650	2	27	-	-	PUNCT
ap-6650	2	28	space	space	NOUN
ap-6650	2	29	ilyas	ilyas	PROPN
ap-6650	2	30	haouam	haouam	PROPN
ap-6650	2	31	université	université	PROPN
ap-6650	2	32	frères	frère	NOUN
ap-6650	2	33	mentouri	mentouri	PROPN
ap-6650	2	34	,	,	PUNCT
ap-6650	2	35	laboratoire	laboratoire	PROPN
ap-6650	2	36	de	de	X
ap-6650	2	37	physique	physique	PROPN
ap-6650	2	38	mathématique	mathématique	X
ap-6650	2	39	et	et	X
ap-6650	2	40	de	de	X
ap-6650	2	41	physique	physique	PROPN
ap-6650	2	42	subatomique	subatomique	NOUN
ap-6650	2	43	(	(	PUNCT
ap-6650	2	44	lpmps	lpmp	NOUN
ap-6650	2	45	)	)	PUNCT
ap-6650	2	46	,	,	PUNCT
ap-6650	2	47	constantine	constantine	PROPN
ap-6650	2	48	25000	25000	NUM
ap-6650	2	49	,	,	PUNCT
ap-6650	2	50	algeria	algeria	PROPN
ap-6650	2	51	correspondence	correspondence	NOUN
ap-6650	2	52	:	:	PUNCT
ap-6650	2	53	ilyashaouam@live.fr	ilyashaouam@live.fr	PROPN
ap-6650	2	54	abstract	abstract	NOUN
ap-6650	2	55	.	.	PUNCT
ap-6650	3	1	in	in	ADP
ap-6650	3	2	this	this	DET
ap-6650	3	3	paper	paper	NOUN
ap-6650	3	4	,	,	PUNCT
ap-6650	3	5	we	we	PRON
ap-6650	3	6	obtained	obtain	VERB
ap-6650	3	7	the	the	DET
ap-6650	3	8	three	three	NUM
ap-6650	3	9	-	-	PUNCT
ap-6650	3	10	dimensional	dimensional	ADJ
ap-6650	3	11	pauli	pauli	NOUN
ap-6650	3	12	equation	equation	NOUN
ap-6650	3	13	for	for	ADP
ap-6650	3	14	a	a	DET
ap-6650	3	15	spin-1/2	spin-1/2	NOUN
ap-6650	3	16	particle	particle	NOUN
ap-6650	3	17	in	in	ADP
ap-6650	3	18	the	the	DET
ap-6650	3	19	presence	presence	NOUN
ap-6650	3	20	of	of	ADP
ap-6650	3	21	an	an	DET
ap-6650	3	22	electromagnetic	electromagnetic	ADJ
ap-6650	3	23	field	field	NOUN
ap-6650	3	24	in	in	ADP
ap-6650	3	25	a	a	DET
ap-6650	3	26	noncommutative	noncommutative	ADJ
ap-6650	3	27	phase	phase	NOUN
ap-6650	3	28	-	-	PUNCT
ap-6650	3	29	space	space	NOUN
ap-6650	3	30	as	as	ADV
ap-6650	3	31	well	well	ADV
ap-6650	3	32	as	as	ADP
ap-6650	3	33	the	the	DET
ap-6650	3	34	corresponding	corresponding	ADJ
ap-6650	3	35	deformed	deform	VERB
ap-6650	3	36	continuity	continuity	NOUN
ap-6650	3	37	equation	equation	NOUN
ap-6650	3	38	,	,	PUNCT
ap-6650	3	39	where	where	SCONJ
ap-6650	3	40	the	the	DET
ap-6650	3	41	cases	case	NOUN
ap-6650	3	42	of	of	ADP
ap-6650	3	43	a	a	DET
ap-6650	3	44	constant	constant	ADJ
ap-6650	3	45	and	and	CCONJ
ap-6650	3	46	non	non	ADJ
ap-6650	3	47	-	-	ADJ
ap-6650	3	48	constant	constant	ADJ
ap-6650	3	49	magnetic	magnetic	ADJ
ap-6650	3	50	fields	field	NOUN
ap-6650	3	51	are	be	AUX
ap-6650	3	52	considered	consider	VERB
ap-6650	3	53	.	.	PUNCT
ap-6650	4	1	due	due	ADP
ap-6650	4	2	to	to	ADP
ap-6650	4	3	the	the	DET
ap-6650	4	4	absence	absence	NOUN
ap-6650	4	5	of	of	ADP
ap-6650	4	6	the	the	DET
ap-6650	4	7	current	current	ADJ
ap-6650	4	8	magnetization	magnetization	NOUN
ap-6650	4	9	term	term	NOUN
ap-6650	4	10	in	in	ADP
ap-6650	4	11	the	the	DET
ap-6650	4	12	deformed	deform	VERB
ap-6650	4	13	continuity	continuity	NOUN
ap-6650	4	14	equation	equation	NOUN
ap-6650	4	15	as	as	SCONJ
ap-6650	4	16	expected	expect	VERB
ap-6650	4	17	,	,	PUNCT
ap-6650	4	18	we	we	PRON
ap-6650	4	19	had	have	VERB
ap-6650	4	20	to	to	PART
ap-6650	4	21	extract	extract	VERB
ap-6650	4	22	it	it	PRON
ap-6650	4	23	from	from	ADP
ap-6650	4	24	the	the	DET
ap-6650	4	25	noncommutative	noncommutative	PROPN
ap-6650	4	26	pauli	pauli	PROPN
ap-6650	4	27	equation	equation	NOUN
ap-6650	4	28	itself	itself	PRON
ap-6650	4	29	without	without	ADP
ap-6650	4	30	modifying	modify	VERB
ap-6650	4	31	the	the	DET
ap-6650	4	32	continuity	continuity	NOUN
ap-6650	4	33	equation	equation	NOUN
ap-6650	4	34	.	.	PUNCT
ap-6650	5	1	it	it	PRON
ap-6650	5	2	is	be	AUX
ap-6650	5	3	shown	show	VERB
ap-6650	5	4	that	that	SCONJ
ap-6650	5	5	the	the	DET
ap-6650	5	6	non	non	ADJ
ap-6650	5	7	-	-	ADJ
ap-6650	5	8	constant	constant	ADJ
ap-6650	5	9	magnetic	magnetic	ADJ
ap-6650	5	10	field	field	NOUN
ap-6650	5	11	lifts	lift	VERB
ap-6650	5	12	the	the	DET
ap-6650	5	13	order	order	NOUN
ap-6650	5	14	of	of	ADP
ap-6650	5	15	the	the	DET
ap-6650	5	16	noncommutativity	noncommutativity	NOUN
ap-6650	5	17	parameter	parameter	NOUN
ap-6650	5	18	in	in	ADP
ap-6650	5	19	both	both	CCONJ
ap-6650	5	20	the	the	DET
ap-6650	5	21	pauli	pauli	PROPN
ap-6650	5	22	equation	equation	NOUN
ap-6650	5	23	and	and	CCONJ
ap-6650	5	24	the	the	DET
ap-6650	5	25	corresponding	corresponding	ADJ
ap-6650	5	26	continuity	continuity	NOUN
ap-6650	5	27	equation	equation	NOUN
ap-6650	5	28	.	.	PUNCT
ap-6650	6	1	however	however	ADV
ap-6650	6	2	,	,	PUNCT
ap-6650	6	3	we	we	PRON
ap-6650	6	4	successfully	successfully	ADV
ap-6650	6	5	examined	examine	VERB
ap-6650	6	6	the	the	DET
ap-6650	6	7	effect	effect	NOUN
ap-6650	6	8	of	of	ADP
ap-6650	6	9	the	the	DET
ap-6650	6	10	noncommutativity	noncommutativity	NOUN
ap-6650	6	11	on	on	ADP
ap-6650	6	12	the	the	DET
ap-6650	6	13	current	current	ADJ
ap-6650	6	14	density	density	NOUN
ap-6650	6	15	and	and	CCONJ
ap-6650	6	16	the	the	DET
ap-6650	6	17	magnetization	magnetization	NOUN
ap-6650	6	18	current	current	ADJ
ap-6650	6	19	.	.	PUNCT
ap-6650	7	1	by	by	ADP
ap-6650	7	2	using	use	VERB
ap-6650	7	3	a	a	DET
ap-6650	7	4	classical	classical	ADJ
ap-6650	7	5	treatment	treatment	NOUN
ap-6650	7	6	,	,	PUNCT
ap-6650	7	7	we	we	PRON
ap-6650	7	8	derived	derive	VERB
ap-6650	7	9	the	the	DET
ap-6650	7	10	semi	semi	ADJ
ap-6650	7	11	-	-	ADJ
ap-6650	7	12	classical	classical	ADJ
ap-6650	7	13	noncommutative	noncommutative	ADJ
ap-6650	7	14	partition	partition	NOUN
ap-6650	7	15	function	function	NOUN
ap-6650	7	16	of	of	ADP
ap-6650	7	17	the	the	DET
ap-6650	7	18	three	three	NUM
ap-6650	7	19	-	-	PUNCT
ap-6650	7	20	dimensional	dimensional	ADJ
ap-6650	7	21	pauli	pauli	NOUN
ap-6650	7	22	system	system	NOUN
ap-6650	7	23	of	of	ADP
ap-6650	7	24	the	the	DET
ap-6650	7	25	one	one	NUM
ap-6650	7	26	-	-	PUNCT
ap-6650	7	27	particle	particle	NOUN
ap-6650	7	28	and	and	CCONJ
ap-6650	7	29	n	n	CCONJ
ap-6650	7	30	-	-	PUNCT
ap-6650	7	31	particle	particle	NOUN
ap-6650	7	32	systems	system	NOUN
ap-6650	7	33	.	.	PUNCT
ap-6650	8	1	then	then	ADV
ap-6650	8	2	,	,	PUNCT
ap-6650	8	3	we	we	PRON
ap-6650	8	4	employed	employ	VERB
ap-6650	8	5	it	it	PRON
ap-6650	8	6	for	for	ADP
ap-6650	8	7	calculating	calculate	VERB
ap-6650	8	8	the	the	DET
ap-6650	8	9	corresponding	corresponding	ADJ
ap-6650	8	10	helmholtz	helmholtz	NOUN
ap-6650	8	11	free	free	ADJ
ap-6650	8	12	energy	energy	NOUN
ap-6650	8	13	followed	follow	VERB
ap-6650	8	14	by	by	ADP
ap-6650	8	15	the	the	DET
ap-6650	8	16	magnetization	magnetization	NOUN
ap-6650	8	17	and	and	CCONJ
ap-6650	8	18	the	the	DET
ap-6650	8	19	magnetic	magnetic	ADJ
ap-6650	8	20	susceptibility	susceptibility	NOUN
ap-6650	8	21	of	of	ADP
ap-6650	8	22	electrons	electron	NOUN
ap-6650	8	23	in	in	ADP
ap-6650	8	24	both	both	CCONJ
ap-6650	8	25	commutative	commutative	ADJ
ap-6650	8	26	and	and	CCONJ
ap-6650	8	27	noncommutative	noncommutative	ADJ
ap-6650	8	28	phase	phase	NOUN
ap-6650	8	29	-	-	PUNCT
ap-6650	8	30	spaces	space	NOUN
ap-6650	8	31	.	.	PUNCT
ap-6650	9	1	knowing	know	VERB
ap-6650	9	2	that	that	SCONJ
ap-6650	9	3	with	with	ADP
ap-6650	9	4	both	both	CCONJ
ap-6650	9	5	the	the	DET
ap-6650	9	6	three	three	NUM
ap-6650	9	7	-	-	PUNCT
ap-6650	9	8	dimensional	dimensional	ADJ
ap-6650	9	9	bopp	bopp	VERB
ap-6650	9	10	-	-	PUNCT
ap-6650	9	11	shift	shift	NOUN
ap-6650	9	12	transformation	transformation	NOUN
ap-6650	9	13	and	and	CCONJ
ap-6650	9	14	the	the	DET
ap-6650	9	15	moyal	moyal	ADV
ap-6650	9	16	-	-	PUNCT
ap-6650	9	17	weyl	weyl	VERB
ap-6650	9	18	product	product	NOUN
ap-6650	9	19	,	,	PUNCT
ap-6650	9	20	we	we	PRON
ap-6650	9	21	introduced	introduce	VERB
ap-6650	9	22	the	the	DET
ap-6650	9	23	phase	phase	NOUN
ap-6650	9	24	-	-	PUNCT
ap-6650	9	25	space	space	NOUN
ap-6650	9	26	noncommutativity	noncommutativity	NOUN
ap-6650	9	27	in	in	ADP
ap-6650	9	28	the	the	DET
ap-6650	9	29	problems	problem	NOUN
ap-6650	9	30	in	in	ADP
ap-6650	9	31	question	question	NOUN
ap-6650	9	32	.	.	PUNCT
ap-6650	10	1	keywords	keyword	NOUN
ap-6650	10	2	:	:	PUNCT
ap-6650	10	3	3	3	NUM
ap-6650	10	4	-	-	SYM
ap-6650	10	5	d	d	ADP
ap-6650	10	6	noncommutative	noncommutative	ADJ
ap-6650	10	7	phase	phase	NOUN
ap-6650	10	8	-	-	PUNCT
ap-6650	10	9	space	space	NOUN
ap-6650	10	10	,	,	PUNCT
ap-6650	10	11	pauli	pauli	PROPN
ap-6650	10	12	equation	equation	NOUN
ap-6650	10	13	,	,	PUNCT
ap-6650	10	14	deformed	deform	VERB
ap-6650	10	15	continuity	continuity	NOUN
ap-6650	10	16	equation	equation	NOUN
ap-6650	10	17	,	,	PUNCT
ap-6650	10	18	current	current	ADJ
ap-6650	10	19	magnetization	magnetization	NOUN
ap-6650	10	20	,	,	PUNCT
ap-6650	10	21	semi	semi	ADJ
ap-6650	10	22	-	-	ADJ
ap-6650	10	23	classical	classical	ADJ
ap-6650	10	24	partition	partition	NOUN
ap-6650	10	25	function	function	NOUN
ap-6650	10	26	,	,	PUNCT
ap-6650	10	27	magnetic	magnetic	ADJ
ap-6650	10	28	susceptibilit	susceptibilit	VERB
ap-6650	10	29	.	.	PUNCT
ap-6650	11	1	1	1	X
ap-6650	11	2	.	.	X
ap-6650	11	3	introduction	introduction	NOUN
ap-6650	11	4	it	it	PRON
ap-6650	11	5	is	be	AUX
ap-6650	11	6	well	well	ADV
ap-6650	11	7	known	know	VERB
ap-6650	11	8	that	that	SCONJ
ap-6650	11	9	the	the	DET
ap-6650	11	10	dirac	dirac	NOUN
ap-6650	11	11	equation	equation	NOUN
ap-6650	11	12	is	be	AUX
ap-6650	11	13	the	the	DET
ap-6650	11	14	relativistic	relativistic	ADJ
ap-6650	11	15	wave	wave	NOUN
ap-6650	11	16	equation	equation	NOUN
ap-6650	11	17	that	that	PRON
ap-6650	11	18	describes	describe	VERB
ap-6650	11	19	the	the	DET
ap-6650	11	20	motion	motion	NOUN
ap-6650	11	21	of	of	ADP
ap-6650	11	22	the	the	DET
ap-6650	11	23	spin-1/2	spin-1/2	PROPN
ap-6650	11	24	fermions	fermion	NOUN
ap-6650	11	25	and	and	CCONJ
ap-6650	11	26	the	the	DET
ap-6650	11	27	pauli	pauli	PROPN
ap-6650	11	28	equation	equation	NOUN
ap-6650	11	29	,	,	PUNCT
ap-6650	11	30	which	which	PRON
ap-6650	11	31	is	be	AUX
ap-6650	11	32	a	a	DET
ap-6650	11	33	topic	topic	NOUN
ap-6650	11	34	of	of	ADP
ap-6650	11	35	great	great	ADJ
ap-6650	11	36	interest	interest	NOUN
ap-6650	11	37	in	in	ADP
ap-6650	11	38	physics	physics	NOUN
ap-6650	11	39	,	,	PUNCT
ap-6650	11	40	is	be	AUX
ap-6650	11	41	the	the	DET
ap-6650	11	42	non	non	ADJ
ap-6650	11	43	-	-	ADJ
ap-6650	11	44	relativistic	relativistic	ADJ
ap-6650	11	45	wave	wave	NOUN
ap-6650	11	46	equation	equation	NOUN
ap-6650	11	47	describing	describe	VERB
ap-6650	11	48	it	it	PRON
ap-6650	12	1	[	[	X
ap-6650	12	2	1–4	1–4	NOUN
ap-6650	12	3	]	]	X
ap-6650	12	4	.	.	PUNCT
ap-6650	13	1	it	it	PRON
ap-6650	13	2	is	be	AUX
ap-6650	13	3	relative	relative	ADJ
ap-6650	13	4	to	to	ADP
ap-6650	13	5	the	the	DET
ap-6650	13	6	explanation	explanation	NOUN
ap-6650	13	7	of	of	ADP
ap-6650	13	8	many	many	ADJ
ap-6650	13	9	experimental	experimental	ADJ
ap-6650	13	10	results	result	NOUN
ap-6650	13	11	,	,	PUNCT
ap-6650	13	12	and	and	CCONJ
ap-6650	13	13	its	its	PRON
ap-6650	13	14	probability	probability	NOUN
ap-6650	13	15	current	current	ADJ
ap-6650	13	16	density	density	NOUN
ap-6650	13	17	changed	change	VERB
ap-6650	13	18	to	to	PART
ap-6650	13	19	include	include	VERB
ap-6650	13	20	an	an	DET
ap-6650	13	21	additional	additional	ADJ
ap-6650	13	22	spin	spin	NOUN
ap-6650	13	23	-	-	PUNCT
ap-6650	13	24	dependent	dependent	ADJ
ap-6650	13	25	term	term	NOUN
ap-6650	13	26	recognized	recognize	VERB
ap-6650	13	27	as	as	ADP
ap-6650	13	28	the	the	DET
ap-6650	13	29	spin	spin	NOUN
ap-6650	14	1	current	current	ADJ
ap-6650	14	2	[	[	X
ap-6650	14	3	5–7	5–7	NOUN
ap-6650	14	4	]	]	X
ap-6650	14	5	.	.	PUNCT
ap-6650	15	1	pauli	pauli	PROPN
ap-6650	15	2	equation	equation	NOUN
ap-6650	15	3	is	be	AUX
ap-6650	15	4	shown	show	VERB
ap-6650	15	5	in	in	ADP
ap-6650	15	6	[	[	X
ap-6650	15	7	8–12	8–12	NOUN
ap-6650	15	8	]	]	PUNCT
ap-6650	15	9	as	as	ADP
ap-6650	15	10	the	the	DET
ap-6650	15	11	non	non	ADJ
ap-6650	15	12	-	-	ADJ
ap-6650	15	13	relativistic	relativistic	ADJ
ap-6650	15	14	limit	limit	NOUN
ap-6650	15	15	of	of	ADP
ap-6650	15	16	the	the	DET
ap-6650	15	17	dirac	dirac	NOUN
ap-6650	15	18	equation	equation	NOUN
ap-6650	15	19	.	.	PUNCT
ap-6650	16	1	historically	historically	ADV
ap-6650	16	2	,	,	PUNCT
ap-6650	16	3	pauli	pauli	PROPN
ap-6650	16	4	(	(	PUNCT
ap-6650	16	5	1927	1927	NUM
ap-6650	16	6	)	)	PUNCT
ap-6650	16	7	presented	present	VERB
ap-6650	16	8	his	his	PRON
ap-6650	16	9	famous	famous	ADJ
ap-6650	16	10	spin	spin	NOUN
ap-6650	16	11	matrices	matrix	NOUN
ap-6650	16	12	[	[	X
ap-6650	16	13	13	13	NUM
ap-6650	16	14	]	]	PUNCT
ap-6650	16	15	for	for	ADP
ap-6650	16	16	adjusting	adjust	VERB
ap-6650	16	17	the	the	DET
ap-6650	16	18	non	non	ADJ
ap-6650	16	19	-	-	ADJ
ap-6650	16	20	relativistic	relativistic	ADJ
ap-6650	16	21	schrödinger	schrödinger	ADJ
ap-6650	16	22	equation	equation	NOUN
ap-6650	16	23	to	to	PART
ap-6650	16	24	account	account	VERB
ap-6650	16	25	for	for	ADP
ap-6650	16	26	goudsmit	goudsmit	NOUN
ap-6650	16	27	-	-	PUNCT
ap-6650	16	28	uhlenbeck	uhlenbeck	NOUN
ap-6650	16	29	’s	’s	PART
ap-6650	16	30	hypothesis	hypothesis	NOUN
ap-6650	16	31	(	(	PUNCT
ap-6650	16	32	1925	1925	NUM
ap-6650	16	33	)	)	PUNCT
ap-6650	17	1	[	[	X
ap-6650	17	2	14	14	NUM
ap-6650	17	3	,	,	PUNCT
ap-6650	17	4	15	15	NUM
ap-6650	17	5	]	]	PUNCT
ap-6650	17	6	.	.	PUNCT
ap-6650	18	1	therefore	therefore	ADV
ap-6650	18	2	,	,	PUNCT
ap-6650	18	3	he	he	PRON
ap-6650	18	4	applied	apply	VERB
ap-6650	18	5	an	an	DET
ap-6650	18	6	ansatz	ansatz	NOUN
ap-6650	18	7	for	for	ADP
ap-6650	18	8	adding	add	VERB
ap-6650	18	9	a	a	DET
ap-6650	18	10	phenomenological	phenomenological	ADJ
ap-6650	18	11	term	term	NOUN
ap-6650	18	12	to	to	ADP
ap-6650	18	13	the	the	DET
ap-6650	18	14	ordinary	ordinary	ADJ
ap-6650	18	15	non	non	ADJ
ap-6650	18	16	-	-	ADJ
ap-6650	18	17	relativistic	relativistic	ADJ
ap-6650	18	18	hamiltonian	hamiltonian	NOUN
ap-6650	18	19	in	in	ADP
ap-6650	18	20	the	the	DET
ap-6650	18	21	presence	presence	NOUN
ap-6650	18	22	of	of	ADP
ap-6650	18	23	an	an	DET
ap-6650	18	24	electromagnetic	electromagnetic	ADJ
ap-6650	18	25	field	field	NOUN
ap-6650	18	26	,	,	PUNCT
ap-6650	18	27	the	the	DET
ap-6650	18	28	interaction	interaction	NOUN
ap-6650	18	29	energy	energy	NOUN
ap-6650	18	30	of	of	ADP
ap-6650	18	31	a	a	DET
ap-6650	18	32	magnetic	magnetic	ADJ
ap-6650	18	33	field	field	NOUN
ap-6650	18	34	and	and	CCONJ
ap-6650	18	35	electronic	electronic	ADJ
ap-6650	18	36	magnetic	magnetic	ADJ
ap-6650	18	37	moment	moment	NOUN
ap-6650	18	38	relative	relative	ADJ
ap-6650	18	39	to	to	ADP
ap-6650	18	40	the	the	DET
ap-6650	18	41	intrinsic	intrinsic	ADJ
ap-6650	18	42	spin	spin	NOUN
ap-6650	18	43	angular	angular	ADJ
ap-6650	18	44	momentum	momentum	NOUN
ap-6650	18	45	of	of	ADP
ap-6650	18	46	the	the	DET
ap-6650	18	47	electron	electron	NOUN
ap-6650	18	48	.	.	PUNCT
ap-6650	19	1	describing	describe	VERB
ap-6650	19	2	this	this	DET
ap-6650	19	3	spin	spin	NOUN
ap-6650	19	4	angular	angular	ADJ
ap-6650	19	5	momentum	momentum	NOUN
ap-6650	19	6	through	through	ADP
ap-6650	19	7	the	the	DET
ap-6650	19	8	spin	spin	NOUN
ap-6650	19	9	matrices	matrix	NOUN
ap-6650	19	10	requires	require	VERB
ap-6650	19	11	replacing	replace	VERB
ap-6650	19	12	the	the	DET
ap-6650	19	13	complex	complex	ADJ
ap-6650	19	14	scalar	scalar	ADJ
ap-6650	19	15	wave	wave	NOUN
ap-6650	19	16	function	function	NOUN
ap-6650	19	17	by	by	ADP
ap-6650	19	18	a	a	DET
ap-6650	19	19	two	two	NUM
ap-6650	19	20	-	-	PUNCT
ap-6650	19	21	component	component	NOUN
ap-6650	19	22	spinor	spinor	NOUN
ap-6650	19	23	wave	wave	NOUN
ap-6650	19	24	function	function	NOUN
ap-6650	19	25	in	in	ADP
ap-6650	19	26	the	the	DET
ap-6650	19	27	wave	wave	NOUN
ap-6650	19	28	equation	equation	NOUN
ap-6650	19	29	.	.	PUNCT
ap-6650	20	1	since	since	SCONJ
ap-6650	20	2	then	then	ADV
ap-6650	20	3	,	,	PUNCT
ap-6650	20	4	the	the	DET
ap-6650	20	5	study	study	NOUN
ap-6650	20	6	of	of	ADP
ap-6650	20	7	the	the	DET
ap-6650	20	8	pauli	pauli	PROPN
ap-6650	20	9	equation	equation	NOUN
ap-6650	20	10	became	become	VERB
ap-6650	20	11	a	a	DET
ap-6650	20	12	matter	matter	NOUN
ap-6650	20	13	of	of	ADP
ap-6650	20	14	considerable	considerable	ADJ
ap-6650	20	15	attention	attention	NOUN
ap-6650	20	16	.	.	PUNCT
ap-6650	21	1	in	in	ADP
ap-6650	21	2	1928	1928	NUM
ap-6650	21	3	,	,	PUNCT
ap-6650	21	4	when	when	SCONJ
ap-6650	21	5	dirac	dirac	NOUN
ap-6650	21	6	presented	present	VERB
ap-6650	21	7	his	his	PRON
ap-6650	21	8	relativistic	relativistic	ADJ
ap-6650	21	9	free	free	ADJ
ap-6650	21	10	wave	wave	NOUN
ap-6650	21	11	equation	equation	NOUN
ap-6650	21	12	in	in	ADP
ap-6650	21	13	addition	addition	NOUN
ap-6650	21	14	to	to	ADP
ap-6650	21	15	the	the	DET
ap-6650	21	16	minimal	minimal	ADJ
ap-6650	21	17	coupling	couple	VERB
ap-6650	21	18	replacement	replacement	NOUN
ap-6650	21	19	to	to	PART
ap-6650	21	20	include	include	VERB
ap-6650	21	21	electromagnetic	electromagnetic	ADJ
ap-6650	21	22	interactions	interaction	NOUN
ap-6650	21	23	[	[	X
ap-6650	21	24	16	16	NUM
ap-6650	21	25	]	]	PUNCT
ap-6650	21	26	,	,	PUNCT
ap-6650	21	27	he	he	PRON
ap-6650	21	28	showed	show	VERB
ap-6650	21	29	that	that	SCONJ
ap-6650	21	30	his	his	PRON
ap-6650	21	31	equation	equation	NOUN
ap-6650	21	32	contained	contain	VERB
ap-6650	21	33	a	a	DET
ap-6650	21	34	term	term	NOUN
ap-6650	21	35	involving	involve	VERB
ap-6650	21	36	the	the	DET
ap-6650	21	37	electron	electron	NOUN
ap-6650	21	38	magnetic	magnetic	ADJ
ap-6650	21	39	moment	moment	NOUN
ap-6650	21	40	interacting	interact	VERB
ap-6650	21	41	with	with	ADP
ap-6650	21	42	a	a	DET
ap-6650	21	43	magnetic	magnetic	ADJ
ap-6650	21	44	field	field	NOUN
ap-6650	21	45	,	,	PUNCT
ap-6650	21	46	which	which	PRON
ap-6650	21	47	was	be	AUX
ap-6650	21	48	the	the	DET
ap-6650	21	49	same	same	ADJ
ap-6650	21	50	one	one	NOUN
ap-6650	21	51	inserted	insert	VERB
ap-6650	21	52	by	by	ADP
ap-6650	21	53	hand	hand	NOUN
ap-6650	21	54	in	in	ADP
ap-6650	21	55	pauli	pauli	PROPN
ap-6650	21	56	’s	’s	PART
ap-6650	21	57	equation	equation	NOUN
ap-6650	21	58	.	.	PUNCT
ap-6650	22	1	after	after	ADP
ap-6650	22	2	that	that	PRON
ap-6650	22	3	,	,	PUNCT
ap-6650	22	4	it	it	PRON
ap-6650	22	5	became	become	VERB
ap-6650	22	6	common	common	ADJ
ap-6650	22	7	to	to	PART
ap-6650	22	8	count	count	VERB
ap-6650	22	9	an	an	DET
ap-6650	22	10	electron	electron	NOUN
ap-6650	22	11	spin	spin	NOUN
ap-6650	22	12	as	as	ADP
ap-6650	22	13	a	a	DET
ap-6650	22	14	relativistic	relativistic	ADJ
ap-6650	22	15	phenomenon	phenomenon	NOUN
ap-6650	22	16	,	,	PUNCT
ap-6650	22	17	and	and	CCONJ
ap-6650	22	18	the	the	DET
ap-6650	22	19	corresponding	corresponding	ADJ
ap-6650	22	20	spin-1/2	spin-1/2	NOUN
ap-6650	22	21	term	term	NOUN
ap-6650	22	22	could	could	AUX
ap-6650	22	23	be	be	AUX
ap-6650	22	24	inserted	insert	VERB
ap-6650	22	25	into	into	ADP
ap-6650	22	26	the	the	DET
ap-6650	22	27	spin-0	spin-0	NUM
ap-6650	22	28	non	non	ADJ
ap-6650	22	29	-	-	ADJ
ap-6650	22	30	relativistic	relativistic	ADJ
ap-6650	22	31	schrödinger	schrödinger	ADJ
ap-6650	22	32	equation	equation	NOUN
ap-6650	22	33	as	as	SCONJ
ap-6650	22	34	will	will	AUX
ap-6650	22	35	be	be	AUX
ap-6650	22	36	discussed	discuss	VERB
ap-6650	22	37	in	in	ADP
ap-6650	22	38	this	this	DET
ap-6650	22	39	article	article	NOUN
ap-6650	22	40	to	to	PART
ap-6650	22	41	see	see	VERB
ap-6650	22	42	how	how	SCONJ
ap-6650	22	43	this	this	PRON
ap-6650	22	44	is	be	AUX
ap-6650	22	45	possible	possible	ADJ
ap-6650	22	46	.	.	PUNCT
ap-6650	23	1	however	however	ADV
ap-6650	23	2	,	,	PUNCT
ap-6650	23	3	motivated	motivate	VERB
ap-6650	23	4	by	by	ADP
ap-6650	23	5	attempts	attempt	NOUN
ap-6650	23	6	to	to	PART
ap-6650	23	7	understand	understand	VERB
ap-6650	23	8	the	the	DET
ap-6650	23	9	string	string	NOUN
ap-6650	23	10	theory	theory	NOUN
ap-6650	23	11	and	and	CCONJ
ap-6650	23	12	describe	describe	VERB
ap-6650	23	13	quantum	quantum	NOUN
ap-6650	23	14	gravitation	gravitation	NOUN
ap-6650	23	15	using	use	VERB
ap-6650	23	16	noncommutative	noncommutative	ADJ
ap-6650	23	17	geometry	geometry	NOUN
ap-6650	23	18	and	and	CCONJ
ap-6650	23	19	by	by	ADP
ap-6650	23	20	trying	try	VERB
ap-6650	23	21	to	to	PART
ap-6650	23	22	draw	draw	VERB
ap-6650	23	23	a	a	DET
ap-6650	23	24	considerable	considerable	ADJ
ap-6650	23	25	attention	attention	NOUN
ap-6650	23	26	to	to	ADP
ap-6650	23	27	the	the	DET
ap-6650	23	28	phenomenological	phenomenological	ADJ
ap-6650	23	29	implications	implication	NOUN
ap-6650	23	30	,	,	PUNCT
ap-6650	23	31	we	we	PRON
ap-6650	23	32	focus	focus	VERB
ap-6650	23	33	on	on	ADP
ap-6650	23	34	studying	study	VERB
ap-6650	23	35	the	the	DET
ap-6650	23	36	problem	problem	NOUN
ap-6650	23	37	of	of	ADP
ap-6650	23	38	a	a	DET
ap-6650	23	39	non	non	ADJ
ap-6650	23	40	-	-	ADJ
ap-6650	23	41	relativistic	relativistic	ADJ
ap-6650	23	42	spin-1/2	spin-1/2	NOUN
ap-6650	23	43	particle	particle	NOUN
ap-6650	23	44	in	in	ADP
ap-6650	23	45	the	the	DET
ap-6650	23	46	presence	presence	NOUN
ap-6650	23	47	of	of	ADP
ap-6650	23	48	an	an	DET
ap-6650	23	49	electromagnetic	electromagnetic	ADJ
ap-6650	23	50	field	field	NOUN
ap-6650	23	51	within	within	ADP
ap-6650	23	52	3	3	NUM
ap-6650	23	53	-	-	PUNCT
ap-6650	23	54	dimensional	dimensional	ADJ
ap-6650	23	55	noncommutative	noncommutative	ADJ
ap-6650	23	56	phase	phase	NOUN
ap-6650	23	57	-	-	PUNCT
ap-6650	23	58	space	space	NOUN
ap-6650	23	59	.	.	PUNCT
ap-6650	24	1	as	as	ADP
ap-6650	24	2	a	a	DET
ap-6650	24	3	mathematical	mathematical	ADJ
ap-6650	24	4	theory	theory	NOUN
ap-6650	24	5	,	,	PUNCT
ap-6650	24	6	noncommutative	noncommutative	ADJ
ap-6650	24	7	geometry	geometry	NOUN
ap-6650	24	8	is	be	AUX
ap-6650	24	9	by	by	ADP
ap-6650	24	10	now	now	ADV
ap-6650	24	11	well	well	ADV
ap-6650	24	12	established	establish	VERB
ap-6650	24	13	,	,	PUNCT
ap-6650	24	14	although	although	SCONJ
ap-6650	24	15	at	at	ADP
ap-6650	24	16	first	first	ADV
ap-6650	24	17	,	,	PUNCT
ap-6650	24	18	its	its	PRON
ap-6650	24	19	progress	progress	NOUN
ap-6650	24	20	has	have	AUX
ap-6650	24	21	been	be	AUX
ap-6650	24	22	narrowly	narrowly	ADV
ap-6650	24	23	restricted	restrict	VERB
ap-6650	24	24	to	to	ADP
ap-6650	24	25	some	some	DET
ap-6650	24	26	branches	branch	NOUN
ap-6650	24	27	of	of	ADP
ap-6650	24	28	physics	physics	NOUN
ap-6650	24	29	such	such	ADJ
ap-6650	24	30	as	as	ADP
ap-6650	24	31	quantum	quantum	NOUN
ap-6650	24	32	mechanics	mechanic	NOUN
ap-6650	24	33	.	.	PUNCT
ap-6650	25	1	however	however	ADV
ap-6650	25	2	,	,	PUNCT
ap-6650	25	3	recently	recently	ADV
ap-6650	25	4	,	,	PUNCT
ap-6650	25	5	the	the	DET
ap-6650	25	6	noncommutative	noncommutative	ADJ
ap-6650	25	7	geometry	geometry	NOUN
ap-6650	25	8	has	have	AUX
ap-6650	25	9	become	become	VERB
ap-6650	25	10	a	a	DET
ap-6650	25	11	topic	topic	NOUN
ap-6650	25	12	of	of	ADP
ap-6650	25	13	great	great	ADJ
ap-6650	25	14	interest	interest	NOUN
ap-6650	26	1	[	[	X
ap-6650	26	2	17–23	17–23	NUM
ap-6650	26	3	]	]	PUNCT
ap-6650	26	4	.	.	PUNCT
ap-6650	27	1	it	it	PRON
ap-6650	27	2	has	have	AUX
ap-6650	27	3	been	be	AUX
ap-6650	27	4	finding	find	VERB
ap-6650	27	5	applications	application	NOUN
ap-6650	27	6	in	in	ADP
ap-6650	27	7	many	many	ADJ
ap-6650	27	8	sectors	sector	NOUN
ap-6650	27	9	of	of	ADP
ap-6650	27	10	physics	physics	NOUN
ap-6650	27	11	and	and	CCONJ
ap-6650	27	12	has	have	AUX
ap-6650	27	13	rapidly	rapidly	ADV
ap-6650	27	14	become	become	VERB
ap-6650	27	15	involved	involved	ADJ
ap-6650	27	16	in	in	ADP
ap-6650	27	17	them	they	PRON
ap-6650	27	18	,	,	PUNCT
ap-6650	27	19	continuing	continue	VERB
ap-6650	27	20	to	to	PART
ap-6650	27	21	promote	promote	VERB
ap-6650	27	22	fruitful	fruitful	ADJ
ap-6650	27	23	ideas	idea	NOUN
ap-6650	27	24	and	and	CCONJ
ap-6650	27	25	the	the	DET
ap-6650	27	26	search	search	NOUN
ap-6650	27	27	for	for	ADP
ap-6650	27	28	a	a	DET
ap-6650	27	29	better	well	ADJ
ap-6650	27	30	understanding	understanding	NOUN
ap-6650	27	31	.	.	PUNCT
ap-6650	28	1	such	such	ADJ
ap-6650	28	2	as	as	ADP
ap-6650	28	3	in	in	ADP
ap-6650	28	4	the	the	DET
ap-6650	28	5	quantum	quantum	NOUN
ap-6650	28	6	gravity	gravity	NOUN
ap-6650	28	7	[	[	X
ap-6650	28	8	24	24	NUM
ap-6650	28	9	]	]	PUNCT
ap-6650	28	10	;	;	PUNCT
ap-6650	28	11	the	the	DET
ap-6650	28	12	standard	standard	ADJ
ap-6650	28	13	model	model	NOUN
ap-6650	28	14	of	of	ADP
ap-6650	28	15	fundamental	fundamental	ADJ
ap-6650	28	16	interactions	interaction	NOUN
ap-6650	28	17	[	[	X
ap-6650	28	18	25	25	NUM
ap-6650	28	19	]	]	X
ap-6650	28	20	;	;	PUNCT
ap-6650	28	21	as	as	ADV
ap-6650	28	22	well	well	ADV
ap-6650	28	23	as	as	ADP
ap-6650	28	24	in	in	ADP
ap-6650	28	25	the	the	DET
ap-6650	28	26	string	string	NOUN
ap-6650	28	27	theory	theory	NOUN
ap-6650	28	28	[	[	X
ap-6650	28	29	26	26	NUM
ap-6650	28	30	]	]	X
ap-6650	28	31	;	;	PUNCT
ap-6650	28	32	and	and	CCONJ
ap-6650	28	33	its	its	PRON
ap-6650	28	34	implication	implication	NOUN
ap-6650	28	35	in	in	ADP
ap-6650	28	36	hopf	hopf	ADJ
ap-6650	28	37	algebras	algebra	NOUN
ap-6650	29	1	[	[	X
ap-6650	29	2	27	27	NUM
ap-6650	29	3	]	]	PUNCT
ap-6650	29	4	gives	give	VERB
ap-6650	29	5	the	the	DET
ap-6650	29	6	connes	conne	NOUN
ap-6650	29	7	–	–	PUNCT
ap-6650	29	8	kreimer	kreimer	NOUN
ap-6650	29	9	230	230	NUM
ap-6650	29	10	https://doi.org/10.14311/ap.2021.61.0230	https://doi.org/10.14311/ap.2021.61.0230	PROPN
ap-6650	29	11	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-6650	29	12	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-6650	29	13	vol	vol	NOUN
ap-6650	29	14	.	.	PROPN
ap-6650	30	1	61	61	NUM
ap-6650	30	2	no	no	NOUN
ap-6650	30	3	.	.	PUNCT
ap-6650	31	1	1/2021	1/2021	NUM
ap-6650	31	2	on	on	ADP
ap-6650	31	3	the	the	DET
ap-6650	31	4	three	three	NUM
ap-6650	31	5	-	-	PUNCT
ap-6650	31	6	dimensional	dimensional	ADJ
ap-6650	31	7	pauli	pauli	PROPN
ap-6650	31	8	equation	equation	NOUN
ap-6650	31	9	in	in	ADP
ap-6650	31	10	noncommutative	noncommutative	ADJ
ap-6650	31	11	phase	phase	NOUN
ap-6650	31	12	-	-	PUNCT
ap-6650	31	13	space	space	NOUN
ap-6650	31	14	hopf	hopf	NOUN
ap-6650	31	15	algebras	algebra	VERB
ap-6650	31	16	[	[	X
ap-6650	31	17	28–30	28–30	NUM
ap-6650	31	18	]	]	X
ap-6650	31	19	etc	etc	X
ap-6650	31	20	.	.	X
ap-6650	32	1	there	there	PRON
ap-6650	32	2	are	be	VERB
ap-6650	32	3	many	many	ADJ
ap-6650	32	4	papers	paper	NOUN
ap-6650	32	5	devoted	devote	VERB
ap-6650	32	6	to	to	ADP
ap-6650	32	7	the	the	DET
ap-6650	32	8	study	study	NOUN
ap-6650	32	9	of	of	ADP
ap-6650	32	10	such	such	ADJ
ap-6650	32	11	various	various	ADJ
ap-6650	32	12	aspects	aspect	NOUN
ap-6650	32	13	especially	especially	ADV
ap-6650	32	14	in	in	ADP
ap-6650	32	15	quantum	quantum	ADJ
ap-6650	32	16	field	field	NOUN
ap-6650	32	17	theory	theory	NOUN
ap-6650	32	18	[	[	X
ap-6650	32	19	31–33	31–33	NUM
ap-6650	32	20	]	]	PUNCT
ap-6650	32	21	and	and	CCONJ
ap-6650	32	22	quantum	quantum	ADJ
ap-6650	32	23	mechanics	mechanic	NOUN
ap-6650	32	24	[	[	X
ap-6650	32	25	34–36	34–36	NUM
ap-6650	32	26	]	]	PUNCT
ap-6650	32	27	.	.	PUNCT
ap-6650	33	1	this	this	DET
ap-6650	33	2	paper	paper	NOUN
ap-6650	33	3	is	be	AUX
ap-6650	33	4	organized	organize	VERB
ap-6650	33	5	as	as	SCONJ
ap-6650	33	6	follows	follow	VERB
ap-6650	33	7	.	.	PUNCT
ap-6650	34	1	in	in	ADP
ap-6650	34	2	section	section	NOUN
ap-6650	34	3	2	2	NUM
ap-6650	34	4	,	,	PUNCT
ap-6650	34	5	we	we	PRON
ap-6650	34	6	present	present	VERB
ap-6650	34	7	an	an	DET
ap-6650	34	8	analysis	analysis	NOUN
ap-6650	34	9	review	review	NOUN
ap-6650	34	10	of	of	ADP
ap-6650	34	11	noncommutative	noncommutative	ADJ
ap-6650	34	12	geometry	geometry	NOUN
ap-6650	34	13	,	,	PUNCT
ap-6650	34	14	in	in	ADP
ap-6650	34	15	particular	particular	ADJ
ap-6650	34	16	both	both	CCONJ
ap-6650	34	17	the	the	DET
ap-6650	34	18	three	three	NUM
ap-6650	34	19	-	-	PUNCT
ap-6650	34	20	dimensional	dimensional	ADJ
ap-6650	34	21	bopp	bopp	VERB
ap-6650	34	22	-	-	PUNCT
ap-6650	34	23	shift	shift	NOUN
ap-6650	34	24	transformation	transformation	NOUN
ap-6650	34	25	and	and	CCONJ
ap-6650	34	26	the	the	DET
ap-6650	34	27	moyal	moyal	ADV
ap-6650	34	28	-	-	PUNCT
ap-6650	34	29	weyl	weyl	VERB
ap-6650	34	30	product	product	NOUN
ap-6650	34	31	.	.	PUNCT
ap-6650	35	1	in	in	ADP
ap-6650	35	2	section	section	NOUN
ap-6650	35	3	3	3	NUM
ap-6650	35	4	,	,	PUNCT
ap-6650	35	5	we	we	PRON
ap-6650	35	6	investigate	investigate	VERB
ap-6650	35	7	the	the	DET
ap-6650	35	8	three	three	NUM
ap-6650	35	9	-	-	PUNCT
ap-6650	35	10	dimensional	dimensional	ADJ
ap-6650	35	11	pauli	pauli	NOUN
ap-6650	35	12	equation	equation	NOUN
ap-6650	35	13	in	in	ADP
ap-6650	35	14	the	the	DET
ap-6650	35	15	presence	presence	NOUN
ap-6650	35	16	of	of	ADP
ap-6650	35	17	an	an	DET
ap-6650	35	18	electromagnetic	electromagnetic	ADJ
ap-6650	35	19	field	field	NOUN
ap-6650	35	20	and	and	CCONJ
ap-6650	35	21	the	the	DET
ap-6650	35	22	corresponding	corresponding	ADJ
ap-6650	35	23	continuity	continuity	NOUN
ap-6650	35	24	equation	equation	NOUN
ap-6650	35	25	.	.	PUNCT
ap-6650	36	1	furthermore	furthermore	ADV
ap-6650	36	2	,	,	PUNCT
ap-6650	36	3	we	we	PRON
ap-6650	36	4	derived	derive	VERB
ap-6650	36	5	the	the	DET
ap-6650	36	6	current	current	ADJ
ap-6650	36	7	magnetization	magnetization	NOUN
ap-6650	36	8	term	term	NOUN
ap-6650	36	9	in	in	ADP
ap-6650	36	10	the	the	DET
ap-6650	36	11	deformed	deform	VERB
ap-6650	36	12	continuity	continuity	NOUN
ap-6650	36	13	equation	equation	NOUN
ap-6650	36	14	.	.	PUNCT
ap-6650	37	1	section	section	NOUN
ap-6650	37	2	4	4	NUM
ap-6650	37	3	is	be	AUX
ap-6650	37	4	devoted	devote	VERB
ap-6650	37	5	to	to	ADP
ap-6650	37	6	calculating	calculate	VERB
ap-6650	37	7	the	the	DET
ap-6650	37	8	semi	semi	ADJ
ap-6650	37	9	-	-	ADJ
ap-6650	37	10	classical	classical	ADJ
ap-6650	37	11	noncommutative	noncommutative	ADJ
ap-6650	37	12	partition	partition	NOUN
ap-6650	37	13	function	function	NOUN
ap-6650	37	14	of	of	ADP
ap-6650	37	15	the	the	DET
ap-6650	37	16	pauli	pauli	PROPN
ap-6650	37	17	system	system	NOUN
ap-6650	37	18	of	of	ADP
ap-6650	37	19	the	the	DET
ap-6650	37	20	one	one	NUM
ap-6650	37	21	-	-	PUNCT
ap-6650	37	22	particle	particle	NOUN
ap-6650	37	23	and	and	CCONJ
ap-6650	37	24	n	n	CCONJ
ap-6650	37	25	-	-	PUNCT
ap-6650	37	26	particle	particle	NOUN
ap-6650	37	27	systems	system	NOUN
ap-6650	37	28	.	.	PUNCT
ap-6650	38	1	consequently	consequently	ADV
ap-6650	38	2	,	,	PUNCT
ap-6650	38	3	we	we	PRON
ap-6650	38	4	obtain	obtain	VERB
ap-6650	38	5	the	the	DET
ap-6650	38	6	corresponding	corresponding	ADJ
ap-6650	38	7	magnetization	magnetization	NOUN
ap-6650	38	8	and	and	CCONJ
ap-6650	38	9	the	the	DET
ap-6650	38	10	magnetic	magnetic	ADJ
ap-6650	38	11	susceptibility	susceptibility	NOUN
ap-6650	38	12	through	through	ADP
ap-6650	38	13	the	the	DET
ap-6650	38	14	helmholtz	helmholtz	NOUN
ap-6650	38	15	free	free	ADJ
ap-6650	38	16	energy	energy	NOUN
ap-6650	38	17	,	,	PUNCT
ap-6650	38	18	all	all	PRON
ap-6650	38	19	in	in	ADP
ap-6650	38	20	both	both	CCONJ
ap-6650	38	21	commutative	commutative	ADJ
ap-6650	38	22	and	and	CCONJ
ap-6650	38	23	noncommutative	noncommutative	ADJ
ap-6650	38	24	phase	phase	NOUN
ap-6650	38	25	-	-	PUNCT
ap-6650	38	26	spaces	space	NOUN
ap-6650	38	27	and	and	CCONJ
ap-6650	38	28	within	within	ADP
ap-6650	38	29	a	a	DET
ap-6650	38	30	classical	classical	ADJ
ap-6650	38	31	limit	limit	NOUN
ap-6650	38	32	.	.	PUNCT
ap-6650	39	1	therefore	therefore	ADV
ap-6650	39	2	,	,	PUNCT
ap-6650	39	3	concluding	conclude	VERB
ap-6650	39	4	with	with	ADP
ap-6650	39	5	some	some	DET
ap-6650	39	6	remarks	remark	NOUN
ap-6650	39	7	.	.	PUNCT
ap-6650	40	1	2	2	X
ap-6650	40	2	.	.	X
ap-6650	40	3	review	review	NOUN
ap-6650	40	4	of	of	ADP
ap-6650	40	5	noncommutative	noncommutative	ADJ
ap-6650	40	6	algebra	algebra	PROPN
ap-6650	40	7	firstly	firstly	ADV
ap-6650	40	8	,	,	PUNCT
ap-6650	40	9	we	we	PRON
ap-6650	40	10	present	present	VERB
ap-6650	40	11	the	the	DET
ap-6650	40	12	most	most	ADV
ap-6650	40	13	essential	essential	ADJ
ap-6650	40	14	formulas	formula	NOUN
ap-6650	40	15	of	of	ADP
ap-6650	40	16	noncommutative	noncommutative	ADJ
ap-6650	40	17	algebra	algebra	PROPN
ap-6650	40	18	[	[	X
ap-6650	40	19	36	36	NUM
ap-6650	40	20	]	]	PUNCT
ap-6650	40	21	.	.	PUNCT
ap-6650	41	1	it	it	PRON
ap-6650	41	2	is	be	AUX
ap-6650	41	3	well	well	ADV
ap-6650	41	4	known	know	VERB
ap-6650	41	5	that	that	SCONJ
ap-6650	41	6	at	at	ADP
ap-6650	41	7	very	very	ADV
ap-6650	41	8	small	small	ADJ
ap-6650	41	9	scales	scale	NOUN
ap-6650	41	10	such	such	ADJ
ap-6650	41	11	as	as	ADP
ap-6650	41	12	the	the	DET
ap-6650	41	13	string	string	NOUN
ap-6650	41	14	scale	scale	NOUN
ap-6650	41	15	,	,	PUNCT
ap-6650	41	16	the	the	DET
ap-6650	41	17	position	position	NOUN
ap-6650	41	18	coordinates	coordinate	NOUN
ap-6650	41	19	do	do	AUX
ap-6650	41	20	not	not	PART
ap-6650	41	21	commute	commute	VERB
ap-6650	41	22	with	with	ADP
ap-6650	41	23	each	each	DET
ap-6650	41	24	other	other	ADJ
ap-6650	41	25	,	,	PUNCT
ap-6650	41	26	neither	neither	CCONJ
ap-6650	41	27	do	do	VERB
ap-6650	41	28	the	the	DET
ap-6650	41	29	momenta	momenta	NOUN
ap-6650	41	30	.	.	PUNCT
ap-6650	42	1	let	let	VERB
ap-6650	42	2	us	we	PRON
ap-6650	42	3	accept	accept	VERB
ap-6650	42	4	,	,	PUNCT
ap-6650	42	5	in	in	ADP
ap-6650	42	6	a	a	DET
ap-6650	42	7	d	d	ADJ
ap-6650	42	8	-	-	ADJ
ap-6650	42	9	dimensional	dimensional	ADJ
ap-6650	42	10	noncommutative	noncommutative	ADJ
ap-6650	42	11	phase	phase	NOUN
ap-6650	42	12	-	-	PUNCT
ap-6650	42	13	space	space	NOUN
ap-6650	42	14	,	,	PUNCT
ap-6650	42	15	the	the	DET
ap-6650	42	16	operators	operator	NOUN
ap-6650	42	17	of	of	ADP
ap-6650	42	18	coordinates	coordinate	NOUN
ap-6650	42	19	and	and	CCONJ
ap-6650	42	20	momenta	momenta	NOUN
ap-6650	42	21	xnci	xnci	PROPN
ap-6650	42	22	and	and	CCONJ
ap-6650	42	23	pnci	pnci	PROPN
ap-6650	42	24	,	,	PUNCT
ap-6650	42	25	respectively	respectively	ADV
ap-6650	42	26	.	.	PUNCT
ap-6650	43	1	the	the	DET
ap-6650	43	2	noncommutative	noncommutative	ADJ
ap-6650	43	3	formulation	formulation	NOUN
ap-6650	43	4	of	of	ADP
ap-6650	43	5	quantum	quantum	ADJ
ap-6650	43	6	mechanics	mechanic	NOUN
ap-6650	43	7	corresponds	correspond	VERB
ap-6650	43	8	to	to	ADP
ap-6650	43	9	the	the	DET
ap-6650	43	10	following	follow	VERB
ap-6650	43	11	heisenberg	heisenberg	PROPN
ap-6650	43	12	-	-	PUNCT
ap-6650	43	13	like	like	ADJ
ap-6650	43	14	commutation	commutation	NOUN
ap-6650	43	15	relations	relation	NOUN
ap-6650	43	16	[	[	PUNCT
ap-6650	43	17	xncµ	xncµ	NOUN
ap-6650	43	18	,	,	PUNCT
ap-6650	43	19	x	x	PROPN
ap-6650	43	20	nc	nc	PROPN
ap-6650	43	21	ν	ν	X
ap-6650	43	22	]	]	PUNCT
ap-6650	43	23	=	=	PUNCT
ap-6650	43	24	iθµν	iθµν	NOUN
ap-6650	43	25	,	,	PUNCT
ap-6650	43	26	[	[	PUNCT
ap-6650	43	27	pncµ	pncµ	NOUN
ap-6650	43	28	,	,	PUNCT
ap-6650	43	29	p	p	PROPN
ap-6650	43	30	nc	nc	PROPN
ap-6650	43	31	ν	ν	X
ap-6650	43	32	]	]	PUNCT
ap-6650	44	1	=	=	PUNCT
ap-6650	44	2	iηµν	iηµν	PROPN
ap-6650	44	3	,	,	PUNCT
ap-6650	44	4	[	[	PUNCT
ap-6650	44	5	xncµ	xncµ	NOUN
ap-6650	44	6	,	,	PUNCT
ap-6650	44	7	p	p	PROPN
ap-6650	44	8	nc	nc	PROPN
ap-6650	44	9	ν	ν	X
ap-6650	44	10	]	]	PUNCT
ap-6650	44	11	=	=	PUNCT
ap-6650	44	12	i~̃δµν	i~̃δµν	PROPN
ap-6650	44	13	,	,	PUNCT
ap-6650	44	14	(	(	PUNCT
ap-6650	44	15	µ	µ	NOUN
ap-6650	44	16	,	,	PUNCT
ap-6650	44	17	ν	ν	X
ap-6650	44	18	=	=	SYM
ap-6650	44	19	1	1	NUM
ap-6650	44	20	,	,	PUNCT
ap-6650	44	21	..	..	PUNCT
ap-6650	44	22	d	d	X
ap-6650	44	23	)	)	PUNCT
ap-6650	44	24	,	,	PUNCT
ap-6650	44	25	(	(	PUNCT
ap-6650	44	26	1	1	X
ap-6650	44	27	)	)	PUNCT
ap-6650	44	28	the	the	DET
ap-6650	44	29	effective	effective	ADJ
ap-6650	44	30	planck	planck	NOUN
ap-6650	44	31	constant	constant	ADJ
ap-6650	44	32	is	be	AUX
ap-6650	44	33	the	the	DET
ap-6650	44	34	deformed	deform	VERB
ap-6650	44	35	planck	planck	NOUN
ap-6650	44	36	constant	constant	ADJ
ap-6650	44	37	,	,	PUNCT
ap-6650	44	38	which	which	PRON
ap-6650	44	39	is	be	AUX
ap-6650	44	40	given	give	VERB
ap-6650	44	41	by	by	ADP
ap-6650	44	42	~̃	~̃	PUNCT
ap-6650	44	43	=	=	SYM
ap-6650	44	44	αβ~	αβ~	PROPN
ap-6650	44	45	+	+	CCONJ
ap-6650	44	46	tr[θη	tr[θη	PROPN
ap-6650	44	47	]	]	X
ap-6650	44	48	4αβ~	4αβ~	NOUN
ap-6650	44	49	,	,	PUNCT
ap-6650	44	50	(	(	PUNCT
ap-6650	44	51	2	2	X
ap-6650	44	52	)	)	PUNCT
ap-6650	44	53	where	where	SCONJ
ap-6650	44	54	tr[θη	tr[θη	VERB
ap-6650	44	55	]	]	X
ap-6650	44	56	4αβ~	4αβ~	NOUN
ap-6650	44	57	�	�	NOUN
ap-6650	44	58	1	1	NUM
ap-6650	44	59	is	be	AUX
ap-6650	44	60	the	the	DET
ap-6650	44	61	condition	condition	NOUN
ap-6650	44	62	of	of	ADP
ap-6650	44	63	consistency	consistency	NOUN
ap-6650	44	64	in	in	ADP
ap-6650	44	65	quantum	quantum	ADJ
ap-6650	44	66	mechanics	mechanic	NOUN
ap-6650	44	67	.	.	PUNCT
ap-6650	45	1	θµν	θµν	NOUN
ap-6650	45	2	,	,	PUNCT
ap-6650	45	3	ηµν	ηµν	PRON
ap-6650	45	4	are	be	AUX
ap-6650	45	5	constant	constant	ADJ
ap-6650	45	6	antisymmetric	antisymmetric	ADJ
ap-6650	45	7	d×	d×	NOUN
ap-6650	45	8	d	d	NOUN
ap-6650	45	9	matrices	matrix	NOUN
ap-6650	45	10	and	and	CCONJ
ap-6650	45	11	δµν	δµν	NOUN
ap-6650	45	12	is	be	AUX
ap-6650	45	13	the	the	DET
ap-6650	45	14	identity	identity	NOUN
ap-6650	45	15	matrix	matrix	NOUN
ap-6650	45	16	.	.	PUNCT
ap-6650	46	1	it	it	PRON
ap-6650	46	2	is	be	AUX
ap-6650	46	3	shown	show	VERB
ap-6650	46	4	that	that	SCONJ
ap-6650	46	5	xnci	xnci	PROPN
ap-6650	46	6	and	and	CCONJ
ap-6650	46	7	pnci	pnci	PROPN
ap-6650	46	8	can	can	AUX
ap-6650	46	9	be	be	AUX
ap-6650	46	10	represented	represent	VERB
ap-6650	46	11	in	in	ADP
ap-6650	46	12	terms	term	NOUN
ap-6650	46	13	of	of	ADP
ap-6650	46	14	coordinates	coordinate	NOUN
ap-6650	46	15	xi	xi	X
ap-6650	46	16	and	and	CCONJ
ap-6650	46	17	momenta	momenta	PROPN
ap-6650	46	18	pj	pj	PROPN
ap-6650	46	19	in	in	ADP
ap-6650	46	20	usual	usual	ADJ
ap-6650	46	21	quantum	quantum	ADJ
ap-6650	46	22	mechanics	mechanic	NOUN
ap-6650	46	23	through	through	ADP
ap-6650	46	24	the	the	DET
ap-6650	46	25	so	so	ADV
ap-6650	46	26	-	-	PUNCT
ap-6650	46	27	called	call	VERB
ap-6650	46	28	generalized	generalize	VERB
ap-6650	46	29	bopp	bopp	VERB
ap-6650	46	30	-	-	PUNCT
ap-6650	46	31	shift	shift	NOUN
ap-6650	46	32	as	as	SCONJ
ap-6650	46	33	follows	follow	VERB
ap-6650	46	34	[	[	X
ap-6650	46	35	34	34	NUM
ap-6650	46	36	]	]	X
ap-6650	46	37	xncµ	xncµ	NOUN
ap-6650	46	38	=	=	NOUN
ap-6650	46	39	αxµ	αxµ	NOUN
ap-6650	46	40	−	−	NOUN
ap-6650	46	41	1	1	NUM
ap-6650	46	42	2α	2α	NOUN
ap-6650	46	43	~	~	SYM
ap-6650	46	44	θµνpν	θµνpν	NOUN
ap-6650	46	45	,	,	PUNCT
ap-6650	46	46	and	and	CCONJ
ap-6650	46	47	pncµ	pncµ	NOUN
ap-6650	46	48	=	=	SYM
ap-6650	46	49	βpµ	βpµ	NOUN
ap-6650	47	1	+	+	CCONJ
ap-6650	47	2	1	1	NUM
ap-6650	47	3	2β	2β	NUM
ap-6650	47	4	~	~	PUNCT
ap-6650	47	5	ηµνxν	ηµνxν	NOUN
ap-6650	47	6	,	,	PUNCT
ap-6650	47	7	(	(	PUNCT
ap-6650	47	8	3	3	X
ap-6650	47	9	)	)	PUNCT
ap-6650	47	10	with	with	ADP
ap-6650	47	11	α	α	PROPN
ap-6650	47	12	=	=	SYM
ap-6650	47	13	1−	1−	NUM
ap-6650	47	14	θη	θη	PROPN
ap-6650	47	15	8~2	8~2	NUM
ap-6650	47	16	and	and	CCONJ
ap-6650	47	17	β	β	AUX
ap-6650	47	18	=	=	NOUN
ap-6650	47	19	1	1	NUM
ap-6650	47	20	α	α	NOUN
ap-6650	47	21	being	be	AUX
ap-6650	47	22	scaling	scale	VERB
ap-6650	47	23	constants	constant	NOUN
ap-6650	47	24	.	.	PUNCT
ap-6650	48	1	to	to	ADP
ap-6650	48	2	the	the	DET
ap-6650	48	3	1rst	1rst	NUM
ap-6650	48	4	order	order	NOUN
ap-6650	48	5	of	of	ADP
ap-6650	48	6	θ	θ	PROPN
ap-6650	48	7	and	and	CCONJ
ap-6650	48	8	η	η	PROPN
ap-6650	48	9	,	,	PUNCT
ap-6650	48	10	in	in	ADP
ap-6650	48	11	the	the	DET
ap-6650	48	12	calculations	calculation	NOUN
ap-6650	48	13	we	we	PRON
ap-6650	48	14	take	take	VERB
ap-6650	48	15	α	α	NOUN
ap-6650	48	16	=	=	NOUN
ap-6650	48	17	β	β	X
ap-6650	48	18	=	=	SYM
ap-6650	48	19	1	1	NUM
ap-6650	48	20	,	,	PUNCT
ap-6650	48	21	so	so	SCONJ
ap-6650	48	22	the	the	DET
ap-6650	48	23	equations	equation	NOUN
ap-6650	48	24	(	(	PUNCT
ap-6650	48	25	3	3	NUM
ap-6650	48	26	,	,	PUNCT
ap-6650	48	27	2	2	NUM
ap-6650	48	28	)	)	PUNCT
ap-6650	48	29	become	become	VERB
ap-6650	48	30	xncµ	xncµ	NOUN
ap-6650	49	1	=	=	PUNCT
ap-6650	49	2	xµ	xµ	ADJ
ap-6650	50	1	−	−	NUM
ap-6650	50	2	1	1	NUM
ap-6650	50	3	2	2	NUM
ap-6650	50	4	~	~	NUM
ap-6650	50	5	θµνpν	θµνpν	NOUN
ap-6650	50	6	,	,	PUNCT
ap-6650	50	7	pncµ	pncµ	NOUN
ap-6650	50	8	=	=	PUNCT
ap-6650	50	9	pµ	pµ	PROPN
ap-6650	50	10	+	+	NOUN
ap-6650	50	11	1	1	NUM
ap-6650	50	12	2	2	NUM
ap-6650	50	13	~	~	NOUN
ap-6650	50	14	ηµνxν	ηµνxν	NOUN
ap-6650	50	15	,	,	PUNCT
ap-6650	50	16	and	and	CCONJ
ap-6650	51	1	~̃	~̃	PUNCT
ap-6650	51	2	=	=	SYM
ap-6650	51	3	~	~	PUNCT
ap-6650	51	4	+	+	CCONJ
ap-6650	51	5	tr[θη	tr[θη	PROPN
ap-6650	51	6	]	]	X
ap-6650	51	7	4~	4~	NOUN
ap-6650	51	8	.	.	PUNCT
ap-6650	52	1	(	(	PUNCT
ap-6650	52	2	4	4	X
ap-6650	52	3	)	)	PUNCT
ap-6650	52	4	if	if	SCONJ
ap-6650	52	5	the	the	DET
ap-6650	52	6	system	system	NOUN
ap-6650	52	7	in	in	ADP
ap-6650	52	8	which	which	PRON
ap-6650	52	9	we	we	PRON
ap-6650	52	10	study	study	VERB
ap-6650	52	11	the	the	DET
ap-6650	52	12	effects	effect	NOUN
ap-6650	52	13	of	of	ADP
ap-6650	52	14	noncommutativity	noncommutativity	NOUN
ap-6650	52	15	is	be	AUX
ap-6650	52	16	three	three	NUM
ap-6650	52	17	-	-	PUNCT
ap-6650	52	18	dimensional	dimensional	ADJ
ap-6650	52	19	,	,	PUNCT
ap-6650	52	20	we	we	PRON
ap-6650	52	21	limit	limit	VERB
ap-6650	52	22	ourselves	ourselves	PRON
ap-6650	52	23	to	to	ADP
ap-6650	52	24	the	the	DET
ap-6650	52	25	following	follow	VERB
ap-6650	52	26	noncommutative	noncommutative	ADJ
ap-6650	52	27	algebra	algebra	PROPN
ap-6650	52	28	[	[	PUNCT
ap-6650	52	29	xncj	xncj	NOUN
ap-6650	52	30	,	,	PUNCT
ap-6650	52	31	x	x	PROPN
ap-6650	52	32	nc	nc	PROPN
ap-6650	52	33	k	k	X
ap-6650	52	34	]	]	PUNCT
ap-6650	53	1	=	=	PUNCT
ap-6650	53	2	i	i	PRON
ap-6650	53	3	1	1	NUM
ap-6650	53	4	2εjklθl	2εjklθl	NUM
ap-6650	53	5	,	,	PUNCT
ap-6650	53	6	[	[	PUNCT
ap-6650	53	7	pncj	pncj	INTJ
ap-6650	53	8	,	,	PUNCT
ap-6650	53	9	p	p	PROPN
ap-6650	53	10	nc	nc	PROPN
ap-6650	53	11	k	k	X
ap-6650	53	12	]	]	PUNCT
ap-6650	54	1	=	=	PUNCT
ap-6650	54	2	i	i	PRON
ap-6650	54	3	1	1	NUM
ap-6650	54	4	2εjklηl	2εjklηl	NUM
ap-6650	54	5	,	,	PUNCT
ap-6650	54	6	[	[	PUNCT
ap-6650	54	7	xncj	xncj	NOUN
ap-6650	54	8	,	,	PUNCT
ap-6650	54	9	p	p	PROPN
ap-6650	54	10	nc	nc	PROPN
ap-6650	54	11	k	k	X
ap-6650	54	12	]	]	PUNCT
ap-6650	55	1	=	=	PUNCT
ap-6650	55	2	i	i	INTJ
ap-6650	55	3	(	(	PUNCT
ap-6650	55	4	~	~	PUNCT
ap-6650	55	5	+	+	CCONJ
ap-6650	55	6	θη	θη	PROPN
ap-6650	55	7	4~	4~	NOUN
ap-6650	55	8	)	)	PUNCT
ap-6650	55	9	δjk	δjk	NOUN
ap-6650	55	10	,	,	PUNCT
ap-6650	55	11	(	(	PUNCT
ap-6650	55	12	j	j	NOUN
ap-6650	55	13	,	,	PUNCT
ap-6650	55	14	k	k	NOUN
ap-6650	55	15	,	,	PUNCT
ap-6650	55	16	l	l	NOUN
ap-6650	55	17	=	=	SYM
ap-6650	55	18	1	1	NUM
ap-6650	55	19	,	,	PUNCT
ap-6650	55	20	2	2	NUM
ap-6650	55	21	,	,	PUNCT
ap-6650	55	22	3	3	NUM
ap-6650	55	23	)	)	PUNCT
ap-6650	55	24	,	,	PUNCT
ap-6650	55	25	(	(	PUNCT
ap-6650	55	26	5	5	X
ap-6650	55	27	)	)	PUNCT
ap-6650	55	28	θl	θl	ADP
ap-6650	55	29	=	=	PUNCT
ap-6650	55	30	(	(	PUNCT
ap-6650	55	31	0	0	NUM
ap-6650	55	32	,	,	PUNCT
ap-6650	55	33	0,θ	0,θ	NUM
ap-6650	55	34	)	)	PUNCT
ap-6650	55	35	,	,	PUNCT
ap-6650	55	36	ηl	ηl	ADP
ap-6650	55	37	=	=	SYM
ap-6650	55	38	(	(	PUNCT
ap-6650	55	39	0	0	NUM
ap-6650	55	40	,	,	PUNCT
ap-6650	55	41	0	0	NUM
ap-6650	55	42	,	,	PUNCT
ap-6650	55	43	η	η	NOUN
ap-6650	55	44	)	)	PUNCT
ap-6650	55	45	are	be	AUX
ap-6650	55	46	the	the	DET
ap-6650	55	47	real	real	ADV
ap-6650	55	48	-	-	PUNCT
ap-6650	55	49	valued	value	VERB
ap-6650	55	50	noncommutative	noncommutative	ADJ
ap-6650	55	51	parameters	parameter	NOUN
ap-6650	55	52	with	with	ADP
ap-6650	55	53	the	the	DET
ap-6650	55	54	dimension	dimension	NOUN
ap-6650	55	55	of	of	ADP
ap-6650	55	56	length2	length2	PROPN
ap-6650	55	57	,	,	PUNCT
ap-6650	55	58	momentum2	momentum2	PROPN
ap-6650	55	59	respectively	respectively	ADV
ap-6650	55	60	,	,	PUNCT
ap-6650	55	61	they	they	PRON
ap-6650	55	62	are	be	AUX
ap-6650	55	63	assumed	assume	VERB
ap-6650	55	64	to	to	PART
ap-6650	55	65	be	be	AUX
ap-6650	55	66	extremely	extremely	ADV
ap-6650	55	67	small	small	ADJ
ap-6650	55	68	.	.	PUNCT
ap-6650	56	1	and	and	CCONJ
ap-6650	56	2	εjkl	εjkl	NOUN
ap-6650	56	3	is	be	AUX
ap-6650	56	4	the	the	DET
ap-6650	56	5	levi	levi	PROPN
ap-6650	56	6	-	-	PUNCT
ap-6650	56	7	civita	civita	PROPN
ap-6650	56	8	permutation	permutation	NOUN
ap-6650	56	9	tensor	tensor	NOUN
ap-6650	56	10	.	.	PUNCT
ap-6650	57	1	therefore	therefore	ADV
ap-6650	57	2	,	,	PUNCT
ap-6650	57	3	we	we	PRON
ap-6650	57	4	have	have	VERB
ap-6650	57	5	xnci	xnci	PROPN
ap-6650	58	1	=	=	PRON
ap-6650	58	2	xi	xi	ADP
ap-6650	58	3	−	−	NUM
ap-6650	59	1	1	1	NUM
ap-6650	59	2	4	4	NUM
ap-6650	59	3	~	~	SYM
ap-6650	59	4	εijkθkpj	εijkθkpj	NOUN
ap-6650	59	5	:	:	PUNCT
ap-6650	59	6			PRON
ap-6650	59	7	xnc	xnc	X
ap-6650	60	1	=	=	SYM
ap-6650	60	2	x−	x−	PROPN
ap-6650	60	3	1	1	NUM
ap-6650	60	4	4	4	NUM
ap-6650	60	5	~	~	SYM
ap-6650	60	6	θpy	θpy	PROPN
ap-6650	60	7	ync	ync	NOUN
ap-6650	60	8	=	=	PROPN
ap-6650	60	9	y	y	PROPN
ap-6650	61	1	+	+	CCONJ
ap-6650	61	2	1	1	NUM
ap-6650	61	3	4	4	NUM
ap-6650	61	4	~	~	NOUN
ap-6650	61	5	θpx	θpx	ADJ
ap-6650	61	6	znc	znc	X
ap-6650	61	7	=	=	SYM
ap-6650	61	8	z	z	PROPN
ap-6650	61	9	,	,	PUNCT
ap-6650	61	10	pnci	pnci	PROPN
ap-6650	61	11	=	=	SYM
ap-6650	62	1	pi	pi	NOUN
ap-6650	63	1	+	+	CCONJ
ap-6650	63	2	1	1	NUM
ap-6650	63	3	4	4	NUM
ap-6650	63	4	~	~	NOUN
ap-6650	63	5	εijkηkxj	εijkηkxj	NOUN
ap-6650	63	6	:	:	PUNCT
ap-6650	63	7			PRON
ap-6650	63	8	pncx	pncx	VERB
ap-6650	63	9	=	=	SYM
ap-6650	63	10	px	px	PROPN
ap-6650	64	1	+	+	NOUN
ap-6650	64	2	1	1	NUM
ap-6650	64	3	4	4	NUM
ap-6650	64	4	~	~	NUM
ap-6650	64	5	ηy	ηy	ADJ
ap-6650	64	6	pncy	pncy	NOUN
ap-6650	64	7	=	=	PROPN
ap-6650	64	8	py	py	PROPN
ap-6650	65	1	−	−	NOUN
ap-6650	65	2	1	1	NUM
ap-6650	65	3	4	4	NUM
ap-6650	65	4	~	~	PUNCT
ap-6650	65	5	ηx	ηx	NOUN
ap-6650	65	6	pncz	pncz	PROPN
ap-6650	65	7	=	=	SYM
ap-6650	65	8	pz	pz	PROPN
ap-6650	65	9	.	.	PUNCT
ap-6650	66	1	(	(	PUNCT
ap-6650	66	2	6	6	NUM
ap-6650	66	3	)	)	PUNCT
ap-6650	66	4	in	in	ADP
ap-6650	66	5	noncommutative	noncommutative	ADJ
ap-6650	66	6	quantum	quantum	ADJ
ap-6650	66	7	mechanics	mechanic	NOUN
ap-6650	66	8	,	,	PUNCT
ap-6650	66	9	it	it	PRON
ap-6650	66	10	is	be	AUX
ap-6650	66	11	quite	quite	ADV
ap-6650	66	12	possible	possible	ADJ
ap-6650	66	13	that	that	SCONJ
ap-6650	66	14	we	we	PRON
ap-6650	66	15	replace	replace	VERB
ap-6650	66	16	the	the	DET
ap-6650	66	17	usual	usual	ADJ
ap-6650	66	18	product	product	NOUN
ap-6650	66	19	with	with	ADP
ap-6650	66	20	the	the	DET
ap-6650	66	21	moyal	moyal	ADV
ap-6650	66	22	-	-	PUNCT
ap-6650	66	23	weyl	weyl	ADJ
ap-6650	66	24	(	(	PUNCT
ap-6650	66	25	?	?	PUNCT
ap-6650	66	26	)	)	PUNCT
ap-6650	66	27	product	product	NOUN
ap-6650	66	28	,	,	PUNCT
ap-6650	66	29	then	then	ADV
ap-6650	66	30	the	the	DET
ap-6650	66	31	quantum	quantum	ADJ
ap-6650	66	32	mechanical	mechanical	ADJ
ap-6650	66	33	system	system	NOUN
ap-6650	66	34	will	will	AUX
ap-6650	66	35	simply	simply	ADV
ap-6650	66	36	become	become	VERB
ap-6650	66	37	the	the	DET
ap-6650	66	38	noncommutative	noncommutative	ADJ
ap-6650	66	39	quantum	quantum	ADJ
ap-6650	66	40	mechanical	mechanical	ADJ
ap-6650	66	41	system	system	NOUN
ap-6650	66	42	.	.	PUNCT
ap-6650	67	1	let	let	VERB
ap-6650	67	2	h	h	NOUN
ap-6650	67	3	(	(	PUNCT
ap-6650	67	4	x	x	X
ap-6650	67	5	,	,	PUNCT
ap-6650	67	6	p	p	X
ap-6650	67	7	)	)	PUNCT
ap-6650	67	8	be	be	AUX
ap-6650	67	9	the	the	DET
ap-6650	67	10	hamiltonian	hamiltonian	ADJ
ap-6650	67	11	operator	operator	NOUN
ap-6650	67	12	of	of	ADP
ap-6650	67	13	the	the	DET
ap-6650	67	14	usual	usual	ADJ
ap-6650	67	15	quantum	quantum	NOUN
ap-6650	67	16	system	system	NOUN
ap-6650	67	17	,	,	PUNCT
ap-6650	67	18	then	then	ADV
ap-6650	67	19	the	the	DET
ap-6650	67	20	corresponding	correspond	VERB
ap-6650	67	21	schrödinger	schrödinger	ADJ
ap-6650	67	22	equation	equation	NOUN
ap-6650	67	23	on	on	ADP
ap-6650	67	24	noncommutative	noncommutative	ADJ
ap-6650	67	25	quantum	quantum	ADJ
ap-6650	67	26	mechanics	mechanic	NOUN
ap-6650	67	27	is	be	AUX
ap-6650	67	28	typically	typically	ADV
ap-6650	67	29	written	write	VERB
ap-6650	67	30	as	as	ADP
ap-6650	67	31	h	h	NOUN
ap-6650	67	32	(	(	PUNCT
ap-6650	67	33	x	x	X
ap-6650	67	34	,	,	PUNCT
ap-6650	67	35	p	p	NOUN
ap-6650	67	36	)	)	PUNCT
ap-6650	67	37	?	?	PUNCT
ap-6650	68	1	ψ	ψ	X
ap-6650	68	2	(	(	PUNCT
ap-6650	68	3	x	x	X
ap-6650	68	4	,	,	PUNCT
ap-6650	68	5	p	p	NOUN
ap-6650	68	6	)	)	PUNCT
ap-6650	68	7	=	=	SYM
ap-6650	68	8	eψ	eψ	INTJ
ap-6650	68	9	(	(	PUNCT
ap-6650	68	10	x	x	X
ap-6650	68	11	,	,	PUNCT
ap-6650	68	12	p	p	NOUN
ap-6650	68	13	)	)	PUNCT
ap-6650	68	14	.	.	PUNCT
ap-6650	69	1	(	(	PUNCT
ap-6650	69	2	7	7	X
ap-6650	69	3	)	)	SYM
ap-6650	69	4	231	231	NUM
ap-6650	69	5	ilyas	ilyas	PROPN
ap-6650	69	6	haouam	haouam	VERB
ap-6650	69	7	acta	acta	PROPN
ap-6650	69	8	polytechnica	polytechnica	PROPN
ap-6650	69	9	the	the	DET
ap-6650	69	10	definition	definition	NOUN
ap-6650	69	11	of	of	ADP
ap-6650	69	12	moyal	moyal	ADV
ap-6650	69	13	-	-	PUNCT
ap-6650	69	14	weyl	weyl	VERB
ap-6650	69	15	product	product	NOUN
ap-6650	69	16	between	between	ADP
ap-6650	69	17	two	two	NUM
ap-6650	69	18	arbitrary	arbitrary	ADJ
ap-6650	69	19	functions	function	NOUN
ap-6650	69	20	f(x	f(x	PROPN
ap-6650	69	21	,	,	PUNCT
ap-6650	69	22	p	p	NOUN
ap-6650	69	23	)	)	PUNCT
ap-6650	69	24	and	and	CCONJ
ap-6650	69	25	g(x	g(x	NOUN
ap-6650	69	26	,	,	PUNCT
ap-6650	69	27	p	p	NOUN
ap-6650	69	28	)	)	PUNCT
ap-6650	69	29	in	in	ADP
ap-6650	69	30	phase	phase	NOUN
ap-6650	69	31	-	-	PUNCT
ap-6650	69	32	space	space	NOUN
ap-6650	69	33	is	be	AUX
ap-6650	69	34	given	give	VERB
ap-6650	69	35	by	by	ADP
ap-6650	69	36	[	[	X
ap-6650	69	37	37	37	NUM
ap-6650	69	38	]	]	PUNCT
ap-6650	69	39	(	(	PUNCT
ap-6650	69	40	f	f	X
ap-6650	69	41	?	?	PUNCT
ap-6650	70	1	g)(x	g)(x	PROPN
ap-6650	70	2	,	,	PUNCT
ap-6650	70	3	p	p	NOUN
ap-6650	70	4	)	)	PUNCT
ap-6650	70	5	=	=	SYM
ap-6650	70	6	exp	exp	NOUN
ap-6650	70	7	[	[	PUNCT
ap-6650	70	8	i2θab∂xa∂xb	i2θab∂xa∂xb	NUM
ap-6650	70	9	+	+	PUNCT
ap-6650	71	1	i	i	PROPN
ap-6650	71	2	2ηab∂pa∂pb	2ηab∂pa∂pb	NOUN
ap-6650	71	3	]	]	X
ap-6650	71	4	f	f	X
ap-6650	71	5	(	(	PUNCT
ap-6650	71	6	xa	xa	PROPN
ap-6650	71	7	,	,	PUNCT
ap-6650	71	8	pa	pa	PROPN
ap-6650	71	9	)	)	PUNCT
ap-6650	71	10	g	g	PROPN
ap-6650	71	11	(	(	PUNCT
ap-6650	71	12	xb	xb	PROPN
ap-6650	71	13	,	,	PUNCT
ap-6650	71	14	pb	pb	PROPN
ap-6650	71	15	)	)	PUNCT
ap-6650	71	16	=	=	SYM
ap-6650	71	17	f(x	f(x	PROPN
ap-6650	71	18	,	,	PUNCT
ap-6650	71	19	p)g(x	p)g(x	ADJ
ap-6650	71	20	,	,	PUNCT
ap-6650	71	21	p	p	X
ap-6650	71	22	)	)	PUNCT
ap-6650	72	1	+	+	CCONJ
ap-6650	72	2	∑	∑	PUNCT
ap-6650	72	3	n=1	n=1	PROPN
ap-6650	72	4	1	1	NUM
ap-6650	72	5	n	n	CCONJ
ap-6650	72	6	!	!	PUNCT
ap-6650	73	1	(	(	PUNCT
ap-6650	73	2	i	i	NOUN
ap-6650	73	3	2	2	NUM
ap-6650	73	4	)	)	PUNCT
ap-6650	73	5	n	n	PRON
ap-6650	73	6	θa1b1	θa1b1	PROPN
ap-6650	73	7	...	...	PUNCT
ap-6650	73	8	θanbn∂xa1	θanbn∂xa1	PROPN
ap-6650	73	9	...	...	SYM
ap-6650	73	10	∂xakf(x	∂xakf(x	PROPN
ap-6650	73	11	,	,	PUNCT
ap-6650	73	12	p)∂xb1	p)∂xb1	PROPN
ap-6650	73	13	...	...	PUNCT
ap-6650	73	14	∂xbkg(x	∂xbkg(x	X
ap-6650	73	15	,	,	PUNCT
ap-6650	73	16	p	p	X
ap-6650	73	17	)	)	PUNCT
ap-6650	74	1	+	+	CCONJ
ap-6650	74	2	∑	∑	PUNCT
ap-6650	74	3	n=1	n=1	PROPN
ap-6650	74	4	1	1	NUM
ap-6650	74	5	n	n	CCONJ
ap-6650	74	6	!	!	PUNCT
ap-6650	75	1	(	(	PUNCT
ap-6650	75	2	i	i	NOUN
ap-6650	75	3	2	2	NUM
ap-6650	75	4	)	)	PUNCT
ap-6650	75	5	n	n	PRON
ap-6650	75	6	ηa1b1	ηa1b1	PROPN
ap-6650	75	7	...	...	PUNCT
ap-6650	75	8	ηanbn∂pa1	ηanbn∂pa1	NOUN
ap-6650	75	9	...	...	PUNCT
ap-6650	75	10	∂pakf(x	∂pakf(x	NOUN
ap-6650	75	11	,	,	PUNCT
ap-6650	75	12	p)∂pb1	p)∂pb1	NOUN
ap-6650	75	13	...	...	PUNCT
ap-6650	76	1	∂pbkg(x	∂pbkg(x	X
ap-6650	76	2	,	,	PUNCT
ap-6650	76	3	p	p	NOUN
ap-6650	76	4	)	)	PUNCT
ap-6650	76	5	,	,	PUNCT
ap-6650	76	6	(	(	PUNCT
ap-6650	76	7	8)	8)	NUM
ap-6650	76	8	with	with	ADP
ap-6650	76	9	f(x	f(x	PROPN
ap-6650	76	10	,	,	PUNCT
ap-6650	76	11	p	p	NOUN
ap-6650	76	12	)	)	PUNCT
ap-6650	76	13	and	and	CCONJ
ap-6650	76	14	g(x	g(x	NOUN
ap-6650	76	15	,	,	PUNCT
ap-6650	76	16	p	p	NOUN
ap-6650	76	17	)	)	PUNCT
ap-6650	76	18	assumed	assume	VERB
ap-6650	76	19	to	to	PART
ap-6650	76	20	be	be	AUX
ap-6650	76	21	infinitely	infinitely	ADV
ap-6650	76	22	differentiable	differentiable	ADJ
ap-6650	76	23	.	.	PUNCT
ap-6650	77	1	if	if	SCONJ
ap-6650	77	2	we	we	PRON
ap-6650	77	3	consider	consider	VERB
ap-6650	77	4	the	the	DET
ap-6650	77	5	case	case	NOUN
ap-6650	77	6	of	of	ADP
ap-6650	77	7	a	a	DET
ap-6650	77	8	noncommutative	noncommutative	ADJ
ap-6650	77	9	space	space	NOUN
ap-6650	77	10	,	,	PUNCT
ap-6650	77	11	the	the	DET
ap-6650	77	12	definition	definition	NOUN
ap-6650	77	13	of	of	ADP
ap-6650	77	14	moyal	moyal	ADV
ap-6650	77	15	-	-	PUNCT
ap-6650	77	16	weyl	weyl	VERB
ap-6650	77	17	product	product	NOUN
ap-6650	77	18	will	will	AUX
ap-6650	77	19	be	be	AUX
ap-6650	77	20	reduced	reduce	VERB
ap-6650	77	21	to	to	ADP
ap-6650	77	22	[	[	X
ap-6650	77	23	38	38	NUM
ap-6650	77	24	]	]	PUNCT
ap-6650	77	25	(	(	PUNCT
ap-6650	77	26	f	f	X
ap-6650	77	27	?	?	PUNCT
ap-6650	78	1	g)(x	g)(x	PROPN
ap-6650	78	2	)	)	PUNCT
ap-6650	78	3	=	=	SYM
ap-6650	78	4	exp	exp	NOUN
ap-6650	78	5	[	[	PUNCT
ap-6650	78	6	i2θab∂xa∂xb	i2θab∂xa∂xb	X
ap-6650	78	7	]	]	SYM
ap-6650	78	8	f	f	X
ap-6650	78	9	(	(	PUNCT
ap-6650	78	10	xa	xa	PROPN
ap-6650	78	11	)	)	PUNCT
ap-6650	78	12	g	g	PROPN
ap-6650	78	13	(	(	PUNCT
ap-6650	78	14	xb	xb	PROPN
ap-6650	78	15	)	)	PUNCT
ap-6650	78	16	=	=	PUNCT
ap-6650	78	17	f(x)g(x	f(x)g(x	X
ap-6650	78	18	)	)	PUNCT
ap-6650	79	1	+	+	CCONJ
ap-6650	79	2	∑	∑	PUNCT
ap-6650	79	3	n=1	n=1	PROPN
ap-6650	79	4	1	1	NUM
ap-6650	79	5	n	n	CCONJ
ap-6650	79	6	!	!	PUNCT
ap-6650	80	1	(	(	PUNCT
ap-6650	80	2	i	i	NOUN
ap-6650	80	3	2	2	NUM
ap-6650	80	4	)	)	PUNCT
ap-6650	80	5	n	n	PRON
ap-6650	80	6	θa1b1	θa1b1	PROPN
ap-6650	80	7	...	...	PUNCT
ap-6650	80	8	θanbn∂a1	θanbn∂a1	NUM
ap-6650	80	9	...	...	PUNCT
ap-6650	81	1	∂akf(x)∂b1	∂akf(x)∂b1	PRON
ap-6650	81	2	...	...	PUNCT
ap-6650	81	3	∂bkg(x	∂bkg(x	ADJ
ap-6650	81	4	)	)	PUNCT
ap-6650	81	5	.	.	PUNCT
ap-6650	82	1	(	(	PUNCT
ap-6650	82	2	9	9	NUM
ap-6650	82	3	)	)	PUNCT
ap-6650	82	4	due	due	ADP
ap-6650	82	5	to	to	ADP
ap-6650	82	6	the	the	DET
ap-6650	82	7	nature	nature	NOUN
ap-6650	82	8	of	of	ADP
ap-6650	82	9	the	the	DET
ap-6650	82	10	?	?	NOUN
ap-6650	82	11	product	product	NOUN
ap-6650	82	12	,	,	PUNCT
ap-6650	82	13	the	the	DET
ap-6650	82	14	noncommutative	noncommutative	ADJ
ap-6650	82	15	field	field	NOUN
ap-6650	82	16	theories	theory	NOUN
ap-6650	82	17	for	for	ADP
ap-6650	82	18	low	low	ADJ
ap-6650	82	19	-	-	PUNCT
ap-6650	82	20	energy	energy	NOUN
ap-6650	82	21	fields	field	NOUN
ap-6650	82	22	(	(	PUNCT
ap-6650	82	23	e2	e2	PROPN
ap-6650	82	24	>	>	X
ap-6650	82	25	1	1	NUM
ap-6650	82	26	/	/	SYM
ap-6650	82	27	θ	θ	NOUN
ap-6650	82	28	)	)	PUNCT
ap-6650	82	29	at	at	ADP
ap-6650	82	30	a	a	DET
ap-6650	82	31	classical	classical	ADJ
ap-6650	82	32	level	level	NOUN
ap-6650	82	33	are	be	AUX
ap-6650	82	34	completely	completely	ADV
ap-6650	82	35	reduced	reduce	VERB
ap-6650	82	36	to	to	ADP
ap-6650	82	37	their	their	PRON
ap-6650	82	38	commutative	commutative	ADJ
ap-6650	82	39	versions	version	NOUN
ap-6650	82	40	.	.	PUNCT
ap-6650	83	1	however	however	ADV
ap-6650	83	2	,	,	PUNCT
ap-6650	83	3	this	this	PRON
ap-6650	83	4	is	be	AUX
ap-6650	83	5	just	just	ADV
ap-6650	83	6	the	the	DET
ap-6650	83	7	classical	classical	ADJ
ap-6650	83	8	result	result	NOUN
ap-6650	83	9	and	and	CCONJ
ap-6650	83	10	quantum	quantum	ADJ
ap-6650	83	11	corrections	correction	NOUN
ap-6650	83	12	always	always	ADV
ap-6650	83	13	reveal	reveal	VERB
ap-6650	83	14	the	the	DET
ap-6650	83	15	effects	effect	NOUN
ap-6650	83	16	of	of	ADP
ap-6650	83	17	θ	θ	PROPN
ap-6650	83	18	even	even	ADV
ap-6650	83	19	at	at	ADP
ap-6650	83	20	low	low	ADJ
ap-6650	83	21	-	-	PUNCT
ap-6650	83	22	energies	energy	NOUN
ap-6650	83	23	.	.	PUNCT
ap-6650	84	1	on	on	ADP
ap-6650	84	2	a	a	DET
ap-6650	84	3	noncommutative	noncommutative	ADJ
ap-6650	84	4	phase	phase	NOUN
ap-6650	84	5	-	-	PUNCT
ap-6650	84	6	space	space	NOUN
ap-6650	84	7	the	the	DET
ap-6650	84	8	?	?	NOUN
ap-6650	84	9	product	product	NOUN
ap-6650	84	10	can	can	AUX
ap-6650	84	11	be	be	AUX
ap-6650	84	12	replaced	replace	VERB
ap-6650	84	13	by	by	ADP
ap-6650	84	14	a	a	DET
ap-6650	84	15	bopp	bopp	PROPN
ap-6650	84	16	’s	’s	PART
ap-6650	84	17	shift	shift	NOUN
ap-6650	84	18	,	,	PUNCT
ap-6650	84	19	i.e.	i.e.	X
ap-6650	84	20	,	,	PUNCT
ap-6650	84	21	the	the	DET
ap-6650	84	22	?	?	NOUN
ap-6650	84	23	product	product	NOUN
ap-6650	84	24	can	can	AUX
ap-6650	84	25	be	be	AUX
ap-6650	84	26	changed	change	VERB
ap-6650	84	27	into	into	ADP
ap-6650	84	28	the	the	DET
ap-6650	84	29	ordinary	ordinary	ADJ
ap-6650	84	30	product	product	NOUN
ap-6650	84	31	by	by	ADP
ap-6650	84	32	replacing	replace	VERB
ap-6650	84	33	h	h	NOUN
ap-6650	84	34	(	(	PUNCT
ap-6650	84	35	x	x	NOUN
ap-6650	84	36	,	,	PUNCT
ap-6650	84	37	p	p	NOUN
ap-6650	84	38	)	)	PUNCT
ap-6650	84	39	with	with	ADP
ap-6650	84	40	h	h	PROPN
ap-6650	84	41	(	(	PUNCT
ap-6650	84	42	xnc	xnc	PROPN
ap-6650	84	43	,	,	PUNCT
ap-6650	84	44	pnc	pnc	PROPN
ap-6650	84	45	)	)	PUNCT
ap-6650	84	46	.	.	PUNCT
ap-6650	85	1	thus	thus	ADV
ap-6650	85	2	,	,	PUNCT
ap-6650	85	3	the	the	DET
ap-6650	85	4	corresponding	corresponding	ADJ
ap-6650	85	5	noncommutative	noncommutative	ADJ
ap-6650	85	6	schrödinger	schrödinger	ADJ
ap-6650	85	7	equation	equation	NOUN
ap-6650	85	8	can	can	AUX
ap-6650	85	9	be	be	AUX
ap-6650	85	10	written	write	VERB
ap-6650	85	11	as	as	ADP
ap-6650	85	12	h	h	NOUN
ap-6650	85	13	(	(	PUNCT
ap-6650	85	14	x	x	X
ap-6650	85	15	,	,	PUNCT
ap-6650	85	16	p	p	NOUN
ap-6650	85	17	)	)	PUNCT
ap-6650	85	18	?	?	PUNCT
ap-6650	86	1	ψ	ψ	X
ap-6650	86	2	(	(	PUNCT
ap-6650	86	3	x	x	X
ap-6650	86	4	,	,	PUNCT
ap-6650	86	5	p	p	NOUN
ap-6650	86	6	)	)	PUNCT
ap-6650	86	7	=	=	SYM
ap-6650	86	8	h	h	NOUN
ap-6650	86	9	(	(	PUNCT
ap-6650	86	10	xi	xi	ADP
ap-6650	86	11	−	−	PROPN
ap-6650	86	12	1	1	NUM
ap-6650	86	13	2	2	NUM
ap-6650	86	14	~	~	NOUN
ap-6650	86	15	θijpj	θijpj	NOUN
ap-6650	86	16	,	,	PUNCT
ap-6650	86	17	pµ	pµ	X
ap-6650	86	18	+	+	NOUN
ap-6650	86	19	1	1	NUM
ap-6650	86	20	2	2	NUM
ap-6650	86	21	~	~	NOUN
ap-6650	86	22	ηµνxν	ηµνxν	NOUN
ap-6650	86	23	)	)	PUNCT
ap-6650	86	24	ψ	ψ	NOUN
ap-6650	86	25	=	=	X
ap-6650	86	26	eψ	eψ	PROPN
ap-6650	86	27	.	.	PUNCT
ap-6650	87	1	(	(	PUNCT
ap-6650	87	2	10	10	NUM
ap-6650	87	3	)	)	PUNCT
ap-6650	87	4	note	note	NOUN
ap-6650	87	5	that	that	SCONJ
ap-6650	87	6	θ	θ	PROPN
ap-6650	87	7	and	and	CCONJ
ap-6650	87	8	η	η	PROPN
ap-6650	87	9	terms	term	NOUN
ap-6650	87	10	can	can	AUX
ap-6650	87	11	always	always	ADV
ap-6650	87	12	be	be	AUX
ap-6650	87	13	treated	treat	VERB
ap-6650	87	14	as	as	ADP
ap-6650	87	15	a	a	DET
ap-6650	87	16	perturbation	perturbation	NOUN
ap-6650	87	17	in	in	ADP
ap-6650	87	18	quantum	quantum	ADJ
ap-6650	87	19	mechanics	mechanic	NOUN
ap-6650	87	20	.	.	PUNCT
ap-6650	88	1	if	if	SCONJ
ap-6650	88	2	θ	θ	PROPN
ap-6650	88	3	=	=	SYM
ap-6650	88	4	η	η	PROPN
ap-6650	88	5	=	=	SYM
ap-6650	88	6	0	0	PROPN
ap-6650	88	7	,	,	PUNCT
ap-6650	88	8	the	the	DET
ap-6650	88	9	noncommutative	noncommutative	ADJ
ap-6650	88	10	algebra	algebra	NOUN
ap-6650	88	11	reduces	reduce	VERB
ap-6650	88	12	to	to	ADP
ap-6650	88	13	the	the	DET
ap-6650	88	14	ordinary	ordinary	ADJ
ap-6650	88	15	commutative	commutative	ADJ
ap-6650	88	16	one	one	NUM
ap-6650	88	17	.	.	PUNCT
ap-6650	89	1	3	3	X
ap-6650	89	2	.	.	X
ap-6650	89	3	pauli	pauli	PROPN
ap-6650	89	4	equation	equation	NOUN
ap-6650	89	5	in	in	ADP
ap-6650	89	6	noncommutative	noncommutative	ADJ
ap-6650	89	7	phase	phase	NOUN
ap-6650	89	8	-	-	PUNCT
ap-6650	89	9	space	space	NOUN
ap-6650	89	10	3.1	3.1	NUM
ap-6650	89	11	.	.	PUNCT
ap-6650	90	1	formulation	formulation	NOUN
ap-6650	90	2	of	of	ADP
ap-6650	90	3	noncommutative	noncommutative	PROPN
ap-6650	90	4	pauli	pauli	PROPN
ap-6650	90	5	equation	equation	NOUN
ap-6650	90	6	the	the	DET
ap-6650	90	7	pauli	pauli	PROPN
ap-6650	90	8	equation	equation	NOUN
ap-6650	90	9	is	be	AUX
ap-6650	90	10	the	the	DET
ap-6650	90	11	formulation	formulation	NOUN
ap-6650	90	12	of	of	ADP
ap-6650	90	13	the	the	DET
ap-6650	90	14	schrödinger	schrödinger	ADJ
ap-6650	90	15	equation	equation	NOUN
ap-6650	90	16	for	for	ADP
ap-6650	90	17	spin-1/2	spin-1/2	NOUN
ap-6650	90	18	particles	particle	NOUN
ap-6650	90	19	,	,	PUNCT
ap-6650	90	20	which	which	PRON
ap-6650	90	21	was	be	AUX
ap-6650	90	22	formulated	formulate	VERB
ap-6650	90	23	by	by	ADP
ap-6650	90	24	w.	w.	PROPN
ap-6650	90	25	pauli	pauli	PROPN
ap-6650	90	26	in	in	ADP
ap-6650	90	27	1927	1927	NUM
ap-6650	90	28	.	.	PUNCT
ap-6650	91	1	it	it	PRON
ap-6650	91	2	takes	take	VERB
ap-6650	91	3	into	into	ADP
ap-6650	91	4	account	account	NOUN
ap-6650	91	5	the	the	DET
ap-6650	91	6	interaction	interaction	NOUN
ap-6650	91	7	of	of	ADP
ap-6650	91	8	the	the	DET
ap-6650	91	9	particle	particle	NOUN
ap-6650	91	10	’s	’s	PART
ap-6650	91	11	spin	spin	NOUN
ap-6650	91	12	with	with	ADP
ap-6650	91	13	an	an	DET
ap-6650	91	14	electromagnetic	electromagnetic	ADJ
ap-6650	91	15	field	field	NOUN
ap-6650	91	16	.	.	PUNCT
ap-6650	92	1	in	in	ADP
ap-6650	92	2	other	other	ADJ
ap-6650	92	3	words	word	NOUN
ap-6650	92	4	,	,	PUNCT
ap-6650	92	5	it	it	PRON
ap-6650	92	6	is	be	AUX
ap-6650	92	7	the	the	DET
ap-6650	92	8	nonrelativistic	nonrelativistic	ADJ
ap-6650	92	9	limit	limit	NOUN
ap-6650	92	10	of	of	ADP
ap-6650	92	11	the	the	DET
ap-6650	92	12	dirac	dirac	NOUN
ap-6650	92	13	equation	equation	NOUN
ap-6650	92	14	.	.	PUNCT
ap-6650	93	1	furthermore	furthermore	ADV
ap-6650	93	2	,	,	PUNCT
ap-6650	93	3	the	the	DET
ap-6650	93	4	pauli	pauli	PROPN
ap-6650	93	5	equation	equation	NOUN
ap-6650	93	6	could	could	AUX
ap-6650	93	7	be	be	AUX
ap-6650	93	8	extracted	extract	VERB
ap-6650	93	9	from	from	ADP
ap-6650	93	10	other	other	ADJ
ap-6650	93	11	relativistic	relativistic	ADJ
ap-6650	93	12	higher	high	ADJ
ap-6650	93	13	spin	spin	NOUN
ap-6650	93	14	equations	equation	NOUN
ap-6650	93	15	such	such	ADJ
ap-6650	93	16	as	as	ADP
ap-6650	93	17	the	the	DET
ap-6650	93	18	dkp	dkp	NOUN
ap-6650	93	19	equation	equation	NOUN
ap-6650	93	20	considering	consider	VERB
ap-6650	93	21	the	the	DET
ap-6650	93	22	particle	particle	NOUN
ap-6650	93	23	interacting	interact	VERB
ap-6650	93	24	with	with	ADP
ap-6650	93	25	an	an	DET
ap-6650	93	26	electromagnetic	electromagnetic	ADJ
ap-6650	93	27	field	field	NOUN
ap-6650	93	28	[	[	X
ap-6650	93	29	37	37	NUM
ap-6650	93	30	]	]	PUNCT
ap-6650	93	31	.	.	PUNCT
ap-6650	94	1	the	the	DET
ap-6650	94	2	nonrelativistic	nonrelativistic	ADJ
ap-6650	94	3	schrödinger	schrödinger	ADJ
ap-6650	94	4	equation	equation	NOUN
ap-6650	94	5	that	that	PRON
ap-6650	94	6	describes	describe	VERB
ap-6650	94	7	an	an	DET
ap-6650	94	8	electron	electron	NOUN
ap-6650	94	9	in	in	ADP
ap-6650	94	10	interaction	interaction	NOUN
ap-6650	94	11	with	with	ADP
ap-6650	94	12	an	an	DET
ap-6650	94	13	electromagnetic	electromagnetic	ADJ
ap-6650	94	14	potential	potential	NOUN
ap-6650	94	15	(	(	PUNCT
ap-6650	94	16	a0	a0	NOUN
ap-6650	94	17	,	,	PUNCT
ap-6650	94	18	−→	−→	NOUN
ap-6650	94	19	a	a	PRON
ap-6650	94	20	)	)	PUNCT
ap-6650	94	21	(	(	PUNCT
ap-6650	94	22	−̂→p	−̂→p	X
ap-6650	94	23	is	be	AUX
ap-6650	94	24	replaced	replace	VERB
ap-6650	94	25	with	with	ADP
ap-6650	94	26	−̂→π	−̂→π	PROPN
ap-6650	94	27	=	=	PUNCT
ap-6650	94	28	−̂→p	−̂→p	PROPN
ap-6650	95	1	−	−	NOUN
ap-6650	95	2	e	e	NOUN
ap-6650	95	3	c	c	AUX
ap-6650	95	4	−→	−→	VERB
ap-6650	95	5	a	a	PRON
ap-6650	95	6	and	and	CCONJ
ap-6650	95	7	ê	ê	PROPN
ap-6650	95	8	with	with	ADP
ap-6650	95	9	ε̂	ε̂	NOUN
ap-6650	95	10	=	=	SYM
ap-6650	95	11	i~	i~	PROPN
ap-6650	95	12	∂	∂	NOUN
ap-6650	95	13	∂t	∂t	PROPN
ap-6650	95	14	−	−	PROPN
ap-6650	95	15	eφ	eφ	PROPN
ap-6650	95	16	)	)	PUNCT
ap-6650	95	17	is	be	AUX
ap-6650	95	18	1	1	NUM
ap-6650	95	19	2	2	NUM
ap-6650	95	20	m	m	NOUN
ap-6650	95	21	(	(	PUNCT
ap-6650	95	22	−̂→p	−̂→p	NUM
ap-6650	95	23	−	−	NOUN
ap-6650	95	24	e	e	NOUN
ap-6650	95	25	c	c	AUX
ap-6650	95	26	−→	−→	VERB
ap-6650	95	27	a	a	DET
ap-6650	95	28	(	(	PUNCT
ap-6650	95	29	r	r	NOUN
ap-6650	95	30	)	)	PUNCT
ap-6650	95	31	)	)	PUNCT
ap-6650	95	32	2	2	NUM
ap-6650	95	33	ψ	ψ	X
ap-6650	95	34	(	(	PUNCT
ap-6650	95	35	r	r	NOUN
ap-6650	95	36	,	,	PUNCT
ap-6650	95	37	t	t	PROPN
ap-6650	95	38	)	)	PUNCT
ap-6650	95	39	+	+	NUM
ap-6650	95	40	eφ	eφ	NOUN
ap-6650	95	41	(	(	PUNCT
ap-6650	95	42	r)ψ	r)ψ	X
ap-6650	95	43	(	(	PUNCT
ap-6650	95	44	r	r	NOUN
ap-6650	95	45	,	,	PUNCT
ap-6650	95	46	t	t	NOUN
ap-6650	95	47	)	)	PUNCT
ap-6650	95	48	=	=	SYM
ap-6650	95	49	i~	i~	PROPN
ap-6650	95	50	∂	∂	NUM
ap-6650	95	51	∂t	∂t	PROPN
ap-6650	95	52	ψ	ψ	X
ap-6650	95	53	(	(	PUNCT
ap-6650	95	54	r	r	NOUN
ap-6650	95	55	,	,	PUNCT
ap-6650	95	56	t	t	PROPN
ap-6650	95	57	)	)	PUNCT
ap-6650	95	58	,	,	PUNCT
ap-6650	95	59	(	(	PUNCT
ap-6650	95	60	11	11	NUM
ap-6650	95	61	)	)	PUNCT
ap-6650	95	62	where	where	SCONJ
ap-6650	95	63	−̂→p	−̂→p	ADV
ap-6650	95	64	=	=	SYM
ap-6650	95	65	i~	i~	ADJ
ap-6650	95	66	−→	−→	NOUN
ap-6650	95	67	∇	∇	NOUN
ap-6650	95	68	is	be	AUX
ap-6650	95	69	the	the	DET
ap-6650	95	70	momentum	momentum	NOUN
ap-6650	95	71	operator	operator	NOUN
ap-6650	95	72	,	,	PUNCT
ap-6650	95	73	m	m	PROPN
ap-6650	95	74	,	,	PUNCT
ap-6650	95	75	e	e	X
ap-6650	95	76	are	be	AUX
ap-6650	95	77	the	the	DET
ap-6650	95	78	mass	mass	NOUN
ap-6650	95	79	and	and	CCONJ
ap-6650	95	80	charge	charge	NOUN
ap-6650	95	81	of	of	ADP
ap-6650	95	82	the	the	DET
ap-6650	95	83	electron	electron	NOUN
ap-6650	95	84	,	,	PUNCT
ap-6650	95	85	and	and	CCONJ
ap-6650	95	86	c	c	NOUN
ap-6650	95	87	is	be	AUX
ap-6650	95	88	the	the	DET
ap-6650	95	89	speed	speed	NOUN
ap-6650	95	90	of	of	ADP
ap-6650	95	91	light	light	NOUN
ap-6650	95	92	.	.	PUNCT
ap-6650	96	1	ψ	ψ	X
ap-6650	96	2	(	(	PUNCT
ap-6650	96	3	r	r	NOUN
ap-6650	96	4	,	,	PUNCT
ap-6650	96	5	t	t	PROPN
ap-6650	96	6	)	)	PUNCT
ap-6650	96	7	is	be	AUX
ap-6650	96	8	the	the	DET
ap-6650	96	9	schrödinger	schrödinger	NOUN
ap-6650	96	10	’s	’s	PART
ap-6650	96	11	scalar	scalar	ADJ
ap-6650	96	12	wave	wave	NOUN
ap-6650	96	13	function	function	NOUN
ap-6650	96	14	.	.	PUNCT
ap-6650	97	1	the	the	DET
ap-6650	97	2	appearance	appearance	NOUN
ap-6650	97	3	of	of	ADP
ap-6650	97	4	real	real	ADV
ap-6650	97	5	-	-	PUNCT
ap-6650	97	6	valued	value	VERB
ap-6650	97	7	electromagnetic	electromagnetic	ADJ
ap-6650	97	8	coulomb	coulomb	NOUN
ap-6650	97	9	and	and	CCONJ
ap-6650	97	10	vector	vector	NOUN
ap-6650	97	11	potentials	potential	NOUN
ap-6650	97	12	,	,	PUNCT
ap-6650	97	13	φ	φ	PROPN
ap-6650	97	14	(	(	PUNCT
ap-6650	97	15	−→r	−→r	PROPN
ap-6650	97	16	,	,	PUNCT
ap-6650	97	17	t	t	PROPN
ap-6650	97	18	)	)	PUNCT
ap-6650	97	19	and	and	CCONJ
ap-6650	97	20	−→a	−→a	PROPN
ap-6650	97	21	(	(	PUNCT
ap-6650	97	22	−→r	−→r	NOUN
ap-6650	97	23	,	,	PUNCT
ap-6650	97	24	t	t	PROPN
ap-6650	97	25	)	)	PUNCT
ap-6650	97	26	,	,	PUNCT
ap-6650	97	27	is	be	AUX
ap-6650	97	28	a	a	DET
ap-6650	97	29	consequence	consequence	NOUN
ap-6650	97	30	of	of	ADP
ap-6650	97	31	using	use	VERB
ap-6650	97	32	the	the	DET
ap-6650	97	33	gauge	gauge	NOUN
ap-6650	97	34	-	-	PUNCT
ap-6650	97	35	invariant	invariant	ADJ
ap-6650	97	36	minimal	minimal	ADJ
ap-6650	97	37	coupling	coupling	NOUN
ap-6650	97	38	assumption	assumption	NOUN
ap-6650	97	39	to	to	PART
ap-6650	97	40	describe	describe	VERB
ap-6650	97	41	the	the	DET
ap-6650	97	42	interaction	interaction	NOUN
ap-6650	97	43	with	with	ADP
ap-6650	97	44	the	the	DET
ap-6650	97	45	external	external	ADJ
ap-6650	97	46	magnetic	magnetic	ADJ
ap-6650	97	47	and	and	CCONJ
ap-6650	97	48	electric	electric	ADJ
ap-6650	97	49	fields	field	NOUN
ap-6650	97	50	defined	define	VERB
ap-6650	97	51	by	by	ADP
ap-6650	97	52	−→	−→	NOUN
ap-6650	97	53	e	e	NOUN
ap-6650	97	54	=	=	SYM
ap-6650	97	55	−−→∇φ−	−−→∇φ−	PROPN
ap-6650	97	56	1	1	NUM
ap-6650	97	57	c	c	NOUN
ap-6650	97	58	∂	∂	NUM
ap-6650	97	59	−→	−→	NOUN
ap-6650	97	60	a	a	DET
ap-6650	97	61	∂t	∂t	PROPN
ap-6650	97	62	,	,	PUNCT
ap-6650	97	63	−→	−→	NOUN
ap-6650	97	64	b	b	X
ap-6650	97	65	=	=	SYM
ap-6650	97	66	−→∇	−→∇	PROPN
ap-6650	97	67	×−→a	×−→a	PROPN
ap-6650	97	68	.	.	PUNCT
ap-6650	98	1	(	(	PUNCT
ap-6650	98	2	12	12	NUM
ap-6650	98	3	)	)	PUNCT
ap-6650	98	4	however	however	ADV
ap-6650	98	5	,	,	PUNCT
ap-6650	98	6	the	the	DET
ap-6650	98	7	electron	electron	NOUN
ap-6650	98	8	gains	gain	VERB
ap-6650	98	9	potential	potential	ADJ
ap-6650	98	10	energy	energy	NOUN
ap-6650	98	11	when	when	SCONJ
ap-6650	98	12	the	the	DET
ap-6650	98	13	spin	spin	NOUN
ap-6650	98	14	interacts	interact	VERB
ap-6650	98	15	with	with	ADP
ap-6650	98	16	the	the	DET
ap-6650	98	17	magnetic	magnetic	ADJ
ap-6650	98	18	field	field	NOUN
ap-6650	98	19	,	,	PUNCT
ap-6650	98	20	therefore	therefore	ADV
ap-6650	98	21	,	,	PUNCT
ap-6650	98	22	the	the	DET
ap-6650	98	23	pauli	pauli	PROPN
ap-6650	98	24	equation	equation	NOUN
ap-6650	98	25	of	of	ADP
ap-6650	98	26	an	an	DET
ap-6650	98	27	electron	electron	NOUN
ap-6650	98	28	with	with	ADP
ap-6650	98	29	a	a	DET
ap-6650	98	30	spin	spin	NOUN
ap-6650	98	31	is	be	AUX
ap-6650	98	32	given	give	VERB
ap-6650	98	33	by	by	ADP
ap-6650	98	34	[	[	X
ap-6650	98	35	1	1	NUM
ap-6650	98	36	,	,	PUNCT
ap-6650	98	37	8	8	NUM
ap-6650	98	38	]	]	SYM
ap-6650	98	39	1	1	NUM
ap-6650	98	40	2	2	NUM
ap-6650	98	41	m	m	VERB
ap-6650	98	42	(	(	PUNCT
ap-6650	98	43	−→σ	−→σ	VERB
ap-6650	98	44	.−̂→π	.−̂→π	PUNCT
ap-6650	98	45	)	)	PUNCT
ap-6650	98	46	2	2	NUM
ap-6650	98	47	ψ	ψ	X
ap-6650	98	48	(	(	PUNCT
ap-6650	98	49	r	r	NOUN
ap-6650	98	50	,	,	PUNCT
ap-6650	98	51	t	t	PROPN
ap-6650	98	52	)	)	PUNCT
ap-6650	98	53	+	+	CCONJ
ap-6650	98	54	eφψ	eφψ	PROPN
ap-6650	98	55	(	(	PUNCT
ap-6650	98	56	r	r	NOUN
ap-6650	98	57	,	,	PUNCT
ap-6650	98	58	t	t	PROPN
ap-6650	98	59	)	)	PUNCT
ap-6650	98	60	=	=	SYM
ap-6650	98	61	1	1	NUM
ap-6650	98	62	2	2	NUM
ap-6650	98	63	m	m	VERB
ap-6650	98	64	(	(	PUNCT
ap-6650	98	65	−̂→p	−̂→p	NUM
ap-6650	98	66	−	−	NOUN
ap-6650	98	67	e	e	NOUN
ap-6650	98	68	c	c	AUX
ap-6650	98	69	−→	−→	VERB
ap-6650	98	70	a	a	DET
ap-6650	98	71	)	)	SYM
ap-6650	98	72	2	2	NUM
ap-6650	98	73	ψ	ψ	X
ap-6650	98	74	(	(	PUNCT
ap-6650	98	75	r	r	NOUN
ap-6650	98	76	,	,	PUNCT
ap-6650	98	77	t	t	PROPN
ap-6650	98	78	)	)	PUNCT
ap-6650	98	79	+	+	CCONJ
ap-6650	99	1	eφψ	eφψ	PROPN
ap-6650	99	2	(	(	PUNCT
ap-6650	99	3	r	r	NOUN
ap-6650	99	4	,	,	PUNCT
ap-6650	99	5	t	t	PROPN
ap-6650	99	6	)	)	PUNCT
ap-6650	99	7	+	+	CCONJ
ap-6650	99	8	µb	µb	VERB
ap-6650	99	9	−→σ	−→σ	VERB
ap-6650	99	10	.	.	PUNCT
ap-6650	100	1	−→	−→	NOUN
ap-6650	100	2	bψ	bψ	NOUN
ap-6650	100	3	(	(	PUNCT
ap-6650	100	4	r	r	NOUN
ap-6650	100	5	,	,	PUNCT
ap-6650	100	6	t	t	PROPN
ap-6650	100	7	)	)	PUNCT
ap-6650	100	8	=	=	SYM
ap-6650	101	1	i~	i~	PROPN
ap-6650	101	2	∂	∂	NUM
ap-6650	101	3	∂t	∂t	PROPN
ap-6650	101	4	ψ	ψ	X
ap-6650	101	5	(	(	PUNCT
ap-6650	101	6	r	r	NOUN
ap-6650	101	7	,	,	PUNCT
ap-6650	101	8	t	t	PROPN
ap-6650	101	9	)	)	PUNCT
ap-6650	101	10	,	,	PUNCT
ap-6650	101	11	(	(	PUNCT
ap-6650	101	12	13	13	NUM
ap-6650	101	13	)	)	PUNCT
ap-6650	101	14	where	where	SCONJ
ap-6650	101	15	ψ	ψ	X
ap-6650	101	16	(	(	PUNCT
ap-6650	101	17	r	r	NOUN
ap-6650	101	18	,	,	PUNCT
ap-6650	101	19	t	t	PROPN
ap-6650	101	20	)	)	PUNCT
ap-6650	101	21	=	=	SYM
ap-6650	101	22	(	(	PUNCT
ap-6650	101	23	ψ1	ψ1	ADJ
ap-6650	101	24	ψ2	ψ2	NOUN
ap-6650	101	25	)	)	PUNCT
ap-6650	101	26	t	t	PROPN
ap-6650	101	27	is	be	AUX
ap-6650	101	28	the	the	DET
ap-6650	101	29	spinor	spinor	NOUN
ap-6650	101	30	wave	wave	NOUN
ap-6650	101	31	function	function	NOUN
ap-6650	101	32	,	,	PUNCT
ap-6650	101	33	which	which	PRON
ap-6650	101	34	replaces	replace	VERB
ap-6650	101	35	the	the	DET
ap-6650	101	36	scalar	scalar	ADJ
ap-6650	101	37	wave	wave	NOUN
ap-6650	101	38	function	function	NOUN
ap-6650	101	39	.	.	PUNCT
ap-6650	102	1	with	with	ADP
ap-6650	102	2	µb	µb	NOUN
ap-6650	102	3	=	=	PUNCT
ap-6650	102	4	|e|~	|e|~	NUM
ap-6650	102	5	2mc	2mc	NOUN
ap-6650	102	6	=	=	X
ap-6650	103	1	9.27×	9.27×	PROPN
ap-6650	103	2	10−24jt−1	10−24jt−1	NUM
ap-6650	103	3	being	be	AUX
ap-6650	103	4	the	the	DET
ap-6650	103	5	bohr	bohr	NOUN
ap-6650	103	6	’s	’s	PART
ap-6650	103	7	magneton	magneton	PROPN
ap-6650	103	8	,	,	PUNCT
ap-6650	103	9	−→b	−→b	PROPN
ap-6650	103	10	is	be	AUX
ap-6650	103	11	the	the	DET
ap-6650	103	12	applied	apply	VERB
ap-6650	103	13	magnetic	magnetic	ADJ
ap-6650	103	14	field	field	NOUN
ap-6650	103	15	vector	vector	NOUN
ap-6650	103	16	and	and	CCONJ
ap-6650	103	17	µb−→σ	µb−→σ	X
ap-6650	103	18	represents	represent	VERB
ap-6650	103	19	the	the	DET
ap-6650	103	20	magnetic	magnetic	ADJ
ap-6650	103	21	moment	moment	NOUN
ap-6650	103	22	.	.	PUNCT
ap-6650	104	1	−→σ	−→σ	PROPN
ap-6650	104	2	’s	’	VERB
ap-6650	104	3	being	be	AUX
ap-6650	104	4	the	the	DET
ap-6650	104	5	three	three	NUM
ap-6650	104	6	pauli	pauli	PROPN
ap-6650	104	7	matrices	matrix	NOUN
ap-6650	104	8	(	(	PUNCT
ap-6650	104	9	tr−→σ	tr−→σ	PROPN
ap-6650	104	10	=	=	SYM
ap-6650	104	11	0	0	NUM
ap-6650	104	12	)	)	PUNCT
ap-6650	104	13	,	,	PUNCT
ap-6650	104	14	which	which	PRON
ap-6650	104	15	obey	obey	VERB
ap-6650	104	16	the	the	DET
ap-6650	104	17	following	follow	VERB
ap-6650	104	18	algebra	algebra	NOUN
ap-6650	104	19	[	[	X
ap-6650	104	20	σi	σi	NOUN
ap-6650	104	21	,	,	PUNCT
ap-6650	104	22	σj	σj	VERB
ap-6650	104	23	]	]	PUNCT
ap-6650	104	24	=	=	SYM
ap-6650	104	25	2iεijkσk	2iεijkσk	NUM
ap-6650	104	26	,	,	PUNCT
ap-6650	104	27	(	(	PUNCT
ap-6650	104	28	14	14	NUM
ap-6650	104	29	)	)	PUNCT
ap-6650	104	30	232	232	NUM
ap-6650	104	31	vol	vol	NOUN
ap-6650	104	32	.	.	PUNCT
ap-6650	105	1	61	61	NUM
ap-6650	105	2	no	no	NOUN
ap-6650	105	3	.	.	PUNCT
ap-6650	106	1	1/2021	1/2021	NUM
ap-6650	106	2	on	on	ADP
ap-6650	106	3	the	the	DET
ap-6650	106	4	three	three	NUM
ap-6650	106	5	-	-	PUNCT
ap-6650	106	6	dimensional	dimensional	ADJ
ap-6650	106	7	pauli	pauli	PROPN
ap-6650	106	8	equation	equation	NOUN
ap-6650	106	9	in	in	ADP
ap-6650	106	10	noncommutative	noncommutative	ADJ
ap-6650	106	11	phase	phase	NOUN
ap-6650	106	12	-	-	PUNCT
ap-6650	106	13	space	space	NOUN
ap-6650	106	14	σiσj	σiσj	ADJ
ap-6650	106	15	=	=	NOUN
ap-6650	106	16	δiji	δiji	NOUN
ap-6650	106	17	+	+	CCONJ
ap-6650	107	1	i	i	PROPN
ap-6650	107	2	∑	∑	PROPN
ap-6650	107	3	k	k	PROPN
ap-6650	107	4	εijkσk	εijkσk	PROPN
ap-6650	107	5	,	,	PUNCT
ap-6650	107	6	(	(	PUNCT
ap-6650	107	7	15	15	NUM
ap-6650	107	8	)	)	PUNCT
ap-6650	107	9	(	(	PUNCT
ap-6650	107	10	−→σ	−→σ	VERB
ap-6650	107	11	.−̂→a	.−̂→a	NOUN
ap-6650	107	12	)	)	PUNCT
ap-6650	107	13	(	(	PUNCT
ap-6650	107	14	−→σ	−→σ	VERB
ap-6650	107	15	.−̂→b	.−̂→b	NOUN
ap-6650	107	16	)	)	PUNCT
ap-6650	108	1	=	=	PUNCT
ap-6650	108	2	−̂→a	−̂→a	NOUN
ap-6650	108	3	.−̂→b	.−̂→b	PUNCT
ap-6650	109	1	+	+	CCONJ
ap-6650	109	2	i−→σ	i−→σ	PROPN
ap-6650	109	3	.	.	PUNCT
ap-6650	110	1	(	(	PUNCT
ap-6650	110	2	−̂→a	−̂→a	NOUN
ap-6650	110	3	×	×	NOUN
ap-6650	110	4	−̂→	−̂→	NOUN
ap-6650	110	5	b	b	NOUN
ap-6650	110	6	)	)	PUNCT
ap-6650	110	7	,	,	PUNCT
ap-6650	110	8	(	(	PUNCT
ap-6650	110	9	16	16	NUM
ap-6650	110	10	)	)	PUNCT
ap-6650	110	11	−̂→a	−̂→a	NOUN
ap-6650	110	12	,	,	PUNCT
ap-6650	110	13	−̂→b	−̂→b	NOUN
ap-6650	110	14	are	be	AUX
ap-6650	110	15	any	any	DET
ap-6650	110	16	two	two	NUM
ap-6650	110	17	vector	vector	NOUN
ap-6650	110	18	operators	operator	NOUN
ap-6650	110	19	that	that	PRON
ap-6650	110	20	commute	commute	VERB
ap-6650	110	21	with	with	ADP
ap-6650	110	22	−→σ	−→σ	PROPN
ap-6650	110	23	.	.	PUNCT
ap-6650	111	1	it	it	PRON
ap-6650	111	2	must	must	AUX
ap-6650	111	3	be	be	AUX
ap-6650	111	4	emphasized	emphasize	VERB
ap-6650	111	5	that	that	SCONJ
ap-6650	111	6	the	the	DET
ap-6650	111	7	third	third	ADJ
ap-6650	111	8	term	term	NOUN
ap-6650	111	9	of	of	ADP
ap-6650	111	10	equation	equation	NOUN
ap-6650	111	11	(	(	PUNCT
ap-6650	111	12	13	13	NUM
ap-6650	111	13	)	)	PUNCT
ap-6650	111	14	is	be	AUX
ap-6650	111	15	the	the	DET
ap-6650	111	16	zeeman	zeeman	PROPN
ap-6650	111	17	term	term	NOUN
ap-6650	111	18	,	,	PUNCT
ap-6650	111	19	which	which	PRON
ap-6650	111	20	is	be	AUX
ap-6650	111	21	generated	generate	VERB
ap-6650	111	22	automatically	automatically	ADV
ap-6650	111	23	by	by	ADP
ap-6650	111	24	using	use	VERB
ap-6650	111	25	feature	feature	NOUN
ap-6650	111	26	(	(	PUNCT
ap-6650	111	27	16	16	NUM
ap-6650	111	28	)	)	PUNCT
ap-6650	111	29	with	with	ADP
ap-6650	111	30	a	a	DET
ap-6650	111	31	correct	correct	ADJ
ap-6650	111	32	g	g	NOUN
ap-6650	111	33	-	-	PUNCT
ap-6650	111	34	factor	factor	NOUN
ap-6650	111	35	of	of	ADP
ap-6650	111	36	g	g	NOUN
ap-6650	111	37	=	=	SYM
ap-6650	111	38	2	2	NUM
ap-6650	111	39	as	as	SCONJ
ap-6650	111	40	reduced	reduce	VERB
ap-6650	111	41	in	in	ADP
ap-6650	111	42	the	the	DET
ap-6650	111	43	bohr	bohr	NOUN
ap-6650	111	44	’s	’s	PART
ap-6650	111	45	magneton	magneton	PROPN
ap-6650	111	46	rather	rather	ADV
ap-6650	111	47	than	than	ADP
ap-6650	111	48	being	be	AUX
ap-6650	111	49	introduced	introduce	VERB
ap-6650	111	50	by	by	ADP
ap-6650	111	51	hand	hand	NOUN
ap-6650	111	52	as	as	ADP
ap-6650	111	53	a	a	DET
ap-6650	111	54	phenomenological	phenomenological	ADJ
ap-6650	111	55	term	term	NOUN
ap-6650	111	56	,	,	PUNCT
ap-6650	111	57	as	as	SCONJ
ap-6650	111	58	is	be	AUX
ap-6650	111	59	usually	usually	ADV
ap-6650	111	60	done	do	VERB
ap-6650	111	61	.	.	PUNCT
ap-6650	112	1	the	the	DET
ap-6650	112	2	pauli	pauli	PROPN
ap-6650	112	3	equation	equation	NOUN
ap-6650	112	4	in	in	ADP
ap-6650	112	5	a	a	DET
ap-6650	112	6	noncommutative	noncommutative	ADJ
ap-6650	112	7	phase	phase	NOUN
ap-6650	112	8	-	-	PUNCT
ap-6650	112	9	space	space	NOUN
ap-6650	112	10	is	be	AUX
ap-6650	112	11	h	h	NOUN
ap-6650	112	12	(	(	PUNCT
ap-6650	112	13	xnc	xnc	PROPN
ap-6650	112	14	,	,	PUNCT
ap-6650	112	15	pnc)ψ	pnc)ψ	PROPN
ap-6650	112	16	(	(	PUNCT
ap-6650	112	17	xnc	xnc	PROPN
ap-6650	112	18	,	,	PUNCT
ap-6650	112	19	t	t	PROPN
ap-6650	112	20	)	)	PUNCT
ap-6650	113	1	=	=	SYM
ap-6650	113	2	h	h	NOUN
ap-6650	113	3	(	(	PUNCT
ap-6650	113	4	x	x	NOUN
ap-6650	113	5	,	,	PUNCT
ap-6650	113	6	pnc	pnc	PROPN
ap-6650	113	7	)	)	PUNCT
ap-6650	113	8	?	?	PUNCT
ap-6650	114	1	ψ	ψ	X
ap-6650	114	2	(	(	PUNCT
ap-6650	114	3	x	x	X
ap-6650	114	4	,	,	PUNCT
ap-6650	114	5	t	t	PROPN
ap-6650	114	6	)	)	PUNCT
ap-6650	114	7	=	=	PUNCT
ap-6650	115	1	e	e	X
ap-6650	115	2	i	i	ADP
ap-6650	115	3	2	2	NUM
ap-6650	115	4	θab∂xa∂xbh	θab∂xa∂xbh	NUM
ap-6650	115	5	(	(	PUNCT
ap-6650	115	6	xa	xa	PROPN
ap-6650	115	7	,	,	PUNCT
ap-6650	115	8	pnc)ψ	pnc)ψ	PROPN
ap-6650	115	9	(	(	PUNCT
ap-6650	115	10	xb	xb	PROPN
ap-6650	115	11	,	,	PUNCT
ap-6650	115	12	t	t	PROPN
ap-6650	115	13	)	)	PUNCT
ap-6650	115	14	=	=	SYM
ap-6650	116	1	i~	i~	PROPN
ap-6650	116	2	∂	∂	NUM
ap-6650	116	3	∂t	∂t	PROPN
ap-6650	116	4	ψ	ψ	X
ap-6650	116	5	(	(	PUNCT
ap-6650	116	6	x	x	PROPN
ap-6650	116	7	,	,	PUNCT
ap-6650	116	8	t	t	PROPN
ap-6650	116	9	)	)	PUNCT
ap-6650	116	10	.	.	PUNCT
ap-6650	117	1	(	(	PUNCT
ap-6650	117	2	17	17	NUM
ap-6650	117	3	)	)	PUNCT
ap-6650	117	4	here	here	ADV
ap-6650	117	5	we	we	PRON
ap-6650	117	6	achieved	achieve	VERB
ap-6650	117	7	the	the	DET
ap-6650	117	8	noncommutativity	noncommutativity	NOUN
ap-6650	117	9	in	in	ADP
ap-6650	117	10	space	space	NOUN
ap-6650	117	11	using	use	VERB
ap-6650	117	12	moyal	moyal	ADJ
ap-6650	117	13	?	?	PUNCT
ap-6650	117	14	product	product	NOUN
ap-6650	117	15	,	,	PUNCT
ap-6650	117	16	and	and	CCONJ
ap-6650	117	17	then	then	ADV
ap-6650	117	18	the	the	DET
ap-6650	117	19	noncommutativity	noncommutativity	NOUN
ap-6650	117	20	in	in	ADP
ap-6650	117	21	phase	phase	NOUN
ap-6650	117	22	through	through	ADP
ap-6650	117	23	bopp	bopp	VERB
ap-6650	117	24	-	-	PUNCT
ap-6650	117	25	shift	shift	NOUN
ap-6650	117	26	.	.	PUNCT
ap-6650	118	1	using	use	VERB
ap-6650	118	2	equation	equation	NOUN
ap-6650	118	3	(	(	PUNCT
ap-6650	118	4	9	9	NUM
ap-6650	118	5	)	)	PUNCT
ap-6650	118	6	,	,	PUNCT
ap-6650	118	7	we	we	PRON
ap-6650	118	8	have	have	VERB
ap-6650	118	9	h	h	NOUN
ap-6650	118	10	(	(	PUNCT
ap-6650	118	11	xnc	xnc	PROPN
ap-6650	118	12	,	,	PUNCT
ap-6650	118	13	pnc)ψ	pnc)ψ	PROPN
ap-6650	118	14	(	(	PUNCT
ap-6650	118	15	xnc	xnc	PROPN
ap-6650	118	16	,	,	PUNCT
ap-6650	118	17	t	t	PROPN
ap-6650	118	18	)	)	PUNCT
ap-6650	118	19	=	=	PUNCT
ap-6650	119	1	=	=	PRON
ap-6650	119	2	{	{	PUNCT
ap-6650	119	3	h	h	NOUN
ap-6650	119	4	(	(	PUNCT
ap-6650	119	5	x	x	PROPN
ap-6650	119	6	,	,	PUNCT
ap-6650	119	7	pnc	pnc	PROPN
ap-6650	119	8	)	)	PUNCT
ap-6650	120	1	+	+	CCONJ
ap-6650	120	2	i	i	PRON
ap-6650	120	3	2θab∂ah	2θab∂ah	NUM
ap-6650	120	4	(	(	PUNCT
ap-6650	120	5	x	x	NOUN
ap-6650	120	6	,	,	PUNCT
ap-6650	120	7	pnc	pnc	PROPN
ap-6650	120	8	)	)	PUNCT
ap-6650	120	9	∂b	∂b	PROPN
ap-6650	120	10	+	+	CCONJ
ap-6650	120	11	∑	∑	PUNCT
ap-6650	120	12	n=2	n=2	ADV
ap-6650	120	13	1	1	NUM
ap-6650	120	14	n	n	NOUN
ap-6650	120	15	!	!	PUNCT
ap-6650	121	1	(	(	PUNCT
ap-6650	121	2	i	i	NOUN
ap-6650	121	3	2	2	NUM
ap-6650	121	4	)	)	PUNCT
ap-6650	121	5	n	n	PRON
ap-6650	121	6	θa1b1	θa1b1	PROPN
ap-6650	121	7	...	...	PUNCT
ap-6650	121	8	θanbn∂a1	θanbn∂a1	NUM
ap-6650	121	9	...	...	PUNCT
ap-6650	122	1	∂akh	∂akh	NUM
ap-6650	122	2	(	(	PUNCT
ap-6650	122	3	x	x	NOUN
ap-6650	122	4	,	,	PUNCT
ap-6650	122	5	pnc	pnc	PROPN
ap-6650	122	6	)	)	PUNCT
ap-6650	122	7	∂b1	∂b1	PROPN
ap-6650	122	8	...	...	PUNCT
ap-6650	122	9	∂bk	∂bk	ADJ
ap-6650	122	10	}	}	PUNCT
ap-6650	122	11	ψ	ψ	X
ap-6650	122	12	.	.	PUNCT
ap-6650	123	1	(	(	PUNCT
ap-6650	123	2	18	18	NUM
ap-6650	123	3	)	)	PUNCT
ap-6650	123	4	in	in	ADP
ap-6650	123	5	the	the	DET
ap-6650	123	6	case	case	NOUN
ap-6650	123	7	of	of	ADP
ap-6650	123	8	a	a	DET
ap-6650	123	9	constant	constant	ADJ
ap-6650	123	10	real	real	ADJ
ap-6650	123	11	magnetic	magnetic	ADJ
ap-6650	123	12	field	field	NOUN
ap-6650	123	13	−→b	−→b	NOUN
ap-6650	123	14	=	=	SYM
ap-6650	123	15	(	(	PUNCT
ap-6650	123	16	0	0	NUM
ap-6650	123	17	,	,	PUNCT
ap-6650	123	18	0	0	NUM
ap-6650	123	19	,	,	PUNCT
ap-6650	123	20	b	b	NOUN
ap-6650	123	21	)	)	PUNCT
ap-6650	124	1	=	=	PUNCT
ap-6650	124	2	b−→e	b−→e	ADP
ap-6650	124	3	3	3	NUM
ap-6650	124	4	oriented	orient	VERB
ap-6650	124	5	along	along	ADP
ap-6650	124	6	the	the	DET
ap-6650	124	7	axis	axis	NOUN
ap-6650	124	8	(	(	PUNCT
ap-6650	124	9	oz	oz	NOUN
ap-6650	124	10	)	)	PUNCT
ap-6650	124	11	,	,	PUNCT
ap-6650	124	12	which	which	PRON
ap-6650	124	13	is	be	AUX
ap-6650	124	14	often	often	ADV
ap-6650	124	15	referred	refer	VERB
ap-6650	124	16	to	to	ADP
ap-6650	124	17	as	as	ADP
ap-6650	124	18	the	the	DET
ap-6650	124	19	landau	landau	NOUN
ap-6650	124	20	system	system	NOUN
ap-6650	124	21	.	.	PUNCT
ap-6650	125	1	we	we	PRON
ap-6650	125	2	have	have	VERB
ap-6650	125	3	the	the	DET
ap-6650	125	4	following	follow	VERB
ap-6650	125	5	symmetric	symmetric	ADJ
ap-6650	125	6	gauge	gauge	NOUN
ap-6650	125	7	−→	−→	NOUN
ap-6650	125	8	a	a	DET
ap-6650	125	9	=	=	X
ap-6650	125	10	−→	−→	NOUN
ap-6650	125	11	b	b	PROPN
ap-6650	125	12	×−→r	×−→r	NOUN
ap-6650	125	13	2	2	NUM
ap-6650	125	14	=	=	SYM
ap-6650	125	15	b	b	SYM
ap-6650	125	16	2	2	NUM
ap-6650	125	17	(	(	PUNCT
ap-6650	125	18	−y	−y	NOUN
ap-6650	125	19	,	,	PUNCT
ap-6650	125	20	x	x	X
ap-6650	125	21	,	,	PUNCT
ap-6650	125	22	0	0	NUM
ap-6650	125	23	)	)	PUNCT
ap-6650	125	24	,	,	PUNCT
ap-6650	125	25	with	with	ADP
ap-6650	125	26	a0	a0	PROPN
ap-6650	125	27	(	(	PUNCT
ap-6650	125	28	x	x	NOUN
ap-6650	125	29	)	)	PUNCT
ap-6650	125	30	=	=	SYM
ap-6650	125	31	eφ	eφ	PROPN
ap-6650	125	32	=	=	SYM
ap-6650	125	33	0	0	PROPN
ap-6650	125	34	.	.	PUNCT
ap-6650	126	1	(	(	PUNCT
ap-6650	126	2	19	19	NUM
ap-6650	126	3	)	)	PUNCT
ap-6650	126	4	therefore	therefore	ADV
ap-6650	126	5	,	,	PUNCT
ap-6650	126	6	the	the	DET
ap-6650	126	7	derivations	derivation	NOUN
ap-6650	126	8	in	in	ADP
ap-6650	126	9	the	the	DET
ap-6650	126	10	equation	equation	NOUN
ap-6650	126	11	(	(	PUNCT
ap-6650	126	12	18	18	NUM
ap-6650	126	13	)	)	PUNCT
ap-6650	126	14	shut	shut	VERB
ap-6650	126	15	down	down	ADP
ap-6650	126	16	approximately	approximately	ADV
ap-6650	126	17	in	in	ADP
ap-6650	126	18	the	the	DET
ap-6650	126	19	first	first	ADJ
ap-6650	126	20	-	-	PUNCT
ap-6650	126	21	order	order	NOUN
ap-6650	126	22	of	of	ADP
ap-6650	126	23	θ	θ	PROPN
ap-6650	126	24	,	,	PUNCT
ap-6650	126	25	then	then	ADV
ap-6650	126	26	the	the	DET
ap-6650	126	27	noncommutative	noncommutative	PROPN
ap-6650	126	28	pauli	pauli	PROPN
ap-6650	126	29	equation	equation	NOUN
ap-6650	126	30	in	in	ADP
ap-6650	126	31	the	the	DET
ap-6650	126	32	presence	presence	NOUN
ap-6650	126	33	of	of	ADP
ap-6650	126	34	a	a	DET
ap-6650	126	35	uniform	uniform	ADJ
ap-6650	126	36	magnetic	magnetic	ADJ
ap-6650	126	37	field	field	NOUN
ap-6650	126	38	can	can	AUX
ap-6650	126	39	be	be	AUX
ap-6650	126	40	written	write	VERB
ap-6650	126	41	as	as	SCONJ
ap-6650	126	42	follows	follow	VERB
ap-6650	126	43	h	h	NOUN
ap-6650	126	44	(	(	PUNCT
ap-6650	126	45	x	x	NOUN
ap-6650	126	46	,	,	PUNCT
ap-6650	126	47	pnc	pnc	PROPN
ap-6650	126	48	)	)	PUNCT
ap-6650	126	49	?	?	PUNCT
ap-6650	127	1	ψ	ψ	X
ap-6650	127	2	(	(	PUNCT
ap-6650	127	3	x	x	X
ap-6650	127	4	)	)	PUNCT
ap-6650	127	5	=	=	PRON
ap-6650	127	6	{	{	PUNCT
ap-6650	127	7	1	1	NUM
ap-6650	127	8	2	2	NUM
ap-6650	127	9	m	m	NOUN
ap-6650	127	10	(	(	PUNCT
ap-6650	127	11	−→p	−→p	NOUN
ap-6650	127	12	nc	nc	NOUN
ap-6650	127	13	−	−	PROPN
ap-6650	127	14	e	e	NOUN
ap-6650	127	15	c	c	AUX
ap-6650	127	16	−→	−→	VERB
ap-6650	127	17	a	a	DET
ap-6650	127	18	(	(	PUNCT
ap-6650	127	19	x	x	NOUN
ap-6650	127	20	)	)	PUNCT
ap-6650	127	21	)	)	PUNCT
ap-6650	127	22	2	2	NUM
ap-6650	127	23	+	+	CCONJ
ap-6650	127	24	µb	µb	VERB
ap-6650	127	25	−→σ	−→σ	VERB
ap-6650	127	26	.	.	PUNCT
ap-6650	128	1	−→	−→	NOUN
ap-6650	128	2	b	b	PROPN
ap-6650	129	1	+	+	CCONJ
ap-6650	129	2	ie	ie	X
ap-6650	129	3	4mcθab∂a	4mcθab∂a	NOUN
ap-6650	129	4	(	(	PUNCT
ap-6650	129	5	e	e	NOUN
ap-6650	129	6	c	c	AUX
ap-6650	129	7	−→	−→	VERB
ap-6650	129	8	a	a	DET
ap-6650	129	9	2	2	NUM
ap-6650	129	10	−	−	NOUN
ap-6650	129	11	2−→p	2−→p	NUM
ap-6650	129	12	nc.−→a	nc.−→a	ADJ
ap-6650	129	13	)	)	PUNCT
ap-6650	129	14	∂b	∂b	PROPN
ap-6650	129	15	}	}	PUNCT
ap-6650	129	16	ψ	ψ	PROPN
ap-6650	129	17	(	(	PUNCT
ap-6650	129	18	x	x	X
ap-6650	129	19	)	)	PUNCT
ap-6650	129	20	+	+	NUM
ap-6650	129	21	0(θ2	0(θ2	NUM
ap-6650	129	22	)	)	PUNCT
ap-6650	129	23	,	,	PUNCT
ap-6650	129	24	(	(	PUNCT
ap-6650	129	25	20	20	NUM
ap-6650	129	26	)	)	PUNCT
ap-6650	129	27	with	with	ADP
ap-6650	129	28	[	[	X
ap-6650	129	29	−→p	−→p	X
ap-6650	129	30	nc,−→a	nc,−→a	X
ap-6650	129	31	]	]	X
ap-6650	129	32	=	=	SYM
ap-6650	130	1	0	0	X
ap-6650	130	2	.	.	PUNCT
ap-6650	131	1	we	we	PRON
ap-6650	131	2	now	now	ADV
ap-6650	131	3	make	make	VERB
ap-6650	131	4	use	use	NOUN
ap-6650	131	5	of	of	ADP
ap-6650	131	6	the	the	DET
ap-6650	131	7	bopp	bopp	ADJ
ap-6650	131	8	-	-	PUNCT
ap-6650	131	9	shift	shift	NOUN
ap-6650	131	10	transformation	transformation	NOUN
ap-6650	131	11	(	(	PUNCT
ap-6650	131	12	4	4	NUM
ap-6650	131	13	)	)	PUNCT
ap-6650	131	14	,	,	PUNCT
ap-6650	131	15	in	in	ADP
ap-6650	131	16	the	the	DET
ap-6650	131	17	momentum	momentum	NOUN
ap-6650	131	18	operator	operator	NOUN
ap-6650	131	19	to	to	PART
ap-6650	131	20	obtain	obtain	VERB
ap-6650	131	21	h	h	NOUN
ap-6650	131	22	(	(	PUNCT
ap-6650	131	23	xnc	xnc	PROPN
ap-6650	131	24	,	,	PUNCT
ap-6650	131	25	pnc)ψ	pnc)ψ	PROPN
ap-6650	131	26	(	(	PUNCT
ap-6650	131	27	xnc	xnc	PROPN
ap-6650	131	28	,	,	PUNCT
ap-6650	131	29	t	t	PROPN
ap-6650	131	30	)	)	PUNCT
ap-6650	131	31	=	=	PRON
ap-6650	131	32	{	{	PUNCT
ap-6650	131	33	1	1	NUM
ap-6650	131	34	2	2	NUM
ap-6650	131	35	m	m	VERB
ap-6650	131	36	(	(	PUNCT
ap-6650	131	37	pi	pi	NOUN
ap-6650	132	1	+	+	CCONJ
ap-6650	132	2	1	1	NUM
ap-6650	132	3	2	2	NUM
ap-6650	132	4	~	~	NOUN
ap-6650	132	5	ηijxj	ηijxj	NOUN
ap-6650	132	6	−	−	PROPN
ap-6650	132	7	e	e	X
ap-6650	132	8	cai	cai	X
ap-6650	132	9	)	)	PUNCT
ap-6650	132	10	2	2	NUM
ap-6650	132	11	+	+	CCONJ
ap-6650	132	12	µb	µb	VERB
ap-6650	132	13	−→σ	−→σ	VERB
ap-6650	132	14	.	.	PUNCT
ap-6650	133	1	−→	−→	NOUN
ap-6650	133	2	b	b	PROPN
ap-6650	133	3	−	−	PROPN
ap-6650	134	1	ie	ie	X
ap-6650	134	2	4mcθab∂a	4mcθab∂a	PROPN
ap-6650	134	3	(	(	PUNCT
ap-6650	134	4	2	2	NUM
ap-6650	134	5	(	(	PUNCT
ap-6650	134	6	pi	pi	NOUN
ap-6650	134	7	+	+	CCONJ
ap-6650	134	8	1	1	NUM
ap-6650	134	9	2	2	NUM
ap-6650	134	10	~	~	NOUN
ap-6650	134	11	ηijxj	ηijxj	NOUN
ap-6650	134	12	)	)	PUNCT
ap-6650	134	13	ai	ai	VERB
ap-6650	134	14	−	−	PROPN
ap-6650	134	15	e	e	NOUN
ap-6650	134	16	c	c	NOUN
ap-6650	134	17	−→	−→	VERB
ap-6650	134	18	a	a	DET
ap-6650	134	19	2	2	NUM
ap-6650	134	20	)	)	PUNCT
ap-6650	134	21	∂b	∂b	PROPN
ap-6650	134	22	}	}	PUNCT
ap-6650	134	23	ψ(x	ψ(x	PROPN
ap-6650	134	24	,	,	PUNCT
ap-6650	134	25	t	t	PROPN
ap-6650	134	26	)	)	PUNCT
ap-6650	134	27	=	=	SYM
ap-6650	135	1	i~	i~	PROPN
ap-6650	135	2	∂	∂	NUM
ap-6650	135	3	∂tψ	∂tψ	PROPN
ap-6650	135	4	(	(	PUNCT
ap-6650	135	5	x	x	X
ap-6650	135	6	,	,	PUNCT
ap-6650	135	7	t	t	PROPN
ap-6650	135	8	)	)	PUNCT
ap-6650	135	9	,	,	PUNCT
ap-6650	135	10	(	(	PUNCT
ap-6650	135	11	21	21	NUM
ap-6650	135	12	)	)	PUNCT
ap-6650	135	13	we	we	PRON
ap-6650	135	14	rewrite	rewrite	VERB
ap-6650	135	15	the	the	DET
ap-6650	135	16	above	above	ADJ
ap-6650	135	17	equation	equation	NOUN
ap-6650	135	18	in	in	ADP
ap-6650	135	19	a	a	DET
ap-6650	135	20	more	more	ADV
ap-6650	135	21	compact	compact	ADJ
ap-6650	135	22	form	form	NOUN
ap-6650	135	23	h	h	NOUN
ap-6650	135	24	(	(	PUNCT
ap-6650	135	25	x	x	NOUN
ap-6650	135	26	,	,	PUNCT
ap-6650	135	27	pnc	pnc	PROPN
ap-6650	135	28	)	)	PUNCT
ap-6650	135	29	?	?	PUNCT
ap-6650	136	1	ψ	ψ	X
ap-6650	136	2	(	(	PUNCT
ap-6650	136	3	x	x	X
ap-6650	136	4	,	,	PUNCT
ap-6650	136	5	t	t	PROPN
ap-6650	136	6	)	)	PUNCT
ap-6650	136	7	=	=	PRON
ap-6650	136	8	{	{	PUNCT
ap-6650	136	9	1	1	NUM
ap-6650	136	10	2	2	NUM
ap-6650	136	11	m	m	NOUN
ap-6650	136	12	(	(	PUNCT
ap-6650	136	13	−→p	−→p	NOUN
ap-6650	136	14	−	−	PROPN
ap-6650	136	15	e	e	NOUN
ap-6650	136	16	c	c	AUX
ap-6650	136	17	−→	−→	VERB
ap-6650	136	18	a	a	PRON
ap-6650	136	19	)	)	PUNCT
ap-6650	136	20	2	2	NUM
ap-6650	136	21	−	−	NOUN
ap-6650	136	22	1	1	NUM
ap-6650	136	23	2	2	NUM
ap-6650	136	24	m	m	NOUN
ap-6650	136	25	(	(	PUNCT
ap-6650	136	26	−→x	−→x	PROPN
ap-6650	136	27	×−→p	×−→p	NOUN
ap-6650	136	28	)	)	PUNCT
ap-6650	136	29	.−→η	.−→η	PUNCT
ap-6650	137	1	−	−	NOUN
ap-6650	137	2	1	1	NUM
ap-6650	137	3	2	2	NUM
ap-6650	137	4	m	m	NOUN
ap-6650	137	5	e	e	NOUN
ap-6650	137	6	c~	c~	PROPN
ap-6650	137	7	(	(	PUNCT
ap-6650	137	8	−→x	−→x	PRON
ap-6650	137	9	×−→a	×−→a	PROPN
ap-6650	137	10	(	(	PUNCT
ap-6650	137	11	x	x	NOUN
ap-6650	137	12	)	)	PUNCT
ap-6650	137	13	)	)	PUNCT
ap-6650	137	14	.−→η	.−→η	PUNCT
ap-6650	138	1	+	+	PUNCT
ap-6650	138	2	1	1	NUM
ap-6650	138	3	8m~2	8m~2	NUM
ap-6650	138	4	ηijηαβxjxβ	ηijηαβxjxβ	ADV
ap-6650	138	5	+	+	CCONJ
ap-6650	138	6	µb	µb	VERB
ap-6650	138	7	−→σ	−→σ	VERB
ap-6650	138	8	.	.	PUNCT
ap-6650	139	1	−→	−→	NOUN
ap-6650	139	2	b	b	PROPN
ap-6650	139	3	+	+	CCONJ
ap-6650	139	4	e	e	NOUN
ap-6650	139	5	4	4	NUM
ap-6650	139	6	~	~	SYM
ap-6650	139	7	mc	mc	X
ap-6650	139	8	(	(	PUNCT
ap-6650	139	9	−→	−→	NOUN
ap-6650	139	10	∇	∇	X
ap-6650	139	11	(	(	PUNCT
ap-6650	139	12	2−→p	2−→p	NUM
ap-6650	139	13	.−→a	.−→a	PUNCT
ap-6650	140	1	−	−	NUM
ap-6650	140	2	1	1	NUM
ap-6650	140	3	2~	2~	PROPN
ap-6650	140	4	(	(	PUNCT
ap-6650	140	5	−→x	−→x	ADJ
ap-6650	140	6	×−→a	×−→a	PROPN
ap-6650	140	7	(	(	PUNCT
ap-6650	140	8	x	x	NOUN
ap-6650	140	9	)	)	PUNCT
ap-6650	140	10	)	)	PUNCT
ap-6650	140	11	.−→η	.−→η	PUNCT
ap-6650	141	1	−	−	X
ap-6650	142	1	e	e	NOUN
ap-6650	142	2	c	c	NOUN
ap-6650	142	3	−→	−→	VERB
ap-6650	142	4	a	a	DET
ap-6650	142	5	2	2	NUM
ap-6650	142	6	)	)	PUNCT
ap-6650	142	7	×−→p	×−→p	PROPN
ap-6650	142	8	)	)	PUNCT
ap-6650	142	9	.	.	PUNCT
ap-6650	143	1	−→θ	−→θ	ADJ
ap-6650	143	2	}	}	SYM
ap-6650	143	3	ψ	ψ	PROPN
ap-6650	143	4	(	(	PUNCT
ap-6650	143	5	x	x	NOUN
ap-6650	143	6	,	,	PUNCT
ap-6650	143	7	t	t	PROPN
ap-6650	143	8	)	)	PUNCT
ap-6650	143	9	.	.	PUNCT
ap-6650	144	1	(	(	PUNCT
ap-6650	144	2	22	22	X
ap-6650	144	3	)	)	PUNCT
ap-6650	144	4	we	we	PRON
ap-6650	144	5	restrict	restrict	VERB
ap-6650	144	6	ourselves	ourselves	PRON
ap-6650	144	7	only	only	ADV
ap-6650	144	8	to	to	ADP
ap-6650	144	9	the	the	DET
ap-6650	144	10	first	first	ADJ
ap-6650	144	11	-	-	PUNCT
ap-6650	144	12	order	order	NOUN
ap-6650	144	13	of	of	ADP
ap-6650	144	14	the	the	DET
ap-6650	144	15	parameter	parameter	PROPN
ap-6650	144	16	η	η	PROPN
ap-6650	144	17	.	.	PROPN
ap-6650	144	18	the	the	DET
ap-6650	144	19	only	only	ADJ
ap-6650	144	20	reason	reason	NOUN
ap-6650	144	21	behind	behind	ADP
ap-6650	144	22	this	this	DET
ap-6650	144	23	consideration	consideration	NOUN
ap-6650	144	24	is	be	AUX
ap-6650	144	25	the	the	DET
ap-6650	144	26	balance	balance	NOUN
ap-6650	144	27	with	with	ADP
ap-6650	144	28	the	the	DET
ap-6650	144	29	noncommutativity	noncommutativity	NOUN
ap-6650	144	30	in	in	ADP
ap-6650	144	31	the	the	DET
ap-6650	144	32	space	space	NOUN
ap-6650	144	33	considered	consider	VERB
ap-6650	144	34	in	in	ADP
ap-6650	144	35	the	the	DET
ap-6650	144	36	case	case	NOUN
ap-6650	144	37	of	of	ADP
ap-6650	144	38	a	a	DET
ap-6650	144	39	constant	constant	ADJ
ap-6650	144	40	magnetic	magnetic	ADJ
ap-6650	144	41	field	field	NOUN
ap-6650	144	42	.	.	PUNCT
ap-6650	145	1	thus	thus	ADV
ap-6650	145	2	we	we	PRON
ap-6650	145	3	now	now	ADV
ap-6650	145	4	have	have	VERB
ap-6650	145	5	h	h	NOUN
ap-6650	145	6	(	(	PUNCT
ap-6650	145	7	x	x	NOUN
ap-6650	145	8	,	,	PUNCT
ap-6650	145	9	pnc	pnc	PROPN
ap-6650	145	10	)	)	PUNCT
ap-6650	145	11	?	?	PUNCT
ap-6650	146	1	ψ	ψ	X
ap-6650	146	2	(	(	PUNCT
ap-6650	146	3	x	x	X
ap-6650	146	4	,	,	PUNCT
ap-6650	146	5	t	t	PROPN
ap-6650	146	6	)	)	PUNCT
ap-6650	146	7	=	=	PRON
ap-6650	146	8	{	{	PUNCT
ap-6650	146	9	1	1	NUM
ap-6650	146	10	2	2	NUM
ap-6650	146	11	m	m	NOUN
ap-6650	146	12	(	(	PUNCT
ap-6650	146	13	−→p	−→p	NOUN
ap-6650	146	14	−	−	PROPN
ap-6650	146	15	e	e	NOUN
ap-6650	146	16	c	c	AUX
ap-6650	146	17	−→	−→	VERB
ap-6650	146	18	a	a	PRON
ap-6650	146	19	)	)	PUNCT
ap-6650	146	20	2	2	NUM
ap-6650	146	21	−	−	NOUN
ap-6650	146	22	1	1	NUM
ap-6650	146	23	2	2	NUM
ap-6650	146	24	m	m	NOUN
ap-6650	146	25	−→	−→	NOUN
ap-6650	146	26	l	l	NOUN
ap-6650	146	27	.−→η	.−→η	PUNCT
ap-6650	147	1	−	−	X
ap-6650	147	2	e	e	SYM
ap-6650	147	3	2mc~	2mc~	NUM
ap-6650	147	4	(	(	PUNCT
ap-6650	147	5	−→x	−→x	ADJ
ap-6650	147	6	×−→a	×−→a	PROPN
ap-6650	147	7	(	(	PUNCT
ap-6650	147	8	x	x	NOUN
ap-6650	147	9	)	)	PUNCT
ap-6650	147	10	)	)	PUNCT
ap-6650	147	11	.−→η	.−→η	PROPN
ap-6650	148	1	+	+	CCONJ
ap-6650	148	2	µb	µb	VERB
ap-6650	148	3	−→σ	−→σ	VERB
ap-6650	148	4	.	.	PUNCT
ap-6650	149	1	−→	−→	NOUN
ap-6650	149	2	b	b	PROPN
ap-6650	149	3	+	+	CCONJ
ap-6650	149	4	e	e	X
ap-6650	149	5	4mc~	4mc~	PROPN
ap-6650	149	6	(	(	PUNCT
ap-6650	149	7	−→	−→	NOUN
ap-6650	149	8	∇	∇	X
ap-6650	149	9	(	(	PUNCT
ap-6650	149	10	2−→p	2−→p	NUM
ap-6650	149	11	.−→a	.−→a	X
ap-6650	150	1	(	(	PUNCT
ap-6650	150	2	x)−	x)−	PROPN
ap-6650	150	3	1	1	NUM
ap-6650	150	4	2~	2~	PROPN
ap-6650	150	5	(	(	PUNCT
ap-6650	150	6	−→x	−→x	ADJ
ap-6650	150	7	×−→a	×−→a	PROPN
ap-6650	150	8	(	(	PUNCT
ap-6650	150	9	x	x	NOUN
ap-6650	150	10	)	)	PUNCT
ap-6650	150	11	)	)	PUNCT
ap-6650	150	12	.−→η	.−→η	PUNCT
ap-6650	151	1	−	−	X
ap-6650	152	1	e	e	NOUN
ap-6650	152	2	c	c	NOUN
ap-6650	152	3	−→	−→	VERB
ap-6650	152	4	a	a	DET
ap-6650	152	5	2	2	NUM
ap-6650	152	6	)	)	PUNCT
ap-6650	152	7	×−→p	×−→p	PROPN
ap-6650	152	8	)	)	PUNCT
ap-6650	152	9	.	.	PUNCT
ap-6650	153	1	−→θ	−→θ	ADJ
ap-6650	153	2	}	}	SYM
ap-6650	153	3	ψ	ψ	PROPN
ap-6650	153	4	(	(	PUNCT
ap-6650	153	5	x	x	NOUN
ap-6650	153	6	,	,	PUNCT
ap-6650	153	7	t	t	PROPN
ap-6650	153	8	)	)	PUNCT
ap-6650	153	9	)	)	PUNCT
ap-6650	154	1	=	=	PUNCT
ap-6650	154	2	i~	i~	PROPN
ap-6650	154	3	∂	∂	NUM
ap-6650	154	4	∂tψ	∂tψ	PROPN
ap-6650	154	5	(	(	PUNCT
ap-6650	154	6	x	x	X
ap-6650	154	7	,	,	PUNCT
ap-6650	154	8	t	t	PROPN
ap-6650	154	9	)	)	PUNCT
ap-6650	154	10	.	.	PUNCT
ap-6650	155	1	(	(	PUNCT
ap-6650	155	2	23	23	NUM
ap-6650	155	3	)	)	PUNCT
ap-6650	155	4	the	the	DET
ap-6650	155	5	existence	existence	NOUN
ap-6650	155	6	of	of	ADP
ap-6650	155	7	a	a	DET
ap-6650	155	8	pauli	pauli	PROPN
ap-6650	155	9	equation	equation	NOUN
ap-6650	155	10	for	for	ADP
ap-6650	155	11	all	all	DET
ap-6650	155	12	orders	order	NOUN
ap-6650	155	13	of	of	ADP
ap-6650	155	14	the	the	DET
ap-6650	155	15	θ	θ	PROPN
ap-6650	155	16	parameter	parameter	NOUN
ap-6650	155	17	is	be	AUX
ap-6650	155	18	explicitly	explicitly	ADV
ap-6650	155	19	relative	relative	ADJ
ap-6650	155	20	to	to	ADP
ap-6650	155	21	the	the	DET
ap-6650	155	22	magnetic	magnetic	ADJ
ap-6650	155	23	field	field	NOUN
ap-6650	155	24	.	.	PUNCT
ap-6650	156	1	in	in	ADP
ap-6650	156	2	the	the	DET
ap-6650	156	3	case	case	NOUN
ap-6650	156	4	of	of	ADP
ap-6650	156	5	a	a	DET
ap-6650	156	6	non	non	ADJ
ap-6650	156	7	-	-	ADJ
ap-6650	156	8	constant	constant	ADJ
ap-6650	156	9	magnetic	magnetic	ADJ
ap-6650	156	10	field	field	NOUN
ap-6650	156	11	,	,	PUNCT
ap-6650	156	12	we	we	PRON
ap-6650	156	13	introduce	introduce	VERB
ap-6650	156	14	a	a	DET
ap-6650	156	15	function	function	NOUN
ap-6650	156	16	depending	depend	VERB
ap-6650	156	17	on	on	ADP
ap-6650	156	18	x	x	PUNCT
ap-6650	156	19	in	in	ADP
ap-6650	156	20	the	the	DET
ap-6650	156	21	landau	landau	NOUN
ap-6650	156	22	gauge	gauge	NOUN
ap-6650	156	23	as	as	ADP
ap-6650	156	24	a2	a2	PROPN
ap-6650	156	25	=	=	SYM
ap-6650	156	26	xbf(x	xbf(x	PROPN
ap-6650	156	27	)	)	PUNCT
ap-6650	156	28	,	,	PUNCT
ap-6650	156	29	which	which	PRON
ap-6650	156	30	gives	give	VERB
ap-6650	156	31	us	we	PRON
ap-6650	156	32	a	a	DET
ap-6650	156	33	non	non	ADJ
ap-6650	156	34	-	-	ADJ
ap-6650	156	35	constant	constant	ADJ
ap-6650	156	36	magnetic	magnetic	ADJ
ap-6650	156	37	field	field	NOUN
ap-6650	156	38	.	.	PUNCT
ap-6650	157	1	the	the	DET
ap-6650	157	2	magnetic	magnetic	ADJ
ap-6650	157	3	field	field	NOUN
ap-6650	157	4	can	can	AUX
ap-6650	157	5	be	be	AUX
ap-6650	157	6	easily	easily	ADV
ap-6650	157	7	calculated	calculate	VERB
ap-6650	157	8	using	use	VERB
ap-6650	157	9	the	the	DET
ap-6650	157	10	second	second	ADJ
ap-6650	157	11	equation	equation	NOUN
ap-6650	157	12	of	of	ADP
ap-6650	157	13	equation	equation	NOUN
ap-6650	157	14	(	(	PUNCT
ap-6650	157	15	12	12	NUM
ap-6650	157	16	)	)	PUNCT
ap-6650	157	17	as	as	SCONJ
ap-6650	157	18	follows	follow	VERB
ap-6650	157	19	[	[	X
ap-6650	157	20	33	33	NUM
ap-6650	157	21	]	]	X
ap-6650	157	22	−→	−→	NOUN
ap-6650	157	23	b	b	PROPN
ap-6650	157	24	(	(	PUNCT
ap-6650	157	25	x	x	NOUN
ap-6650	157	26	)	)	PUNCT
ap-6650	157	27	=	=	SYM
ap-6650	157	28	bf(x)−→e	bf(x)−→e	PROPN
ap-6650	157	29	3	3	NUM
ap-6650	157	30	.	.	PUNCT
ap-6650	158	1	(	(	PUNCT
ap-6650	158	2	24	24	NUM
ap-6650	158	3	)	)	PUNCT
ap-6650	158	4	if	if	SCONJ
ap-6650	158	5	we	we	PRON
ap-6650	158	6	specify	specify	VERB
ap-6650	158	7	f(x	f(x	PROPN
ap-6650	158	8	)	)	PUNCT
ap-6650	158	9	,	,	PUNCT
ap-6650	158	10	we	we	PRON
ap-6650	158	11	obtain	obtain	VERB
ap-6650	158	12	different	different	ADJ
ap-6650	158	13	classes	class	NOUN
ap-6650	158	14	of	of	ADP
ap-6650	158	15	the	the	DET
ap-6650	158	16	non	non	ADJ
ap-6650	158	17	-	-	ADJ
ap-6650	158	18	constant	constant	ADJ
ap-6650	158	19	magnetic	magnetic	ADJ
ap-6650	158	20	field	field	NOUN
ap-6650	158	21	.	.	PUNCT
ap-6650	159	1	if	if	SCONJ
ap-6650	159	2	we	we	PRON
ap-6650	159	3	take	take	VERB
ap-6650	159	4	f(x	f(x	PROPN
ap-6650	159	5	)	)	PUNCT
ap-6650	160	1	=	=	SYM
ap-6650	160	2	1	1	NUM
ap-6650	160	3	in	in	ADP
ap-6650	160	4	this	this	DET
ap-6650	160	5	case	case	NOUN
ap-6650	160	6	,	,	PUNCT
ap-6650	160	7	we	we	PRON
ap-6650	160	8	get	get	VERB
ap-6650	160	9	a	a	DET
ap-6650	160	10	constant	constant	ADJ
ap-6650	160	11	magnetic	magnetic	ADJ
ap-6650	160	12	field	field	NOUN
ap-6650	160	13	.	.	PUNCT
ap-6650	161	1	having	have	VERB
ap-6650	161	2	the	the	DET
ap-6650	161	3	equation	equation	NOUN
ap-6650	161	4	(	(	PUNCT
ap-6650	161	5	23	23	NUM
ap-6650	161	6	)	)	PUNCT
ap-6650	161	7	on	on	ADP
ap-6650	161	8	hand	hand	NOUN
ap-6650	161	9	,	,	PUNCT
ap-6650	161	10	we	we	PRON
ap-6650	161	11	calculate	calculate	VERB
ap-6650	161	12	the	the	DET
ap-6650	161	13	probability	probability	NOUN
ap-6650	161	14	density	density	NOUN
ap-6650	161	15	and	and	CCONJ
ap-6650	161	16	the	the	DET
ap-6650	161	17	current	current	ADJ
ap-6650	161	18	density	density	NOUN
ap-6650	161	19	.	.	PUNCT
ap-6650	162	1	233	233	NUM
ap-6650	162	2	ilyas	ilyas	PROPN
ap-6650	162	3	haouam	haouam	VERB
ap-6650	162	4	acta	acta	PROPN
ap-6650	162	5	polytechnica	polytechnica	PROPN
ap-6650	162	6	3.2	3.2	NUM
ap-6650	162	7	.	.	PUNCT
ap-6650	163	1	deformed	deform	VERB
ap-6650	163	2	continuity	continuity	NOUN
ap-6650	163	3	equation	equation	NOUN
ap-6650	163	4	in	in	ADP
ap-6650	163	5	the	the	DET
ap-6650	163	6	following	following	NOUN
ap-6650	163	7	we	we	PRON
ap-6650	163	8	calculate	calculate	VERB
ap-6650	163	9	the	the	DET
ap-6650	163	10	current	current	ADJ
ap-6650	163	11	density	density	NOUN
ap-6650	163	12	,	,	PUNCT
ap-6650	163	13	which	which	PRON
ap-6650	163	14	results	result	VERB
ap-6650	163	15	from	from	ADP
ap-6650	163	16	the	the	DET
ap-6650	163	17	pauli	pauli	PROPN
ap-6650	163	18	equation	equation	NOUN
ap-6650	163	19	(	(	PUNCT
ap-6650	163	20	23	23	NUM
ap-6650	163	21	)	)	PUNCT
ap-6650	163	22	that	that	PRON
ap-6650	163	23	describes	describe	VERB
ap-6650	163	24	a	a	DET
ap-6650	163	25	system	system	NOUN
ap-6650	163	26	of	of	ADP
ap-6650	163	27	two	two	NUM
ap-6650	163	28	coupled	couple	VERB
ap-6650	163	29	differential	differential	ADJ
ap-6650	163	30	equations	equation	NOUN
ap-6650	163	31	for	for	ADP
ap-6650	163	32	ψ1	ψ1	NOUN
ap-6650	163	33	and	and	CCONJ
ap-6650	163	34	ψ2	ψ2	NOUN
ap-6650	163	35	.	.	PUNCT
ap-6650	164	1	by	by	ADP
ap-6650	164	2	putting	put	VERB
ap-6650	164	3	qη	qη	NOUN
ap-6650	164	4	=	=	PUNCT
ap-6650	164	5	q∗η	q∗η	NOUN
ap-6650	164	6	=	=	SYM
ap-6650	164	7	(	(	PUNCT
ap-6650	164	8	−→x	−→x	NUM
ap-6650	164	9	×−→a	×−→a	PROPN
ap-6650	164	10	(	(	PUNCT
ap-6650	164	11	x	x	NOUN
ap-6650	164	12	)	)	PUNCT
ap-6650	164	13	)	)	PUNCT
ap-6650	164	14	.−→η	.−→η	PROPN
ap-6650	164	15	,	,	PUNCT
ap-6650	164	16	qθ	qθ	PROPN
ap-6650	164	17	=	=	SYM
ap-6650	164	18	(	(	PUNCT
ap-6650	164	19	−→	−→	NOUN
ap-6650	164	20	∇	∇	X
ap-6650	164	21	(	(	PUNCT
ap-6650	164	22	2−→p	2−→p	NUM
ap-6650	164	23	.−→a	.−→a	X
ap-6650	165	1	(	(	PUNCT
ap-6650	165	2	x)−	x)−	PROPN
ap-6650	165	3	1	1	NUM
ap-6650	165	4	2	2	NUM
ap-6650	165	5	~	~	NOUN
ap-6650	165	6	qη	qη	NOUN
ap-6650	165	7	−	−	NOUN
ap-6650	165	8	e	e	NOUN
ap-6650	166	1	c	c	NOUN
ap-6650	166	2	−→	−→	VERB
ap-6650	166	3	a	a	DET
ap-6650	166	4	2	2	NUM
ap-6650	166	5	(	(	PUNCT
ap-6650	166	6	x	x	NOUN
ap-6650	166	7	)	)	PUNCT
ap-6650	166	8	)	)	PUNCT
ap-6650	166	9	×−→p	×−→p	PROPN
ap-6650	166	10	)	)	PUNCT
ap-6650	166	11	.	.	PUNCT
ap-6650	167	1	−→θ	−→θ	X
ap-6650	167	2	=	=	PUNCT
ap-6650	167	3	(	(	PUNCT
ap-6650	167	4	−→	−→	PROPN
ap-6650	167	5	∇v	∇v	PROPN
ap-6650	167	6	(	(	PUNCT
ap-6650	167	7	x)×−→p	x)×−→p	PROPN
ap-6650	167	8	)	)	PUNCT
ap-6650	167	9	.	.	PUNCT
ap-6650	168	1	−→θ	−→θ	ADJ
ap-6650	168	2	,	,	PUNCT
ap-6650	168	3	(	(	PUNCT
ap-6650	168	4	25	25	NUM
ap-6650	168	5	)	)	PUNCT
ap-6650	168	6	the	the	DET
ap-6650	168	7	noncommutative	noncommutative	PROPN
ap-6650	168	8	pauli	pauli	PROPN
ap-6650	168	9	equation	equation	NOUN
ap-6650	168	10	in	in	ADP
ap-6650	168	11	the	the	DET
ap-6650	168	12	presence	presence	NOUN
ap-6650	168	13	of	of	ADP
ap-6650	168	14	a	a	DET
ap-6650	168	15	uniform	uniform	ADJ
ap-6650	168	16	magnetic	magnetic	ADJ
ap-6650	168	17	field	field	NOUN
ap-6650	168	18	simply	simply	ADV
ap-6650	168	19	reads	read	VERB
ap-6650	168	20	{	{	PUNCT
ap-6650	168	21	1	1	NUM
ap-6650	168	22	2	2	NUM
ap-6650	168	23	m	m	NOUN
ap-6650	168	24	(	(	PUNCT
ap-6650	168	25	−~2−→∇2	−~2−→∇2	NUM
ap-6650	168	26	+	+	CCONJ
ap-6650	169	1	ie~	ie~	PROPN
ap-6650	169	2	c	c	NOUN
ap-6650	169	3	(	(	PUNCT
ap-6650	169	4	−→	−→	ADJ
ap-6650	169	5	∇	∇	NOUN
ap-6650	169	6	.	.	PUNCT
ap-6650	170	1	−→	−→	ADV
ap-6650	170	2	a	a	DET
ap-6650	170	3	+	+	NOUN
ap-6650	170	4	−→a.−→∇	−→a.−→∇	NOUN
ap-6650	170	5	)	)	PUNCT
ap-6650	171	1	+	+	CCONJ
ap-6650	171	2	e2	e2	PROPN
ap-6650	171	3	c2	c2	PROPN
ap-6650	171	4	−→	−→	NOUN
ap-6650	171	5	a	a	DET
ap-6650	171	6	2	2	NUM
ap-6650	171	7	)	)	PUNCT
ap-6650	171	8	−	−	ADP
ap-6650	171	9	−→	−→	ADJ
ap-6650	171	10	l	l	NOUN
ap-6650	171	11	.−→η	.−→η	PROPN
ap-6650	171	12	2	2	NUM
ap-6650	171	13	m	m	NOUN
ap-6650	171	14	−	−	NOUN
ap-6650	171	15	eqη	eqη	NOUN
ap-6650	171	16	2mc~	2mc~	PROPN
ap-6650	171	17	+	+	CCONJ
ap-6650	171	18	µb	µb	VERB
ap-6650	171	19	−→σ	−→σ	VERB
ap-6650	171	20	.	.	PUNCT
ap-6650	172	1	−→	−→	NOUN
ap-6650	172	2	b	b	PROPN
ap-6650	172	3	+	+	CCONJ
ap-6650	172	4	eqθ	eqθ	NOUN
ap-6650	172	5	4mc~	4mc~	ADJ
ap-6650	172	6	}	}	PUNCT
ap-6650	172	7	ψ	ψ	X
ap-6650	172	8	=	=	SYM
ap-6650	172	9	i~	i~	PROPN
ap-6650	172	10	∂	∂	NOUN
ap-6650	172	11	∂t	∂t	PROPN
ap-6650	172	12	ψ	ψ	PROPN
ap-6650	172	13	.	.	PUNCT
ap-6650	173	1	(	(	PUNCT
ap-6650	173	2	26	26	NUM
ap-6650	173	3	)	)	PUNCT
ap-6650	173	4	knowing	know	VERB
ap-6650	173	5	that	that	SCONJ
ap-6650	173	6	−→σ	−→σ	PROPN
ap-6650	173	7	,	,	PUNCT
ap-6650	173	8	−→l	−→l	PROPN
ap-6650	173	9	are	be	AUX
ap-6650	173	10	hermitian	hermitian	ADJ
ap-6650	173	11	and	and	CCONJ
ap-6650	173	12	the	the	DET
ap-6650	173	13	magnetic	magnetic	ADJ
ap-6650	173	14	field	field	NOUN
ap-6650	173	15	is	be	AUX
ap-6650	173	16	real	real	ADJ
ap-6650	173	17	,	,	PUNCT
ap-6650	173	18	and	and	CCONJ
ap-6650	173	19	q∗θ	q∗θ	PROPN
ap-6650	173	20	is	be	AUX
ap-6650	173	21	the	the	DET
ap-6650	173	22	adjoint	adjoint	NOUN
ap-6650	173	23	of	of	ADP
ap-6650	173	24	qθ	qθ	PROPN
ap-6650	173	25	,	,	PUNCT
ap-6650	173	26	the	the	DET
ap-6650	173	27	adjoint	adjoint	NOUN
ap-6650	173	28	equation	equation	NOUN
ap-6650	173	29	of	of	ADP
ap-6650	173	30	equation	equation	NOUN
ap-6650	173	31	(	(	PUNCT
ap-6650	173	32	26	26	NUM
ap-6650	173	33	)	)	PUNCT
ap-6650	173	34	reads	read	VERB
ap-6650	173	35	1	1	NUM
ap-6650	173	36	2	2	NUM
ap-6650	173	37	m	m	NOUN
ap-6650	173	38	{	{	PUNCT
ap-6650	173	39	−~2−→∇2ψ†	−~2−→∇2ψ†	PROPN
ap-6650	173	40	−	−	PROPN
ap-6650	174	1	ie~	ie~	PROPN
ap-6650	174	2	c	c	PROPN
ap-6650	174	3	(	(	PUNCT
ap-6650	174	4	−→	−→	ADJ
ap-6650	174	5	∇	∇	NOUN
ap-6650	174	6	.	.	PUNCT
ap-6650	175	1	−→	−→	ADV
ap-6650	175	2	a	a	DET
ap-6650	175	3	+	+	NOUN
ap-6650	175	4	−→a.−→∇	−→a.−→∇	NOUN
ap-6650	175	5	)	)	PUNCT
ap-6650	175	6	ψ†	ψ†	PROPN
ap-6650	176	1	+	+	CCONJ
ap-6650	176	2	e2	e2	PROPN
ap-6650	176	3	c2	c2	PROPN
ap-6650	176	4	−→	−→	NOUN
ap-6650	176	5	a	a	DET
ap-6650	176	6	2ψ†	2ψ†	PROPN
ap-6650	176	7	}	}	PUNCT
ap-6650	176	8	−	−	ADP
ap-6650	176	9	−→	−→	NOUN
ap-6650	176	10	l	l	NOUN
ap-6650	176	11	.−→η	.−→η	PROPN
ap-6650	176	12	2	2	NUM
ap-6650	176	13	m	m	NOUN
ap-6650	176	14	ψ†	ψ†	VERB
ap-6650	176	15	−	−	PROPN
ap-6650	176	16	eqη	eqη	PROPN
ap-6650	176	17	2mc	2mc	NOUN
ap-6650	176	18	~	~	PUNCT
ap-6650	176	19	ψ	ψ	X
ap-6650	176	20	†	†	PROPN
ap-6650	176	21	+	+	CCONJ
ap-6650	176	22	µb	µb	ADP
ap-6650	176	23	−→σ	−→σ	VERB
ap-6650	176	24	.	.	PUNCT
ap-6650	177	1	−→	−→	NOUN
ap-6650	177	2	bψ†	bψ†	PROPN
ap-6650	177	3	+	+	NOUN
ap-6650	177	4	e	e	NOUN
ap-6650	177	5	4mc	4mc	NOUN
ap-6650	177	6	~	~	PUNCT
ap-6650	177	7	ψ	ψ	X
ap-6650	177	8	†q∗θ	†q∗θ	NOUN
ap-6650	177	9	=	=	PUNCT
ap-6650	177	10	=	=	SYM
ap-6650	177	11	−i~∂ψ	−i~∂ψ	PROPN
ap-6650	177	12	†	†	PROPN
ap-6650	177	13	∂t	∂t	PROPN
ap-6650	177	14	.	.	PUNCT
ap-6650	178	1	(	(	PUNCT
ap-6650	178	2	27	27	NUM
ap-6650	178	3	)	)	PUNCT
ap-6650	178	4	here	here	ADV
ap-6650	178	5	∗	∗	NOUN
ap-6650	178	6	,	,	PUNCT
ap-6650	178	7	†	†	PROPN
ap-6650	178	8	stand	stand	VERB
ap-6650	178	9	for	for	ADP
ap-6650	178	10	the	the	DET
ap-6650	178	11	complex	complex	ADJ
ap-6650	178	12	conjugation	conjugation	NOUN
ap-6650	178	13	of	of	ADP
ap-6650	178	14	the	the	DET
ap-6650	178	15	potentials	potential	NOUN
ap-6650	178	16	,	,	PUNCT
ap-6650	178	17	operators	operator	NOUN
ap-6650	178	18	and	and	CCONJ
ap-6650	178	19	for	for	ADP
ap-6650	178	20	the	the	DET
ap-6650	178	21	wave	wave	NOUN
ap-6650	178	22	-	-	PUNCT
ap-6650	178	23	functions	function	NOUN
ap-6650	178	24	,	,	PUNCT
ap-6650	178	25	respectively	respectively	ADV
ap-6650	178	26	.	.	PUNCT
ap-6650	179	1	to	to	PART
ap-6650	179	2	find	find	VERB
ap-6650	179	3	the	the	DET
ap-6650	179	4	continuity	continuity	NOUN
ap-6650	179	5	equation	equation	NOUN
ap-6650	179	6	,	,	PUNCT
ap-6650	179	7	we	we	PRON
ap-6650	179	8	multiply	multiply	VERB
ap-6650	179	9	equation	equation	NOUN
ap-6650	179	10	(	(	PUNCT
ap-6650	179	11	26	26	NUM
ap-6650	179	12	)	)	PUNCT
ap-6650	179	13	from	from	ADP
ap-6650	179	14	left	leave	VERB
ap-6650	179	15	by	by	ADP
ap-6650	179	16	ψ†	ψ†	NOUN
ap-6650	179	17	and	and	CCONJ
ap-6650	179	18	equation	equation	NOUN
ap-6650	179	19	(	(	PUNCT
ap-6650	179	20	27	27	NUM
ap-6650	179	21	)	)	PUNCT
ap-6650	179	22	from	from	ADP
ap-6650	179	23	the	the	DET
ap-6650	179	24	right	right	NOUN
ap-6650	179	25	by	by	ADP
ap-6650	179	26	ψ	ψ	NOUN
ap-6650	179	27	,	,	PUNCT
ap-6650	179	28	making	make	VERB
ap-6650	179	29	the	the	DET
ap-6650	179	30	subtraction	subtraction	NOUN
ap-6650	179	31	of	of	ADP
ap-6650	179	32	these	these	DET
ap-6650	179	33	equations	equation	NOUN
ap-6650	179	34	yields	yield	VERB
ap-6650	179	35	−~2	−~2	ADV
ap-6650	179	36	2	2	NUM
ap-6650	179	37	m	m	NOUN
ap-6650	179	38	{	{	PUNCT
ap-6650	179	39	ψ†	ψ†	VERB
ap-6650	179	40	−→	−→	ADJ
ap-6650	179	41	∇2ψ	∇2ψ	PRON
ap-6650	180	1	−	−	PROPN
ap-6650	181	1	(	(	PUNCT
ap-6650	181	2	−→	−→	NOUN
ap-6650	181	3	∇2ψ†	∇2ψ†	NOUN
ap-6650	181	4	)	)	PUNCT
ap-6650	182	1	ψ	ψ	X
ap-6650	182	2	}	}	PUNCT
ap-6650	182	3	+	+	CCONJ
ap-6650	182	4	ie~	ie~	PROPN
ap-6650	182	5	2mc	2mc	NOUN
ap-6650	182	6	{	{	PUNCT
ap-6650	182	7	ψ†	ψ†	PUNCT
ap-6650	182	8	(	(	PUNCT
ap-6650	182	9	−→	−→	ADJ
ap-6650	182	10	∇	∇	NOUN
ap-6650	182	11	.	.	PUNCT
ap-6650	183	1	−→	−→	ADV
ap-6650	183	2	a	a	DET
ap-6650	183	3	+	+	NOUN
ap-6650	183	4	−→a.−→∇	−→a.−→∇	NOUN
ap-6650	183	5	)	)	PUNCT
ap-6650	183	6	ψ	ψ	X
ap-6650	184	1	+	+	X
ap-6650	184	2	[	[	X
ap-6650	184	3	(	(	PUNCT
ap-6650	184	4	−→	−→	NOUN
ap-6650	184	5	∇.	∇.	ADV
ap-6650	184	6	−→	−→	NOUN
ap-6650	184	7	a	a	DET
ap-6650	184	8	+	+	NOUN
ap-6650	184	9	−→a.−→∇	−→a.−→∇	NOUN
ap-6650	184	10	)	)	PUNCT
ap-6650	184	11	ψ†	ψ†	PUNCT
ap-6650	184	12	]	]	PUNCT
ap-6650	185	1	ψ	ψ	X
ap-6650	185	2	}	}	PUNCT
ap-6650	185	3	+	+	CCONJ
ap-6650	185	4	e	e	X
ap-6650	185	5	4mc~	4mc~	PROPN
ap-6650	185	6	(	(	PUNCT
ap-6650	185	7	ψ†qθψ	ψ†qθψ	ADP
ap-6650	185	8	−	−	PROPN
ap-6650	185	9	ψ†q∗θψ	ψ†q∗θψ	NOUN
ap-6650	185	10	)	)	PUNCT
ap-6650	185	11	=	=	PUNCT
ap-6650	186	1	i~	i~	PROPN
ap-6650	186	2	(	(	PUNCT
ap-6650	186	3	ψ†	ψ†	ADJ
ap-6650	186	4	∂∂tψ	∂∂tψ	NOUN
ap-6650	186	5	+	+	CCONJ
ap-6650	186	6	ψ	ψ	SYM
ap-6650	186	7	∂	∂	NUM
ap-6650	186	8	∂tψ	∂tψ	PROPN
ap-6650	186	9	†	†	PROPN
ap-6650	186	10	)	)	PUNCT
ap-6650	186	11	,	,	PUNCT
ap-6650	186	12	(	(	PUNCT
ap-6650	186	13	28	28	NUM
ap-6650	186	14	)	)	PUNCT
ap-6650	186	15	after	after	ADP
ap-6650	186	16	some	some	DET
ap-6650	186	17	minor	minor	ADJ
ap-6650	186	18	simplefications	simplefication	NOUN
ap-6650	186	19	,	,	PUNCT
ap-6650	186	20	we	we	PRON
ap-6650	186	21	have	have	VERB
ap-6650	186	22	−~	−~	NUM
ap-6650	186	23	2mdiv	2mdiv	NUM
ap-6650	186	24	{	{	PUNCT
ap-6650	186	25	ψ†	ψ†	VERB
ap-6650	186	26	−→	−→	NOUN
ap-6650	186	27	∇ψ	∇ψ	PROPN
ap-6650	186	28	−	−	NOUN
ap-6650	186	29	ψ	ψ	ADP
ap-6650	186	30	−→	−→	NOUN
ap-6650	186	31	∇ψ†	∇ψ†	PROPN
ap-6650	186	32	}	}	PUNCT
ap-6650	187	1	+	+	CCONJ
ap-6650	187	2	ie	ie	PRON
ap-6650	187	3	mc	mc	PROPN
ap-6650	187	4	div	div	X
ap-6650	187	5	{	{	PUNCT
ap-6650	187	6	−→	−→	NOUN
ap-6650	187	7	aψ†ψ	aψ†ψ	PROPN
ap-6650	187	8	}	}	PUNCT
ap-6650	188	1	+	+	CCONJ
ap-6650	188	2	e	e	X
ap-6650	188	3	4mc~2	4mc~2	NOUN
ap-6650	188	4	(	(	PUNCT
ap-6650	188	5	ψ†qθψ	ψ†qθψ	ADP
ap-6650	188	6	−	−	PROPN
ap-6650	188	7	ψ†q∗θψ	ψ†q∗θψ	NOUN
ap-6650	188	8	)	)	PUNCT
ap-6650	188	9	=	=	SYM
ap-6650	189	1	i	i	PRON
ap-6650	189	2	∂	∂	NOUN
ap-6650	189	3	∂t	∂t	PROPN
ap-6650	189	4	ψ†ψ	ψ†ψ	PROPN
ap-6650	189	5	.	.	PUNCT
ap-6650	190	1	(	(	PUNCT
ap-6650	190	2	29	29	NUM
ap-6650	190	3	)	)	PUNCT
ap-6650	190	4	this	this	PRON
ap-6650	190	5	will	will	AUX
ap-6650	190	6	be	be	AUX
ap-6650	190	7	recognized	recognize	VERB
ap-6650	190	8	as	as	ADP
ap-6650	190	9	the	the	DET
ap-6650	190	10	deformed	deform	VERB
ap-6650	190	11	continuity	continuity	NOUN
ap-6650	190	12	equation	equation	NOUN
ap-6650	190	13	.	.	PUNCT
ap-6650	191	1	the	the	DET
ap-6650	191	2	obtained	obtain	VERB
ap-6650	191	3	equation	equation	NOUN
ap-6650	191	4	(	(	PUNCT
ap-6650	191	5	29	29	NUM
ap-6650	191	6	)	)	PUNCT
ap-6650	191	7	contains	contain	VERB
ap-6650	191	8	a	a	DET
ap-6650	191	9	new	new	ADJ
ap-6650	191	10	quantity	quantity	NOUN
ap-6650	191	11	,	,	PUNCT
ap-6650	191	12	which	which	PRON
ap-6650	191	13	is	be	AUX
ap-6650	191	14	the	the	DET
ap-6650	191	15	deformation	deformation	NOUN
ap-6650	191	16	due	due	ADP
ap-6650	191	17	to	to	ADP
ap-6650	191	18	the	the	DET
ap-6650	191	19	effect	effect	NOUN
ap-6650	191	20	of	of	ADP
ap-6650	191	21	the	the	DET
ap-6650	191	22	phase	phase	NOUN
ap-6650	191	23	-	-	PUNCT
ap-6650	191	24	space	space	NOUN
ap-6650	191	25	noncommutativity	noncommutativity	NOUN
ap-6650	191	26	on	on	ADP
ap-6650	191	27	the	the	DET
ap-6650	191	28	pauli	pauli	PROPN
ap-6650	191	29	equation	equation	NOUN
ap-6650	191	30	.	.	PUNCT
ap-6650	192	1	the	the	DET
ap-6650	192	2	third	third	ADJ
ap-6650	192	3	term	term	NOUN
ap-6650	192	4	on	on	ADP
ap-6650	192	5	the	the	DET
ap-6650	192	6	left	left	ADJ
ap-6650	192	7	-	-	PUNCT
ap-6650	192	8	hand	hand	NOUN
ap-6650	192	9	side	side	NOUN
ap-6650	192	10	,	,	PUNCT
ap-6650	192	11	which	which	PRON
ap-6650	192	12	is	be	AUX
ap-6650	192	13	the	the	DET
ap-6650	192	14	deformation	deformation	NOUN
ap-6650	192	15	quantity	quantity	NOUN
ap-6650	192	16	,	,	PUNCT
ap-6650	192	17	can	can	AUX
ap-6650	192	18	be	be	AUX
ap-6650	192	19	simplified	simplify	VERB
ap-6650	192	20	as	as	SCONJ
ap-6650	192	21	follows	follow	VERB
ap-6650	192	22	ie	ie	PRON
ap-6650	192	23	4mc~2	4mc~2	PROPN
ap-6650	192	24	(	(	PUNCT
ap-6650	192	25	ψ†qθψ	ψ†qθψ	ADP
ap-6650	192	26	−	−	PROPN
ap-6650	192	27	ψ†q∗θψ	ψ†q∗θψ	PROPN
ap-6650	192	28	)	)	PUNCT
ap-6650	192	29	=	=	SYM
ap-6650	193	1	ie	ie	X
ap-6650	193	2	4mc~2	4mc~2	NOUN
ap-6650	193	3	(	(	PUNCT
ap-6650	193	4	ψ†	ψ†	PROPN
ap-6650	193	5	(	(	PUNCT
ap-6650	193	6	v	v	NOUN
ap-6650	193	7	(	(	PUNCT
ap-6650	193	8	x	x	NOUN
ap-6650	193	9	)	)	PUNCT
ap-6650	193	10	?	?	PUNCT
ap-6650	194	1	ψ)−	ψ)−	PROPN
ap-6650	194	2	(	(	PUNCT
ap-6650	194	3	ψ†	ψ†	ADJ
ap-6650	194	4	?	?	PUNCT
ap-6650	195	1	v	v	X
ap-6650	195	2	(	(	PUNCT
ap-6650	195	3	x	x	NOUN
ap-6650	195	4	)	)	PUNCT
ap-6650	195	5	)	)	PUNCT
ap-6650	196	1	ψ	ψ	X
ap-6650	196	2	)	)	PUNCT
ap-6650	196	3	,	,	PUNCT
ap-6650	196	4	(	(	PUNCT
ap-6650	196	5	30	30	X
ap-6650	196	6	)	)	PUNCT
ap-6650	196	7	using	use	VERB
ap-6650	196	8	the	the	DET
ap-6650	196	9	propriety	propriety	NOUN
ap-6650	196	10	(	(	PUNCT
ap-6650	196	11	−→a	−→a	PROPN
ap-6650	196	12	×−→b	×−→b	PROPN
ap-6650	196	13	)	)	PUNCT
ap-6650	196	14	.−→c	.−→c	PUNCT
ap-6650	197	1	=	=	PUNCT
ap-6650	197	2	−→a	−→a	PROPN
ap-6650	197	3	.	.	PUNCT
ap-6650	198	1	(	(	PUNCT
ap-6650	198	2	−→	−→	NOUN
ap-6650	198	3	b	b	PROPN
ap-6650	198	4	×−→c	×−→c	PROPN
ap-6650	198	5	)	)	PUNCT
ap-6650	199	1	=	=	PUNCT
ap-6650	200	1	−→b	−→b	INTJ
ap-6650	200	2	.	.	PUNCT
ap-6650	201	1	(	(	PUNCT
ap-6650	201	2	−→c	−→c	PROPN
ap-6650	201	3	×−→a	×−→a	PROPN
ap-6650	201	4	)	)	PUNCT
ap-6650	201	5	,	,	PUNCT
ap-6650	201	6	we	we	PRON
ap-6650	201	7	must	must	AUX
ap-6650	201	8	also	also	ADV
ap-6650	201	9	pay	pay	VERB
ap-6650	201	10	attention	attention	NOUN
ap-6650	201	11	to	to	ADP
ap-6650	201	12	the	the	DET
ap-6650	201	13	order	order	NOUN
ap-6650	201	14	,	,	PUNCT
ap-6650	201	15	ψ†	ψ†	VERB
ap-6650	201	16	is	be	AUX
ap-6650	201	17	the	the	DET
ap-6650	201	18	first	first	ADJ
ap-6650	201	19	and	and	CCONJ
ap-6650	201	20	ψ	ψ	X
ap-6650	201	21	the	the	DET
ap-6650	201	22	second	second	ADJ
ap-6650	201	23	factor	factor	NOUN
ap-6650	201	24	,	,	PUNCT
ap-6650	201	25	we	we	PRON
ap-6650	201	26	have	have	VERB
ap-6650	201	27	ie	ie	X
ap-6650	201	28	4mc~2	4mc~2	NOUN
ap-6650	201	29	(	(	PUNCT
ap-6650	201	30	ψ†qθψ	ψ†qθψ	ADP
ap-6650	201	31	−	−	PROPN
ap-6650	201	32	ψ†q∗θψ	ψ†q∗θψ	NOUN
ap-6650	201	33	)	)	PUNCT
ap-6650	201	34	=	=	PUNCT
ap-6650	202	1	e	e	X
ap-6650	202	2	8mc~2	8mc~2	NUM
ap-6650	202	3	divv	divv	NOUN
ap-6650	202	4	(	(	PUNCT
ap-6650	202	5	x	x	X
ap-6650	202	6	)	)	PUNCT
ap-6650	202	7	(	(	PUNCT
ap-6650	202	8	−→θ	−→θ	NUM
ap-6650	202	9	×−→∇	×−→∇	NOUN
ap-6650	202	10	(	(	PUNCT
ap-6650	202	11	ψ†ψ	ψ†ψ	NUM
ap-6650	202	12	)	)	PUNCT
ap-6650	202	13	)	)	PUNCT
ap-6650	203	1	=	=	NOUN
ap-6650	203	2	div	div	X
ap-6650	203	3	−→	−→	NOUN
ap-6650	203	4	ξ	ξ	PROPN
ap-6650	203	5	nc	nc	PROPN
ap-6650	203	6	.	.	PROPN
ap-6650	203	7	(	(	PUNCT
ap-6650	203	8	31	31	NUM
ap-6650	203	9	)	)	PUNCT
ap-6650	203	10	using	use	VERB
ap-6650	203	11	the	the	DET
ap-6650	203	12	following	follow	VERB
ap-6650	203	13	identity	identity	NOUN
ap-6650	203	14	also	also	ADV
ap-6650	203	15	gives	give	VERB
ap-6650	203	16	the	the	DET
ap-6650	203	17	same	same	ADJ
ap-6650	203	18	equation	equation	NOUN
ap-6650	203	19	as	as	ADP
ap-6650	203	20	above	above	ADP
ap-6650	203	21	[	[	X
ap-6650	203	22	6	6	NUM
ap-6650	203	23	]	]	X
ap-6650	203	24	υ†	υ†	NOUN
ap-6650	203	25	(	(	PUNCT
ap-6650	203	26	−→π	−→π	PROPN
ap-6650	203	27	τ)−	τ)−	PROPN
ap-6650	203	28	(	(	PUNCT
ap-6650	203	29	−→π	−→π	PROPN
ap-6650	203	30	υ)†	υ)†	PROPN
ap-6650	203	31	τ	τ	PROPN
ap-6650	203	32	=	=	SYM
ap-6650	203	33	−i~−→∇	−i~−→∇	PROPN
ap-6650	203	34	(	(	PUNCT
ap-6650	203	35	υ†τ	υ†τ	NUM
ap-6650	203	36	)	)	PUNCT
ap-6650	203	37	,	,	PUNCT
ap-6650	203	38	(	(	PUNCT
ap-6650	203	39	32	32	NUM
ap-6650	203	40	)	)	PUNCT
ap-6650	203	41	where	where	SCONJ
ap-6650	203	42	υ	υ	NOUN
ap-6650	203	43	,	,	PUNCT
ap-6650	203	44	τ	τ	PROPN
ap-6650	203	45	are	be	AUX
ap-6650	203	46	arbitrary	arbitrary	ADJ
ap-6650	203	47	two	two	NUM
ap-6650	203	48	-	-	PUNCT
ap-6650	203	49	component	component	NOUN
ap-6650	203	50	spinor	spinor	NOUN
ap-6650	203	51	.	.	PUNCT
ap-6650	204	1	noting	note	VERB
ap-6650	204	2	that	that	SCONJ
ap-6650	204	3	−→a	−→a	PROPN
ap-6650	204	4	does	do	AUX
ap-6650	204	5	not	not	PART
ap-6650	204	6	appear	appear	VERB
ap-6650	204	7	on	on	ADP
ap-6650	204	8	the	the	DET
ap-6650	204	9	right	right	ADJ
ap-6650	204	10	-	-	PUNCT
ap-6650	204	11	hand	hand	NOUN
ap-6650	204	12	side	side	NOUN
ap-6650	204	13	of	of	ADP
ap-6650	204	14	the	the	DET
ap-6650	204	15	identity	identity	NOUN
ap-6650	204	16	;	;	PUNCT
ap-6650	204	17	and	and	CCONJ
ap-6650	204	18	that	that	SCONJ
ap-6650	204	19	this	this	DET
ap-6650	204	20	identity	identity	NOUN
ap-6650	204	21	is	be	AUX
ap-6650	204	22	related	relate	VERB
ap-6650	204	23	to	to	ADP
ap-6650	204	24	the	the	DET
ap-6650	204	25	fact	fact	NOUN
ap-6650	204	26	that	that	SCONJ
ap-6650	204	27	−→π	−→π	PROPN
ap-6650	204	28	is	be	AUX
ap-6650	204	29	hermitian	hermitian	ADJ
ap-6650	204	30	.	.	PUNCT
ap-6650	205	1	it	it	PRON
ap-6650	205	2	is	be	AUX
ap-6650	205	3	evident	evident	ADJ
ap-6650	205	4	that	that	SCONJ
ap-6650	205	5	the	the	DET
ap-6650	205	6	noncommutativity	noncommutativity	NOUN
ap-6650	205	7	affects	affect	VERB
ap-6650	205	8	the	the	DET
ap-6650	205	9	current	current	ADJ
ap-6650	205	10	density	density	NOUN
ap-6650	205	11	,	,	PUNCT
ap-6650	205	12	and	and	CCONJ
ap-6650	205	13	the	the	DET
ap-6650	205	14	deformation	deformation	NOUN
ap-6650	205	15	quantity	quantity	NOUN
ap-6650	205	16	may	may	AUX
ap-6650	205	17	apear	apear	VERB
ap-6650	205	18	as	as	ADP
ap-6650	205	19	a	a	DET
ap-6650	205	20	correction	correction	NOUN
ap-6650	205	21	to	to	ADP
ap-6650	205	22	it	it	PRON
ap-6650	205	23	.	.	PUNCT
ap-6650	206	1	the	the	DET
ap-6650	206	2	deformed	deform	VERB
ap-6650	206	3	current	current	ADJ
ap-6650	206	4	density	density	NOUN
ap-6650	206	5	satisfies	satisfy	VERB
ap-6650	206	6	the	the	DET
ap-6650	206	7	current	current	ADJ
ap-6650	206	8	conservation	conservation	NOUN
ap-6650	206	9	,	,	PUNCT
ap-6650	206	10	which	which	PRON
ap-6650	206	11	means	mean	VERB
ap-6650	206	12	that	that	SCONJ
ap-6650	206	13	we	we	PRON
ap-6650	206	14	have	have	VERB
ap-6650	206	15	a	a	DET
ap-6650	206	16	conservation	conservation	NOUN
ap-6650	206	17	of	of	ADP
ap-6650	206	18	the	the	DET
ap-6650	206	19	continuity	continuity	NOUN
ap-6650	206	20	equation	equation	NOUN
ap-6650	206	21	in	in	ADP
ap-6650	206	22	the	the	DET
ap-6650	206	23	noncommutative	noncommutative	ADJ
ap-6650	206	24	phase	phase	NOUN
ap-6650	206	25	-	-	PUNCT
ap-6650	206	26	space	space	NOUN
ap-6650	206	27	.	.	PUNCT
ap-6650	207	1	equation	equation	NOUN
ap-6650	207	2	(	(	PUNCT
ap-6650	207	3	29	29	NUM
ap-6650	207	4	)	)	PUNCT
ap-6650	207	5	may	may	AUX
ap-6650	207	6	be	be	AUX
ap-6650	207	7	contracted	contract	VERB
ap-6650	207	8	as	as	ADP
ap-6650	207	9	∂ρ	∂ρ	PROPN
ap-6650	207	10	∂t	∂t	PROPN
ap-6650	208	1	+	+	PROPN
ap-6650	208	2	−→∇	−→∇	PROPN
ap-6650	208	3	.−→j	.−→j	PROPN
ap-6650	208	4	nc	nc	PROPN
ap-6650	209	1	=	=	NOUN
ap-6650	209	2	0	0	PROPN
ap-6650	209	3	,	,	PUNCT
ap-6650	209	4	(	(	PUNCT
ap-6650	209	5	33	33	NUM
ap-6650	209	6	)	)	PUNCT
ap-6650	209	7	where	where	SCONJ
ap-6650	209	8	ρ	ρ	NOUN
ap-6650	209	9	=	=	SYM
ap-6650	209	10	ψ†ψ	ψ†ψ	NOUN
ap-6650	210	1	=	=	SYM
ap-6650	210	2	|ψ|2	|ψ|2	PROPN
ap-6650	210	3	,	,	PUNCT
ap-6650	210	4	(	(	PUNCT
ap-6650	210	5	34	34	NUM
ap-6650	210	6	)	)	PUNCT
ap-6650	210	7	234	234	NUM
ap-6650	210	8	vol	vol	NOUN
ap-6650	210	9	.	.	PUNCT
ap-6650	211	1	61	61	NUM
ap-6650	211	2	no	no	NOUN
ap-6650	211	3	.	.	PUNCT
ap-6650	212	1	1/2021	1/2021	NUM
ap-6650	212	2	on	on	ADP
ap-6650	212	3	the	the	DET
ap-6650	212	4	three	three	NUM
ap-6650	212	5	-	-	PUNCT
ap-6650	212	6	dimensional	dimensional	ADJ
ap-6650	212	7	pauli	pauli	PROPN
ap-6650	212	8	equation	equation	NOUN
ap-6650	212	9	in	in	ADP
ap-6650	212	10	noncommutative	noncommutative	ADJ
ap-6650	212	11	phase	phase	NOUN
ap-6650	212	12	-	-	PUNCT
ap-6650	212	13	space	space	NOUN
ap-6650	212	14	is	be	AUX
ap-6650	212	15	the	the	DET
ap-6650	212	16	probability	probability	NOUN
ap-6650	212	17	density	density	NOUN
ap-6650	212	18	and	and	CCONJ
ap-6650	212	19	−→	−→	NOUN
ap-6650	212	20	j	j	PROPN
ap-6650	212	21	nc	nc	PROPN
ap-6650	212	22	=	=	PROPN
ap-6650	212	23	−→j	−→j	PROPN
ap-6650	213	1	+	+	NOUN
ap-6650	213	2	−→ξ	−→ξ	X
ap-6650	213	3	nc	nc	X
ap-6650	213	4	=	=	PROPN
ap-6650	213	5	−i~2	−i~2	PROPN
ap-6650	213	6	m	m	AUX
ap-6650	213	7	{	{	PUNCT
ap-6650	213	8	ψ†	ψ†	VERB
ap-6650	213	9	−→	−→	NOUN
ap-6650	213	10	∇ψ	∇ψ	PROPN
ap-6650	213	11	−	−	NOUN
ap-6650	213	12	ψ	ψ	ADP
ap-6650	213	13	−→	−→	NOUN
ap-6650	213	14	∇ψ†	∇ψ†	PROPN
ap-6650	213	15	}	}	PUNCT
ap-6650	213	16	−	−	PROPN
ap-6650	214	1	e	e	X
ap-6650	214	2	mc	mc	X
ap-6650	214	3	{	{	PUNCT
ap-6650	214	4	−→	−→	NOUN
ap-6650	214	5	aψ†ψ	aψ†ψ	PROPN
ap-6650	214	6	}	}	PUNCT
ap-6650	214	7	+	+	ADP
ap-6650	214	8	−→ξ	−→ξ	X
ap-6650	214	9	nc	nc	X
ap-6650	214	10	,	,	PUNCT
ap-6650	214	11	(	(	PUNCT
ap-6650	214	12	35	35	NUM
ap-6650	214	13	)	)	PUNCT
ap-6650	214	14	is	be	AUX
ap-6650	214	15	the	the	DET
ap-6650	214	16	deformed	deform	VERB
ap-6650	214	17	current	current	ADJ
ap-6650	214	18	density	density	NOUN
ap-6650	214	19	of	of	ADP
ap-6650	214	20	the	the	DET
ap-6650	214	21	electrons	electron	NOUN
ap-6650	214	22	.	.	PUNCT
ap-6650	215	1	the	the	DET
ap-6650	215	2	deformation	deformation	NOUN
ap-6650	215	3	quantity	quantity	NOUN
ap-6650	215	4	is	be	AUX
ap-6650	215	5	−→	−→	NOUN
ap-6650	215	6	ξ	ξ	X
ap-6650	215	7	nc	nc	PROPN
ap-6650	215	8	=	=	SYM
ap-6650	215	9	e	e	PROPN
ap-6650	215	10	8mc~2v	8mc~2v	PROPN
ap-6650	215	11	(	(	PUNCT
ap-6650	215	12	x	x	X
ap-6650	215	13	)	)	PUNCT
ap-6650	215	14	(	(	PUNCT
ap-6650	215	15	−→θ	−→θ	NUM
ap-6650	215	16	×−→∇	×−→∇	NOUN
ap-6650	215	17	(	(	PUNCT
ap-6650	215	18	ψ†ψ	ψ†ψ	NUM
ap-6650	215	19	)	)	PUNCT
ap-6650	215	20	)	)	PUNCT
ap-6650	216	1	=	=	PUNCT
ap-6650	216	2	e	e	X
ap-6650	216	3	8mc~2	8mc~2	PROPN
ap-6650	216	4	(	(	PUNCT
ap-6650	216	5	2−→p	2−→p	NUM
ap-6650	216	6	.−→a	.−→a	PUNCT
ap-6650	217	1	−	−	NUM
ap-6650	217	2	1	1	NUM
ap-6650	217	3	2	2	NUM
ap-6650	217	4	~	~	NOUN
ap-6650	217	5	qη	qη	NOUN
ap-6650	217	6	−	−	NOUN
ap-6650	217	7	e	e	NOUN
ap-6650	218	1	c	c	NOUN
ap-6650	218	2	−→	−→	VERB
ap-6650	218	3	a	a	DET
ap-6650	218	4	2	2	NUM
ap-6650	218	5	)	)	PUNCT
ap-6650	218	6	(	(	PUNCT
ap-6650	218	7	−→θ	−→θ	ADJ
ap-6650	218	8	×−→∇	×−→∇	NOUN
ap-6650	218	9	(	(	PUNCT
ap-6650	218	10	ψ†ψ	ψ†ψ	NUM
ap-6650	218	11	)	)	PUNCT
ap-6650	218	12	)	)	PUNCT
ap-6650	218	13	.	.	PUNCT
ap-6650	219	1	(	(	PUNCT
ap-6650	219	2	36	36	NUM
ap-6650	219	3	)	)	PUNCT
ap-6650	219	4	furthermore	furthermore	ADV
ap-6650	219	5	,	,	PUNCT
ap-6650	219	6	the	the	DET
ap-6650	219	7	deformed	deform	VERB
ap-6650	219	8	continuity	continuity	NOUN
ap-6650	219	9	equation	equation	NOUN
ap-6650	219	10	for	for	ADP
ap-6650	219	11	all	all	DET
ap-6650	219	12	orders	order	NOUN
ap-6650	219	13	of	of	ADP
ap-6650	219	14	θ	θ	PROPN
ap-6650	219	15	is	be	AUX
ap-6650	219	16	proportional	proportional	ADJ
ap-6650	219	17	to	to	ADP
ap-6650	219	18	the	the	DET
ap-6650	219	19	magnetic	magnetic	ADJ
ap-6650	219	20	field	field	NOUN
ap-6650	220	1	−→b	−→b	INTJ
ap-6650	220	2	.	.	PUNCT
ap-6650	221	1	in	in	ADP
ap-6650	221	2	fact	fact	NOUN
ap-6650	221	3	,	,	PUNCT
ap-6650	221	4	one	one	PRON
ap-6650	221	5	can	can	AUX
ap-6650	221	6	explicitly	explicitly	ADV
ap-6650	221	7	calculate	calculate	VERB
ap-6650	221	8	the	the	DET
ap-6650	221	9	conserved	conserved	ADJ
ap-6650	221	10	current	current	NOUN
ap-6650	221	11	for	for	ADP
ap-6650	221	12	all	all	DET
ap-6650	221	13	orders	order	NOUN
ap-6650	221	14	of	of	ADP
ap-6650	221	15	θ	θ	PROPN
ap-6650	221	16	in	in	ADP
ap-6650	221	17	the	the	DET
ap-6650	221	18	case	case	NOUN
ap-6650	221	19	of	of	ADP
ap-6650	221	20	a	a	DET
ap-6650	221	21	non	non	ADJ
ap-6650	221	22	-	-	ADJ
ap-6650	221	23	constant	constant	ADJ
ap-6650	221	24	magnetic	magnetic	ADJ
ap-6650	221	25	field	field	NOUN
ap-6650	221	26	,	,	PUNCT
ap-6650	221	27	thus	thus	ADV
ap-6650	221	28	using	use	VERB
ap-6650	221	29	equation	equation	NOUN
ap-6650	221	30	(	(	PUNCT
ap-6650	221	31	24	24	NUM
ap-6650	221	32	)	)	PUNCT
ap-6650	221	33	,	,	PUNCT
ap-6650	221	34	we	we	PRON
ap-6650	221	35	have	have	VERB
ap-6650	221	36	∂ρ	∂ρ	PROPN
ap-6650	221	37	∂t	∂t	PROPN
ap-6650	222	1	+	+	PROPN
ap-6650	222	2	−→∇	−→∇	PROPN
ap-6650	222	3	.−→j	.−→j	PUNCT
ap-6650	223	1	+	+	CCONJ
ap-6650	223	2	ie	ie	X
ap-6650	223	3	4mc~2	4mc~2	NOUN
ap-6650	223	4	{	{	PUNCT
ap-6650	223	5	ψ†	ψ†	PUNCT
ap-6650	223	6	(	(	PUNCT
ap-6650	223	7	v	v	NOUN
ap-6650	223	8	(	(	PUNCT
ap-6650	223	9	x	x	NOUN
ap-6650	223	10	)	)	PUNCT
ap-6650	223	11	?	?	PUNCT
ap-6650	224	1	ψ)−	ψ)−	PROPN
ap-6650	224	2	(	(	PUNCT
ap-6650	224	3	ψ†	ψ†	ADJ
ap-6650	224	4	?	?	PUNCT
ap-6650	225	1	v	v	X
ap-6650	225	2	(	(	PUNCT
ap-6650	225	3	x	x	NOUN
ap-6650	225	4	)	)	PUNCT
ap-6650	225	5	)	)	PUNCT
ap-6650	226	1	ψ	ψ	X
ap-6650	226	2	}	}	PUNCT
ap-6650	226	3	=	=	SYM
ap-6650	226	4	0	0	NUM
ap-6650	226	5	,	,	PUNCT
ap-6650	226	6	(	(	PUNCT
ap-6650	226	7	37	37	NUM
ap-6650	226	8	)	)	PUNCT
ap-6650	226	9	we	we	PRON
ap-6650	226	10	calculate	calculate	VERB
ap-6650	226	11	the	the	DET
ap-6650	226	12	nth	nth	NOUN
ap-6650	226	13	order	order	NOUN
ap-6650	226	14	term	term	NOUN
ap-6650	226	15	in	in	ADP
ap-6650	226	16	the	the	DET
ap-6650	226	17	general	general	ADJ
ap-6650	226	18	deformed	deform	VERB
ap-6650	226	19	continuity	continuity	NOUN
ap-6650	226	20	equation	equation	NOUN
ap-6650	226	21	(	(	PUNCT
ap-6650	226	22	37	37	NUM
ap-6650	226	23	)	)	PUNCT
ap-6650	226	24	as	as	SCONJ
ap-6650	226	25	follows	follow	VERB
ap-6650	226	26	ψ†	ψ†	NOUN
ap-6650	226	27	(	(	PUNCT
ap-6650	226	28	v	v	NOUN
ap-6650	226	29	(	(	PUNCT
ap-6650	226	30	x	x	NOUN
ap-6650	226	31	)	)	PUNCT
ap-6650	226	32	?	?	PUNCT
ap-6650	227	1	ψ)−	ψ)−	PROPN
ap-6650	227	2	(	(	PUNCT
ap-6650	227	3	ψ†	ψ†	ADJ
ap-6650	227	4	?	?	PUNCT
ap-6650	228	1	v	v	X
ap-6650	228	2	(	(	PUNCT
ap-6650	228	3	x	x	NOUN
ap-6650	228	4	)	)	PUNCT
ap-6650	228	5	)	)	PUNCT
ap-6650	229	1	ψ	ψ	ADP
ap-6650	229	2	∣∣	∣∣	NUM
ap-6650	229	3	nth	nth	NOUN
ap-6650	229	4	=	=	SYM
ap-6650	229	5	1	1	NUM
ap-6650	229	6	n	n	CCONJ
ap-6650	229	7	!	!	PUNCT
ap-6650	230	1	(	(	PUNCT
ap-6650	230	2	i	i	NOUN
ap-6650	230	3	2	2	NUM
ap-6650	230	4	)	)	PUNCT
ap-6650	230	5	n	n	PRON
ap-6650	230	6	θa1b1	θa1b1	PROPN
ap-6650	230	7	...	...	PUNCT
ap-6650	230	8	θanbn	θanbn	NOUN
ap-6650	230	9	×	×	NOUN
ap-6650	230	10	(	(	PUNCT
ap-6650	230	11	ψ†∂a1	ψ†∂a1	PROPN
ap-6650	230	12	...	...	PUNCT
ap-6650	230	13	∂akv	∂akv	X
ap-6650	230	14	(	(	PUNCT
ap-6650	230	15	x	x	X
ap-6650	230	16	)	)	PUNCT
ap-6650	230	17	∂b1	∂b1	PROPN
ap-6650	230	18	...	...	PUNCT
ap-6650	230	19	∂bkψ	∂bkψ	NUM
ap-6650	230	20	−	−	ADP
ap-6650	231	1	∂a1	∂a1	NOUN
ap-6650	231	2	...	...	PUNCT
ap-6650	231	3	∂akψ	∂akψ	X
ap-6650	231	4	†	†	X
ap-6650	231	5	(	(	PUNCT
ap-6650	231	6	∂b1	∂b1	PROPN
ap-6650	231	7	...	...	PUNCT
ap-6650	231	8	∂bkv	∂bkv	NUM
ap-6650	231	9	(	(	PUNCT
ap-6650	231	10	x))ψ	x))ψ	X
ap-6650	231	11	+	+	X
ap-6650	231	12	(	(	PUNCT
ap-6650	231	13	−1)ncc	−1)ncc	NUM
ap-6650	231	14	.	.	PUNCT
ap-6650	231	15	)	)	PUNCT
ap-6650	231	16	.	.	PUNCT
ap-6650	232	1	(	(	PUNCT
ap-6650	232	2	38	38	NUM
ap-6650	232	3	)	)	PUNCT
ap-6650	232	4	we	we	PRON
ap-6650	232	5	note	note	VERB
ap-6650	232	6	the	the	DET
ap-6650	232	7	absence	absence	NOUN
ap-6650	232	8	of	of	ADP
ap-6650	232	9	the	the	DET
ap-6650	232	10	magnetization	magnetization	NOUN
ap-6650	232	11	current	current	ADJ
ap-6650	232	12	term	term	NOUN
ap-6650	232	13	in	in	ADP
ap-6650	232	14	equation	equation	NOUN
ap-6650	232	15	(	(	PUNCT
ap-6650	232	16	35	35	NUM
ap-6650	232	17	)	)	PUNCT
ap-6650	232	18	,	,	PUNCT
ap-6650	232	19	as	as	ADP
ap-6650	232	20	in	in	ADP
ap-6650	232	21	commutative	commutative	ADJ
ap-6650	232	22	case	case	NOUN
ap-6650	232	23	when	when	SCONJ
ap-6650	232	24	this	this	PRON
ap-6650	232	25	was	be	AUX
ap-6650	232	26	asserted	assert	VERB
ap-6650	232	27	by	by	ADP
ap-6650	232	28	authors	author	NOUN
ap-6650	232	29	[	[	X
ap-6650	232	30	1	1	NUM
ap-6650	232	31	,	,	PUNCT
ap-6650	232	32	4	4	NUM
ap-6650	232	33	,	,	PUNCT
ap-6650	232	34	8	8	NUM
ap-6650	232	35	,	,	PUNCT
ap-6650	232	36	13	13	NUM
ap-6650	232	37	,	,	PUNCT
ap-6650	232	38	16	16	NUM
ap-6650	232	39	,	,	PUNCT
ap-6650	232	40	27	27	NUM
ap-6650	232	41	]	]	PUNCT
ap-6650	232	42	,	,	PUNCT
ap-6650	232	43	where	where	SCONJ
ap-6650	232	44	at	at	ADP
ap-6650	232	45	first	first	ADV
ap-6650	232	46	,	,	PUNCT
ap-6650	232	47	they	they	PRON
ap-6650	232	48	attempted	attempt	VERB
ap-6650	232	49	to	to	PART
ap-6650	232	50	cover	cover	VERB
ap-6650	232	51	this	this	DET
ap-6650	232	52	deficiency	deficiency	NOUN
ap-6650	232	53	by	by	ADP
ap-6650	232	54	explaining	explain	VERB
ap-6650	232	55	how	how	SCONJ
ap-6650	232	56	to	to	PART
ap-6650	232	57	derive	derive	VERB
ap-6650	232	58	this	this	DET
ap-6650	232	59	additional	additional	ADJ
ap-6650	232	60	term	term	NOUN
ap-6650	232	61	from	from	ADP
ap-6650	232	62	the	the	DET
ap-6650	232	63	non	non	ADJ
ap-6650	232	64	-	-	ADJ
ap-6650	232	65	relativistic	relativistic	ADJ
ap-6650	232	66	limit	limit	NOUN
ap-6650	232	67	of	of	ADP
ap-6650	232	68	the	the	DET
ap-6650	232	69	relativistic	relativistic	ADJ
ap-6650	232	70	dirac	dirac	NOUN
ap-6650	232	71	probability	probability	NOUN
ap-6650	232	72	current	current	ADJ
ap-6650	232	73	density	density	NOUN
ap-6650	232	74	.	.	PUNCT
ap-6650	233	1	then	then	ADV
ap-6650	233	2	,	,	PUNCT
ap-6650	233	3	nowakowski	nowakowski	ADJ
ap-6650	233	4	and	and	CCONJ
ap-6650	233	5	others	other	NOUN
ap-6650	233	6	[	[	X
ap-6650	233	7	6	6	NUM
ap-6650	233	8	]	]	PUNCT
ap-6650	233	9	provided	provide	VERB
ap-6650	233	10	a	a	DET
ap-6650	233	11	superb	superb	ADJ
ap-6650	233	12	explanation	explanation	NOUN
ap-6650	233	13	of	of	ADP
ap-6650	233	14	how	how	SCONJ
ap-6650	233	15	to	to	PART
ap-6650	233	16	extract	extract	VERB
ap-6650	233	17	this	this	DET
ap-6650	233	18	term	term	NOUN
ap-6650	233	19	through	through	ADP
ap-6650	233	20	the	the	DET
ap-6650	233	21	non	non	ADJ
ap-6650	233	22	-	-	ADJ
ap-6650	233	23	relativistic	relativistic	ADJ
ap-6650	233	24	pauli	pauli	PROPN
ap-6650	233	25	equation	equation	NOUN
ap-6650	233	26	itself	itself	PRON
ap-6650	233	27	.	.	PUNCT
ap-6650	234	1	knowing	know	VERB
ap-6650	234	2	that	that	SCONJ
ap-6650	234	3	,	,	PUNCT
ap-6650	234	4	in	in	ADP
ap-6650	234	5	a	a	DET
ap-6650	234	6	commutative	commutative	ADJ
ap-6650	234	7	background	background	NOUN
ap-6650	234	8	,	,	PUNCT
ap-6650	234	9	the	the	DET
ap-6650	234	10	magnetization	magnetization	NOUN
ap-6650	234	11	current	current	ADJ
ap-6650	234	12	−→j	−→j	PROPN
ap-6650	234	13	m	m	VERB
ap-6650	234	14	from	from	ADP
ap-6650	234	15	the	the	DET
ap-6650	234	16	probability	probability	NOUN
ap-6650	234	17	current	current	NOUN
ap-6650	234	18	of	of	ADP
ap-6650	234	19	the	the	DET
ap-6650	234	20	pauli	pauli	PROPN
ap-6650	234	21	equation	equation	NOUN
ap-6650	234	22	is	be	AUX
ap-6650	234	23	proportional	proportional	ADJ
ap-6650	234	24	to	to	PART
ap-6650	234	25	−→∇	−→∇	VERB
ap-6650	234	26	×	×	NOUN
ap-6650	234	27	(	(	PUNCT
ap-6650	234	28	ψ†−→σ	ψ†−→σ	PROPN
ap-6650	234	29	ψ	ψ	NOUN
ap-6650	234	30	)	)	PUNCT
ap-6650	234	31	.	.	PUNCT
ap-6650	235	1	however	however	ADV
ap-6650	235	2	,	,	PUNCT
ap-6650	235	3	the	the	DET
ap-6650	235	4	existence	existence	NOUN
ap-6650	235	5	of	of	ADP
ap-6650	235	6	such	such	DET
ap-6650	235	7	an	an	DET
ap-6650	235	8	additional	additional	ADJ
ap-6650	235	9	term	term	NOUN
ap-6650	235	10	is	be	AUX
ap-6650	235	11	important	important	ADJ
ap-6650	235	12	and	and	CCONJ
ap-6650	235	13	it	it	PRON
ap-6650	235	14	should	should	AUX
ap-6650	235	15	be	be	AUX
ap-6650	235	16	discussed	discuss	VERB
ap-6650	235	17	when	when	SCONJ
ap-6650	235	18	talking	talk	VERB
ap-6650	235	19	about	about	ADP
ap-6650	235	20	the	the	DET
ap-6650	235	21	probability	probability	NOUN
ap-6650	235	22	current	current	NOUN
ap-6650	235	23	of	of	ADP
ap-6650	235	24	spin-1/2	spin-1/2	NOUN
ap-6650	235	25	particles	particle	NOUN
ap-6650	235	26	.	.	PUNCT
ap-6650	236	1	in	in	ADP
ap-6650	236	2	following	follow	VERB
ap-6650	236	3	,	,	PUNCT
ap-6650	236	4	we	we	PRON
ap-6650	236	5	try	try	VERB
ap-6650	236	6	to	to	PART
ap-6650	236	7	derive	derive	VERB
ap-6650	236	8	the	the	DET
ap-6650	236	9	current	current	ADJ
ap-6650	236	10	magnetization	magnetization	NOUN
ap-6650	236	11	in	in	ADP
ap-6650	236	12	a	a	DET
ap-6650	236	13	noncommutative	noncommutative	ADJ
ap-6650	236	14	background	background	NOUN
ap-6650	236	15	without	without	ADP
ap-6650	236	16	changing	change	VERB
ap-6650	236	17	the	the	DET
ap-6650	236	18	continuity	continuity	NOUN
ap-6650	236	19	equation	equation	NOUN
ap-6650	236	20	,	,	PUNCT
ap-6650	236	21	and	and	CCONJ
ap-6650	236	22	seek	seek	VERB
ap-6650	236	23	if	if	SCONJ
ap-6650	236	24	such	such	DET
ap-6650	236	25	an	an	DET
ap-6650	236	26	additional	additional	ADJ
ap-6650	236	27	term	term	NOUN
ap-6650	236	28	is	be	AUX
ap-6650	236	29	affected	affect	VERB
ap-6650	236	30	by	by	ADP
ap-6650	236	31	the	the	DET
ap-6650	236	32	noncommutativity	noncommutativity	NOUN
ap-6650	236	33	or	or	CCONJ
ap-6650	236	34	not	not	PART
ap-6650	236	35	.	.	PUNCT
ap-6650	237	1	3.3	3.3	NUM
ap-6650	237	2	.	.	PUNCT
ap-6650	238	1	derivation	derivation	NOUN
ap-6650	238	2	of	of	ADP
ap-6650	238	3	the	the	DET
ap-6650	238	4	magnetization	magnetization	NOUN
ap-6650	238	5	current	current	ADJ
ap-6650	238	6	at	at	ADP
ap-6650	238	7	first	first	ADV
ap-6650	238	8	,	,	PUNCT
ap-6650	238	9	it	it	PRON
ap-6650	238	10	must	must	AUX
ap-6650	238	11	be	be	AUX
ap-6650	238	12	clarified	clarify	VERB
ap-6650	238	13	that	that	SCONJ
ap-6650	238	14	the	the	DET
ap-6650	238	15	authors	author	NOUN
ap-6650	238	16	nowakowski	nowakowski	ADJ
ap-6650	238	17	and	and	CCONJ
ap-6650	238	18	others	other	NOUN
ap-6650	238	19	(	(	PUNCT
ap-6650	238	20	2011	2011	NUM
ap-6650	238	21	)	)	PUNCT
ap-6650	238	22	in	in	ADP
ap-6650	238	23	[	[	X
ap-6650	238	24	4	4	NUM
ap-6650	238	25	,	,	PUNCT
ap-6650	238	26	6	6	NUM
ap-6650	238	27	]	]	PUNCT
ap-6650	238	28	derived	derive	VERB
ap-6650	238	29	the	the	DET
ap-6650	238	30	non	non	ADJ
ap-6650	238	31	-	-	ADJ
ap-6650	238	32	relativistic	relativistic	ADJ
ap-6650	238	33	current	current	ADJ
ap-6650	238	34	density	density	NOUN
ap-6650	238	35	for	for	ADP
ap-6650	238	36	a	a	DET
ap-6650	238	37	spin-1/2	spin-1/2	NOUN
ap-6650	238	38	particle	particle	NOUN
ap-6650	238	39	using	use	VERB
ap-6650	238	40	minimally	minimally	ADV
ap-6650	238	41	coupled	couple	VERB
ap-6650	238	42	pauli	pauli	PROPN
ap-6650	238	43	equation	equation	NOUN
ap-6650	238	44	.	.	PUNCT
ap-6650	239	1	in	in	ADP
ap-6650	239	2	contrast	contrast	NOUN
ap-6650	239	3	,	,	PUNCT
ap-6650	239	4	wilkes	wilkes	PROPN
ap-6650	239	5	,	,	PUNCT
ap-6650	239	6	j.	j.	PROPN
ap-6650	239	7	m	m	PROPN
ap-6650	239	8	(	(	PUNCT
ap-6650	239	9	2020	2020	NUM
ap-6650	239	10	)	)	PUNCT
ap-6650	239	11	in	in	ADP
ap-6650	239	12	[	[	X
ap-6650	239	13	39	39	NUM
ap-6650	239	14	]	]	PUNCT
ap-6650	239	15	derived	derive	VERB
ap-6650	239	16	the	the	DET
ap-6650	239	17	non	non	ADJ
ap-6650	239	18	-	-	ADJ
ap-6650	239	19	relativistic	relativistic	ADJ
ap-6650	239	20	current	current	ADJ
ap-6650	239	21	density	density	NOUN
ap-6650	239	22	for	for	ADP
ap-6650	239	23	a	a	DET
ap-6650	239	24	free	free	ADJ
ap-6650	239	25	spin-1/2	spin-1/2	NOUN
ap-6650	239	26	particle	particle	NOUN
ap-6650	239	27	using	use	VERB
ap-6650	239	28	directly	directly	ADV
ap-6650	239	29	free	free	ADJ
ap-6650	239	30	pauli	pauli	PROPN
ap-6650	239	31	equation	equation	NOUN
ap-6650	239	32	.	.	PUNCT
ap-6650	240	1	however	however	ADV
ap-6650	240	2	,	,	PUNCT
ap-6650	240	3	we	we	PRON
ap-6650	240	4	show	show	VERB
ap-6650	240	5	here	here	ADV
ap-6650	240	6	that	that	SCONJ
ap-6650	240	7	the	the	DET
ap-6650	240	8	current	current	ADJ
ap-6650	240	9	density	density	NOUN
ap-6650	240	10	can	can	AUX
ap-6650	240	11	be	be	AUX
ap-6650	240	12	derived	derive	VERB
ap-6650	240	13	from	from	ADP
ap-6650	240	14	the	the	DET
ap-6650	240	15	minimally	minimally	ADV
ap-6650	240	16	coupled	couple	VERB
ap-6650	240	17	pauli	pauli	PROPN
ap-6650	240	18	equation	equation	NOUN
ap-6650	240	19	in	in	ADP
ap-6650	240	20	a	a	DET
ap-6650	240	21	noncommutative	noncommutative	ADJ
ap-6650	240	22	phase	phase	NOUN
ap-6650	240	23	-	-	PUNCT
ap-6650	240	24	space	space	NOUN
ap-6650	240	25	.	.	PUNCT
ap-6650	241	1	starting	start	VERB
ap-6650	241	2	with	with	ADP
ap-6650	241	3	the	the	DET
ap-6650	241	4	noncommutative	noncommutative	ADJ
ap-6650	241	5	minimally	minimally	ADV
ap-6650	241	6	coupled	couple	VERB
ap-6650	241	7	pauli	pauli	PROPN
ap-6650	241	8	equation	equation	NOUN
ap-6650	241	9	written	write	VERB
ap-6650	241	10	in	in	ADP
ap-6650	241	11	the	the	DET
ap-6650	241	12	form	form	NOUN
ap-6650	241	13	hncpauliψ	hncpauliψ	NOUN
ap-6650	241	14	=	=	NOUN
ap-6650	241	15	1	1	NUM
ap-6650	241	16	2	2	NUM
ap-6650	241	17	m	m	VERB
ap-6650	241	18	(	(	PUNCT
ap-6650	241	19	−→σ	−→σ	NUM
ap-6650	241	20	.−̂→π	.−̂→π	PUNCT
ap-6650	241	21	nc)2	nc)2	NOUN
ap-6650	241	22	ψ	ψ	X
ap-6650	241	23	=	=	SYM
ap-6650	241	24	i~	i~	PROPN
ap-6650	241	25	∂	∂	NOUN
ap-6650	241	26	∂t	∂t	PROPN
ap-6650	241	27	ψ	ψ	PROPN
ap-6650	241	28	,	,	PUNCT
ap-6650	241	29	(	(	PUNCT
ap-6650	241	30	39	39	NUM
ap-6650	241	31	)	)	PUNCT
ap-6650	241	32	we	we	PRON
ap-6650	241	33	multiply	multiply	VERB
ap-6650	241	34	the	the	DET
ap-6650	241	35	above	above	ADJ
ap-6650	241	36	equation	equation	NOUN
ap-6650	241	37	from	from	ADP
ap-6650	241	38	left	leave	VERB
ap-6650	241	39	by	by	ADP
ap-6650	241	40	ψ†	ψ†	PROPN
ap-6650	241	41	and	and	CCONJ
ap-6650	241	42	the	the	DET
ap-6650	241	43	adjoint	adjoint	NOUN
ap-6650	241	44	equation	equation	NOUN
ap-6650	241	45	of	of	ADP
ap-6650	241	46	equation	equation	NOUN
ap-6650	241	47	(	(	PUNCT
ap-6650	241	48	39	39	NUM
ap-6650	241	49	)	)	PUNCT
ap-6650	241	50	from	from	ADP
ap-6650	241	51	the	the	DET
ap-6650	241	52	right	right	NOUN
ap-6650	241	53	by	by	ADP
ap-6650	241	54	ψ	ψ	NOUN
ap-6650	241	55	,	,	PUNCT
ap-6650	241	56	the	the	DET
ap-6650	241	57	subtraction	subtraction	NOUN
ap-6650	241	58	of	of	ADP
ap-6650	241	59	these	these	DET
ap-6650	241	60	equations	equation	NOUN
ap-6650	241	61	yields	yield	VERB
ap-6650	241	62	the	the	DET
ap-6650	241	63	following	follow	VERB
ap-6650	241	64	continuity	continuity	NOUN
ap-6650	241	65	equation	equation	NOUN
ap-6650	241	66	2	2	NUM
ap-6650	241	67	m	m	VERB
ap-6650	241	68	{	{	PUNCT
ap-6650	241	69	(	(	PUNCT
ap-6650	241	70	(	(	PUNCT
ap-6650	241	71	−→σ	−→σ	NUM
ap-6650	241	72	.−̂→π	.−̂→π	PUNCT
ap-6650	241	73	nc)2	nc)2	NOUN
ap-6650	241	74	ψ	ψ	NOUN
ap-6650	241	75	)	)	PUNCT
ap-6650	241	76	†	†	PROPN
ap-6650	241	77	ψ	ψ	X
ap-6650	242	1	−	−	PROPN
ap-6650	242	2	ψ†	ψ†	PUNCT
ap-6650	242	3	(	(	PUNCT
ap-6650	242	4	−→σ	−→σ	NUM
ap-6650	242	5	.−̂→π	.−̂→π	PUNCT
ap-6650	242	6	nc)2	nc)2	NOUN
ap-6650	242	7	ψ	ψ	NOUN
ap-6650	242	8	}	}	PUNCT
ap-6650	242	9	=	=	SYM
ap-6650	242	10	i~	i~	PROPN
ap-6650	242	11	(	(	PUNCT
ap-6650	242	12	ψ†	ψ†	VERB
ap-6650	242	13	∂ψ	∂ψ	PROPN
ap-6650	243	1	∂t	∂t	PROPN
ap-6650	243	2	+	+	CCONJ
ap-6650	243	3	ψ	ψ	X
ap-6650	243	4	∂ψ†	∂ψ†	X
ap-6650	243	5	∂t	∂t	PROPN
ap-6650	243	6	)	)	PUNCT
ap-6650	243	7	,	,	PUNCT
ap-6650	243	8	(	(	PUNCT
ap-6650	243	9	40	40	NUM
ap-6650	243	10	)	)	PUNCT
ap-6650	243	11	noting	note	VERB
ap-6650	243	12	that	that	SCONJ
ap-6650	243	13	the	the	DET
ap-6650	243	14	noncommutativity	noncommutativity	NOUN
ap-6650	243	15	of	of	ADP
ap-6650	243	16	πnc	πnc	NOUN
ap-6650	243	17	has	have	AUX
ap-6650	243	18	led	lead	VERB
ap-6650	243	19	us	we	PRON
ap-6650	243	20	to	to	PART
ap-6650	243	21	express	express	VERB
ap-6650	243	22	the	the	DET
ap-6650	243	23	two	two	NUM
ap-6650	243	24	terms	term	NOUN
ap-6650	243	25	as	as	SCONJ
ap-6650	243	26	follows	follow	VERB
ap-6650	243	27	i	i	PRON
ap-6650	243	28	2m~	2m~	VERB
ap-6650	243	29	∑	∑	PROPN
ap-6650	243	30	i	i	PROPN
ap-6650	243	31	,	,	PUNCT
ap-6650	243	32	j	j	PROPN
ap-6650	243	33	{	{	PUNCT
ap-6650	243	34	(	(	PUNCT
ap-6650	243	35	π̂incπ̂jncψ)†	π̂incπ̂jncψ)†	PUNCT
ap-6650	243	36	σjσiψ	σjσiψ	NOUN
ap-6650	243	37	−	−	PROPN
ap-6650	243	38	ψ†σiσj	ψ†σiσj	PROPN
ap-6650	243	39	(	(	PUNCT
ap-6650	243	40	π̂incπ̂jncψ	π̂incπ̂jncψ	NOUN
ap-6650	243	41	)	)	PUNCT
ap-6650	243	42	}	}	PUNCT
ap-6650	244	1	=	=	PUNCT
ap-6650	244	2	∂ρ	∂ρ	PROPN
ap-6650	244	3	∂t	∂t	PROPN
ap-6650	244	4	.	.	PUNCT
ap-6650	245	1	(	(	PUNCT
ap-6650	245	2	41	41	NUM
ap-6650	245	3	)	)	PUNCT
ap-6650	245	4	while	while	SCONJ
ap-6650	245	5	with	with	ADP
ap-6650	245	6	only	only	ADJ
ap-6650	245	7	pi	pi	NOUN
ap-6650	245	8	,	,	PUNCT
ap-6650	245	9	we	we	PRON
ap-6650	245	10	would	would	AUX
ap-6650	245	11	have	have	VERB
ap-6650	245	12	no	no	DET
ap-6650	245	13	reason	reason	NOUN
ap-6650	245	14	for	for	ADP
ap-6650	245	15	preferring	prefer	VERB
ap-6650	245	16	pipjψ	pipjψ	NOUN
ap-6650	245	17	over	over	ADP
ap-6650	245	18	pjpiψ	pjpiψ	PROPN
ap-6650	245	19	.	.	PUNCT
ap-6650	246	1	it	it	PRON
ap-6650	246	2	is	be	AUX
ap-6650	246	3	easy	easy	ADJ
ap-6650	246	4	to	to	PART
ap-6650	246	5	verify	verify	VERB
ap-6650	246	6	that	that	SCONJ
ap-6650	246	7	the	the	DET
ap-6650	246	8	identity	identity	NOUN
ap-6650	246	9	(	(	PUNCT
ap-6650	246	10	32	32	NUM
ap-6650	246	11	)	)	PUNCT
ap-6650	246	12	remains	remain	VERB
ap-6650	246	13	valid	valid	ADJ
ap-6650	246	14	for	for	ADP
ap-6650	246	15	−→π	−→π	PROPN
ap-6650	246	16	nc	nc	PROPN
ap-6650	246	17	because	because	SCONJ
ap-6650	246	18	of	of	ADP
ap-6650	246	19	the	the	DET
ap-6650	246	20	fact	fact	NOUN
ap-6650	246	21	that	that	SCONJ
ap-6650	246	22	−→π	−→π	PROPN
ap-6650	246	23	nc	nc	PROPN
ap-6650	246	24	is	be	AUX
ap-6650	246	25	hermitian	hermitian	ADJ
ap-6650	246	26	.	.	PUNCT
ap-6650	247	1	therefore	therefore	ADV
ap-6650	247	2	,	,	PUNCT
ap-6650	247	3	through	through	ADP
ap-6650	247	4	identity	identity	NOUN
ap-6650	247	5	(	(	PUNCT
ap-6650	247	6	32	32	NUM
ap-6650	247	7	)	)	PUNCT
ap-6650	247	8	,	,	PUNCT
ap-6650	247	9	we	we	PRON
ap-6650	247	10	have	have	VERB
ap-6650	247	11	−1	−1	NOUN
ap-6650	247	12	2	2	NUM
ap-6650	247	13	m	m	NOUN
ap-6650	247	14	∑	∑	PROPN
ap-6650	247	15	i	i	PROPN
ap-6650	247	16	,	,	PUNCT
ap-6650	247	17	j	j	PROPN
ap-6650	247	18	∇i	∇i	PROPN
ap-6650	247	19	{	{	PUNCT
ap-6650	247	20	(	(	PUNCT
ap-6650	247	21	π̂jncψ)†	π̂jncψ)†	ADV
ap-6650	247	22	σjσiψ	σjσiψ	NOUN
ap-6650	247	23	+	+	CCONJ
ap-6650	247	24	ψ†σiσj	ψ†σiσj	PROPN
ap-6650	247	25	(	(	PUNCT
ap-6650	247	26	π̂jncψ	π̂jncψ	X
ap-6650	247	27	)	)	PUNCT
ap-6650	247	28	}	}	PUNCT
ap-6650	248	1	+	+	CCONJ
ap-6650	249	1	i	i	PRON
ap-6650	249	2	2m~	2m~	VERB
ap-6650	249	3	∑	∑	PROPN
ap-6650	249	4	i	i	PROPN
ap-6650	249	5	,	,	PUNCT
ap-6650	249	6	j	j	PROPN
ap-6650	249	7	{	{	PUNCT
ap-6650	249	8	(	(	PUNCT
ap-6650	249	9	π̂jncψ)†	π̂jncψ)†	ADV
ap-6650	249	10	σjσi	σjσi	NOUN
ap-6650	249	11	(	(	PUNCT
ap-6650	249	12	π̂incψ)−	π̂incψ)−	X
ap-6650	249	13	(	(	PUNCT
ap-6650	249	14	π̂incψ)†	π̂incψ)†	ADJ
ap-6650	249	15	σiσj	σiσj	ADJ
ap-6650	249	16	(	(	PUNCT
ap-6650	249	17	π̂jncψ	π̂jncψ	X
ap-6650	249	18	)	)	PUNCT
ap-6650	249	19	}	}	PUNCT
ap-6650	250	1	=	=	SYM
ap-6650	250	2	∂ρ	∂ρ	PROPN
ap-6650	250	3	∂t	∂t	PROPN
ap-6650	250	4	,	,	PUNCT
ap-6650	250	5	(	(	PUNCT
ap-6650	250	6	42	42	NUM
ap-6650	250	7	)	)	PUNCT
ap-6650	250	8	235	235	NUM
ap-6650	250	9	ilyas	ilyas	PROPN
ap-6650	250	10	haouam	haouam	PROPN
ap-6650	250	11	acta	acta	PROPN
ap-6650	250	12	polytechnica	polytechnica	PROPN
ap-6650	250	13	then	then	ADV
ap-6650	250	14	−1	−1	NOUN
ap-6650	250	15	2	2	NUM
ap-6650	250	16	m	m	PROPN
ap-6650	250	17	∑	∑	PROPN
ap-6650	250	18	i	i	PROPN
ap-6650	250	19	,	,	PUNCT
ap-6650	250	20	j	j	PROPN
ap-6650	250	21	∇i	∇i	PROPN
ap-6650	250	22	{	{	PUNCT
ap-6650	250	23	(	(	PUNCT
ap-6650	250	24	π̂jncψ)†	π̂jncψ)†	ADV
ap-6650	250	25	σjσiψ	σjσiψ	NOUN
ap-6650	250	26	+	+	CCONJ
ap-6650	250	27	ψ†σiσj	ψ†σiσj	PROPN
ap-6650	250	28	(	(	PUNCT
ap-6650	250	29	π̂jncψ	π̂jncψ	X
ap-6650	250	30	)	)	PUNCT
ap-6650	250	31	}	}	PUNCT
ap-6650	250	32	=	=	SYM
ap-6650	250	33	∂ρ	∂ρ	PROPN
ap-6650	250	34	∂t	∂t	PROPN
ap-6650	250	35	.	.	PUNCT
ap-6650	251	1	(	(	PUNCT
ap-6650	251	2	43	43	X
ap-6650	251	3	)	)	PUNCT
ap-6650	251	4	knowing	know	VERB
ap-6650	251	5	that	that	SCONJ
ap-6650	251	6	the	the	DET
ap-6650	251	7	2nd	2nd	ADJ
ap-6650	251	8	sum	sum	NOUN
ap-6650	251	9	in	in	ADP
ap-6650	251	10	equation	equation	NOUN
ap-6650	251	11	(	(	PUNCT
ap-6650	251	12	42	42	NUM
ap-6650	251	13	)	)	PUNCT
ap-6650	251	14	gives	give	VERB
ap-6650	251	15	zero	zero	NUM
ap-6650	251	16	by	by	ADP
ap-6650	251	17	swapping	swap	VERB
ap-6650	251	18	i	i	PRON
ap-6650	251	19	and	and	CCONJ
ap-6650	251	20	j	j	PROPN
ap-6650	251	21	for	for	ADP
ap-6650	251	22	one	one	NUM
ap-6650	251	23	of	of	ADP
ap-6650	251	24	the	the	DET
ap-6650	251	25	sums	sum	NOUN
ap-6650	251	26	,	,	PUNCT
ap-6650	251	27	then	then	ADV
ap-6650	251	28	the	the	DET
ap-6650	251	29	probability	probability	NOUN
ap-6650	251	30	current	current	ADJ
ap-6650	251	31	vector	vector	NOUN
ap-6650	251	32	from	from	ADP
ap-6650	251	33	the	the	DET
ap-6650	251	34	above	above	ADJ
ap-6650	251	35	continuity	continuity	NOUN
ap-6650	251	36	equation	equation	NOUN
ap-6650	251	37	is	be	AUX
ap-6650	251	38	ji	ji	PROPN
ap-6650	251	39	=	=	NOUN
ap-6650	252	1	1	1	NUM
ap-6650	252	2	2	2	NUM
ap-6650	252	3	m	m	PROPN
ap-6650	252	4	∑	∑	PROPN
ap-6650	252	5	j	j	PROPN
ap-6650	252	6	{	{	PUNCT
ap-6650	252	7	(	(	PUNCT
ap-6650	252	8	π̂jncψ)†	π̂jncψ)†	ADV
ap-6650	252	9	σjσiψ	σjσiψ	NOUN
ap-6650	252	10	+	+	CCONJ
ap-6650	252	11	ψ†σiσj	ψ†σiσj	PROPN
ap-6650	252	12	(	(	PUNCT
ap-6650	252	13	π̂jncψ	π̂jncψ	X
ap-6650	252	14	)	)	PUNCT
ap-6650	252	15	}	}	PUNCT
ap-6650	252	16	.	.	PUNCT
ap-6650	253	1	(	(	PUNCT
ap-6650	253	2	44	44	NUM
ap-6650	253	3	)	)	PUNCT
ap-6650	253	4	using	use	VERB
ap-6650	253	5	the	the	DET
ap-6650	253	6	property	property	NOUN
ap-6650	253	7	(	(	PUNCT
ap-6650	253	8	15	15	NUM
ap-6650	253	9	)	)	PUNCT
ap-6650	253	10	,	,	PUNCT
ap-6650	253	11	equation	equation	NOUN
ap-6650	253	12	(	(	PUNCT
ap-6650	253	13	44	44	NUM
ap-6650	253	14	)	)	PUNCT
ap-6650	253	15	becomes	become	VERB
ap-6650	253	16	ji	ji	NOUN
ap-6650	253	17	=	=	NOUN
ap-6650	253	18	1	1	NUM
ap-6650	253	19	2	2	NUM
ap-6650	253	20	m	m	PROPN
ap-6650	253	21	∑	∑	PROPN
ap-6650	253	22	j	j	PROPN
ap-6650	253	23	{	{	PUNCT
ap-6650	253	24	(	(	PUNCT
ap-6650	253	25	π̂jncψ)†	π̂jncψ)†	ADV
ap-6650	253	26	ψ	ψ	X
ap-6650	253	27	+	+	CCONJ
ap-6650	253	28	ψ†	ψ†	INTJ
ap-6650	253	29	(	(	PUNCT
ap-6650	253	30	π̂jncψ	π̂jncψ	X
ap-6650	253	31	)	)	PUNCT
ap-6650	254	1	+	+	CCONJ
ap-6650	254	2	i	i	PRON
ap-6650	254	3	∑	∑	X
ap-6650	254	4	k	k	X
ap-6650	254	5	[	[	PUNCT
ap-6650	254	6	εjik	εjik	NOUN
ap-6650	254	7	(	(	PUNCT
ap-6650	254	8	π̂jncψ)†	π̂jncψ)†	ADV
ap-6650	254	9	σkψ	σkψ	ADJ
ap-6650	254	10	+	+	CCONJ
ap-6650	254	11	εijkψ	εijkψ	PROPN
ap-6650	254	12	†σk	†σk	NUM
ap-6650	254	13	(	(	PUNCT
ap-6650	254	14	π̂jncψ	π̂jncψ	X
ap-6650	254	15	)	)	PUNCT
ap-6650	254	16	]	]	PUNCT
ap-6650	254	17	}	}	PUNCT
ap-6650	254	18	,	,	PUNCT
ap-6650	254	19	(	(	PUNCT
ap-6650	254	20	45	45	NUM
ap-6650	254	21	)	)	PUNCT
ap-6650	254	22	with	with	ADP
ap-6650	254	23	εjik	εjik	NOUN
ap-6650	254	24	=	=	SYM
ap-6650	254	25	−εijk	−εijk	NOUN
ap-6650	254	26	,	,	PUNCT
ap-6650	254	27	and	and	CCONJ
ap-6650	254	28	using	use	VERB
ap-6650	254	29	one	one	NUM
ap-6650	254	30	more	more	ADJ
ap-6650	254	31	time	time	NOUN
ap-6650	254	32	identity	identity	NOUN
ap-6650	254	33	(	(	PUNCT
ap-6650	254	34	32	32	NUM
ap-6650	254	35	)	)	PUNCT
ap-6650	254	36	,	,	PUNCT
ap-6650	254	37	we	we	PRON
ap-6650	254	38	find	find	VERB
ap-6650	254	39	(	(	PUNCT
ap-6650	254	40	this	this	PRON
ap-6650	254	41	is	be	AUX
ap-6650	254	42	similar	similar	ADJ
ap-6650	254	43	to	to	ADP
ap-6650	254	44	investigation	investigation	NOUN
ap-6650	254	45	by	by	ADP
ap-6650	254	46	[	[	X
ap-6650	254	47	6	6	NUM
ap-6650	254	48	]	]	PUNCT
ap-6650	254	49	in	in	ADP
ap-6650	254	50	the	the	DET
ap-6650	254	51	case	case	NOUN
ap-6650	254	52	of	of	ADP
ap-6650	254	53	commutative	commutative	ADJ
ap-6650	254	54	phase	phase	NOUN
ap-6650	254	55	-	-	PUNCT
ap-6650	254	56	space	space	NOUN
ap-6650	254	57	)	)	PUNCT
ap-6650	255	1	ji	ji	NOUN
ap-6650	256	1	=	=	NOUN
ap-6650	256	2	1	1	NUM
ap-6650	256	3	2	2	NUM
ap-6650	256	4	m	m	NOUN
ap-6650	256	5	[	[	PUNCT
ap-6650	256	6	(	(	PUNCT
ap-6650	256	7	p̂jncψ)†	p̂jncψ)†	ADJ
ap-6650	256	8	ψ	ψ	X
ap-6650	256	9	−	−	PROPN
ap-6650	256	10	e	e	X
ap-6650	256	11	c	c	X
ap-6650	256	12	(	(	PUNCT
ap-6650	256	13	ancj	ancj	PROPN
ap-6650	256	14	ψ	ψ	NOUN
ap-6650	256	15	)	)	PUNCT
ap-6650	256	16	†	†	X
ap-6650	256	17	ψ	ψ	PROPN
ap-6650	256	18	+	+	CCONJ
ap-6650	256	19	ψ†p̂j	ψ†p̂j	ADJ
ap-6650	256	20	ncψ	ncψ	NOUN
ap-6650	256	21	−	−	PROPN
ap-6650	256	22	e	e	X
ap-6650	256	23	c	c	NOUN
ap-6650	256	24	ψ†ancj	ψ†ancj	ADP
ap-6650	256	25	ψ	ψ	NOUN
ap-6650	256	26	]	]	PUNCT
ap-6650	257	1	+	+	CCONJ
ap-6650	257	2	~	~	PUNCT
ap-6650	257	3	2	2	NUM
ap-6650	257	4	m	m	PROPN
ap-6650	257	5	∑	∑	PROPN
ap-6650	257	6	j	j	PROPN
ap-6650	257	7	,	,	PUNCT
ap-6650	257	8	k	k	PROPN
ap-6650	257	9	εijk∇j	εijk∇j	PROPN
ap-6650	257	10	(	(	PUNCT
ap-6650	257	11	ψ†σkψ	ψ†σkψ	PROPN
ap-6650	257	12	)	)	PUNCT
ap-6650	257	13	.	.	PUNCT
ap-6650	258	1	(	(	PUNCT
ap-6650	258	2	46	46	NUM
ap-6650	258	3	)	)	PUNCT
ap-6650	258	4	in	in	ADP
ap-6650	258	5	the	the	DET
ap-6650	258	6	right	right	ADJ
ap-6650	258	7	-	-	PUNCT
ap-6650	258	8	hand	hand	NOUN
ap-6650	258	9	side	side	NOUN
ap-6650	258	10	of	of	ADP
ap-6650	258	11	the	the	DET
ap-6650	258	12	above	above	ADJ
ap-6650	258	13	equation	equation	NOUN
ap-6650	258	14	,	,	PUNCT
ap-6650	258	15	the	the	DET
ap-6650	258	16	first	first	ADJ
ap-6650	258	17	term	term	NOUN
ap-6650	258	18	will	will	AUX
ap-6650	258	19	be	be	AUX
ap-6650	258	20	interpreted	interpret	VERB
ap-6650	258	21	as	as	ADP
ap-6650	258	22	the	the	DET
ap-6650	258	23	noncommutative	noncommutative	ADJ
ap-6650	258	24	current	current	ADJ
ap-6650	258	25	vector	vector	NOUN
ap-6650	258	26	−→j	−→j	PROPN
ap-6650	258	27	nc	nc	PROPN
ap-6650	258	28	given	give	VERB
ap-6650	258	29	by	by	ADP
ap-6650	258	30	equation	equation	NOUN
ap-6650	258	31	(	(	PUNCT
ap-6650	258	32	36	36	NUM
ap-6650	258	33	)	)	PUNCT
ap-6650	258	34	,	,	PUNCT
ap-6650	258	35	and	and	CCONJ
ap-6650	258	36	the	the	DET
ap-6650	258	37	second	second	ADJ
ap-6650	258	38	term	term	NOUN
ap-6650	258	39	is	be	AUX
ap-6650	258	40	the	the	DET
ap-6650	258	41	requested	request	VERB
ap-6650	258	42	additional	additional	ADJ
ap-6650	258	43	term	term	NOUN
ap-6650	258	44	,	,	PUNCT
ap-6650	258	45	namely	namely	ADV
ap-6650	258	46	current	current	ADJ
ap-6650	258	47	magnetization	magnetization	NOUN
ap-6650	258	48	−→j	−→j	PROPN
ap-6650	258	49	m	m	NOUN
ap-6650	258	50	,	,	PUNCT
ap-6650	258	51	where	where	SCONJ
ap-6650	258	52	j	j	PROPN
ap-6650	258	53	mi	mi	PROPN
ap-6650	259	1	=	=	PROPN
ap-6650	259	2	~	~	PUNCT
ap-6650	259	3	2	2	NUM
ap-6650	259	4	m	m	NOUN
ap-6650	259	5	(	(	PUNCT
ap-6650	259	6	−→	−→	ADJ
ap-6650	259	7	∇	∇	X
ap-6650	259	8	×	×	NOUN
ap-6650	259	9	(	(	PUNCT
ap-6650	259	10	ψ†−→σ	ψ†−→σ	X
ap-6650	259	11	ψ	ψ	NOUN
ap-6650	259	12	)	)	PUNCT
ap-6650	259	13	)	)	PUNCT
ap-6650	259	14	i	i	PRON
ap-6650	259	15	.	.	PUNCT
ap-6650	260	1	(	(	PUNCT
ap-6650	260	2	47	47	NUM
ap-6650	260	3	)	)	PUNCT
ap-6650	260	4	furthermore	furthermore	ADV
ap-6650	260	5	,	,	PUNCT
ap-6650	260	6	−→j	−→j	PROPN
ap-6650	260	7	m	m	VERB
ap-6650	260	8	can	can	AUX
ap-6650	260	9	also	also	ADV
ap-6650	260	10	be	be	AUX
ap-6650	260	11	shown	show	VERB
ap-6650	260	12	to	to	PART
ap-6650	260	13	be	be	AUX
ap-6650	260	14	a	a	DET
ap-6650	260	15	part	part	NOUN
ap-6650	260	16	of	of	ADP
ap-6650	260	17	the	the	DET
ap-6650	260	18	conserved	conserve	VERB
ap-6650	260	19	noether	noether	ADJ
ap-6650	260	20	current	current	ADJ
ap-6650	261	1	[	[	X
ap-6650	261	2	40	40	NUM
ap-6650	261	3	]	]	PUNCT
ap-6650	261	4	,	,	PUNCT
ap-6650	261	5	resulting	result	VERB
ap-6650	261	6	from	from	ADP
ap-6650	261	7	the	the	DET
ap-6650	261	8	invariance	invariance	NOUN
ap-6650	261	9	of	of	ADP
ap-6650	261	10	the	the	DET
ap-6650	261	11	pauli	pauli	PROPN
ap-6650	261	12	lagrangian	lagrangian	NOUN
ap-6650	261	13	under	under	ADP
ap-6650	261	14	the	the	DET
ap-6650	261	15	global	global	ADJ
ap-6650	261	16	phase	phase	NOUN
ap-6650	261	17	transformation	transformation	NOUN
ap-6650	261	18	u(1	u(1	PROPN
ap-6650	261	19	)	)	PUNCT
ap-6650	261	20	.	.	PUNCT
ap-6650	262	1	what	what	PRON
ap-6650	262	2	can	can	AUX
ap-6650	262	3	be	be	AUX
ap-6650	262	4	concluded	conclude	VERB
ap-6650	262	5	here	here	ADV
ap-6650	262	6	is	be	AUX
ap-6650	262	7	that	that	SCONJ
ap-6650	262	8	the	the	DET
ap-6650	262	9	magnetization	magnetization	NOUN
ap-6650	262	10	current	current	NOUN
ap-6650	262	11	is	be	AUX
ap-6650	262	12	not	not	PART
ap-6650	262	13	affected	affect	VERB
ap-6650	262	14	by	by	ADP
ap-6650	262	15	the	the	DET
ap-6650	262	16	noncommutativity	noncommutativity	NOUN
ap-6650	262	17	,	,	PUNCT
ap-6650	262	18	perhaps	perhaps	ADV
ap-6650	262	19	because	because	SCONJ
ap-6650	262	20	the	the	DET
ap-6650	262	21	spin	spin	NOUN
ap-6650	262	22	operator	operator	NOUN
ap-6650	262	23	could	could	AUX
ap-6650	262	24	not	not	PART
ap-6650	262	25	be	be	AUX
ap-6650	262	26	affected	affect	VERB
ap-6650	262	27	by	by	ADP
ap-6650	262	28	the	the	DET
ap-6650	262	29	noncommutativity	noncommutativity	NOUN
ap-6650	262	30	.	.	PUNCT
ap-6650	263	1	this	this	PRON
ap-6650	263	2	is	be	AUX
ap-6650	263	3	in	in	ADP
ap-6650	263	4	contrast	contrast	NOUN
ap-6650	263	5	to	to	ADP
ap-6650	263	6	what	what	PRON
ap-6650	263	7	was	be	AUX
ap-6650	263	8	previously	previously	ADV
ap-6650	263	9	found	find	VERB
ap-6650	263	10	around	around	ADP
ap-6650	263	11	the	the	DET
ap-6650	263	12	current	current	ADJ
ap-6650	263	13	density	density	NOUN
ap-6650	263	14	,	,	PUNCT
ap-6650	263	15	which	which	PRON
ap-6650	263	16	showed	show	VERB
ap-6650	263	17	a	a	DET
ap-6650	263	18	great	great	ADJ
ap-6650	263	19	influence	influence	NOUN
ap-6650	263	20	of	of	ADP
ap-6650	263	21	the	the	DET
ap-6650	263	22	noncommutativity	noncommutativity	NOUN
ap-6650	263	23	.	.	PUNCT
ap-6650	264	1	4	4	X
ap-6650	264	2	.	.	X
ap-6650	264	3	noncommutative	noncommutative	ADJ
ap-6650	264	4	semi	semi	ADJ
ap-6650	264	5	-	-	ADJ
ap-6650	264	6	classical	classical	ADJ
ap-6650	264	7	partition	partition	NOUN
ap-6650	264	8	function	function	NOUN
ap-6650	264	9	in	in	ADP
ap-6650	264	10	this	this	DET
ap-6650	264	11	part	part	NOUN
ap-6650	264	12	of	of	ADP
ap-6650	264	13	our	our	PRON
ap-6650	264	14	work	work	NOUN
ap-6650	264	15	,	,	PUNCT
ap-6650	264	16	we	we	PRON
ap-6650	264	17	investigate	investigate	VERB
ap-6650	264	18	the	the	DET
ap-6650	264	19	magnetization	magnetization	NOUN
ap-6650	264	20	and	and	CCONJ
ap-6650	264	21	the	the	DET
ap-6650	264	22	magnetic	magnetic	ADJ
ap-6650	264	23	susceptibility	susceptibility	NOUN
ap-6650	264	24	quantities	quantity	NOUN
ap-6650	264	25	of	of	ADP
ap-6650	264	26	our	our	PRON
ap-6650	264	27	pauli	pauli	PROPN
ap-6650	264	28	system	system	NOUN
ap-6650	264	29	using	use	VERB
ap-6650	264	30	the	the	DET
ap-6650	264	31	partition	partition	NOUN
ap-6650	264	32	function	function	NOUN
ap-6650	264	33	in	in	ADP
ap-6650	264	34	a	a	DET
ap-6650	264	35	noncommutative	noncommutative	ADJ
ap-6650	264	36	phase	phase	NOUN
ap-6650	264	37	-	-	PUNCT
ap-6650	264	38	space	space	NOUN
ap-6650	264	39	.	.	PUNCT
ap-6650	265	1	we	we	PRON
ap-6650	265	2	concentrate	concentrate	VERB
ap-6650	265	3	,	,	PUNCT
ap-6650	265	4	at	at	ADP
ap-6650	265	5	first	first	ADV
ap-6650	265	6	,	,	PUNCT
ap-6650	265	7	on	on	ADP
ap-6650	265	8	the	the	DET
ap-6650	265	9	calculation	calculation	NOUN
ap-6650	265	10	of	of	ADP
ap-6650	265	11	the	the	DET
ap-6650	265	12	semi	semi	ADJ
ap-6650	265	13	-	-	ADJ
ap-6650	265	14	classical	classical	ADJ
ap-6650	265	15	partition	partition	NOUN
ap-6650	265	16	function	function	NOUN
ap-6650	265	17	.	.	PUNCT
ap-6650	266	1	our	our	PRON
ap-6650	266	2	studied	studied	ADJ
ap-6650	266	3	system	system	NOUN
ap-6650	266	4	is	be	AUX
ap-6650	266	5	semi	semi	ADJ
ap-6650	266	6	-	-	ADJ
ap-6650	266	7	classical	classical	ADJ
ap-6650	266	8	,	,	PUNCT
ap-6650	266	9	so	so	SCONJ
ap-6650	266	10	our	our	PRON
ap-6650	266	11	system	system	NOUN
ap-6650	266	12	is	be	AUX
ap-6650	266	13	not	not	PART
ap-6650	266	14	completely	completely	ADV
ap-6650	266	15	classical	classical	ADJ
ap-6650	266	16	but	but	CCONJ
ap-6650	266	17	contains	contain	VERB
ap-6650	266	18	a	a	DET
ap-6650	266	19	quantum	quantum	NOUN
ap-6650	266	20	interaction	interaction	NOUN
ap-6650	266	21	concerning	concern	VERB
ap-6650	266	22	the	the	DET
ap-6650	266	23	spin	spin	NOUN
ap-6650	266	24	,	,	PUNCT
ap-6650	266	25	therefore	therefore	ADV
ap-6650	266	26	,	,	PUNCT
ap-6650	266	27	the	the	DET
ap-6650	266	28	noncommutative	noncommutative	ADJ
ap-6650	266	29	partition	partition	NOUN
ap-6650	266	30	function	function	NOUN
ap-6650	266	31	is	be	AUX
ap-6650	266	32	separable	separable	ADJ
ap-6650	266	33	into	into	ADP
ap-6650	266	34	two	two	NUM
ap-6650	266	35	independent	independent	ADJ
ap-6650	266	36	parts	part	NOUN
ap-6650	266	37	as	as	SCONJ
ap-6650	266	38	follows	follow	VERB
ap-6650	266	39	znc	znc	ADJ
ap-6650	266	40	=	=	NOUN
ap-6650	266	41	zncclaszncl	zncclaszncl	NOUN
ap-6650	266	42	,	,	PUNCT
ap-6650	266	43	(	(	PUNCT
ap-6650	266	44	48	48	NUM
ap-6650	266	45	)	)	PUNCT
ap-6650	266	46	where	where	SCONJ
ap-6650	266	47	zncl	zncl	NOUN
ap-6650	266	48	is	be	AUX
ap-6650	266	49	the	the	DET
ap-6650	266	50	non	non	ADJ
ap-6650	266	51	-	-	ADJ
ap-6650	266	52	classical	classical	ADJ
ap-6650	266	53	part	part	NOUN
ap-6650	266	54	of	of	ADP
ap-6650	266	55	the	the	DET
ap-6650	266	56	partition	partition	NOUN
ap-6650	266	57	function	function	NOUN
ap-6650	266	58	.	.	PUNCT
ap-6650	267	1	to	to	PART
ap-6650	267	2	study	study	VERB
ap-6650	267	3	our	our	PRON
ap-6650	267	4	noncommutative	noncommutative	ADJ
ap-6650	267	5	classical	classical	ADJ
ap-6650	267	6	partition	partition	NOUN
ap-6650	267	7	function	function	NOUN
ap-6650	267	8	,	,	PUNCT
ap-6650	267	9	we	we	PRON
ap-6650	267	10	assume	assume	VERB
ap-6650	267	11	that	that	SCONJ
ap-6650	267	12	the	the	DET
ap-6650	267	13	passage	passage	NOUN
ap-6650	267	14	between	between	ADP
ap-6650	267	15	noncommutative	noncommutative	ADJ
ap-6650	267	16	classical	classical	ADJ
ap-6650	267	17	mechanics	mechanic	NOUN
ap-6650	267	18	and	and	CCONJ
ap-6650	267	19	noncommutative	noncommutative	ADJ
ap-6650	267	20	quantum	quantum	ADJ
ap-6650	267	21	mechanics	mechanic	NOUN
ap-6650	267	22	can	can	AUX
ap-6650	267	23	be	be	AUX
ap-6650	267	24	realized	realize	VERB
ap-6650	267	25	through	through	ADP
ap-6650	267	26	the	the	DET
ap-6650	267	27	following	follow	VERB
ap-6650	267	28	generalized	generalized	ADJ
ap-6650	267	29	dirac	dirac	NOUN
ap-6650	267	30	quantization	quantization	NOUN
ap-6650	267	31	condition	condition	NOUN
ap-6650	268	1	[	[	X
ap-6650	268	2	41–43	41–43	NUM
ap-6650	268	3	]	]	X
ap-6650	268	4	{	{	PUNCT
ap-6650	268	5	f	f	X
ap-6650	268	6	,	,	PUNCT
ap-6650	268	7	g	g	NOUN
ap-6650	268	8	}	}	PUNCT
ap-6650	268	9	=	=	SYM
ap-6650	268	10	1	1	NUM
ap-6650	268	11	i~	i~	PROPN
ap-6650	268	12	[	[	X
ap-6650	268	13	f	f	X
ap-6650	268	14	,	,	PUNCT
ap-6650	268	15	g	g	NOUN
ap-6650	268	16	]	]	PUNCT
ap-6650	268	17	,	,	PUNCT
ap-6650	268	18	(	(	PUNCT
ap-6650	268	19	49	49	NUM
ap-6650	268	20	)	)	PUNCT
ap-6650	268	21	where	where	SCONJ
ap-6650	268	22	f	f	X
ap-6650	268	23	,	,	PUNCT
ap-6650	268	24	g	g	PROPN
ap-6650	268	25	stand	stand	VERB
ap-6650	268	26	for	for	ADP
ap-6650	268	27	the	the	DET
ap-6650	268	28	operators	operator	NOUN
ap-6650	268	29	associated	associate	VERB
ap-6650	268	30	with	with	ADP
ap-6650	268	31	classical	classical	ADJ
ap-6650	268	32	observables	observable	NOUN
ap-6650	268	33	f	f	NOUN
ap-6650	268	34	,	,	PUNCT
ap-6650	268	35	g	g	PROPN
ap-6650	268	36	and	and	CCONJ
ap-6650	268	37	{	{	PUNCT
ap-6650	268	38	,	,	PUNCT
ap-6650	268	39	}	}	PUNCT
ap-6650	268	40	stands	stand	VERB
ap-6650	268	41	for	for	ADP
ap-6650	268	42	poisson	poisson	NOUN
ap-6650	268	43	bracket	bracket	NOUN
ap-6650	268	44	.	.	PUNCT
ap-6650	269	1	using	use	VERB
ap-6650	269	2	the	the	DET
ap-6650	269	3	condition	condition	NOUN
ap-6650	269	4	above	above	ADV
ap-6650	269	5	,	,	PUNCT
ap-6650	269	6	we	we	PRON
ap-6650	269	7	obtain	obtain	VERB
ap-6650	269	8	from	from	ADP
ap-6650	269	9	eq.(5	eq.(5	NOUN
ap-6650	269	10	)	)	PUNCT
ap-6650	269	11	{	{	PUNCT
ap-6650	269	12	xncj	xncj	PROPN
ap-6650	269	13	,	,	PUNCT
ap-6650	269	14	x	x	PROPN
ap-6650	269	15	nc	nc	PROPN
ap-6650	269	16	k	k	PROPN
ap-6650	269	17	}	}	PUNCT
ap-6650	269	18	=	=	PUNCT
ap-6650	269	19	1	1	NUM
ap-6650	269	20	2εjklθl	2εjklθl	NUM
ap-6650	269	21	,	,	PUNCT
ap-6650	269	22	{	{	PUNCT
ap-6650	269	23	pncj	pncj	INTJ
ap-6650	269	24	,	,	PUNCT
ap-6650	269	25	p	p	PROPN
ap-6650	269	26	nc	nc	PROPN
ap-6650	269	27	k	k	PROPN
ap-6650	269	28	}	}	PUNCT
ap-6650	269	29	=	=	PUNCT
ap-6650	269	30	1	1	NUM
ap-6650	269	31	2εjklηl	2εjklηl	NUM
ap-6650	269	32	,	,	PUNCT
ap-6650	269	33	{	{	PUNCT
ap-6650	269	34	xncj	xncj	PROPN
ap-6650	269	35	,	,	PUNCT
ap-6650	269	36	p	p	PROPN
ap-6650	269	37	nc	nc	PROPN
ap-6650	269	38	k	k	PROPN
ap-6650	269	39	}	}	PUNCT
ap-6650	269	40	=	=	PUNCT
ap-6650	269	41	δjk	δjk	NOUN
ap-6650	269	42	+	+	CCONJ
ap-6650	269	43	1	1	NUM
ap-6650	269	44	4~2	4~2	NUM
ap-6650	269	45	θjlηkl	θjlηkl	NOUN
ap-6650	269	46	=	=	PUNCT
ap-6650	269	47	δjk	δjk	NOUN
ap-6650	269	48	,	,	PUNCT
ap-6650	269	49	(	(	PUNCT
ap-6650	269	50	j	j	NOUN
ap-6650	269	51	,	,	PUNCT
ap-6650	269	52	k	k	NOUN
ap-6650	269	53	,	,	PUNCT
ap-6650	269	54	l	l	NOUN
ap-6650	269	55	=	=	SYM
ap-6650	269	56	1	1	NUM
ap-6650	269	57	,	,	PUNCT
ap-6650	269	58	2	2	NUM
ap-6650	269	59	,	,	PUNCT
ap-6650	269	60	3	3	NUM
ap-6650	269	61	)	)	PUNCT
ap-6650	269	62	.	.	PUNCT
ap-6650	270	1	(	(	PUNCT
ap-6650	270	2	50	50	NUM
ap-6650	270	3	)	)	PUNCT
ap-6650	270	4	it	it	PRON
ap-6650	270	5	is	be	AUX
ap-6650	270	6	worth	worth	ADJ
ap-6650	270	7	mentioning	mention	VERB
ap-6650	270	8	that	that	SCONJ
ap-6650	270	9	in	in	ADP
ap-6650	270	10	terms	term	NOUN
ap-6650	270	11	of	of	ADP
ap-6650	270	12	the	the	DET
ap-6650	270	13	classical	classical	ADJ
ap-6650	270	14	limit	limit	NOUN
ap-6650	270	15	,	,	PUNCT
ap-6650	270	16	θη	θη	PROPN
ap-6650	270	17	4~2	4~2	NUM
ap-6650	270	18	�	�	PROPN
ap-6650	270	19	1	1	NUM
ap-6650	270	20	(	(	PUNCT
ap-6650	270	21	check	check	NOUN
ap-6650	270	22	ref	ref	NOUN
ap-6650	270	23	.	.	PUNCT
ap-6650	271	1	[	[	X
ap-6650	271	2	42	42	NUM
ap-6650	271	3	]	]	PUNCT
ap-6650	271	4	)	)	PUNCT
ap-6650	271	5	,	,	PUNCT
ap-6650	271	6	thus	thus	ADV
ap-6650	271	7	{	{	PUNCT
ap-6650	271	8	xncj	xncj	PROPN
ap-6650	271	9	,	,	PUNCT
ap-6650	271	10	p	p	PROPN
ap-6650	271	11	nc	nc	PROPN
ap-6650	271	12	k	k	PROPN
ap-6650	271	13	}	}	PUNCT
ap-6650	271	14	=	=	PUNCT
ap-6650	271	15	δjk	δjk	NOUN
ap-6650	271	16	.	.	PUNCT
ap-6650	272	1	now	now	ADV
ap-6650	272	2	based	base	VERB
ap-6650	272	3	on	on	ADP
ap-6650	272	4	the	the	DET
ap-6650	272	5	proposal	proposal	NOUN
ap-6650	272	6	that	that	SCONJ
ap-6650	272	7	noncommutative	noncommutative	ADJ
ap-6650	272	8	observables	observable	NOUN
ap-6650	272	9	fnc	fnc	PROPN
ap-6650	272	10	correspond	correspond	VERB
ap-6650	272	11	to	to	ADP
ap-6650	272	12	the	the	DET
ap-6650	272	13	commutative	commutative	ADJ
ap-6650	272	14	one	one	NUM
ap-6650	272	15	f	f	NOUN
ap-6650	272	16	(	(	PUNCT
ap-6650	272	17	x	x	X
ap-6650	272	18	,	,	PUNCT
ap-6650	272	19	p	p	NOUN
ap-6650	272	20	)	)	PUNCT
ap-6650	272	21	can	can	AUX
ap-6650	272	22	be	be	AUX
ap-6650	272	23	defined	define	VERB
ap-6650	272	24	by	by	ADP
ap-6650	272	25	[	[	X
ap-6650	272	26	44	44	NUM
ap-6650	272	27	,	,	PUNCT
ap-6650	272	28	45	45	NUM
ap-6650	272	29	]	]	PUNCT
ap-6650	272	30	fnc	fnc	PROPN
ap-6650	272	31	=	=	SYM
ap-6650	272	32	f	f	PROPN
ap-6650	272	33	(	(	PUNCT
ap-6650	272	34	xnc	xnc	PROPN
ap-6650	272	35	,	,	PUNCT
ap-6650	272	36	pnc	pnc	PROPN
ap-6650	272	37	)	)	PUNCT
ap-6650	272	38	,	,	PUNCT
ap-6650	272	39	(	(	PUNCT
ap-6650	272	40	51	51	NUM
ap-6650	272	41	)	)	PUNCT
ap-6650	272	42	and	and	CCONJ
ap-6650	272	43	for	for	ADP
ap-6650	272	44	non	non	ADJ
ap-6650	272	45	-	-	ADJ
ap-6650	272	46	interacting	interacting	ADJ
ap-6650	272	47	particles	particle	NOUN
ap-6650	272	48	,	,	PUNCT
ap-6650	272	49	the	the	DET
ap-6650	272	50	classical	classical	ADJ
ap-6650	272	51	partition	partition	NOUN
ap-6650	272	52	function	function	NOUN
ap-6650	272	53	in	in	ADP
ap-6650	272	54	the	the	DET
ap-6650	272	55	canonical	canonical	ADJ
ap-6650	272	56	ensemble	ensemble	ADJ
ap-6650	272	57	in	in	ADP
ap-6650	272	58	a	a	DET
ap-6650	272	59	noncommutative	noncommutative	ADJ
ap-6650	272	60	phase	phase	NOUN
ap-6650	272	61	-	-	PUNCT
ap-6650	272	62	space	space	NOUN
ap-6650	272	63	is	be	AUX
ap-6650	272	64	given	give	VERB
ap-6650	272	65	by	by	ADP
ap-6650	272	66	the	the	DET
ap-6650	272	67	following	follow	VERB
ap-6650	272	68	formula	formula	NOUN
ap-6650	272	69	[	[	X
ap-6650	272	70	41	41	NUM
ap-6650	272	71	,	,	PUNCT
ap-6650	272	72	42	42	NUM
ap-6650	272	73	]	]	PUNCT
ap-6650	272	74	zncclas	zncclas	PROPN
ap-6650	272	75	=	=	SYM
ap-6650	272	76	1	1	NUM
ap-6650	272	77	n	n	NOUN
ap-6650	272	78	!	!	PUNCT
ap-6650	273	1	(	(	PUNCT
ap-6650	273	2	2π~̃	2π~̃	NUM
ap-6650	273	3	)	)	PUNCT
ap-6650	273	4	3n	3n	NUM
ap-6650	273	5	�	�	PROPN
ap-6650	273	6	e−βh	e−βh	PROPN
ap-6650	273	7	nc	nc	PROPN
ap-6650	273	8	clas(x	clas(x	PROPN
ap-6650	273	9	,	,	PUNCT
ap-6650	273	10	p)d3nxncd3npnc	p)d3nxncd3npnc	PROPN
ap-6650	273	11	,	,	PUNCT
ap-6650	273	12	(	(	PUNCT
ap-6650	273	13	52	52	NUM
ap-6650	273	14	)	)	PUNCT
ap-6650	273	15	236	236	NUM
ap-6650	273	16	vol	vol	NOUN
ap-6650	273	17	.	.	PUNCT
ap-6650	274	1	61	61	NUM
ap-6650	274	2	no	no	NOUN
ap-6650	274	3	.	.	PUNCT
ap-6650	275	1	1/2021	1/2021	NUM
ap-6650	275	2	on	on	ADP
ap-6650	275	3	the	the	DET
ap-6650	275	4	three	three	NUM
ap-6650	275	5	-	-	PUNCT
ap-6650	275	6	dimensional	dimensional	ADJ
ap-6650	275	7	pauli	pauli	PROPN
ap-6650	275	8	equation	equation	NOUN
ap-6650	275	9	in	in	ADP
ap-6650	275	10	noncommutative	noncommutative	ADJ
ap-6650	275	11	phase	phase	NOUN
ap-6650	275	12	-	-	PUNCT
ap-6650	275	13	space	space	NOUN
ap-6650	275	14	which	which	PRON
ap-6650	275	15	is	be	AUX
ap-6650	275	16	written	write	VERB
ap-6650	275	17	for	for	ADP
ap-6650	275	18	an	an	DET
ap-6650	275	19	n	n	PRON
ap-6650	275	20	particles	particle	NOUN
ap-6650	275	21	.	.	PUNCT
ap-6650	276	1	1	1	NUM
ap-6650	276	2	n	n	NOUN
ap-6650	276	3	!	!	PUNCT
ap-6650	276	4	is	be	AUX
ap-6650	276	5	the	the	DET
ap-6650	276	6	gibbs	gibbs	PROPN
ap-6650	276	7	correction	correction	NOUN
ap-6650	276	8	factor	factor	NOUN
ap-6650	276	9	,	,	PUNCT
ap-6650	276	10	considered	consider	VERB
ap-6650	276	11	due	due	ADJ
ap-6650	276	12	to	to	ADP
ap-6650	276	13	accounting	account	VERB
ap-6650	276	14	for	for	ADP
ap-6650	276	15	indistinguishability	indistinguishability	NOUN
ap-6650	276	16	,	,	PUNCT
ap-6650	276	17	which	which	PRON
ap-6650	276	18	means	mean	VERB
ap-6650	276	19	that	that	SCONJ
ap-6650	276	20	there	there	PRON
ap-6650	276	21	are	be	VERB
ap-6650	276	22	n	n	PRON
ap-6650	276	23	!	!	PUNCT
ap-6650	277	1	ways	way	NOUN
ap-6650	277	2	of	of	ADP
ap-6650	277	3	arranging	arrange	VERB
ap-6650	277	4	n	n	DET
ap-6650	277	5	particles	particle	NOUN
ap-6650	277	6	at	at	ADP
ap-6650	277	7	n	n	DET
ap-6650	277	8	sites	site	NOUN
ap-6650	277	9	.	.	PUNCT
ap-6650	278	1	~̃	~̃	PUNCT
ap-6650	278	2	∼	∼	NOUN
ap-6650	278	3	4xnc4pnc	4xnc4pnc	NOUN
ap-6650	278	4	,	,	PUNCT
ap-6650	278	5	with	with	ADP
ap-6650	278	6	1	1	NUM
ap-6650	278	7	~̃3	~̃3	NOUN
ap-6650	278	8	is	be	AUX
ap-6650	278	9	a	a	DET
ap-6650	278	10	factor	factor	NOUN
ap-6650	278	11	that	that	PRON
ap-6650	278	12	makes	make	VERB
ap-6650	278	13	the	the	DET
ap-6650	278	14	volume	volume	NOUN
ap-6650	278	15	of	of	ADP
ap-6650	278	16	the	the	DET
ap-6650	278	17	noncommutative	noncommutative	ADJ
ap-6650	278	18	phase	phase	NOUN
ap-6650	278	19	-	-	PUNCT
ap-6650	278	20	space	space	NOUN
ap-6650	278	21	dimensionless	dimensionless	NOUN
ap-6650	278	22	.	.	PUNCT
ap-6650	279	1	β	β	NOUN
ap-6650	279	2	defined	define	VERB
ap-6650	279	3	as	as	ADP
ap-6650	279	4	1	1	NUM
ap-6650	279	5	kbt	kbt	PROPN
ap-6650	279	6	,	,	PUNCT
ap-6650	279	7	kb	kb	PROPN
ap-6650	279	8	is	be	AUX
ap-6650	279	9	the	the	DET
ap-6650	279	10	boltzmann	boltzmann	PROPN
ap-6650	279	11	constant	constant	PROPN
ap-6650	279	12	,	,	PUNCT
ap-6650	279	13	where	where	SCONJ
ap-6650	279	14	kb	kb	PROPN
ap-6650	279	15	=	=	PROPN
ap-6650	279	16	1.38	1.38	NUM
ap-6650	279	17	×	×	PROPN
ap-6650	279	18	10−23jk−1	10−23jk−1	NUM
ap-6650	279	19	.	.	PUNCT
ap-6650	280	1	the	the	DET
ap-6650	280	2	helmholtz	helmholtz	NOUN
ap-6650	280	3	free	free	ADJ
ap-6650	280	4	energy	energy	NOUN
ap-6650	280	5	is	be	AUX
ap-6650	280	6	f	f	NOUN
ap-6650	280	7	=	=	SYM
ap-6650	280	8	−	−	PROPN
ap-6650	280	9	1	1	NUM
ap-6650	280	10	β	β	NOUN
ap-6650	280	11	lnz	lnz	NOUN
ap-6650	280	12	,	,	PUNCT
ap-6650	280	13	(	(	PUNCT
ap-6650	280	14	53	53	NUM
ap-6650	280	15	)	)	PUNCT
ap-6650	280	16	we	we	PRON
ap-6650	280	17	may	may	AUX
ap-6650	280	18	derive	derive	VERB
ap-6650	280	19	the	the	DET
ap-6650	280	20	magnetization	magnetization	NOUN
ap-6650	280	21	as	as	SCONJ
ap-6650	280	22	follows	follow	VERB
ap-6650	280	23	〈	〈	PROPN
ap-6650	280	24	m	m	NOUN
ap-6650	280	25	〉	〉	NOUN
ap-6650	280	26	=	=	SYM
ap-6650	280	27	−∂f	−∂f	PROPN
ap-6650	280	28	∂b	∂b	PROPN
ap-6650	280	29	.	.	PUNCT
ap-6650	281	1	(	(	PUNCT
ap-6650	281	2	54	54	NUM
ap-6650	281	3	)	)	PUNCT
ap-6650	281	4	for	for	ADP
ap-6650	281	5	a	a	DET
ap-6650	281	6	single	single	ADJ
ap-6650	281	7	particle	particle	NOUN
ap-6650	281	8	,	,	PUNCT
ap-6650	281	9	the	the	DET
ap-6650	281	10	noncommutative	noncommutative	ADJ
ap-6650	281	11	classical	classical	ADJ
ap-6650	281	12	partition	partition	NOUN
ap-6650	281	13	function	function	NOUN
ap-6650	281	14	is	be	AUX
ap-6650	281	15	then	then	ADV
ap-6650	281	16	zncclas,1	zncclas,1	NUM
ap-6650	281	17	=	=	SYM
ap-6650	281	18	1	1	NUM
ap-6650	281	19	h̃3	h̃3	PROPN
ap-6650	281	20	�	�	PROPN
ap-6650	281	21	e−βh	e−βh	PROPN
ap-6650	281	22	nc	nc	PROPN
ap-6650	281	23	clas(x	clas(x	PROPN
ap-6650	281	24	,	,	PUNCT
ap-6650	281	25	p)d3xncd3pnc	p)d3xncd3pnc	PROPN
ap-6650	281	26	,	,	PUNCT
ap-6650	281	27	(	(	PUNCT
ap-6650	281	28	55	55	NUM
ap-6650	281	29	)	)	PUNCT
ap-6650	281	30	where	where	SCONJ
ap-6650	281	31	d3	d3	PROPN
ap-6650	281	32	is	be	AUX
ap-6650	281	33	a	a	DET
ap-6650	281	34	shorthand	shorthand	NOUN
ap-6650	281	35	notation	notation	NOUN
ap-6650	281	36	serving	serve	VERB
ap-6650	281	37	as	as	ADP
ap-6650	281	38	a	a	DET
ap-6650	281	39	reminder	reminder	NOUN
ap-6650	281	40	that	that	SCONJ
ap-6650	281	41	the	the	DET
ap-6650	281	42	x	x	X
ap-6650	281	43	and	and	CCONJ
ap-6650	281	44	p	p	NOUN
ap-6650	281	45	are	be	AUX
ap-6650	281	46	vectors	vector	NOUN
ap-6650	281	47	in	in	ADP
ap-6650	281	48	a	a	DET
ap-6650	281	49	three	three	NUM
ap-6650	281	50	-	-	PUNCT
ap-6650	281	51	dimensional	dimensional	ADJ
ap-6650	281	52	phase	phase	NOUN
ap-6650	281	53	-	-	PUNCT
ap-6650	281	54	space	space	NOUN
ap-6650	281	55	.	.	PUNCT
ap-6650	282	1	the	the	DET
ap-6650	282	2	relation	relation	NOUN
ap-6650	282	3	between	between	ADP
ap-6650	282	4	equation	equation	NOUN
ap-6650	282	5	(	(	PUNCT
ap-6650	282	6	52	52	NUM
ap-6650	282	7	)	)	PUNCT
ap-6650	282	8	and	and	CCONJ
ap-6650	282	9	(	(	PUNCT
ap-6650	282	10	55	55	NUM
ap-6650	282	11	)	)	PUNCT
ap-6650	282	12	is	be	AUX
ap-6650	282	13	given	give	VERB
ap-6650	282	14	by	by	ADP
ap-6650	282	15	the	the	DET
ap-6650	282	16	following	follow	VERB
ap-6650	282	17	formula	formula	NOUN
ap-6650	282	18	zncclas	zncclas	NUM
ap-6650	283	1	=	=	PUNCT
ap-6650	284	1	(	(	PUNCT
ap-6650	284	2	zncclas,1	zncclas,1	NOUN
ap-6650	284	3	)	)	PUNCT
ap-6650	284	4	n	n	PRON
ap-6650	284	5	n	n	NOUN
ap-6650	284	6	!	!	PUNCT
ap-6650	284	7	.	.	PUNCT
ap-6650	285	1	(	(	PUNCT
ap-6650	285	2	56	56	X
ap-6650	285	3	)	)	PUNCT
ap-6650	285	4	knowing	know	VERB
ap-6650	285	5	that	that	SCONJ
ap-6650	285	6	,	,	PUNCT
ap-6650	285	7	using	use	VERB
ap-6650	285	8	equation	equation	NOUN
ap-6650	285	9	(	(	PUNCT
ap-6650	285	10	6	6	NUM
ap-6650	285	11	)	)	PUNCT
ap-6650	285	12	,	,	PUNCT
ap-6650	285	13	we	we	PRON
ap-6650	285	14	have	have	VERB
ap-6650	285	15	d3xncd3pnc	d3xncd3pnc	PROPN
ap-6650	285	16	=	=	SYM
ap-6650	285	17	(	(	PUNCT
ap-6650	285	18	1−	1−	NUM
ap-6650	285	19	θη	θη	PROPN
ap-6650	285	20	8~2	8~2	NUM
ap-6650	285	21	)	)	PUNCT
ap-6650	285	22	d3xd3p	d3xd3p	NOUN
ap-6650	285	23	,	,	PUNCT
ap-6650	285	24	(	(	PUNCT
ap-6650	285	25	57	57	NUM
ap-6650	285	26	)	)	PUNCT
ap-6650	285	27	furthermore	furthermore	ADV
ap-6650	285	28	,	,	PUNCT
ap-6650	285	29	using	use	VERB
ap-6650	285	30	uncertainty	uncertainty	NOUN
ap-6650	285	31	principle	principle	NOUN
ap-6650	285	32	and	and	CCONJ
ap-6650	285	33	according	accord	VERB
ap-6650	285	34	to	to	ADP
ap-6650	285	35	the	the	DET
ap-6650	285	36	third	third	ADJ
ap-6650	285	37	equation	equation	NOUN
ap-6650	285	38	of	of	ADP
ap-6650	285	39	equation	equation	NOUN
ap-6650	285	40	(	(	PUNCT
ap-6650	285	41	4	4	NUM
ap-6650	285	42	)	)	PUNCT
ap-6650	285	43	,	,	PUNCT
ap-6650	285	44	we	we	PRON
ap-6650	285	45	deduce	deduce	VERB
ap-6650	285	46	h̃3	h̃3	NOUN
ap-6650	285	47	=	=	NOUN
ap-6650	285	48	h3	h3	NOUN
ap-6650	285	49	(	(	PUNCT
ap-6650	285	50	1	1	NUM
ap-6650	285	51	+	+	NUM
ap-6650	285	52	3θη	3θη	ADJ
ap-6650	285	53	4~2	4~2	NUM
ap-6650	285	54	)	)	PUNCT
ap-6650	286	1	+	+	ADP
ap-6650	286	2	o	o	X
ap-6650	286	3	(	(	PUNCT
ap-6650	286	4	θ2η2	θ2η2	NOUN
ap-6650	286	5	)	)	PUNCT
ap-6650	286	6	.	.	PUNCT
ap-6650	287	1	(	(	PUNCT
ap-6650	287	2	58	58	NUM
ap-6650	287	3	)	)	PUNCT
ap-6650	287	4	unlike	unlike	ADP
ap-6650	287	5	other	other	ADJ
ap-6650	287	6	works	work	NOUN
ap-6650	287	7	such	such	ADJ
ap-6650	287	8	as	as	ADP
ap-6650	287	9	[	[	X
ap-6650	287	10	41	41	NUM
ap-6650	287	11	]	]	PUNCT
ap-6650	287	12	,	,	PUNCT
ap-6650	287	13	where	where	SCONJ
ap-6650	287	14	the	the	DET
ap-6650	287	15	researchers	researcher	NOUN
ap-6650	287	16	used	use	VERB
ap-6650	287	17	a	a	DET
ap-6650	287	18	different	different	ADJ
ap-6650	287	19	formula	formula	NOUN
ap-6650	287	20	for	for	ADP
ap-6650	287	21	planck	planck	NOUN
ap-6650	287	22	’s	’s	PART
ap-6650	287	23	constant	constant	ADJ
ap-6650	287	24	h̃11	h̃11	NOUN
ap-6650	287	25	=	=	PUNCT
ap-6650	288	1	h̃22	h̃22	PROPN
ap-6650	288	2	6=	6=	NUM
ap-6650	288	3	h̃33	h̃33	PROPN
ap-6650	288	4	,	,	PUNCT
ap-6650	288	5	which	which	PRON
ap-6650	288	6	led	lead	VERB
ap-6650	288	7	to	to	ADP
ap-6650	288	8	a	a	DET
ap-6650	288	9	different	different	ADJ
ap-6650	288	10	formula	formula	NOUN
ap-6650	288	11	of	of	ADP
ap-6650	288	12	h̃3	h̃3	PROPN
ap-6650	288	13	.	.	PROPN
ap-6650	288	14	for	for	ADP
ap-6650	288	15	an	an	DET
ap-6650	288	16	electron	electron	NOUN
ap-6650	288	17	with	with	ADP
ap-6650	288	18	a	a	DET
ap-6650	288	19	spin	spin	NOUN
ap-6650	288	20	in	in	ADP
ap-6650	288	21	interaction	interaction	NOUN
ap-6650	288	22	with	with	ADP
ap-6650	288	23	an	an	DET
ap-6650	288	24	electromagnetic	electromagnetic	ADJ
ap-6650	288	25	potential	potential	NOUN
ap-6650	288	26	,	,	PUNCT
ap-6650	288	27	once	once	SCONJ
ap-6650	288	28	the	the	DET
ap-6650	288	29	magnetic	magnetic	ADJ
ap-6650	288	30	field	field	NOUN
ap-6650	288	31	−→b	−→b	NOUN
ap-6650	288	32	be	be	AUX
ap-6650	288	33	in	in	ADP
ap-6650	288	34	the	the	DET
ap-6650	288	35	z	z	NOUN
ap-6650	288	36	-	-	NOUN
ap-6650	288	37	direction	direction	NOUN
ap-6650	288	38	,	,	PUNCT
ap-6650	288	39	and	and	CCONJ
ap-6650	288	40	by	by	ADP
ap-6650	288	41	equation	equation	NOUN
ap-6650	288	42	(	(	PUNCT
ap-6650	288	43	19	19	NUM
ap-6650	288	44	)	)	PUNCT
ap-6650	288	45	,	,	PUNCT
ap-6650	288	46	bear	bear	VERB
ap-6650	288	47	in	in	ADP
ap-6650	288	48	mind	mind	NOUN
ap-6650	288	49	that	that	SCONJ
ap-6650	288	50	[	[	X
ap-6650	288	51	−→p	−→p	NOUN
ap-6650	288	52	nc,−→anc	nc,−→anc	X
ap-6650	288	53	]	]	PUNCT
ap-6650	288	54	=	=	PUNCT
ap-6650	288	55	0	0	NUM
ap-6650	288	56	,	,	PUNCT
ap-6650	288	57	then	then	ADV
ap-6650	288	58	for	for	ADP
ap-6650	288	59	the	the	DET
ap-6650	288	60	sake	sake	NOUN
ap-6650	288	61	of	of	ADP
ap-6650	288	62	simplicity	simplicity	NOUN
ap-6650	288	63	,	,	PUNCT
ap-6650	288	64	the	the	DET
ap-6650	288	65	noncommutative	noncommutative	PROPN
ap-6650	288	66	pauli	pauli	PROPN
ap-6650	288	67	hamiltonian	hamiltonian	NOUN
ap-6650	288	68	from	from	ADP
ap-6650	288	69	equation	equation	NOUN
ap-6650	288	70	(	(	PUNCT
ap-6650	288	71	23	23	NUM
ap-6650	288	72	)	)	PUNCT
ap-6650	288	73	takes	take	VERB
ap-6650	288	74	the	the	DET
ap-6650	288	75	form	form	NOUN
ap-6650	288	76	hpauli	hpauli	NOUN
ap-6650	288	77	(	(	PUNCT
ap-6650	288	78	xnc	xnc	PROPN
ap-6650	288	79	,	,	PUNCT
ap-6650	288	80	pnc	pnc	PROPN
ap-6650	288	81	)	)	PUNCT
ap-6650	288	82	=	=	SYM
ap-6650	288	83	1	1	NUM
ap-6650	288	84	2	2	NUM
ap-6650	288	85	m	m	VERB
ap-6650	288	86	{	{	PUNCT
ap-6650	288	87	(	(	PUNCT
ap-6650	288	88	−→p	−→p	NOUN
ap-6650	288	89	nc)2	nc)2	NOUN
ap-6650	288	90	−	−	PROPN
ap-6650	288	91	2e	2e	PROPN
ap-6650	288	92	c	c	PROPN
ap-6650	288	93	−→p	−→p	PROPN
ap-6650	288	94	nc	nc	PROPN
ap-6650	288	95	.	.	PROPN
ap-6650	288	96	−→	−→	PROPN
ap-6650	288	97	anc	anc	PROPN
ap-6650	288	98	+	+	CCONJ
ap-6650	288	99	(	(	PUNCT
ap-6650	288	100	e	e	NOUN
ap-6650	288	101	c	c	NOUN
ap-6650	288	102	)	)	PUNCT
ap-6650	288	103	2	2	NUM
ap-6650	288	104	(	(	PUNCT
ap-6650	288	105	−→	−→	ADJ
ap-6650	288	106	anc	anc	PROPN
ap-6650	288	107	)	)	PUNCT
ap-6650	288	108	2	2	NUM
ap-6650	288	109	}	}	PUNCT
ap-6650	288	110	+	+	CCONJ
ap-6650	289	1	µbσ̂zb	µbσ̂zb	PROPN
ap-6650	289	2	.	.	PROPN
ap-6650	289	3	(	(	PUNCT
ap-6650	289	4	59	59	NUM
ap-6650	289	5	)	)	PUNCT
ap-6650	289	6	we	we	PRON
ap-6650	289	7	split	split	VERB
ap-6650	289	8	the	the	DET
ap-6650	289	9	noncommutative	noncommutative	PROPN
ap-6650	289	10	pauli	pauli	PROPN
ap-6650	289	11	hamiltonian	hamiltonian	PROPN
ap-6650	289	12	as	as	SCONJ
ap-6650	289	13	hncpauli	hncpauli	NOUN
ap-6650	289	14	=	=	NOUN
ap-6650	289	15	hnccla	hnccla	VERB
ap-6650	290	1	+	+	NOUN
ap-6650	290	2	hncl	hncl	NOUN
ap-6650	290	3	,	,	PUNCT
ap-6650	290	4	σ	σ	PROPN
ap-6650	290	5	,	,	PUNCT
ap-6650	290	6	with	with	ADP
ap-6650	290	7	hncl	hncl	NOUN
ap-6650	290	8	,	,	PUNCT
ap-6650	290	9	σ	σ	PROPN
ap-6650	291	1	=	=	PUNCT
ap-6650	291	2	µbσ̂zb	µbσ̂zb	PROPN
ap-6650	291	3	.	.	PUNCT
ap-6650	292	1	it	it	PRON
ap-6650	292	2	is	be	AUX
ap-6650	292	3	easy	easy	ADJ
ap-6650	292	4	to	to	PART
ap-6650	292	5	verify	verify	VERB
ap-6650	292	6	that	that	SCONJ
ap-6650	292	7	(	(	PUNCT
ap-6650	292	8	−→p	−→p	NOUN
ap-6650	292	9	nc)2	nc)2	NOUN
ap-6650	292	10	=	=	SYM
ap-6650	292	11	(	(	PUNCT
ap-6650	292	12	pncx	pncx	NOUN
ap-6650	292	13	)	)	PUNCT
ap-6650	292	14	2	2	NUM
ap-6650	293	1	+	+	CCONJ
ap-6650	293	2	(	(	PUNCT
ap-6650	293	3	pncy	pncy	NOUN
ap-6650	293	4	)	)	PUNCT
ap-6650	293	5	2	2	NUM
ap-6650	294	1	+	+	CCONJ
ap-6650	294	2	(	(	PUNCT
ap-6650	294	3	pncz	pncz	NOUN
ap-6650	294	4	)	)	PUNCT
ap-6650	294	5	2	2	NUM
ap-6650	294	6	=	=	SYM
ap-6650	294	7	p2	p2	X
ap-6650	294	8	x	x	PUNCT
ap-6650	294	9	+	+	CCONJ
ap-6650	294	10	p2	p2	PROPN
ap-6650	294	11	y	y	PROPN
ap-6650	294	12	+	+	CCONJ
ap-6650	294	13	p2	p2	PROPN
ap-6650	294	14	z	z	PROPN
ap-6650	294	15	−	−	PROPN
ap-6650	294	16	η	η	PROPN
ap-6650	294	17	2	2	NUM
ap-6650	294	18	~	~	SYM
ap-6650	294	19	lz	lz	X
ap-6650	294	20	+	+	ADJ
ap-6650	294	21	η2	η2	ADJ
ap-6650	294	22	16~2	16~2	NOUN
ap-6650	294	23	(	(	PUNCT
ap-6650	294	24	x2	x2	NOUN
ap-6650	294	25	+	+	CCONJ
ap-6650	294	26	y2	y2	NOUN
ap-6650	294	27	)	)	PUNCT
ap-6650	294	28	,	,	PUNCT
ap-6650	294	29	(	(	PUNCT
ap-6650	294	30	60	60	NUM
ap-6650	294	31	)	)	PUNCT
ap-6650	294	32	−→p	−→p	PROPN
ap-6650	294	33	nc	nc	PROPN
ap-6650	294	34	.	.	PROPN
ap-6650	294	35	−→	−→	PROPN
ap-6650	295	1	a	a	DET
ap-6650	295	2	=	=	X
ap-6650	295	3	pncx	pncx	ADP
ap-6650	295	4	a	a	DET
ap-6650	295	5	nc	nc	PROPN
ap-6650	295	6	x	x	PROPN
ap-6650	295	7	+	+	NUM
ap-6650	295	8	pncy	pncy	NOUN
ap-6650	295	9	a	a	PRON
ap-6650	295	10	nc	nc	PROPN
ap-6650	295	11	y	y	PROPN
ap-6650	295	12	=	=	SYM
ap-6650	295	13	b	b	PROPN
ap-6650	295	14	2	2	NUM
ap-6650	295	15	{	{	PUNCT
ap-6650	295	16	−	−	PROPN
ap-6650	295	17	θ	θ	PROPN
ap-6650	295	18	4~	4~	NOUN
ap-6650	295	19	(	(	PUNCT
ap-6650	295	20	p2	p2	PROPN
ap-6650	295	21	x	x	PUNCT
ap-6650	295	22	+	+	CCONJ
ap-6650	295	23	p2	p2	PROPN
ap-6650	295	24	y	y	PROPN
ap-6650	295	25	)	)	PUNCT
ap-6650	295	26	−	−	PROPN
ap-6650	296	1	η	η	PROPN
ap-6650	296	2	4~	4~	PROPN
ap-6650	296	3	(	(	PUNCT
ap-6650	296	4	y2	y2	PROPN
ap-6650	296	5	+	+	CCONJ
ap-6650	296	6	x2)+	x2)+	PROPN
ap-6650	296	7	(	(	PUNCT
ap-6650	296	8	1	1	NUM
ap-6650	296	9	+	+	CCONJ
ap-6650	296	10	θη	θη	PROPN
ap-6650	296	11	16~2	16~2	NUM
ap-6650	296	12	)	)	PUNCT
ap-6650	296	13	lz	lz	ADP
ap-6650	296	14	}	}	PUNCT
ap-6650	296	15	,	,	PUNCT
ap-6650	296	16	(	(	PUNCT
ap-6650	296	17	61	61	NUM
ap-6650	296	18	)	)	PUNCT
ap-6650	296	19	(	(	PUNCT
ap-6650	296	20	−→	−→	NOUN
ap-6650	296	21	anc	anc	PROPN
ap-6650	296	22	)	)	PUNCT
ap-6650	296	23	2	2	NUM
ap-6650	296	24	=	=	SYM
ap-6650	296	25	(	(	PUNCT
ap-6650	296	26	ancx	ancx	NOUN
ap-6650	296	27	)	)	PUNCT
ap-6650	296	28	2	2	NUM
ap-6650	297	1	+	+	CCONJ
ap-6650	297	2	(	(	PUNCT
ap-6650	297	3	ancy	ancy	NOUN
ap-6650	297	4	)	)	PUNCT
ap-6650	297	5	2	2	NUM
ap-6650	297	6	=	=	SYM
ap-6650	297	7	b2	b2	NOUN
ap-6650	297	8	4	4	NUM
ap-6650	297	9	{	{	PUNCT
ap-6650	297	10	x2	x2	NOUN
ap-6650	298	1	+	+	CCONJ
ap-6650	298	2	y2	y2	NOUN
ap-6650	299	1	−	−	NUM
ap-6650	299	2	θ	θ	NOUN
ap-6650	299	3	2	2	NUM
ap-6650	299	4	~	~	PUNCT
ap-6650	299	5	lz	lz	X
ap-6650	299	6	+	+	ADJ
ap-6650	299	7	θ2	θ2	PROPN
ap-6650	299	8	16~2	16~2	NUM
ap-6650	299	9	(	(	PUNCT
ap-6650	299	10	p2	p2	X
ap-6650	299	11	x	x	PUNCT
ap-6650	299	12	+	+	CCONJ
ap-6650	299	13	p2	p2	PROPN
ap-6650	299	14	y	y	PROPN
ap-6650	299	15	)	)	PUNCT
ap-6650	299	16	}	}	PUNCT
ap-6650	299	17	.	.	PUNCT
ap-6650	300	1	(	(	PUNCT
ap-6650	300	2	62	62	NUM
ap-6650	300	3	)	)	PUNCT
ap-6650	300	4	using	use	VERB
ap-6650	300	5	the	the	DET
ap-6650	300	6	three	three	NUM
ap-6650	300	7	equations	equation	NOUN
ap-6650	300	8	above	above	ADV
ap-6650	300	9	,	,	PUNCT
ap-6650	300	10	our	our	PRON
ap-6650	300	11	noncommutative	noncommutative	ADJ
ap-6650	300	12	classical	classical	ADJ
ap-6650	300	13	hamiltonian	hamiltonian	NOUN
ap-6650	300	14	becomes	become	VERB
ap-6650	300	15	hnccla	hnccla	NOUN
ap-6650	300	16	=	=	SYM
ap-6650	300	17	1	1	NUM
ap-6650	300	18	2m̃	2m̃	PROPN
ap-6650	300	19	(	(	PUNCT
ap-6650	300	20	p2	p2	X
ap-6650	300	21	x	x	PUNCT
ap-6650	301	1	+	+	CCONJ
ap-6650	301	2	p2	p2	PROPN
ap-6650	301	3	y	y	PROPN
ap-6650	301	4	)	)	PUNCT
ap-6650	302	1	+	+	CCONJ
ap-6650	302	2	1	1	NUM
ap-6650	302	3	2mp2	2mp2	NUM
ap-6650	302	4	z	z	NOUN
ap-6650	302	5	−	−	ADP
ap-6650	303	1	ω̃lz	ω̃lz	PROPN
ap-6650	303	2	+	+	CCONJ
ap-6650	303	3	1	1	NUM
ap-6650	303	4	2m̃ω̃	2m̃ω̃	NUM
ap-6650	303	5	2	2	NUM
ap-6650	303	6	(	(	PUNCT
ap-6650	303	7	x2	x2	PROPN
ap-6650	303	8	+	+	CCONJ
ap-6650	303	9	y2	y2	NOUN
ap-6650	303	10	)	)	PUNCT
ap-6650	303	11	,	,	PUNCT
ap-6650	303	12	(	(	PUNCT
ap-6650	303	13	63	63	NUM
ap-6650	303	14	)	)	PUNCT
ap-6650	303	15	where	where	SCONJ
ap-6650	303	16	lz	lz	SCONJ
ap-6650	303	17	=	=	PROPN
ap-6650	303	18	pyx−	pyx−	PROPN
ap-6650	303	19	pxy	pxy	NOUN
ap-6650	303	20	=	=	SYM
ap-6650	303	21	(	(	PUNCT
ap-6650	303	22	xi	xi	X
ap-6650	303	23	×	×	PROPN
ap-6650	303	24	pi)z	pi)z	PROPN
ap-6650	303	25	,	,	PUNCT
ap-6650	303	26	and	and	CCONJ
ap-6650	303	27	m̃	m̃	PROPN
ap-6650	304	1	=	=	SYM
ap-6650	304	2	m	m	PROPN
ap-6650	304	3	(	(	PUNCT
ap-6650	304	4	1	1	NUM
ap-6650	304	5	+	+	NUM
ap-6650	304	6	ebθ	ebθ	PROPN
ap-6650	304	7	8c~	8c~	NOUN
ap-6650	304	8	)	)	PUNCT
ap-6650	304	9	2	2	NUM
ap-6650	304	10	,	,	PUNCT
ap-6650	304	11	ω̃	ω̃	NUM
ap-6650	304	12	=	=	SYM
ap-6650	304	13	cη	cη	PROPN
ap-6650	304	14	+	+	NOUN
ap-6650	304	15	2e	2e	NUM
ap-6650	304	16	~	~	SYM
ap-6650	304	17	b	b	NOUN
ap-6650	304	18	4c	4c	NOUN
ap-6650	304	19	~	~	SYM
ap-6650	304	20	m̃	m̃	PROPN
ap-6650	304	21	(	(	PUNCT
ap-6650	304	22	1	1	NUM
ap-6650	304	23	+	+	NUM
ap-6650	304	24	ebθ	ebθ	NOUN
ap-6650	304	25	c8~	c8~	PROPN
ap-6650	304	26	)	)	PUNCT
ap-6650	304	27	and	and	CCONJ
ap-6650	304	28	1	1	NUM
ap-6650	304	29	2m̃ω̃	2m̃ω̃	NUM
ap-6650	304	30	2	2	NUM
ap-6650	304	31	=	=	SYM
ap-6650	304	32	1	1	NUM
ap-6650	304	33	2	2	NUM
ap-6650	304	34	m	m	VERB
ap-6650	304	35	(	(	PUNCT
ap-6650	304	36	ηeb	ηeb	PROPN
ap-6650	304	37	4c~	4c~	PROPN
ap-6650	305	1	+	+	CCONJ
ap-6650	305	2	η2	η2	ADJ
ap-6650	305	3	16~2	16~2	NOUN
ap-6650	305	4	+	+	CCONJ
ap-6650	305	5	e2b2	e2b2	X
ap-6650	305	6	c24	c24	NOUN
ap-6650	305	7	)	)	PUNCT
ap-6650	305	8	.	.	PUNCT
ap-6650	306	1	(	(	PUNCT
ap-6650	306	2	64	64	NUM
ap-6650	306	3	)	)	PUNCT
ap-6650	306	4	237	237	NUM
ap-6650	306	5	ilyas	ilyas	PROPN
ap-6650	306	6	haouam	haouam	PROPN
ap-6650	306	7	acta	acta	PROPN
ap-6650	306	8	polytechnica	polytechnica	PROPN
ap-6650	306	9	now	now	ADV
ap-6650	306	10	,	,	PUNCT
ap-6650	306	11	following	follow	VERB
ap-6650	306	12	the	the	DET
ap-6650	306	13	definition	definition	NOUN
ap-6650	306	14	given	give	VERB
ap-6650	306	15	in	in	ADP
ap-6650	306	16	equation	equation	NOUN
ap-6650	306	17	(	(	PUNCT
ap-6650	306	18	55	55	NUM
ap-6650	306	19	)	)	PUNCT
ap-6650	306	20	,	,	PUNCT
ap-6650	306	21	we	we	PRON
ap-6650	306	22	express	express	VERB
ap-6650	306	23	the	the	DET
ap-6650	306	24	single	single	ADJ
ap-6650	306	25	particle	particle	NOUN
ap-6650	306	26	noncommutative	noncommutative	ADJ
ap-6650	306	27	classical	classical	ADJ
ap-6650	306	28	partition	partition	NOUN
ap-6650	306	29	function	function	NOUN
ap-6650	306	30	as	as	ADP
ap-6650	306	31	znc	znc	X
ap-6650	306	32	clas,1	clas,1	X
ap-6650	306	33	=	=	SYM
ap-6650	306	34	1	1	NUM
ap-6650	306	35	h̃3	h̃3	PROPN
ap-6650	306	36	�	�	PROPN
ap-6650	306	37	e−β	e−β	PROPN
ap-6650	306	38	[	[	PUNCT
ap-6650	306	39	1	1	NUM
ap-6650	306	40	2m̃(p2	2m̃(p2	NUM
ap-6650	306	41	x+p2	x+p2	NOUN
ap-6650	306	42	y)+	y)+	NOUN
ap-6650	306	43	1	1	NUM
ap-6650	306	44	2mp	2mp	ADJ
ap-6650	306	45	2	2	NUM
ap-6650	306	46	z−ω̃lz+	z−ω̃lz+	PROPN
ap-6650	306	47	1	1	NUM
ap-6650	306	48	2	2	NUM
ap-6650	306	49	m̃ω̃	m̃ω̃	PROPN
ap-6650	306	50	2(x2+y2)]d3xncd3pnc	2(x2+y2)]d3xncd3pnc	NUM
ap-6650	306	51	.	.	PUNCT
ap-6650	307	1	(	(	PUNCT
ap-6650	307	2	65	65	NUM
ap-6650	307	3	)	)	PUNCT
ap-6650	307	4	it	it	PRON
ap-6650	307	5	should	should	AUX
ap-6650	307	6	be	be	AUX
ap-6650	307	7	noted	note	VERB
ap-6650	307	8	that	that	SCONJ
ap-6650	307	9	we	we	PRON
ap-6650	307	10	want	want	VERB
ap-6650	307	11	to	to	PART
ap-6650	307	12	factorize	factorize	VERB
ap-6650	307	13	our	our	PRON
ap-6650	307	14	hamiltonian	hamiltonian	NOUN
ap-6650	307	15	into	into	ADP
ap-6650	307	16	momentum	momentum	NOUN
ap-6650	307	17	and	and	CCONJ
ap-6650	307	18	position	position	NOUN
ap-6650	307	19	terms	term	NOUN
ap-6650	307	20	.	.	PUNCT
ap-6650	308	1	this	this	PRON
ap-6650	308	2	is	be	AUX
ap-6650	308	3	not	not	PART
ap-6650	308	4	always	always	ADV
ap-6650	308	5	possible	possible	ADJ
ap-6650	308	6	when	when	SCONJ
ap-6650	308	7	there	there	PRON
ap-6650	308	8	are	be	VERB
ap-6650	308	9	matrices	matrix	NOUN
ap-6650	308	10	(	(	PUNCT
ap-6650	308	11	or	or	CCONJ
ap-6650	308	12	operators	operator	NOUN
ap-6650	308	13	)	)	PUNCT
ap-6650	308	14	in	in	ADP
ap-6650	308	15	the	the	DET
ap-6650	308	16	exponent	exponent	NOUN
ap-6650	308	17	.	.	PUNCT
ap-6650	309	1	however	however	ADV
ap-6650	309	2	,	,	PUNCT
ap-6650	309	3	within	within	ADP
ap-6650	309	4	the	the	DET
ap-6650	309	5	classical	classical	ADJ
ap-6650	309	6	limit	limit	NOUN
ap-6650	309	7	,	,	PUNCT
ap-6650	309	8	it	it	PRON
ap-6650	309	9	is	be	AUX
ap-6650	309	10	possible	possible	ADJ
ap-6650	309	11	.	.	PUNCT
ap-6650	310	1	otherwise	otherwise	ADV
ap-6650	310	2	,	,	PUNCT
ap-6650	310	3	to	to	PART
ap-6650	310	4	separate	separate	VERB
ap-6650	310	5	the	the	DET
ap-6650	310	6	operators	operator	NOUN
ap-6650	310	7	in	in	ADP
ap-6650	310	8	the	the	DET
ap-6650	310	9	exponent	exponent	NOUN
ap-6650	310	10	,	,	PUNCT
ap-6650	310	11	we	we	PRON
ap-6650	310	12	use	use	VERB
ap-6650	310	13	the	the	DET
ap-6650	310	14	baker	baker	PROPN
ap-6650	310	15	-	-	PUNCT
ap-6650	310	16	campbell	campbell	PROPN
ap-6650	310	17	-	-	PUNCT
ap-6650	310	18	hausdorff	hausdorff	PROPN
ap-6650	310	19	(	(	PUNCT
ap-6650	310	20	bch	bch	PROPN
ap-6650	310	21	)	)	PUNCT
ap-6650	310	22	formula	formula	NOUN
ap-6650	310	23	given	give	VERB
ap-6650	310	24	by	by	ADP
ap-6650	310	25	(	(	PUNCT
ap-6650	310	26	first	first	ADJ
ap-6650	310	27	few	few	ADJ
ap-6650	310	28	terms	term	NOUN
ap-6650	310	29	)	)	PUNCT
ap-6650	310	30	e[â+b̂	e[â+b̂	PROPN
ap-6650	310	31	]	]	X
ap-6650	310	32	=	=	SYM
ap-6650	310	33	e[â]e[b̂]e[−	e[â]e[b̂]e[−	PROPN
ap-6650	310	34	1	1	NUM
ap-6650	310	35	2	2	NUM
ap-6650	311	1	[	[	X
ap-6650	311	2	â,b̂]]e	â,b̂]]e	NOUN
ap-6650	311	3	1	1	NUM
ap-6650	311	4	6(2[â,[â,b̂]]+[b̂,[â,b̂	6(2[â,[â,b̂]]+[b̂,[â,b̂	NUM
ap-6650	311	5	]	]	NOUN
ap-6650	311	6	]	]	PUNCT
ap-6650	311	7	)	)	PUNCT
ap-6650	311	8	...	...	PUNCT
ap-6650	312	1	(	(	PUNCT
ap-6650	312	2	66	66	NUM
ap-6650	312	3	)	)	PUNCT
ap-6650	312	4	we	we	PRON
ap-6650	312	5	can	can	AUX
ap-6650	312	6	now	now	ADV
ap-6650	312	7	start	start	VERB
ap-6650	312	8	to	to	PART
ap-6650	312	9	replace	replace	VERB
ap-6650	312	10	some	some	PRON
ap-6650	312	11	of	of	ADP
ap-6650	312	12	the	the	DET
ap-6650	312	13	operators	operator	NOUN
ap-6650	312	14	in	in	ADP
ap-6650	312	15	the	the	DET
ap-6650	312	16	exponent	exponent	NOUN
ap-6650	312	17	znc	znc	X
ap-6650	312	18	clas,1	clas,1	X
ap-6650	312	19	=	=	SYM
ap-6650	312	20	1	1	NUM
ap-6650	312	21	h̃3	h̃3	PROPN
ap-6650	312	22	�	�	PROPN
ap-6650	312	23	e−β	e−β	PROPN
ap-6650	312	24	[	[	PUNCT
ap-6650	312	25	1	1	NUM
ap-6650	312	26	2m̃(p2	2m̃(p2	NUM
ap-6650	312	27	x+p2	x+p2	NOUN
ap-6650	312	28	y)+	y)+	NOUN
ap-6650	312	29	1	1	NUM
ap-6650	312	30	2mp	2mp	ADJ
ap-6650	312	31	2	2	NUM
ap-6650	312	32	z]e−β	z]e−β	NOUN
ap-6650	312	33	[	[	PUNCT
ap-6650	312	34	1	1	NUM
ap-6650	312	35	2	2	NUM
ap-6650	312	36	m̃ω̃	m̃ω̃	NOUN
ap-6650	312	37	2(x2+y2)]eβω̃lzd3pncd3xnc	2(x2+y2)]eβω̃lzd3pncd3xnc	NUM
ap-6650	312	38	.	.	PUNCT
ap-6650	313	1	(	(	PUNCT
ap-6650	313	2	67	67	NUM
ap-6650	313	3	)	)	PUNCT
ap-6650	313	4	we	we	PRON
ap-6650	313	5	should	should	AUX
ap-6650	313	6	expand	expand	VERB
ap-6650	313	7	exponentials	exponential	NOUN
ap-6650	313	8	containing	contain	VERB
ap-6650	313	9	ω̃	ω̃	PROPN
ap-6650	313	10	,	,	PUNCT
ap-6650	313	11	and	and	CCONJ
ap-6650	313	12	by	by	ADP
ap-6650	313	13	considering	consider	VERB
ap-6650	313	14	terms	term	NOUN
ap-6650	313	15	up	up	ADP
ap-6650	313	16	to	to	ADP
ap-6650	313	17	the	the	DET
ap-6650	313	18	second	second	ADJ
ap-6650	313	19	-	-	PUNCT
ap-6650	313	20	order	order	NOUN
ap-6650	313	21	of	of	ADP
ap-6650	313	22	ω̃	ω̃	PROPN
ap-6650	313	23	,	,	PUNCT
ap-6650	313	24	we	we	PRON
ap-6650	313	25	obtain	obtain	VERB
ap-6650	313	26	zncclas,1	zncclas,1	NOUN
ap-6650	313	27	=	=	SYM
ap-6650	313	28	1	1	NUM
ap-6650	313	29	h̃3	h̃3	PROPN
ap-6650	313	30	�	�	PROPN
ap-6650	313	31	e	e	ADP
ap-6650	313	32	−	−	PROPN
ap-6650	313	33	β2	β2	PROPN
ap-6650	313	34	[	[	PUNCT
ap-6650	313	35	p2	p2	PROPN
ap-6650	313	36	x+p2	x+p2	PROPN
ap-6650	313	37	y	y	PROPN
ap-6650	313	38	m̃	m̃	PROPN
ap-6650	313	39	+	+	CCONJ
ap-6650	313	40	p2	p2	PROPN
ap-6650	313	41	z	z	NOUN
ap-6650	313	42	m	m	VERB
ap-6650	313	43	]	]	PUNCT
ap-6650	313	44	(	(	PUNCT
ap-6650	313	45	1	1	NUM
ap-6650	314	1	+	+	CCONJ
ap-6650	314	2	βω̃lz	βω̃lz	NUM
ap-6650	314	3	+	+	CCONJ
ap-6650	314	4	1	1	NUM
ap-6650	314	5	2β	2β	NUM
ap-6650	314	6	2ω̃2l2	2ω̃2l2	PROPN
ap-6650	314	7	z	z	NOUN
ap-6650	314	8	)	)	PUNCT
ap-6650	314	9	(	(	PUNCT
ap-6650	314	10	1−	1−	NUM
ap-6650	314	11	βω̃2	βω̃2	NOUN
ap-6650	314	12	m̃	m̃	NOUN
ap-6650	314	13	2	2	NUM
ap-6650	314	14	(	(	PUNCT
ap-6650	314	15	x2	x2	PROPN
ap-6650	314	16	+	+	CCONJ
ap-6650	314	17	y2	y2	NOUN
ap-6650	314	18	)	)	PUNCT
ap-6650	314	19	)	)	PUNCT
ap-6650	314	20	d3pncd3xnc	d3pncd3xnc	PROPN
ap-6650	314	21	,	,	PUNCT
ap-6650	314	22	(	(	PUNCT
ap-6650	314	23	68	68	NUM
ap-6650	314	24	)	)	PUNCT
ap-6650	314	25	therefore	therefore	ADV
ap-6650	314	26	,	,	PUNCT
ap-6650	314	27	we	we	PRON
ap-6650	314	28	have	have	VERB
ap-6650	314	29	the	the	DET
ap-6650	314	30	appropriate	appropriate	ADJ
ap-6650	314	31	expression	expression	NOUN
ap-6650	314	32	for	for	ADP
ap-6650	314	33	zncclas,1	zncclas,1	NOUN
ap-6650	314	34	znc	znc	X
ap-6650	314	35	clas,1	clas,1	X
ap-6650	314	36	=	=	SYM
ap-6650	314	37	1−	1−	NUM
ap-6650	314	38	7θη	7θη	NOUN
ap-6650	314	39	8~2	8~2	NUM
ap-6650	314	40	h3	h3	PROPN
ap-6650	314	41	�	�	PROPN
ap-6650	314	42	e	e	PROPN
ap-6650	314	43	−β	−β	PROPN
ap-6650	314	44	2	2	NUM
ap-6650	314	45	[	[	PUNCT
ap-6650	314	46	p2x+p2y	p2x+p2y	PROPN
ap-6650	314	47	m̃	m̃	PROPN
ap-6650	314	48	+	+	CCONJ
ap-6650	314	49	p2z	p2z	PROPN
ap-6650	314	50	m	m	VERB
ap-6650	314	51	]	]	X
ap-6650	315	1	d3pd3x+	d3pd3x+	PROPN
ap-6650	315	2	(	(	PUNCT
ap-6650	315	3	1−	1−	NUM
ap-6650	315	4	7θη	7θη	NOUN
ap-6650	315	5	8~2	8~2	NUM
ap-6650	315	6	)	)	PUNCT
ap-6650	316	1	βω̃	βω̃	PROPN
ap-6650	316	2	h3	h3	PROPN
ap-6650	316	3	�	�	PROPN
ap-6650	316	4	e	e	PROPN
ap-6650	316	5	−β	−β	PROPN
ap-6650	316	6	2	2	NUM
ap-6650	316	7	[	[	PUNCT
ap-6650	316	8	p2x+p2y	p2x+p2y	PROPN
ap-6650	316	9	m̃	m̃	PROPN
ap-6650	316	10	+	+	CCONJ
ap-6650	316	11	p2z	p2z	PROPN
ap-6650	316	12	m	m	VERB
ap-6650	316	13	]	]	X
ap-6650	316	14	lzd	lzd	X
ap-6650	316	15	3pd3x	3pd3x	NUM
ap-6650	316	16	+	+	NOUN
ap-6650	316	17	(	(	PUNCT
ap-6650	316	18	1−	1−	NUM
ap-6650	316	19	7θη	7θη	NOUN
ap-6650	316	20	8~2	8~2	NUM
ap-6650	316	21	)	)	PUNCT
ap-6650	316	22	β2ω̃2	β2ω̃2	SYM
ap-6650	316	23	2h3	2h3	NUM
ap-6650	316	24	�	�	PROPN
ap-6650	316	25	e	e	NOUN
ap-6650	316	26	−β	−β	NOUN
ap-6650	316	27	2	2	NUM
ap-6650	316	28	[	[	PUNCT
ap-6650	316	29	p2x+p2y	p2x+p2y	PROPN
ap-6650	316	30	m̃	m̃	PROPN
ap-6650	316	31	+	+	CCONJ
ap-6650	316	32	p2z	p2z	PROPN
ap-6650	316	33	m	m	VERB
ap-6650	316	34	]	]	PUNCT
ap-6650	316	35	l2	l2	PROPN
ap-6650	316	36	zd	zd	PROPN
ap-6650	316	37	3pd3x−	3pd3x−	NUM
ap-6650	316	38	(	(	PUNCT
ap-6650	316	39	1−	1−	NUM
ap-6650	316	40	7θη	7θη	NOUN
ap-6650	316	41	8~2	8~2	NUM
ap-6650	316	42	)	)	PUNCT
ap-6650	316	43	βω̃2	βω̃2	NOUN
ap-6650	316	44	2h3	2h3	NUM
ap-6650	316	45	�	�	PROPN
ap-6650	316	46	e	e	NOUN
ap-6650	316	47	−β	−β	NOUN
ap-6650	316	48	2	2	NUM
ap-6650	316	49	[	[	PUNCT
ap-6650	316	50	p2x+p2y	p2x+p2y	PROPN
ap-6650	316	51	m̃	m̃	PROPN
ap-6650	316	52	+	+	CCONJ
ap-6650	316	53	p2z	p2z	PROPN
ap-6650	316	54	m	m	VERB
ap-6650	316	55	]	]	PUNCT
ap-6650	316	56	(	(	PUNCT
ap-6650	316	57	x2	x2	NOUN
ap-6650	316	58	+	+	CCONJ
ap-6650	316	59	y2	y2	NOUN
ap-6650	316	60	)	)	PUNCT
ap-6650	316	61	d3pd3x	d3pd3x	NOUN
ap-6650	316	62	.	.	PUNCT
ap-6650	317	1	(	(	PUNCT
ap-6650	317	2	69	69	NUM
ap-6650	317	3	)	)	PUNCT
ap-6650	317	4	in	in	ADP
ap-6650	317	5	the	the	DET
ap-6650	317	6	right	right	ADJ
ap-6650	317	7	-	-	PUNCT
ap-6650	317	8	hand	hand	NOUN
ap-6650	317	9	side	side	NOUN
ap-6650	317	10	of	of	ADP
ap-6650	317	11	the	the	DET
ap-6650	317	12	above	above	ADJ
ap-6650	317	13	equation	equation	NOUN
ap-6650	317	14	,	,	PUNCT
ap-6650	317	15	it	it	PRON
ap-6650	317	16	is	be	AUX
ap-6650	317	17	easy	easy	ADJ
ap-6650	317	18	to	to	PART
ap-6650	317	19	check	check	VERB
ap-6650	317	20	that	that	SCONJ
ap-6650	317	21	the	the	DET
ap-6650	317	22	second	second	ADJ
ap-6650	317	23	integral	integral	ADJ
ap-6650	317	24	goes	go	VERB
ap-6650	317	25	to	to	ADP
ap-6650	317	26	zero	zero	NUM
ap-6650	317	27	and	and	CCONJ
ap-6650	317	28	the	the	DET
ap-6650	317	29	third	third	ADJ
ap-6650	317	30	and	and	CCONJ
ap-6650	317	31	last	last	ADJ
ap-6650	317	32	integrals	integral	NOUN
ap-6650	317	33	cancel	cancel	VERB
ap-6650	317	34	each	each	DET
ap-6650	317	35	other	other	ADJ
ap-6650	317	36	,	,	PUNCT
ap-6650	317	37	and	and	CCONJ
ap-6650	317	38	thus	thus	ADV
ap-6650	317	39	we	we	PRON
ap-6650	317	40	obtain	obtain	VERB
ap-6650	317	41	znc	znc	X
ap-6650	317	42	clas,1	clas,1	NOUN
ap-6650	317	43	=	=	SYM
ap-6650	318	1	1−	1−	NUM
ap-6650	318	2	7θη	7θη	NOUN
ap-6650	318	3	8~2	8~2	NUM
ap-6650	318	4	h3	h3	PROPN
ap-6650	318	5	�	�	PROPN
ap-6650	318	6	e	e	PROPN
ap-6650	318	7	−β	−β	PROPN
ap-6650	318	8	2	2	NUM
ap-6650	318	9	[	[	PUNCT
ap-6650	318	10	p2x+p2y	p2x+p2y	PROPN
ap-6650	318	11	m̃	m̃	PROPN
ap-6650	318	12	+	+	CCONJ
ap-6650	318	13	p2z	p2z	PROPN
ap-6650	318	14	m	m	VERB
ap-6650	318	15	]	]	X
ap-6650	318	16	d3pd3x	d3pd3x	NOUN
ap-6650	318	17	.	.	PUNCT
ap-6650	319	1	(	(	PUNCT
ap-6650	319	2	70	70	X
ap-6650	319	3	)	)	PUNCT
ap-6650	319	4	using	use	VERB
ap-6650	319	5	the	the	DET
ap-6650	319	6	integral	integral	ADJ
ap-6650	319	7	of	of	ADP
ap-6650	319	8	gaussian	gaussian	ADJ
ap-6650	319	9	function	function	NOUN
ap-6650	319	10	�	�	PROPN
ap-6650	319	11	e−ax	e−ax	PROPN
ap-6650	319	12	2	2	NUM
ap-6650	319	13	dx	dx	NOUN
ap-6650	319	14	=	=	SYM
ap-6650	319	15	√	√	PROPN
ap-6650	319	16	π	π	PROPN
ap-6650	319	17	a	a	X
ap-6650	319	18	,	,	PUNCT
ap-6650	319	19	we	we	PRON
ap-6650	319	20	have	have	VERB
ap-6650	319	21	znc	znc	VERB
ap-6650	319	22	clas,1	clas,1	ADJ
ap-6650	319	23	=	=	SYM
ap-6650	319	24	1−	1−	NUM
ap-6650	319	25	7θη	7θη	NOUN
ap-6650	319	26	8~2	8~2	NUM
ap-6650	319	27	h3	h3	PROPN
ap-6650	319	28	�	�	PROPN
ap-6650	319	29	d3x	d3x	PROPN
ap-6650	319	30	�	�	PROPN
ap-6650	319	31	e	e	NOUN
ap-6650	319	32	−β	−β	PROPN
ap-6650	319	33	2	2	NUM
ap-6650	319	34	[	[	PUNCT
ap-6650	319	35	p2x+p2y	p2x+p2y	PROPN
ap-6650	319	36	m̃	m̃	PROPN
ap-6650	319	37	+	+	CCONJ
ap-6650	319	38	p2z	p2z	PROPN
ap-6650	319	39	m	m	VERB
ap-6650	319	40	]	]	PUNCT
ap-6650	319	41	d3p	d3p	PROPN
ap-6650	319	42	=	=	PUNCT
ap-6650	319	43	v	v	ADP
ap-6650	319	44	λ3	λ3	PROPN
ap-6650	319	45	1−	1−	NUM
ap-6650	319	46	7θη	7θη	NOUN
ap-6650	319	47	8~2	8~2	NUM
ap-6650	319	48	(	(	PUNCT
ap-6650	319	49	1	1	NUM
ap-6650	319	50	+	+	NUM
ap-6650	319	51	ebθ	ebθ	PROPN
ap-6650	319	52	8c~	8c~	NOUN
ap-6650	319	53	)	)	PUNCT
ap-6650	319	54	2	2	NUM
ap-6650	319	55	,	,	PUNCT
ap-6650	319	56	(	(	PUNCT
ap-6650	319	57	71	71	NUM
ap-6650	319	58	)	)	PUNCT
ap-6650	319	59	where	where	SCONJ
ap-6650	319	60	v	v	NOUN
ap-6650	319	61	,	,	PUNCT
ap-6650	319	62	λ	λ	PROPN
ap-6650	319	63	=	=	SYM
ap-6650	319	64	h	h	PROPN
ap-6650	319	65	(	(	PUNCT
ap-6650	319	66	2mπkbt	2mπkbt	NUM
ap-6650	319	67	)	)	PUNCT
ap-6650	319	68	−	−	NOUN
ap-6650	320	1	1	1	NUM
ap-6650	320	2	2	2	NUM
ap-6650	320	3	are	be	AUX
ap-6650	320	4	the	the	DET
ap-6650	320	5	volume	volume	NOUN
ap-6650	320	6	and	and	CCONJ
ap-6650	320	7	the	the	DET
ap-6650	320	8	thermal	thermal	ADJ
ap-6650	320	9	de	de	X
ap-6650	320	10	broglie	broglie	PROPN
ap-6650	320	11	wavelength	wavelength	NOUN
ap-6650	320	12	,	,	PUNCT
ap-6650	320	13	respectively	respectively	ADV
ap-6650	320	14	.	.	PUNCT
ap-6650	321	1	the	the	DET
ap-6650	321	2	non	non	ADJ
ap-6650	321	3	-	-	ADJ
ap-6650	321	4	classical	classical	ADJ
ap-6650	321	5	partition	partition	NOUN
ap-6650	321	6	function	function	NOUN
ap-6650	321	7	using	use	VERB
ap-6650	321	8	hncl	hncl	NOUN
ap-6650	321	9	,	,	PUNCT
ap-6650	321	10	σ	σ	PROPN
ap-6650	321	11	is	be	AUX
ap-6650	321	12	zncl	zncl	NOUN
ap-6650	321	13	=	=	SYM
ap-6650	321	14	znncl,1	znncl,1	NOUN
ap-6650	321	15	=	=	SYM
ap-6650	321	16	(	(	PUNCT
ap-6650	321	17	∑	∑	PUNCT
ap-6650	321	18	σz=±1	σz=±1	VERB
ap-6650	321	19	eβµb	eβµb	NOUN
ap-6650	321	20	σ̂zb	σ̂zb	NOUN
ap-6650	321	21	)	)	PUNCT
ap-6650	321	22	n	n	NOUN
ap-6650	321	23	=	=	SYM
ap-6650	321	24	2ncoshn	2ncoshn	NUM
ap-6650	321	25	(	(	PUNCT
ap-6650	321	26	βµbb	βµbb	PROPN
ap-6650	321	27	)	)	PUNCT
ap-6650	321	28	.	.	PUNCT
ap-6650	322	1	(	(	PUNCT
ap-6650	322	2	72	72	NUM
ap-6650	322	3	)	)	PUNCT
ap-6650	322	4	finally	finally	ADV
ap-6650	322	5	,	,	PUNCT
ap-6650	322	6	the	the	DET
ap-6650	322	7	pauli	pauli	PROPN
ap-6650	322	8	partition	partition	NOUN
ap-6650	322	9	function	function	NOUN
ap-6650	322	10	for	for	ADP
ap-6650	322	11	a	a	DET
ap-6650	322	12	system	system	NOUN
ap-6650	322	13	of	of	ADP
ap-6650	322	14	n	n	DET
ap-6650	322	15	particles	particle	NOUN
ap-6650	322	16	in	in	ADP
ap-6650	322	17	a	a	DET
ap-6650	322	18	three	three	NUM
ap-6650	322	19	-	-	PUNCT
ap-6650	322	20	dimensional	dimensional	ADJ
ap-6650	322	21	noncommutative	noncommutative	ADJ
ap-6650	322	22	phase	phase	NOUN
ap-6650	322	23	-	-	PUNCT
ap-6650	322	24	spaces	space	NOUN
ap-6650	322	25	is	be	AUX
ap-6650	322	26	znc	znc	ADJ
ap-6650	322	27	=	=	SYM
ap-6650	322	28	(	(	PUNCT
ap-6650	322	29	2v	2v	PROPN
ap-6650	322	30	)	)	PUNCT
ap-6650	322	31	n	n	CCONJ
ap-6650	322	32	λ3nn	λ3nn	NOUN
ap-6650	322	33	!	!	PUNCT
ap-6650	323	1	(	(	PUNCT
ap-6650	323	2	1−	1−	NUM
ap-6650	323	3	7θη	7θη	NOUN
ap-6650	323	4	8~2	8~2	NUM
ap-6650	323	5	)	)	PUNCT
ap-6650	323	6	n	n	PRON
ap-6650	323	7	coshn	coshn	NOUN
ap-6650	323	8	(	(	PUNCT
ap-6650	323	9	βµbb	βµbb	PROPN
ap-6650	323	10	)	)	PUNCT
ap-6650	323	11	(	(	PUNCT
ap-6650	323	12	1	1	NUM
ap-6650	323	13	+	+	NUM
ap-6650	323	14	ebθ	ebθ	PROPN
ap-6650	323	15	8c~	8c~	NOUN
ap-6650	323	16	)	)	PUNCT
ap-6650	323	17	2n	2n	NUM
ap-6650	323	18	.	.	PUNCT
ap-6650	324	1	(	(	PUNCT
ap-6650	324	2	73	73	NUM
ap-6650	324	3	)	)	PUNCT
ap-6650	324	4	238	238	NUM
ap-6650	324	5	vol	vol	NOUN
ap-6650	324	6	.	.	PUNCT
ap-6650	325	1	61	61	NUM
ap-6650	325	2	no	no	NOUN
ap-6650	325	3	.	.	PUNCT
ap-6650	326	1	1/2021	1/2021	NUM
ap-6650	326	2	on	on	ADP
ap-6650	326	3	the	the	DET
ap-6650	326	4	three	three	NUM
ap-6650	326	5	-	-	PUNCT
ap-6650	326	6	dimensional	dimensional	ADJ
ap-6650	326	7	pauli	pauli	PROPN
ap-6650	326	8	equation	equation	NOUN
ap-6650	326	9	in	in	ADP
ap-6650	326	10	noncommutative	noncommutative	ADJ
ap-6650	326	11	phase	phase	NOUN
ap-6650	326	12	-	-	PUNCT
ap-6650	326	13	space	space	NOUN
ap-6650	326	14	in	in	ADP
ap-6650	326	15	the	the	DET
ap-6650	326	16	limit	limit	NOUN
ap-6650	326	17	of	of	ADP
ap-6650	326	18	the	the	DET
ap-6650	326	19	noncommutativity	noncommutativity	NOUN
ap-6650	326	20	,	,	PUNCT
ap-6650	326	21	i.e.	i.e.	X
ap-6650	326	22	θ→	θ→	X
ap-6650	326	23	0	0	NUM
ap-6650	326	24	,	,	PUNCT
ap-6650	326	25	η	η	PROPN
ap-6650	326	26	→	→	X
ap-6650	326	27	0	0	PROPN
ap-6650	326	28	,	,	PUNCT
ap-6650	326	29	the	the	DET
ap-6650	326	30	above	above	ADJ
ap-6650	326	31	expression	expression	NOUN
ap-6650	326	32	of	of	ADP
ap-6650	326	33	znc	znc	PROPN
ap-6650	326	34	tends	tend	VERB
ap-6650	326	35	to	to	ADP
ap-6650	326	36	the	the	DET
ap-6650	326	37	result	result	NOUN
ap-6650	326	38	of	of	ADP
ap-6650	326	39	z	z	NOUN
ap-6650	326	40	in	in	ADP
ap-6650	326	41	the	the	DET
ap-6650	326	42	usual	usual	ADJ
ap-6650	326	43	commutative	commutative	ADJ
ap-6650	326	44	phase	phase	NOUN
ap-6650	326	45	-	-	PUNCT
ap-6650	326	46	space	space	NOUN
ap-6650	326	47	,	,	PUNCT
ap-6650	326	48	which	which	PRON
ap-6650	326	49	is	be	AUX
ap-6650	326	50	z	z	NOUN
ap-6650	326	51	=	=	SYM
ap-6650	326	52	(	(	PUNCT
ap-6650	326	53	2v	2v	PROPN
ap-6650	326	54	)	)	PUNCT
ap-6650	326	55	n	n	CCONJ
ap-6650	326	56	λ3nn	λ3nn	NOUN
ap-6650	326	57	!	!	PUNCT
ap-6650	327	1	cosh	cosh	PROPN
ap-6650	327	2	n	n	PROPN
ap-6650	327	3	(	(	PUNCT
ap-6650	327	4	βµbb	βµbb	PROPN
ap-6650	327	5	)	)	PUNCT
ap-6650	327	6	.	.	PUNCT
ap-6650	328	1	(	(	PUNCT
ap-6650	328	2	74	74	X
ap-6650	328	3	)	)	PUNCT
ap-6650	328	4	using	use	VERB
ap-6650	328	5	formulae	formulae	NOUN
ap-6650	328	6	(	(	PUNCT
ap-6650	328	7	53	53	NUM
ap-6650	328	8	)	)	PUNCT
ap-6650	328	9	and	and	CCONJ
ap-6650	328	10	(	(	PUNCT
ap-6650	328	11	54	54	NUM
ap-6650	328	12	)	)	PUNCT
ap-6650	328	13	,	,	PUNCT
ap-6650	328	14	we	we	PRON
ap-6650	328	15	find	find	VERB
ap-6650	328	16	the	the	DET
ap-6650	328	17	magnetization	magnetization	NOUN
ap-6650	328	18	in	in	ADP
ap-6650	328	19	noncommutative	noncommutative	ADJ
ap-6650	328	20	and	and	CCONJ
ap-6650	328	21	commutative	commutative	ADJ
ap-6650	328	22	phase	phase	NOUN
ap-6650	328	23	-	-	PUNCT
ap-6650	328	24	space	space	NOUN
ap-6650	328	25	,	,	PUNCT
ap-6650	328	26	thus	thus	ADV
ap-6650	328	27	fnc	fnc	VERB
ap-6650	328	28	=	=	PRON
ap-6650	329	1	−n	−n	PROPN
ap-6650	329	2	β	β	X
ap-6650	329	3	ln	ln	X
ap-6650	329	4	(	(	PUNCT
ap-6650	329	5	2v	2v	PROPN
ap-6650	329	6	)	)	PUNCT
ap-6650	330	1	λ3	λ3	PROPN
ap-6650	330	2	(	(	PUNCT
ap-6650	330	3	1−	1−	NUM
ap-6650	330	4	7θη	7θη	NOUN
ap-6650	330	5	8~2	8~2	NUM
ap-6650	330	6	)	)	PUNCT
ap-6650	330	7	cosh	cosh	NOUN
ap-6650	330	8	(	(	PUNCT
ap-6650	330	9	βµbb	βµbb	PROPN
ap-6650	330	10	)	)	PUNCT
ap-6650	330	11	(	(	PUNCT
ap-6650	330	12	1	1	NUM
ap-6650	330	13	+	+	NUM
ap-6650	330	14	ebθ	ebθ	PROPN
ap-6650	330	15	8c~	8c~	NOUN
ap-6650	330	16	)	)	PUNCT
ap-6650	330	17	2	2	NUM
ap-6650	330	18	+	+	SYM
ap-6650	330	19	1	1	NUM
ap-6650	330	20	β	β	NOUN
ap-6650	330	21	lnn	lnn	NOUN
ap-6650	330	22	!	!	PUNCT
ap-6650	330	23	,	,	PUNCT
ap-6650	330	24	(	(	PUNCT
ap-6650	330	25	75	75	NUM
ap-6650	330	26	)	)	PUNCT
ap-6650	330	27	we	we	PRON
ap-6650	330	28	can	can	AUX
ap-6650	330	29	use	use	VERB
ap-6650	330	30	lnn	lnn	NOUN
ap-6650	330	31	!	!	PUNCT
ap-6650	331	1	=	=	PRON
ap-6650	332	1	n	n	PRON
ap-6650	332	2	lnn	lnn	NOUN
ap-6650	332	3	−n	−n	PROPN
ap-6650	332	4	(	(	PUNCT
ap-6650	332	5	stirling	stirling	NOUN
ap-6650	332	6	’s	’s	PART
ap-6650	332	7	formula	formula	NOUN
ap-6650	332	8	)	)	PUNCT
ap-6650	332	9	to	to	PART
ap-6650	332	10	simplify	simplify	VERB
ap-6650	332	11	further	far	ADV
ap-6650	332	12	.	.	PUNCT
ap-6650	333	1	the	the	DET
ap-6650	333	2	noncommutative	noncommutative	ADJ
ap-6650	333	3	magnetization	magnetization	NOUN
ap-6650	333	4	is	be	AUX
ap-6650	333	5	〈	〈	PROPN
ap-6650	333	6	mnc	mnc	PROPN
ap-6650	333	7	〉	〉	PROPN
ap-6650	333	8	=	=	SYM
ap-6650	333	9	−∂f	−∂f	PROPN
ap-6650	333	10	nc	nc	PROPN
ap-6650	333	11	∂b	∂b	PROPN
ap-6650	333	12	=	=	SYM
ap-6650	333	13	2n	2n	NUM
ap-6650	333	14	β	β	X
ap-6650	333	15	eθ	eθ	PROPN
ap-6650	333	16	(	(	PUNCT
ap-6650	333	17	8c~	8c~	NOUN
ap-6650	333	18	+	+	CCONJ
ap-6650	333	19	ebθ	ebθ	NOUN
ap-6650	333	20	)	)	PUNCT
ap-6650	334	1	+	+	NUM
ap-6650	334	2	nµbtanh	nµbtanh	ADJ
ap-6650	334	3	(	(	PUNCT
ap-6650	334	4	βµbb	βµbb	NOUN
ap-6650	334	5	)	)	PUNCT
ap-6650	334	6	.	.	PUNCT
ap-6650	335	1	(	(	PUNCT
ap-6650	335	2	76	76	NUM
ap-6650	335	3	)	)	PUNCT
ap-6650	335	4	the	the	DET
ap-6650	335	5	commutative	commutative	ADJ
ap-6650	335	6	magnetization	magnetization	NOUN
ap-6650	335	7	is	be	AUX
ap-6650	335	8	〈	〈	PROPN
ap-6650	335	9	m	m	NOUN
ap-6650	335	10	〉	〉	NOUN
ap-6650	335	11	=	=	SYM
ap-6650	335	12	−∂f	−∂f	PROPN
ap-6650	335	13	∂b	∂b	PROPN
ap-6650	335	14	=	=	PUNCT
ap-6650	335	15	nµbtanh	nµbtanh	NOUN
ap-6650	335	16	(	(	PUNCT
ap-6650	335	17	βµbb	βµbb	PROPN
ap-6650	335	18	)	)	PUNCT
ap-6650	335	19	,	,	PUNCT
ap-6650	335	20	(	(	PUNCT
ap-6650	335	21	77	77	X
ap-6650	335	22	)	)	PUNCT
ap-6650	335	23	it	it	PRON
ap-6650	335	24	is	be	AUX
ap-6650	335	25	obvious	obvious	ADJ
ap-6650	335	26	that	that	SCONJ
ap-6650	335	27	〈	〈	PROPN
ap-6650	335	28	mnc〉|θ=0	mnc〉|θ=0	NOUN
ap-6650	335	29	=	=	PUNCT
ap-6650	335	30	〈	〈	PROPN
ap-6650	335	31	m	m	NOUN
ap-6650	335	32	〉	〉	NUM
ap-6650	335	33	.	.	PUNCT
ap-6650	336	1	we	we	PRON
ap-6650	336	2	may	may	AUX
ap-6650	336	3	derive	derive	VERB
ap-6650	336	4	the	the	DET
ap-6650	336	5	magnetic	magnetic	ADJ
ap-6650	336	6	susceptibility	susceptibility	NOUN
ap-6650	336	7	of	of	ADP
ap-6650	336	8	electrons	electron	NOUN
ap-6650	336	9	χ	χ	X
ap-6650	336	10	=	=	SYM
ap-6650	336	11	1	1	NUM
ap-6650	336	12	v	v	ADP
ap-6650	336	13	∂〈m	∂〈m	ADJ
ap-6650	336	14	〉	〉	PROPN
ap-6650	336	15	∂b	∂b	PROPN
ap-6650	336	16	in	in	ADP
ap-6650	336	17	a	a	DET
ap-6650	336	18	noncommutative	noncommutative	ADJ
ap-6650	336	19	phase	phase	NOUN
ap-6650	336	20	-	-	PUNCT
ap-6650	336	21	space	space	NOUN
ap-6650	336	22	using	use	VERB
ap-6650	336	23	the	the	DET
ap-6650	336	24	magnetization	magnetization	NOUN
ap-6650	336	25	(	(	PUNCT
ap-6650	336	26	76	76	NUM
ap-6650	336	27	)	)	PUNCT
ap-6650	336	28	by	by	ADP
ap-6650	336	29	χnc	χnc	NOUN
ap-6650	336	30	=	=	PUNCT
ap-6650	336	31	−2	−2	PROPN
ap-6650	336	32	n	n	PRON
ap-6650	336	33	v	v	NOUN
ap-6650	336	34	β	β	X
ap-6650	336	35	(	(	PUNCT
ap-6650	336	36	eθ)2	eθ)2	PROPN
ap-6650	336	37	(	(	PUNCT
ap-6650	336	38	8c~	8c~	NOUN
ap-6650	336	39	+	+	CCONJ
ap-6650	336	40	ebθ)2	ebθ)2	PROPN
ap-6650	336	41	+	+	CCONJ
ap-6650	336	42	n	n	NUM
ap-6650	336	43	v	v	ADP
ap-6650	336	44	βµ2	βµ2	NOUN
ap-6650	336	45	b	b	NOUN
ap-6650	336	46	(	(	PUNCT
ap-6650	336	47	1−	1−	NUM
ap-6650	336	48	tanh2	tanh2	NOUN
ap-6650	336	49	(	(	PUNCT
ap-6650	336	50	βµbb	βµbb	PROPN
ap-6650	336	51	)	)	PUNCT
ap-6650	336	52	)	)	PUNCT
ap-6650	336	53	,	,	PUNCT
ap-6650	336	54	(	(	PUNCT
ap-6650	336	55	78	78	NUM
ap-6650	336	56	)	)	PUNCT
ap-6650	336	57	where	where	SCONJ
ap-6650	336	58	the	the	DET
ap-6650	336	59	commutative	commutative	ADJ
ap-6650	336	60	magnetic	magnetic	ADJ
ap-6650	336	61	susceptibility	susceptibility	NOUN
ap-6650	336	62	χ	χ	X
ap-6650	336	63	=	=	X
ap-6650	336	64	χnc	χnc	VERB
ap-6650	336	65	(	(	PUNCT
ap-6650	336	66	θ	θ	NOUN
ap-6650	336	67	=	=	SYM
ap-6650	336	68	0	0	NUM
ap-6650	336	69	)	)	PUNCT
ap-6650	336	70	is	be	AUX
ap-6650	336	71	χ	χ	NOUN
ap-6650	336	72	=	=	PUNCT
ap-6650	336	73	n	n	NOUN
ap-6650	336	74	v	v	ADP
ap-6650	336	75	βµ2	βµ2	NOUN
ap-6650	336	76	b	b	NOUN
ap-6650	336	77	(	(	PUNCT
ap-6650	336	78	1−	1−	NUM
ap-6650	336	79	tanh2	tanh2	NOUN
ap-6650	336	80	(	(	PUNCT
ap-6650	336	81	βµbb	βµbb	PROPN
ap-6650	336	82	)	)	PUNCT
ap-6650	336	83	)	)	PUNCT
ap-6650	336	84	.	.	PUNCT
ap-6650	337	1	(	(	PUNCT
ap-6650	337	2	79	79	NUM
ap-6650	337	3	)	)	PUNCT
ap-6650	337	4	finally	finally	ADV
ap-6650	337	5	,	,	PUNCT
ap-6650	337	6	we	we	PRON
ap-6650	337	7	conclude	conclude	VERB
ap-6650	337	8	with	with	ADP
ap-6650	337	9	the	the	DET
ap-6650	337	10	following	follow	VERB
ap-6650	337	11	special	special	ADJ
ap-6650	337	12	cases	case	NOUN
ap-6650	337	13	.	.	PUNCT
ap-6650	338	1	let	let	VERB
ap-6650	338	2	us	we	PRON
ap-6650	338	3	first	first	ADV
ap-6650	338	4	consider	consider	VERB
ap-6650	338	5	b	b	NOUN
ap-6650	338	6	=	=	SYM
ap-6650	338	7	0	0	NUM
ap-6650	338	8	,	,	PUNCT
ap-6650	338	9	then	then	ADV
ap-6650	338	10	we	we	PRON
ap-6650	338	11	have	have	VERB
ap-6650	338	12	〈	〈	PROPN
ap-6650	338	13	m	m	NOUN
ap-6650	338	14	〉	〉	NOUN
ap-6650	338	15	=	=	SYM
ap-6650	338	16	0	0	NUM
ap-6650	338	17	;	;	PUNCT
ap-6650	338	18	〈	〈	PROPN
ap-6650	338	19	mnc	mnc	PROPN
ap-6650	338	20	〉	〉	PROPN
ap-6650	338	21	=	=	SYM
ap-6650	338	22	2n	2n	NUM
ap-6650	338	23	β	β	X
ap-6650	338	24	eθ	eθ	X
ap-6650	338	25	8c~	8c~	NOUN
ap-6650	338	26	;	;	PUNCT
ap-6650	338	27	and	and	CCONJ
ap-6650	338	28	χnc	χnc	VERB
ap-6650	338	29	=	=	SYM
ap-6650	338	30	−2	−2	PROPN
ap-6650	338	31	n	n	PRON
ap-6650	338	32	v	v	NOUN
ap-6650	338	33	β	β	X
ap-6650	338	34	(	(	PUNCT
ap-6650	338	35	eθ)2	eθ)2	PROPN
ap-6650	338	36	(	(	PUNCT
ap-6650	338	37	8c~)2	8c~)2	NUM
ap-6650	338	38	+	+	CCONJ
ap-6650	338	39	n	n	NUM
ap-6650	338	40	v	v	ADP
ap-6650	338	41	βµ2	βµ2	NOUN
ap-6650	338	42	b	b	NOUN
ap-6650	338	43	.	.	PUNCT
ap-6650	339	1	(	(	PUNCT
ap-6650	339	2	80	80	NUM
ap-6650	339	3	)	)	PUNCT
ap-6650	339	4	for	for	ADP
ap-6650	339	5	b	b	NOUN
ap-6650	339	6	→∞	→∞	PROPN
ap-6650	339	7	and	and	CCONJ
ap-6650	339	8	t	t	PROPN
ap-6650	339	9	=	=	SYM
ap-6650	339	10	cst	cst	PROPN
ap-6650	339	11	,	,	PUNCT
ap-6650	339	12	tanh	tanh	PROPN
ap-6650	339	13	(	(	PUNCT
ap-6650	339	14	βµbb	βµbb	PROPN
ap-6650	339	15	)	)	PUNCT
ap-6650	339	16	=	=	SYM
ap-6650	340	1	1	1	NUM
ap-6650	340	2	,	,	PUNCT
ap-6650	340	3	we	we	PRON
ap-6650	340	4	obtain	obtain	VERB
ap-6650	340	5	〈	〈	PROPN
ap-6650	341	1	mnc	mnc	PROPN
ap-6650	341	2	〉	〉	PROPN
ap-6650	341	3	=	=	SYM
ap-6650	341	4	〈	〈	PROPN
ap-6650	341	5	m	m	NOUN
ap-6650	341	6	〉	〉	NOUN
ap-6650	341	7	=	=	PUNCT
ap-6650	341	8	nµb	nµb	VERB
ap-6650	341	9	;	;	PUNCT
ap-6650	341	10	and	and	CCONJ
ap-6650	341	11	χnc	χnc	VERB
ap-6650	341	12	=	=	SYM
ap-6650	342	1	χ	χ	ADJ
ap-6650	342	2	∼	∼	NOUN
ap-6650	342	3	0	0	NUM
ap-6650	342	4	.	.	PUNCT
ap-6650	343	1	(	(	PUNCT
ap-6650	343	2	81	81	NUM
ap-6650	343	3	)	)	PUNCT
ap-6650	343	4	as	as	ADV
ap-6650	343	5	well	well	ADV
ap-6650	343	6	when	when	SCONJ
ap-6650	343	7	t	t	PROPN
ap-6650	343	8	→∞,β	→∞,β	PROPN
ap-6650	343	9	→	→	SYM
ap-6650	343	10	0	0	NUM
ap-6650	343	11	(	(	PUNCT
ap-6650	343	12	with	with	SCONJ
ap-6650	343	13	b	b	NOUN
ap-6650	343	14	be	be	AUX
ap-6650	343	15	constant	constant	ADJ
ap-6650	343	16	)	)	PUNCT
ap-6650	343	17	,	,	PUNCT
ap-6650	343	18	tanh	tanh	PROPN
ap-6650	343	19	(	(	PUNCT
ap-6650	343	20	βµbb	βµbb	NOUN
ap-6650	343	21	)	)	PUNCT
ap-6650	344	1	=	=	SYM
ap-6650	344	2	0	0	NUM
ap-6650	344	3	,	,	PUNCT
ap-6650	344	4	we	we	PRON
ap-6650	344	5	obtain	obtain	VERB
ap-6650	344	6	〈	〈	PROPN
ap-6650	344	7	mnc	mnc	PROPN
ap-6650	344	8	〉	〉	PROPN
ap-6650	344	9	→	→	SYM
ap-6650	344	10	∞	∞	PROPN
ap-6650	344	11	,	,	PUNCT
ap-6650	344	12	〈	〈	PROPN
ap-6650	344	13	m	m	PROPN
ap-6650	344	14	〉	〉	NOUN
ap-6650	344	15	=	=	SYM
ap-6650	344	16	0	0	NUM
ap-6650	344	17	;	;	PUNCT
ap-6650	344	18	and	and	CCONJ
ap-6650	344	19	χnc	χnc	VERB
ap-6650	344	20	→∞	→∞	PROPN
ap-6650	344	21	,	,	PUNCT
ap-6650	344	22	χ	χ	X
ap-6650	344	23	=	=	PUNCT
ap-6650	344	24	0	0	PROPN
ap-6650	344	25	.	.	PUNCT
ap-6650	345	1	(	(	PUNCT
ap-6650	345	2	82	82	X
ap-6650	345	3	)	)	PUNCT
ap-6650	345	4	armed	arm	VERB
ap-6650	345	5	with	with	ADP
ap-6650	345	6	the	the	DET
ap-6650	345	7	partition	partition	NOUN
ap-6650	345	8	function	function	NOUN
ap-6650	345	9	z	z	NOUN
ap-6650	345	10	,	,	PUNCT
ap-6650	345	11	we	we	PRON
ap-6650	345	12	can	can	AUX
ap-6650	345	13	compute	compute	VERB
ap-6650	345	14	other	other	ADJ
ap-6650	345	15	important	important	ADJ
ap-6650	345	16	thermal	thermal	ADJ
ap-6650	345	17	quantities	quantity	NOUN
ap-6650	345	18	,	,	PUNCT
ap-6650	345	19	such	such	ADJ
ap-6650	345	20	as	as	ADP
ap-6650	345	21	the	the	DET
ap-6650	345	22	average	average	ADJ
ap-6650	345	23	energy	energy	NOUN
ap-6650	345	24	u	u	NOUN
ap-6650	345	25	=	=	NOUN
ap-6650	345	26	−	−	PROPN
ap-6650	345	27	∂	∂	NOUN
ap-6650	345	28	∂β	∂β	PROPN
ap-6650	345	29	lnz	lnz	NOUN
ap-6650	345	30	,	,	PUNCT
ap-6650	345	31	the	the	DET
ap-6650	345	32	entropy	entropy	NOUN
ap-6650	345	33	s	s	PART
ap-6650	345	34	=	=	NOUN
ap-6650	345	35	lnz	lnz	NOUN
ap-6650	345	36	−	−	NOUN
ap-6650	345	37	β	β	NOUN
ap-6650	345	38	∂	∂	NOUN
ap-6650	345	39	∂β	∂β	PROPN
ap-6650	345	40	lnz	lnz	NOUN
ap-6650	345	41	and	and	CCONJ
ap-6650	345	42	the	the	DET
ap-6650	345	43	specific	specific	ADJ
ap-6650	345	44	heat	heat	NOUN
ap-6650	345	45	c	c	NOUN
ap-6650	346	1	=	=	SYM
ap-6650	346	2	β2	β2	PROPN
ap-6650	346	3	∂2	∂2	PROPN
ap-6650	346	4	∂2β	∂2β	ADJ
ap-6650	346	5	lnz	lnz	NOUN
ap-6650	346	6	.	.	PUNCT
ap-6650	347	1	this	this	PRON
ap-6650	347	2	is	be	AUX
ap-6650	347	3	of	of	ADP
ap-6650	347	4	course	course	NOUN
ap-6650	347	5	in	in	ADP
ap-6650	347	6	both	both	DET
ap-6650	347	7	case	case	NOUN
ap-6650	347	8	of	of	ADP
ap-6650	347	9	noncommutative	noncommutative	ADJ
ap-6650	347	10	and	and	CCONJ
ap-6650	347	11	commutative	commutative	ADJ
ap-6650	347	12	phase	phase	NOUN
ap-6650	347	13	-	-	PUNCT
ap-6650	347	14	spaces	space	NOUN
ap-6650	347	15	.	.	PUNCT
ap-6650	348	1	5	5	X
ap-6650	348	2	.	.	X
ap-6650	348	3	conclusion	conclusion	NOUN
ap-6650	348	4	in	in	ADP
ap-6650	348	5	this	this	DET
ap-6650	348	6	work	work	NOUN
ap-6650	348	7	,	,	PUNCT
ap-6650	348	8	we	we	PRON
ap-6650	348	9	have	have	AUX
ap-6650	348	10	studied	study	VERB
ap-6650	348	11	the	the	DET
ap-6650	348	12	three	three	NUM
ap-6650	348	13	-	-	PUNCT
ap-6650	348	14	dimensional	dimensional	ADJ
ap-6650	348	15	pauli	pauli	NOUN
ap-6650	348	16	equation	equation	NOUN
ap-6650	348	17	and	and	CCONJ
ap-6650	348	18	the	the	DET
ap-6650	348	19	corresponding	corresponding	ADJ
ap-6650	348	20	continuity	continuity	NOUN
ap-6650	348	21	equation	equation	NOUN
ap-6650	348	22	for	for	ADP
ap-6650	348	23	a	a	DET
ap-6650	348	24	spin-1/2	spin-1/2	NOUN
ap-6650	348	25	particle	particle	NOUN
ap-6650	348	26	in	in	ADP
ap-6650	348	27	the	the	DET
ap-6650	348	28	presence	presence	NOUN
ap-6650	348	29	of	of	ADP
ap-6650	348	30	an	an	DET
ap-6650	348	31	electromagnetic	electromagnetic	ADJ
ap-6650	348	32	field	field	NOUN
ap-6650	348	33	in	in	ADP
ap-6650	348	34	a	a	DET
ap-6650	348	35	noncommutative	noncommutative	ADJ
ap-6650	348	36	phase	phase	NOUN
ap-6650	348	37	-	-	PUNCT
ap-6650	348	38	space	space	NOUN
ap-6650	348	39	,	,	PUNCT
ap-6650	348	40	considering	consider	VERB
ap-6650	348	41	constant	constant	ADJ
ap-6650	348	42	and	and	CCONJ
ap-6650	348	43	non	non	ADJ
ap-6650	348	44	-	-	ADJ
ap-6650	348	45	constant	constant	ADJ
ap-6650	348	46	magnetic	magnetic	ADJ
ap-6650	348	47	fields	field	NOUN
ap-6650	348	48	.	.	PUNCT
ap-6650	349	1	it	it	PRON
ap-6650	349	2	is	be	AUX
ap-6650	349	3	shown	show	VERB
ap-6650	349	4	that	that	SCONJ
ap-6650	349	5	the	the	DET
ap-6650	349	6	non	non	ADJ
ap-6650	349	7	-	-	ADJ
ap-6650	349	8	constant	constant	ADJ
ap-6650	349	9	magnetic	magnetic	ADJ
ap-6650	349	10	field	field	NOUN
ap-6650	349	11	lifts	lift	VERB
ap-6650	349	12	the	the	DET
ap-6650	349	13	order	order	NOUN
ap-6650	349	14	of	of	ADP
ap-6650	349	15	the	the	DET
ap-6650	349	16	noncommutativity	noncommutativity	NOUN
ap-6650	349	17	parameter	parameter	NOUN
ap-6650	349	18	in	in	ADP
ap-6650	349	19	both	both	CCONJ
ap-6650	349	20	the	the	DET
ap-6650	349	21	pauli	pauli	PROPN
ap-6650	349	22	equation	equation	NOUN
ap-6650	349	23	and	and	CCONJ
ap-6650	349	24	the	the	DET
ap-6650	349	25	corresponding	corresponding	ADJ
ap-6650	349	26	continuity	continuity	NOUN
ap-6650	349	27	equation	equation	NOUN
ap-6650	349	28	.	.	PUNCT
ap-6650	350	1	given	give	VERB
ap-6650	350	2	the	the	DET
ap-6650	350	3	known	know	VERB
ap-6650	350	4	absence	absence	NOUN
ap-6650	350	5	of	of	ADP
ap-6650	350	6	the	the	DET
ap-6650	350	7	magnetization	magnetization	NOUN
ap-6650	350	8	current	current	ADJ
ap-6650	350	9	term	term	NOUN
ap-6650	350	10	in	in	ADP
ap-6650	350	11	the	the	DET
ap-6650	350	12	continuity	continuity	NOUN
ap-6650	350	13	equation	equation	NOUN
ap-6650	350	14	,	,	PUNCT
ap-6650	350	15	even	even	ADV
ap-6650	350	16	in	in	ADP
ap-6650	350	17	the	the	DET
ap-6650	350	18	noncommutative	noncommutative	ADJ
ap-6650	350	19	phase	phase	NOUN
ap-6650	350	20	-	-	PUNCT
ap-6650	350	21	space	space	NOUN
ap-6650	350	22	as	as	SCONJ
ap-6650	350	23	confirmed	confirm	VERB
ap-6650	350	24	by	by	ADP
ap-6650	350	25	our	our	PRON
ap-6650	350	26	calculations	calculation	NOUN
ap-6650	350	27	,	,	PUNCT
ap-6650	350	28	we	we	PRON
ap-6650	350	29	extracted	extract	VERB
ap-6650	350	30	the	the	DET
ap-6650	350	31	magnetization	magnetization	NOUN
ap-6650	350	32	current	current	ADJ
ap-6650	350	33	term	term	NOUN
ap-6650	350	34	from	from	ADP
ap-6650	350	35	the	the	DET
ap-6650	350	36	pauli	pauli	PROPN
ap-6650	350	37	equation	equation	NOUN
ap-6650	350	38	itself	itself	PRON
ap-6650	350	39	without	without	ADP
ap-6650	350	40	modifying	modify	VERB
ap-6650	350	41	the	the	DET
ap-6650	350	42	continuity	continuity	NOUN
ap-6650	350	43	equation	equation	NOUN
ap-6650	350	44	.	.	PUNCT
ap-6650	351	1	furthermore	furthermore	ADV
ap-6650	351	2	,	,	PUNCT
ap-6650	351	3	we	we	PRON
ap-6650	351	4	found	find	VERB
ap-6650	351	5	that	that	SCONJ
ap-6650	351	6	the	the	DET
ap-6650	351	7	density	density	NOUN
ap-6650	351	8	current	current	NOUN
ap-6650	351	9	is	be	AUX
ap-6650	351	10	conserved	conserve	VERB
ap-6650	351	11	,	,	PUNCT
ap-6650	351	12	which	which	PRON
ap-6650	351	13	means	mean	VERB
ap-6650	351	14	that	that	SCONJ
ap-6650	351	15	we	we	PRON
ap-6650	351	16	have	have	VERB
ap-6650	351	17	a	a	DET
ap-6650	351	18	conservation	conservation	NOUN
ap-6650	351	19	of	of	ADP
ap-6650	351	20	the	the	DET
ap-6650	351	21	deformed	deform	VERB
ap-6650	351	22	continuity	continuity	NOUN
ap-6650	351	23	equation	equation	NOUN
ap-6650	351	24	.	.	PUNCT
ap-6650	352	1	by	by	ADP
ap-6650	352	2	using	use	VERB
ap-6650	352	3	the	the	DET
ap-6650	352	4	classical	classical	ADJ
ap-6650	352	5	treatment	treatment	NOUN
ap-6650	352	6	(	(	PUNCT
ap-6650	352	7	within	within	ADP
ap-6650	352	8	the	the	DET
ap-6650	352	9	classical	classical	ADJ
ap-6650	352	10	limit	limit	NOUN
ap-6650	352	11	)	)	PUNCT
ap-6650	352	12	,	,	PUNCT
ap-6650	352	13	the	the	DET
ap-6650	352	14	magnetization	magnetization	NOUN
ap-6650	352	15	and	and	CCONJ
ap-6650	352	16	the	the	DET
ap-6650	352	17	magnetic	magnetic	ADJ
ap-6650	352	18	susceptibility	susceptibility	NOUN
ap-6650	352	19	quantities	quantity	NOUN
ap-6650	352	20	are	be	AUX
ap-6650	352	21	explicitly	explicitly	ADV
ap-6650	352	22	determined	determine	VERB
ap-6650	352	23	in	in	ADP
ap-6650	352	24	both	both	CCONJ
ap-6650	352	25	commutative	commutative	ADJ
ap-6650	352	26	and	and	CCONJ
ap-6650	352	27	noncommutative	noncommutative	ADJ
ap-6650	352	28	phase	phase	NOUN
ap-6650	352	29	-	-	PUNCT
ap-6650	352	30	spaces	space	NOUN
ap-6650	352	31	through	through	ADP
ap-6650	352	32	a	a	DET
ap-6650	352	33	semiclassical	semiclassical	ADJ
ap-6650	352	34	partition	partition	NOUN
ap-6650	352	35	function	function	NOUN
ap-6650	352	36	of	of	ADP
ap-6650	352	37	the	the	DET
ap-6650	352	38	pauli	pauli	PROPN
ap-6650	352	39	system	system	NOUN
ap-6650	352	40	of	of	ADP
ap-6650	352	41	the	the	DET
ap-6650	352	42	one	one	NUM
ap-6650	352	43	-	-	PUNCT
ap-6650	352	44	particle	particle	NOUN
ap-6650	352	45	and	and	CCONJ
ap-6650	352	46	n	n	CCONJ
ap-6650	352	47	-	-	PUNCT
ap-6650	352	48	particle	particle	NOUN
ap-6650	352	49	systems	system	NOUN
ap-6650	352	50	in	in	ADP
ap-6650	352	51	three	three	NUM
ap-6650	352	52	dimensions	dimension	NOUN
ap-6650	352	53	.	.	PUNCT
ap-6650	353	1	furthermore	furthermore	ADV
ap-6650	353	2	,	,	PUNCT
ap-6650	353	3	to	to	PART
ap-6650	353	4	see	see	VERB
ap-6650	353	5	the	the	DET
ap-6650	353	6	behaviour	behaviour	NOUN
ap-6650	353	7	of	of	ADP
ap-6650	353	8	these	these	DET
ap-6650	353	9	deformed	deform	VERB
ap-6650	353	10	quantities	quantity	NOUN
ap-6650	353	11	,	,	PUNCT
ap-6650	353	12	we	we	PRON
ap-6650	353	13	carried	carry	VERB
ap-6650	353	14	out	out	ADP
ap-6650	353	15	some	some	DET
ap-6650	353	16	special	special	ADJ
ap-6650	353	17	cases	case	NOUN
ap-6650	353	18	in	in	ADP
ap-6650	353	19	commutative	commutative	ADJ
ap-6650	353	20	and	and	CCONJ
ap-6650	353	21	noncommutative	noncommutative	ADJ
ap-6650	353	22	phase	phase	NOUN
ap-6650	353	23	-	-	PUNCT
ap-6650	353	24	spaces	space	NOUN
ap-6650	353	25	.	.	PUNCT
ap-6650	354	1	finally	finally	ADV
ap-6650	354	2	,	,	PUNCT
ap-6650	354	3	we	we	PRON
ap-6650	354	4	can	can	AUX
ap-6650	354	5	say	say	VERB
ap-6650	354	6	that	that	SCONJ
ap-6650	354	7	we	we	PRON
ap-6650	354	8	successfully	successfully	ADV
ap-6650	354	9	examined	examine	VERB
ap-6650	354	10	the	the	DET
ap-6650	354	11	influence	influence	NOUN
ap-6650	354	12	of	of	ADP
ap-6650	354	13	the	the	DET
ap-6650	354	14	noncommutativity	noncommutativity	NOUN
ap-6650	354	15	on	on	ADP
ap-6650	354	16	the	the	DET
ap-6650	354	17	problems	problem	NOUN
ap-6650	354	18	in	in	ADP
ap-6650	354	19	question	question	NOUN
ap-6650	354	20	,	,	PUNCT
ap-6650	354	21	where	where	SCONJ
ap-6650	354	22	the	the	DET
ap-6650	354	23	noncommutativity	noncommutativity	NOUN
ap-6650	354	24	was	be	AUX
ap-6650	354	25	introduced	introduce	VERB
ap-6650	354	26	using	use	VERB
ap-6650	354	27	both	both	CCONJ
ap-6650	354	28	the	the	DET
ap-6650	354	29	three	three	NUM
ap-6650	354	30	-	-	PUNCT
ap-6650	354	31	dimensional	dimensional	ADJ
ap-6650	354	32	bopp	bopp	VERB
ap-6650	354	33	-	-	PUNCT
ap-6650	354	34	shift	shift	NOUN
ap-6650	354	35	transformation	transformation	NOUN
ap-6650	354	36	and	and	CCONJ
ap-6650	354	37	the	the	DET
ap-6650	354	38	moyal	moyal	ADV
ap-6650	354	39	-	-	PUNCT
ap-6650	354	40	weyl	weyl	VERB
ap-6650	354	41	product	product	NOUN
ap-6650	354	42	.	.	PUNCT
ap-6650	355	1	furthermore	furthermore	ADV
ap-6650	355	2	,	,	PUNCT
ap-6650	355	3	the	the	DET
ap-6650	355	4	noncommutative	noncommutative	ADJ
ap-6650	355	5	corrections	correction	NOUN
ap-6650	355	6	to	to	ADP
ap-6650	355	7	the	the	DET
ap-6650	355	8	nonrelativistic	nonrelativistic	ADJ
ap-6650	355	9	pauli	pauli	PROPN
ap-6650	355	10	equation	equation	NOUN
ap-6650	355	11	and	and	CCONJ
ap-6650	355	12	the	the	DET
ap-6650	355	13	continuity	continuity	NOUN
ap-6650	355	14	equation	equation	NOUN
ap-6650	355	15	are	be	AUX
ap-6650	355	16	also	also	ADV
ap-6650	355	17	valid	valid	ADJ
ap-6650	355	18	up	up	ADP
ap-6650	355	19	to	to	ADP
ap-6650	355	20	all	all	DET
ap-6650	355	21	orders	order	NOUN
ap-6650	355	22	in	in	ADP
ap-6650	355	23	the	the	DET
ap-6650	355	24	noncommutative	noncommutative	ADJ
ap-6650	355	25	parameter	parameter	NOUN
ap-6650	355	26	.	.	PUNCT
ap-6650	356	1	our	our	PRON
ap-6650	356	2	results	result	NOUN
ap-6650	356	3	’	'	PUNCT
ap-6650	356	4	limits	limit	NOUN
ap-6650	356	5	are	be	AUX
ap-6650	356	6	in	in	ADP
ap-6650	356	7	good	good	ADJ
ap-6650	356	8	agreement	agreement	NOUN
ap-6650	356	9	with	with	ADP
ap-6650	356	10	those	those	PRON
ap-6650	356	11	obtained	obtain	VERB
ap-6650	356	12	by	by	ADP
ap-6650	356	13	other	other	ADJ
ap-6650	356	14	authors	author	NOUN
ap-6650	356	15	as	as	SCONJ
ap-6650	356	16	discussed	discuss	VERB
ap-6650	356	17	and	and	CCONJ
ap-6650	356	18	in	in	ADP
ap-6650	356	19	the	the	DET
ap-6650	356	20	literature	literature	NOUN
ap-6650	356	21	.	.	PUNCT
ap-6650	357	1	239	239	NUM
ap-6650	357	2	ilyas	ilyas	PROPN
ap-6650	357	3	haouam	haouam	PROPN
ap-6650	357	4	acta	acta	PROPN
ap-6650	357	5	polytechnica	polytechnica	PROPN
ap-6650	357	6	acknowledgements	acknowledgement	NOUN
ap-6650	357	7	the	the	DET
ap-6650	357	8	author	author	NOUN
ap-6650	357	9	would	would	AUX
ap-6650	357	10	like	like	VERB
ap-6650	357	11	to	to	PART
ap-6650	357	12	thank	thank	VERB
ap-6650	357	13	dr	dr	PROPN
ap-6650	357	14	.	.	PROPN
ap-6650	357	15	mojtaba	mojtaba	PROPN
ap-6650	357	16	najafizadeh	najafizadeh	NOUN
ap-6650	357	17	for	for	ADP
ap-6650	357	18	his	his	PRON
ap-6650	357	19	valuable	valuable	ADJ
ap-6650	357	20	discussion	discussion	NOUN
ap-6650	357	21	on	on	ADP
ap-6650	357	22	the	the	DET
ap-6650	357	23	classical	classical	ADJ
ap-6650	357	24	partition	partition	NOUN
ap-6650	357	25	function	function	NOUN
ap-6650	357	26	.	.	PUNCT
ap-6650	358	1	references	reference	NOUN
ap-6650	358	2	[	[	X
ap-6650	358	3	1	1	NUM
ap-6650	358	4	]	]	PUNCT
ap-6650	358	5	w.	w.	PROPN
ap-6650	358	6	greiner	greiner	PROPN
ap-6650	358	7	.	.	PUNCT
ap-6650	358	8	quantum	quantum	PROPN
ap-6650	358	9	mechanics	mechanic	NOUN
ap-6650	358	10	:	:	PUNCT
ap-6650	358	11	an	an	DET
ap-6650	358	12	introduction	introduction	NOUN
ap-6650	358	13	.	.	PUNCT
ap-6650	359	1	springer	springer	NOUN
ap-6650	359	2	,	,	PUNCT
ap-6650	359	3	berlin	berlin	PROPN
ap-6650	359	4	,	,	PUNCT
ap-6650	359	5	4th	4th	ADJ
ap-6650	359	6	edn	edn	NOUN
ap-6650	359	7	.	.	PUNCT
ap-6650	359	8	,	,	PUNCT
ap-6650	359	9	2001	2001	NUM
ap-6650	359	10	.	.	PUNCT
ap-6650	360	1	[	[	X
ap-6650	360	2	2	2	X
ap-6650	360	3	]	]	PUNCT
ap-6650	360	4	e.	e.	PROPN
ap-6650	360	5	ikenberry	ikenberry	PROPN
ap-6650	360	6	.	.	PUNCT
ap-6650	361	1	quantum	quantum	ADJ
ap-6650	361	2	mechanics	mechanic	NOUN
ap-6650	361	3	for	for	ADP
ap-6650	361	4	mathematicians	mathematician	NOUN
ap-6650	361	5	and	and	CCONJ
ap-6650	361	6	physicists	physicist	NOUN
ap-6650	361	7	.	.	PUNCT
ap-6650	362	1	oxford	oxford	PROPN
ap-6650	362	2	,	,	PUNCT
ap-6650	362	3	new	new	PROPN
ap-6650	362	4	york	york	PROPN
ap-6650	362	5	,	,	PUNCT
ap-6650	362	6	1st	1st	ADJ
ap-6650	362	7	edn	edn	PROPN
ap-6650	362	8	.	.	PUNCT
ap-6650	362	9	,	,	PUNCT
ap-6650	362	10	1962	1962	NUM
ap-6650	362	11	.	.	PUNCT
ap-6650	363	1	[	[	X
ap-6650	363	2	3	3	NUM
ap-6650	363	3	]	]	PUNCT
ap-6650	363	4	a.	a.	NOUN
ap-6650	363	5	galindo	galindo	PROPN
ap-6650	363	6	,	,	PUNCT
ap-6650	363	7	c.	c.	PROPN
ap-6650	363	8	sanchez	sanchez	PROPN
ap-6650	363	9	del	del	PROPN
ap-6650	363	10	rio	rio	PROPN
ap-6650	363	11	.	.	PUNCT
ap-6650	364	1	intrinsic	intrinsic	PROPN
ap-6650	364	2	magnetic	magnetic	ADJ
ap-6650	364	3	moment	moment	NOUN
ap-6650	364	4	as	as	ADP
ap-6650	364	5	a	a	DET
ap-6650	364	6	nonrelativistic	nonrelativistic	ADJ
ap-6650	364	7	phenomenon	phenomenon	NOUN
ap-6650	364	8	.	.	PUNCT
ap-6650	365	1	american	american	ADJ
ap-6650	365	2	journal	journal	PROPN
ap-6650	365	3	of	of	ADP
ap-6650	365	4	physics	physics	PROPN
ap-6650	365	5	29(9):582	29(9):582	PROPN
ap-6650	365	6	–	–	PUNCT
ap-6650	365	7	584	584	NUM
ap-6650	365	8	,	,	PUNCT
ap-6650	365	9	1961	1961	NUM
ap-6650	365	10	.	.	PUNCT
ap-6650	366	1	doi:10.1119/1.1937856	doi:10.1119/1.1937856	NOUN
ap-6650	366	2	.	.	PUNCT
ap-6650	367	1	[	[	X
ap-6650	367	2	4	4	NUM
ap-6650	367	3	]	]	PUNCT
ap-6650	367	4	m.	m.	NOUN
ap-6650	367	5	nowakowski	nowakowski	PROPN
ap-6650	367	6	.	.	PUNCT
ap-6650	368	1	the	the	DET
ap-6650	368	2	quantum	quantum	PROPN
ap-6650	368	3	mechanical	mechanical	ADJ
ap-6650	368	4	current	current	NOUN
ap-6650	368	5	of	of	ADP
ap-6650	368	6	the	the	DET
ap-6650	368	7	pauli	pauli	PROPN
ap-6650	368	8	equation	equation	NOUN
ap-6650	368	9	.	.	PUNCT
ap-6650	369	1	american	american	PROPN
ap-6650	369	2	journal	journal	PROPN
ap-6650	369	3	of	of	ADP
ap-6650	369	4	physics	physics	PROPN
ap-6650	369	5	67(10):916	67(10):916	NUM
ap-6650	369	6	–	–	PUNCT
ap-6650	369	7	919	919	NUM
ap-6650	369	8	,	,	PUNCT
ap-6650	369	9	1999	1999	NUM
ap-6650	369	10	.	.	PUNCT
ap-6650	370	1	doi:10.1119/1.19149	doi:10.1119/1.19149	NOUN
ap-6650	370	2	.	.	PUNCT
ap-6650	371	1	[	[	X
ap-6650	371	2	5	5	X
ap-6650	371	3	]	]	PUNCT
ap-6650	371	4	g.	g.	PROPN
ap-6650	371	5	w.	w.	PROPN
ap-6650	371	6	parker	parker	PROPN
ap-6650	371	7	.	.	PUNCT
ap-6650	372	1	spin	spin	VERB
ap-6650	372	2	current	current	ADJ
ap-6650	372	3	density	density	NOUN
ap-6650	372	4	and	and	CCONJ
ap-6650	372	5	the	the	DET
ap-6650	372	6	hyperfine	hyperfine	ADJ
ap-6650	372	7	interaction	interaction	NOUN
ap-6650	372	8	in	in	ADP
ap-6650	372	9	hydrogen	hydrogen	NOUN
ap-6650	372	10	.	.	PUNCT
ap-6650	373	1	american	american	PROPN
ap-6650	373	2	journal	journal	PROPN
ap-6650	373	3	of	of	ADP
ap-6650	373	4	physics	physics	PROPN
ap-6650	373	5	52(1):36	52(1):36	PROPN
ap-6650	373	6	–	–	PUNCT
ap-6650	373	7	39	39	NUM
ap-6650	373	8	,	,	PUNCT
ap-6650	373	9	1984	1984	NUM
ap-6650	373	10	.	.	PUNCT
ap-6650	374	1	doi:10.1119/1.13846	doi:10.1119/1.13846	NOUN
ap-6650	374	2	.	.	PUNCT
ap-6650	375	1	[	[	X
ap-6650	375	2	6	6	NUM
ap-6650	375	3	]	]	PUNCT
ap-6650	375	4	m.	m.	NOUN
ap-6650	375	5	s.	s.	PROPN
ap-6650	375	6	shikakhwa	shikakhwa	PROPN
ap-6650	375	7	,	,	PUNCT
ap-6650	375	8	s.	s.	PROPN
ap-6650	375	9	turgut	turgut	PROPN
ap-6650	375	10	,	,	PUNCT
ap-6650	375	11	n.	n.	PROPN
ap-6650	375	12	k.	k.	PROPN
ap-6650	375	13	pak	pak	PROPN
ap-6650	375	14	.	.	PUNCT
ap-6650	376	1	derivation	derivation	NOUN
ap-6650	376	2	of	of	ADP
ap-6650	376	3	the	the	DET
ap-6650	376	4	magnetization	magnetization	NOUN
ap-6650	376	5	current	current	ADJ
ap-6650	376	6	from	from	ADP
ap-6650	376	7	the	the	DET
ap-6650	376	8	non	non	ADJ
ap-6650	376	9	-	-	ADJ
ap-6650	376	10	relativistic	relativistic	ADJ
ap-6650	376	11	pauli	pauli	PROPN
ap-6650	376	12	equation	equation	NOUN
ap-6650	376	13	:	:	PUNCT
ap-6650	376	14	a	a	DET
ap-6650	376	15	comment	comment	NOUN
ap-6650	376	16	on	on	ADP
ap-6650	376	17	“	"	PUNCT
ap-6650	376	18	the	the	DET
ap-6650	376	19	quantum	quantum	ADJ
ap-6650	376	20	mechanical	mechanical	ADJ
ap-6650	376	21	current	current	NOUN
ap-6650	376	22	of	of	ADP
ap-6650	376	23	the	the	DET
ap-6650	376	24	pauli	pauli	PROPN
ap-6650	376	25	equation	equation	NOUN
ap-6650	376	26	”	"	PUNCT
ap-6650	376	27	by	by	ADP
ap-6650	376	28	marek	marek	PROPN
ap-6650	376	29	nowakowski	nowakowski	PROPN
ap-6650	376	30	.	.	PUNCT
ap-6650	377	1	american	american	PROPN
ap-6650	377	2	journal	journal	PROPN
ap-6650	377	3	of	of	ADP
ap-6650	377	4	physics	physics	PROPN
ap-6650	377	5	79(11):1177	79(11):1177	NUM
ap-6650	377	6	–	–	PUNCT
ap-6650	377	7	1179	1179	NUM
ap-6650	377	8	,	,	PUNCT
ap-6650	377	9	2011	2011	NUM
ap-6650	377	10	.	.	PUNCT
ap-6650	378	1	doi:10.1119/1.3630931	doi:10.1119/1.3630931	NOUN
ap-6650	378	2	.	.	PUNCT
ap-6650	379	1	[	[	X
ap-6650	379	2	7	7	X
ap-6650	379	3	]	]	X
ap-6650	379	4	w.	w.	PROPN
ap-6650	379	5	b.	b.	PROPN
ap-6650	379	6	hodge	hodge	PROPN
ap-6650	379	7	,	,	PUNCT
ap-6650	379	8	s.	s.	PROPN
ap-6650	379	9	v.	v.	PROPN
ap-6650	379	10	migirditch	migirditch	PROPN
ap-6650	379	11	,	,	PUNCT
ap-6650	379	12	w.	w.	PROPN
ap-6650	379	13	c.	c.	PROPN
ap-6650	379	14	kerr	kerr	PROPN
ap-6650	379	15	.	.	PUNCT
ap-6650	380	1	electron	electron	NOUN
ap-6650	380	2	spin	spin	NOUN
ap-6650	380	3	and	and	CCONJ
ap-6650	380	4	probability	probability	VERB
ap-6650	380	5	current	current	ADJ
ap-6650	380	6	density	density	NOUN
ap-6650	380	7	in	in	ADP
ap-6650	380	8	quantum	quantum	ADJ
ap-6650	380	9	mechanics	mechanic	NOUN
ap-6650	380	10	.	.	PUNCT
ap-6650	381	1	american	american	PROPN
ap-6650	381	2	journal	journal	PROPN
ap-6650	381	3	of	of	ADP
ap-6650	381	4	physics	physics	PROPN
ap-6650	381	5	82(7):681	82(7):681	PROPN
ap-6650	381	6	–	–	PUNCT
ap-6650	381	7	690	690	NUM
ap-6650	381	8	,	,	PUNCT
ap-6650	381	9	2014	2014	NUM
ap-6650	381	10	.	.	PUNCT
ap-6650	382	1	doi:10.1119/1.4868094	doi:10.1119/1.4868094	PROPN
ap-6650	382	2	.	.	PUNCT
ap-6650	383	1	[	[	X
ap-6650	383	2	8	8	X
ap-6650	383	3	]	]	PUNCT
ap-6650	383	4	j.	j.	PROPN
ap-6650	383	5	j.	j.	PROPN
ap-6650	383	6	sakurai	sakurai	PROPN
ap-6650	383	7	.	.	PUNCT
ap-6650	384	1	advanced	advanced	ADJ
ap-6650	384	2	quantum	quantum	ADJ
ap-6650	384	3	mechanics	mechanic	NOUN
ap-6650	384	4	.	.	PUNCT
ap-6650	385	1	reading	reading	NOUN
ap-6650	385	2	,	,	PUNCT
ap-6650	385	3	mass	mass	PROPN
ap-6650	385	4	.	.	PUNCT
ap-6650	385	5	:	:	PUNCT
ap-6650	386	1	addison	addison	PROPN
ap-6650	386	2	-	-	PUNCT
ap-6650	386	3	wesley	wesley	PROPN
ap-6650	386	4	pub	pub	PROPN
ap-6650	386	5	.	.	PUNCT
ap-6650	387	1	co.	co.	PROPN
ap-6650	387	2	,	,	PUNCT
ap-6650	387	3	1967	1967	NUM
ap-6650	387	4	.	.	PUNCT
ap-6650	388	1	[	[	X
ap-6650	388	2	9	9	NUM
ap-6650	388	3	]	]	SYM
ap-6650	388	4	i.	i.	PROPN
ap-6650	388	5	haouam	haouam	PROPN
ap-6650	388	6	,	,	PUNCT
ap-6650	388	7	l.	l.	PROPN
ap-6650	388	8	chetouani	chetouani	PROPN
ap-6650	388	9	.	.	PUNCT
ap-6650	389	1	the	the	DET
ap-6650	389	2	foldy	foldy	NOUN
ap-6650	389	3	-	-	PUNCT
ap-6650	389	4	wouthuysen	wouthuysen	NOUN
ap-6650	389	5	transformation	transformation	NOUN
ap-6650	389	6	of	of	ADP
ap-6650	389	7	the	the	DET
ap-6650	389	8	dirac	dirac	NOUN
ap-6650	389	9	equation	equation	NOUN
ap-6650	389	10	in	in	ADP
ap-6650	389	11	noncommutative	noncommutative	ADJ
ap-6650	389	12	phase	phase	NOUN
ap-6650	389	13	-	-	PUNCT
ap-6650	389	14	space	space	NOUN
ap-6650	389	15	.	.	PUNCT
ap-6650	390	1	journal	journal	NOUN
ap-6650	390	2	of	of	ADP
ap-6650	390	3	modern	modern	ADJ
ap-6650	390	4	physics	physics	NOUN
ap-6650	390	5	9(11):2021	9(11):2021	NUM
ap-6650	390	6	–	–	PUNCT
ap-6650	390	7	2034	2034	NUM
ap-6650	390	8	,	,	PUNCT
ap-6650	390	9	2018	2018	NUM
ap-6650	390	10	.	.	PUNCT
ap-6650	391	1	doi:10.4236	doi:10.4236	PROPN
ap-6650	391	2	/	/	SYM
ap-6650	391	3	jmp.2018.911127	jmp.2018.911127	PROPN
ap-6650	391	4	.	.	PUNCT
ap-6650	392	1	[	[	X
ap-6650	392	2	10	10	NUM
ap-6650	392	3	]	]	X
ap-6650	392	4	i.	i.	PROPN
ap-6650	392	5	haouam	haouam	PROPN
ap-6650	392	6	.	.	PUNCT
ap-6650	393	1	the	the	DET
ap-6650	393	2	phase	phase	NOUN
ap-6650	393	3	-	-	PUNCT
ap-6650	393	4	space	space	NOUN
ap-6650	393	5	noncommutativity	noncommutativity	NOUN
ap-6650	393	6	effect	effect	NOUN
ap-6650	393	7	on	on	ADP
ap-6650	393	8	the	the	DET
ap-6650	393	9	large	large	ADJ
ap-6650	393	10	and	and	CCONJ
ap-6650	393	11	small	small	ADJ
ap-6650	393	12	wavefunction	wavefunction	NOUN
ap-6650	393	13	components	component	NOUN
ap-6650	393	14	approach	approach	NOUN
ap-6650	393	15	at	at	ADP
ap-6650	393	16	dirac	dirac	NOUN
ap-6650	393	17	equation	equation	NOUN
ap-6650	393	18	.	.	PUNCT
ap-6650	394	1	open	open	ADJ
ap-6650	394	2	access	access	NOUN
ap-6650	394	3	library	library	PROPN
ap-6650	394	4	journal	journal	NOUN
ap-6650	394	5	5	5	NUM
ap-6650	394	6	:	:	PUNCT
ap-6650	394	7	e4108	e4108	NOUN
ap-6650	394	8	,	,	PUNCT
ap-6650	394	9	2018	2018	NUM
ap-6650	394	10	.	.	PUNCT
ap-6650	395	1	doi:10.4236	doi:10.4236	PROPN
ap-6650	395	2	/	/	SYM
ap-6650	395	3	oalib.1104108	oalib.1104108	PROPN
ap-6650	395	4	.	.	PUNCT
ap-6650	396	1	[	[	X
ap-6650	396	2	11	11	NUM
ap-6650	396	3	]	]	PUNCT
ap-6650	396	4	j.	j.	PROPN
ap-6650	396	5	d.	d.	PROPN
ap-6650	396	6	bjorken	bjorken	VERB
ap-6650	396	7	,	,	PUNCT
ap-6650	396	8	s.	s.	PROPN
ap-6650	396	9	drell	drell	PROPN
ap-6650	396	10	.	.	PUNCT
ap-6650	397	1	relativistic	relativistic	ADJ
ap-6650	397	2	quantum	quantum	ADJ
ap-6650	397	3	mechanics	mechanic	NOUN
ap-6650	397	4	.	.	PUNCT
ap-6650	398	1	mcgraw	mcgraw	PROPN
ap-6650	398	2	-	-	PUNCT
ap-6650	398	3	hill	hill	PROPN
ap-6650	398	4	,	,	PUNCT
ap-6650	398	5	new	new	PROPN
ap-6650	398	6	york	york	PROPN
ap-6650	398	7	,	,	PUNCT
ap-6650	398	8	1964	1964	NUM
ap-6650	398	9	.	.	PUNCT
ap-6650	399	1	[	[	X
ap-6650	399	2	12	12	NUM
ap-6650	399	3	]	]	PUNCT
ap-6650	399	4	l.	l.	PROPN
ap-6650	399	5	l.	l.	PROPN
ap-6650	399	6	foldy	foldy	PROPN
ap-6650	399	7	,	,	PUNCT
ap-6650	399	8	s.	s.	PROPN
ap-6650	399	9	a.	a.	PROPN
ap-6650	399	10	wouthuysen	wouthuysen	PROPN
ap-6650	399	11	.	.	PUNCT
ap-6650	400	1	on	on	ADP
ap-6650	400	2	the	the	DET
ap-6650	400	3	dirac	dirac	NOUN
ap-6650	400	4	theory	theory	NOUN
ap-6650	400	5	of	of	ADP
ap-6650	400	6	spin	spin	NOUN
ap-6650	400	7	1/2	1/2	NUM
ap-6650	400	8	particles	particle	NOUN
ap-6650	400	9	and	and	CCONJ
ap-6650	400	10	its	its	PRON
ap-6650	400	11	non	non	ADJ
ap-6650	400	12	-	-	ADJ
ap-6650	400	13	relativistic	relativistic	ADJ
ap-6650	400	14	limit	limit	NOUN
ap-6650	400	15	.	.	PUNCT
ap-6650	401	1	physical	physical	ADJ
ap-6650	401	2	review	review	NOUN
ap-6650	401	3	78(1):29	78(1):29	NUM
ap-6650	401	4	–	–	PUNCT
ap-6650	401	5	36	36	NUM
ap-6650	401	6	,	,	PUNCT
ap-6650	401	7	1950	1950	NUM
ap-6650	401	8	.	.	PUNCT
ap-6650	402	1	doi:10.1103	doi:10.1103	NOUN
ap-6650	402	2	/	/	SYM
ap-6650	402	3	physrev.78.29	physrev.78.29	NOUN
ap-6650	402	4	.	.	PUNCT
ap-6650	403	1	[	[	X
ap-6650	403	2	13	13	NUM
ap-6650	403	3	]	]	PUNCT
ap-6650	403	4	w.	w.	PROPN
ap-6650	403	5	pauli	pauli	PROPN
ap-6650	403	6	.	.	PUNCT
ap-6650	404	1	zur	zur	PROPN
ap-6650	404	2	quantenmechanik	quantenmechanik	X
ap-6650	404	3	des	des	X
ap-6650	404	4	magnetischen	magnetischen	PROPN
ap-6650	404	5	elektrons	elektron	NOUN
ap-6650	404	6	.	.	PUNCT
ap-6650	405	1	zeitschrift	zeitschrift	PROPN
ap-6650	405	2	für	für	PROPN
ap-6650	405	3	physik	physik	PROPN
ap-6650	405	4	43:601	43:601	NUM
ap-6650	405	5	–	–	PUNCT
ap-6650	405	6	623	623	NUM
ap-6650	405	7	,	,	PUNCT
ap-6650	405	8	1927	1927	NUM
ap-6650	405	9	.	.	PUNCT
ap-6650	406	1	doi:10.1103	doi:10.1103	NOUN
ap-6650	406	2	/	/	SYM
ap-6650	406	3	physrev.78.29	physrev.78.29	NOUN
ap-6650	406	4	.	.	PUNCT
ap-6650	407	1	[	[	X
ap-6650	407	2	14	14	NUM
ap-6650	407	3	]	]	X
ap-6650	407	4	g.	g.	PROPN
ap-6650	407	5	s	s	PROPN
ap-6650	407	6	,	,	PUNCT
ap-6650	407	7	g.	g.	PROPN
ap-6650	407	8	e.	e.	PROPN
ap-6650	407	9	uhlenbeck	uhlenbeck	PROPN
ap-6650	407	10	.	.	PUNCT
ap-6650	408	1	opmerking	opmerke	VERB
ap-6650	408	2	over	over	ADP
ap-6650	408	3	de	de	X
ap-6650	408	4	spectra	spectra	ADJ
ap-6650	408	5	van	van	PROPN
ap-6650	408	6	waterstof	waterstof	NOUN
ap-6650	408	7	en	en	ADP
ap-6650	408	8	helium	helium	NOUN
ap-6650	408	9	.	.	PUNCT
ap-6650	409	1	physica	physica	NOUN
ap-6650	409	2	5:266	5:266	NUM
ap-6650	409	3	–	–	PUNCT
ap-6650	409	4	270	270	NUM
ap-6650	409	5	,	,	PUNCT
ap-6650	409	6	1925	1925	NUM
ap-6650	409	7	.	.	PUNCT
ap-6650	410	1	[	[	X
ap-6650	410	2	15	15	NUM
ap-6650	410	3	]	]	X
ap-6650	410	4	g.	g.	PROPN
ap-6650	410	5	e.	e.	PROPN
ap-6650	410	6	uhlenbeck	uhlenbeck	PROPN
ap-6650	410	7	,	,	PUNCT
ap-6650	410	8	s.	s.	PROPN
ap-6650	410	9	goudsmit	goudsmit	PROPN
ap-6650	410	10	.	.	PUNCT
ap-6650	411	1	ersetzung	ersetzung	PROPN
ap-6650	411	2	der	der	PROPN
ap-6650	411	3	hypothese	hypothese	PROPN
ap-6650	411	4	vom	vom	VERB
ap-6650	411	5	unmechanischen	unmechanischen	PROPN
ap-6650	411	6	zwang	zwang	PROPN
ap-6650	411	7	durch	durch	PROPN
ap-6650	411	8	eine	eine	PROPN
ap-6650	411	9	forderung	forderung	PROPN
ap-6650	411	10	bezüglich	bezüglich	PROPN
ap-6650	411	11	des	des	PROPN
ap-6650	411	12	inneren	inneren	PROPN
ap-6650	411	13	verhaltens	verhaltens	PROPN
ap-6650	411	14	jedes	jede	VERB
ap-6650	411	15	einzelnen	einzelnen	PROPN
ap-6650	411	16	elektrons	elektron	NOUN
ap-6650	411	17	.	.	PUNCT
ap-6650	412	1	die	die	VERB
ap-6650	412	2	naturwissenschaften	naturwissenschaften	NOUN
ap-6650	412	3	13(47	13(47	NUM
ap-6650	412	4	)	)	PUNCT
ap-6650	412	5	.	.	PUNCT
ap-6650	413	1	[	[	X
ap-6650	413	2	16	16	NUM
ap-6650	413	3	]	]	X
ap-6650	413	4	p.	p.	NOUN
ap-6650	413	5	a.	a.	PROPN
ap-6650	413	6	m.	m.	PROPN
ap-6650	413	7	dirac	dirac	PROPN
ap-6650	413	8	,	,	PUNCT
ap-6650	413	9	r.	r.	PROPN
ap-6650	413	10	h.	h.	PROPN
ap-6650	413	11	fowler	fowler	PROPN
ap-6650	413	12	.	.	PUNCT
ap-6650	414	1	the	the	DET
ap-6650	414	2	quantum	quantum	PROPN
ap-6650	414	3	theory	theory	NOUN
ap-6650	414	4	of	of	ADP
ap-6650	414	5	the	the	DET
ap-6650	414	6	electron	electron	NOUN
ap-6650	414	7	.	.	PUNCT
ap-6650	415	1	proceedings	proceeding	NOUN
ap-6650	415	2	of	of	ADP
ap-6650	415	3	the	the	DET
ap-6650	415	4	royal	royal	ADJ
ap-6650	415	5	society	society	NOUN
ap-6650	415	6	of	of	ADP
ap-6650	415	7	london	london	PROPN
ap-6650	415	8	series	series	PROPN
ap-6650	415	9	a	a	PROPN
ap-6650	415	10	,	,	PUNCT
ap-6650	415	11	containing	contain	VERB
ap-6650	415	12	papers	paper	NOUN
ap-6650	415	13	of	of	ADP
ap-6650	415	14	a	a	DET
ap-6650	415	15	mathematical	mathematical	ADJ
ap-6650	415	16	and	and	CCONJ
ap-6650	415	17	physical	physical	ADJ
ap-6650	415	18	character	character	NOUN
ap-6650	415	19	117(778):610	117(778):610	PROPN
ap-6650	415	20	–	–	PUNCT
ap-6650	415	21	624	624	NUM
ap-6650	415	22	,	,	PUNCT
ap-6650	415	23	1928	1928	NUM
ap-6650	415	24	.	.	PUNCT
ap-6650	416	1	doi:10.1098	doi:10.1098	PROPN
ap-6650	416	2	/	/	SYM
ap-6650	416	3	rspa.1928.0023	rspa.1928.0023	NUM
ap-6650	416	4	.	.	PUNCT
ap-6650	417	1	[	[	X
ap-6650	417	2	17	17	NUM
ap-6650	417	3	]	]	PUNCT
ap-6650	417	4	a.	a.	NOUN
ap-6650	417	5	connes	conne	NOUN
ap-6650	417	6	.	.	PUNCT
ap-6650	418	1	non	non	ADJ
ap-6650	418	2	-	-	ADJ
ap-6650	418	3	commutative	commutative	ADJ
ap-6650	418	4	differential	differential	NOUN
ap-6650	418	5	geometry	geometry	NOUN
ap-6650	418	6	.	.	PUNCT
ap-6650	419	1	publications	publication	NOUN
ap-6650	419	2	mathématiques	mathématiques	PROPN
ap-6650	419	3	de	de	X
ap-6650	419	4	l’institut	l’institut	PROPN
ap-6650	419	5	des	des	PROPN
ap-6650	419	6	hautes	haute	NOUN
ap-6650	419	7	études	étude	NOUN
ap-6650	419	8	scientifiques	scientifique	NOUN
ap-6650	419	9	62(1):41	62(1):41	NUM
ap-6650	419	10	–	–	PUNCT
ap-6650	419	11	144	144	NUM
ap-6650	419	12	,	,	PUNCT
ap-6650	419	13	1985	1985	NUM
ap-6650	419	14	.	.	PUNCT
ap-6650	420	1	doi:10.1007	doi:10.1007	NOUN
ap-6650	420	2	/	/	SYM
ap-6650	420	3	bf02698807	bf02698807	ADJ
ap-6650	420	4	.	.	PUNCT
ap-6650	421	1	[	[	X
ap-6650	421	2	18	18	NUM
ap-6650	421	3	]	]	X
ap-6650	421	4	s.	s.	PROPN
ap-6650	421	5	l.	l.	PROPN
ap-6650	421	6	woronowicz	woronowicz	PROPN
ap-6650	421	7	.	.	PUNCT
ap-6650	422	1	twisted	twisted	ADJ
ap-6650	422	2	su	su	PROPN
ap-6650	422	3	(	(	PUNCT
ap-6650	422	4	2	2	NUM
ap-6650	422	5	)	)	PUNCT
ap-6650	422	6	group	group	NOUN
ap-6650	422	7	.	.	PUNCT
ap-6650	423	1	an	an	DET
ap-6650	423	2	example	example	NOUN
ap-6650	423	3	of	of	ADP
ap-6650	423	4	a	a	DET
ap-6650	423	5	non	non	ADJ
ap-6650	423	6	-	-	ADJ
ap-6650	423	7	commutative	commutative	ADJ
ap-6650	423	8	differential	differential	ADJ
ap-6650	423	9	calculus	calculus	NOUN
ap-6650	423	10	.	.	PUNCT
ap-6650	424	1	publications	publication	NOUN
ap-6650	424	2	of	of	ADP
ap-6650	424	3	the	the	DET
ap-6650	424	4	research	research	PROPN
ap-6650	424	5	institute	institute	NOUN
ap-6650	424	6	for	for	ADP
ap-6650	424	7	mathematical	mathematical	ADJ
ap-6650	424	8	sciences	science	NOUN
ap-6650	424	9	23(1):117	23(1):117	NUM
ap-6650	424	10	–	–	PUNCT
ap-6650	424	11	181	181	NUM
ap-6650	424	12	,	,	PUNCT
ap-6650	424	13	1987	1987	NUM
ap-6650	424	14	.	.	PUNCT
ap-6650	425	1	doi:10.2977	doi:10.2977	NOUN
ap-6650	425	2	/	/	SYM
ap-6650	425	3	prims/1195176848	prims/1195176848	NOUN
ap-6650	425	4	.	.	PUNCT
ap-6650	426	1	[	[	X
ap-6650	426	2	19	19	NUM
ap-6650	426	3	]	]	PUNCT
ap-6650	426	4	a.	a.	NOUN
ap-6650	426	5	connes	conne	NOUN
ap-6650	426	6	,	,	PUNCT
ap-6650	426	7	m.	m.	PROPN
ap-6650	426	8	r.	r.	PROPN
ap-6650	426	9	douglas	douglas	PROPN
ap-6650	426	10	,	,	PUNCT
ap-6650	426	11	a.	a.	NOUN
ap-6650	426	12	schwarz	schwarz	PROPN
ap-6650	426	13	.	.	PUNCT
ap-6650	426	14	noncommutative	noncommutative	ADJ
ap-6650	426	15	geometry	geometry	NOUN
ap-6650	426	16	and	and	CCONJ
ap-6650	426	17	matrix	matrix	NOUN
ap-6650	426	18	theory	theory	NOUN
ap-6650	426	19	.	.	PUNCT
ap-6650	427	1	journal	journal	NOUN
ap-6650	427	2	of	of	ADP
ap-6650	427	3	high	high	ADJ
ap-6650	427	4	energy	energy	NOUN
ap-6650	427	5	physics	physics	NOUN
ap-6650	427	6	1998(jhep02):003	1998(jhep02):003	NUM
ap-6650	427	7	,	,	PUNCT
ap-6650	427	8	1998	1998	NUM
ap-6650	427	9	.	.	PUNCT
ap-6650	428	1	doi:10.1088/1126	doi:10.1088/1126	NOUN
ap-6650	428	2	-	-	PUNCT
ap-6650	428	3	6708/1998/02/003	6708/1998/02/003	NUM
ap-6650	428	4	.	.	PUNCT
ap-6650	429	1	[	[	X
ap-6650	429	2	20	20	NUM
ap-6650	429	3	]	]	PUNCT
ap-6650	429	4	m.	m.	NOUN
ap-6650	429	5	m.	m.	NOUN
ap-6650	429	6	sheikh	sheikh	PROPN
ap-6650	429	7	-	-	PUNCT
ap-6650	429	8	jabbari	jabbari	NOUN
ap-6650	429	9	.	.	PUNCT
ap-6650	430	1	c	c	X
ap-6650	430	2	,	,	PUNCT
ap-6650	430	3	p	p	X
ap-6650	430	4	,	,	PUNCT
ap-6650	430	5	and	and	CCONJ
ap-6650	430	6	t	t	PROPN
ap-6650	430	7	invariance	invariance	NOUN
ap-6650	430	8	of	of	ADP
ap-6650	430	9	noncommutative	noncommutative	ADJ
ap-6650	430	10	gauge	gauge	NOUN
ap-6650	430	11	theories	theory	NOUN
ap-6650	430	12	.	.	PUNCT
ap-6650	431	1	physical	physical	ADJ
ap-6650	431	2	review	review	NOUN
ap-6650	431	3	letters	letter	NOUN
ap-6650	431	4	84(23):5265	84(23):5265	NUM
ap-6650	431	5	–	–	PUNCT
ap-6650	431	6	5268	5268	NUM
ap-6650	431	7	,	,	PUNCT
ap-6650	431	8	2000	2000	NUM
ap-6650	431	9	.	.	PUNCT
ap-6650	432	1	doi:10.1103	doi:10.1103	NOUN
ap-6650	432	2	/	/	SYM
ap-6650	432	3	physrevlett.84.5265	physrevlett.84.5265	NOUN
ap-6650	432	4	.	.	PUNCT
ap-6650	433	1	[	[	X
ap-6650	433	2	21	21	NUM
ap-6650	433	3	]	]	X
ap-6650	433	4	e.	e.	PROPN
ap-6650	433	5	di	di	PROPN
ap-6650	433	6	grezia	grezia	PROPN
ap-6650	433	7	,	,	PUNCT
ap-6650	433	8	g.	g.	PROPN
ap-6650	433	9	esposito	esposito	PROPN
ap-6650	433	10	,	,	PUNCT
ap-6650	433	11	a.	a.	NOUN
ap-6650	433	12	funel	funel	PROPN
ap-6650	433	13	,	,	PUNCT
ap-6650	433	14	et	et	PROPN
ap-6650	433	15	al	al	PROPN
ap-6650	433	16	.	.	PROPN
ap-6650	433	17	spacetime	spacetime	PROPN
ap-6650	433	18	noncommutativity	noncommutativity	PROPN
ap-6650	433	19	and	and	CCONJ
ap-6650	433	20	antisymmetric	antisymmetric	ADJ
ap-6650	433	21	tensor	tensor	NOUN
ap-6650	433	22	dynamics	dynamic	NOUN
ap-6650	433	23	in	in	ADP
ap-6650	433	24	the	the	DET
ap-6650	433	25	early	early	ADJ
ap-6650	433	26	universe	universe	NOUN
ap-6650	433	27	.	.	PUNCT
ap-6650	434	1	physical	physical	ADJ
ap-6650	434	2	review	review	PROPN
ap-6650	434	3	d	d	PROPN
ap-6650	434	4	68(10):105012	68(10):105012	PROPN
ap-6650	434	5	,	,	PUNCT
ap-6650	434	6	2003	2003	NUM
ap-6650	434	7	.	.	PUNCT
ap-6650	435	1	doi:10.1103	doi:10.1103	NOUN
ap-6650	435	2	/	/	SYM
ap-6650	435	3	physrevd.68.105012	physrevd.68.105012	NOUN
ap-6650	435	4	.	.	PUNCT
ap-6650	436	1	[	[	X
ap-6650	436	2	22	22	NUM
ap-6650	436	3	]	]	X
ap-6650	436	4	o.	o.	PROPN
ap-6650	436	5	bertolami	bertolami	PROPN
ap-6650	436	6	,	,	PUNCT
ap-6650	436	7	j.	j.	PROPN
ap-6650	436	8	g.	g.	PROPN
ap-6650	436	9	rosa	rosa	PROPN
ap-6650	436	10	,	,	PUNCT
ap-6650	436	11	c.	c.	PROPN
ap-6650	436	12	m.	m.	PROPN
ap-6650	436	13	l.	l.	PROPN
ap-6650	436	14	de	de	PROPN
ap-6650	436	15	aragão	aragão	PROPN
ap-6650	436	16	,	,	PUNCT
ap-6650	436	17	et	et	PROPN
ap-6650	436	18	al	al	PROPN
ap-6650	436	19	.	.	PUNCT
ap-6650	436	20	noncommutative	noncommutative	PROPN
ap-6650	436	21	gravitational	gravitational	ADJ
ap-6650	436	22	quantum	quantum	NOUN
ap-6650	436	23	well	well	NOUN
ap-6650	436	24	.	.	PUNCT
ap-6650	437	1	physical	physical	ADJ
ap-6650	437	2	review	review	PROPN
ap-6650	438	1	d	d	PROPN
ap-6650	438	2	72(2):025010	72(2):025010	NUM
ap-6650	438	3	,	,	PUNCT
ap-6650	438	4	2005	2005	NUM
ap-6650	438	5	.	.	PUNCT
ap-6650	439	1	doi:10.1103	doi:10.1103	NOUN
ap-6650	439	2	/	/	SYM
ap-6650	439	3	physrevd.72.025010	physrevd.72.025010	NOUN
ap-6650	439	4	.	.	PUNCT
ap-6650	440	1	[	[	X
ap-6650	440	2	23	23	NUM
ap-6650	440	3	]	]	PUNCT
ap-6650	440	4	a.	a.	NOUN
ap-6650	440	5	das	das	PROPN
ap-6650	440	6	,	,	PUNCT
ap-6650	440	7	h.	h.	PROPN
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ap-6650	440	10	j.	j.	PROPN
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ap-6650	440	12	,	,	PUNCT
ap-6650	440	13	f.	f.	PROPN
ap-6650	440	14	méndez	méndez	PROPN
ap-6650	440	15	.	.	PUNCT
ap-6650	441	1	non	non	ADJ
ap-6650	441	2	-	-	ADJ
ap-6650	441	3	commutative	commutative	ADJ
ap-6650	441	4	supersymmetric	supersymmetric	ADJ
ap-6650	441	5	quantum	quantum	NOUN
ap-6650	441	6	mechanics	mechanic	NOUN
ap-6650	441	7	.	.	PUNCT
ap-6650	442	1	physics	physics	NOUN
ap-6650	442	2	letters	letter	NOUN
ap-6650	442	3	b	b	PROPN
ap-6650	442	4	670(4	670(4	NUM
ap-6650	442	5	-	-	SYM
ap-6650	442	6	5):407	5):407	NUM
ap-6650	442	7	–	–	PUNCT
ap-6650	442	8	415	415	NUM
ap-6650	442	9	,	,	PUNCT
ap-6650	442	10	2009	2009	NUM
ap-6650	442	11	.	.	PUNCT
ap-6650	443	1	doi:10.1016	doi:10.1016	PROPN
ap-6650	443	2	/	/	SYM
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ap-6650	443	4	.	.	PUNCT
ap-6650	444	1	[	[	X
ap-6650	444	2	24	24	NUM
ap-6650	444	3	]	]	X
ap-6650	444	4	j.	j.	PROPN
ap-6650	444	5	m.	m.	PROPN
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ap-6650	444	7	-	-	PUNCT
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ap-6650	444	9	.	.	PUNCT
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ap-6650	445	6	”	"	PUNCT
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ap-6650	445	10	.	.	PUNCT
ap-6650	446	1	in	in	ADP
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ap-6650	446	5	quantum	quantum	ADJ
ap-6650	446	6	gravity	gravity	NOUN
ap-6650	446	7	,	,	PUNCT
ap-6650	446	8	pp	pp	CCONJ
ap-6650	446	9	.	.	PUNCT
ap-6650	446	10	3	3	NUM
ap-6650	446	11	–	–	SYM
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ap-6650	446	13	.	.	PUNCT
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ap-6650	446	17	.	.	PUNCT
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ap-6650	447	2	-	-	PUNCT
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ap-6650	447	4	-	-	PUNCT
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ap-6650	447	6	-	-	PUNCT
ap-6650	447	7	11897	11897	NUM
ap-6650	447	8	-	-	SYM
ap-6650	447	9	5_1	5_1	NUM
ap-6650	447	10	.	.	PUNCT
ap-6650	448	1	[	[	X
ap-6650	448	2	25	25	NUM
ap-6650	448	3	]	]	X
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ap-6650	448	6	.	.	PUNCT
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ap-6650	449	4	model	model	NOUN
ap-6650	449	5	with	with	ADP
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ap-6650	449	7	geometry	geometry	NOUN
ap-6650	449	8	,	,	PUNCT
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ap-6650	449	11	quantum	quantum	ADJ
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ap-6650	449	13	.	.	PUNCT
ap-6650	450	1	vol	vol	NOUN
ap-6650	450	2	.	.	PUNCT
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ap-6650	451	2	,	,	PUNCT
ap-6650	451	3	p.	p.	NOUN
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ap-6650	451	5	.	.	PUNCT
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ap-6650	452	5	.	.	PUNCT
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ap-6650	453	2	-	-	PUNCT
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ap-6650	453	4	.	.	PUNCT
ap-6650	454	1	[	[	X
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ap-6650	454	3	]	]	X
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ap-6650	454	9	.	.	PUNCT
ap-6650	455	1	string	string	PROPN
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ap-6650	455	4	noncommutative	noncommutative	ADJ
ap-6650	455	5	geometry	geometry	NOUN
ap-6650	455	6	.	.	PUNCT
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ap-6650	456	7	)	)	PUNCT
ap-6650	456	8	,	,	PUNCT
ap-6650	456	9	1999	1999	NUM
ap-6650	456	10	.	.	PUNCT
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ap-6650	457	2	-	-	PUNCT
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ap-6650	457	4	.	.	PUNCT
ap-6650	458	1	[	[	X
ap-6650	458	2	27	27	NUM
ap-6650	458	3	]	]	PUNCT
ap-6650	458	4	k.	k.	PROPN
ap-6650	458	5	christian	christian	PROPN
ap-6650	458	6	.	.	PUNCT
ap-6650	458	7	quantum	quantum	ADJ
ap-6650	458	8	groups	group	NOUN
ap-6650	458	9	.	.	PUNCT
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ap-6650	459	2	texts	text	NOUN
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ap-6650	459	5	155	155	NUM
ap-6650	459	6	.	.	PUNCT
ap-6650	459	7	springer	springer	NOUN
ap-6650	459	8	-	-	PUNCT
ap-6650	459	9	verlag	verlag	PROPN
ap-6650	459	10	,	,	PUNCT
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ap-6650	459	13	,	,	PUNCT
ap-6650	459	14	1995	1995	NUM
ap-6650	459	15	.	.	PUNCT
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ap-6650	460	6	http://dx.doi.org/10.1119/1.4868094	http://dx.doi.org/10.1119/1.4868094	VERB
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ap-6650	461	17	.	.	PROPN
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ap-6650	462	2	no	no	NOUN
ap-6650	462	3	.	.	PUNCT
ap-6650	463	1	1/2021	1/2021	NUM
ap-6650	463	2	on	on	ADP
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ap-6650	463	4	three	three	NUM
ap-6650	463	5	-	-	PUNCT
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ap-6650	463	7	pauli	pauli	PROPN
ap-6650	463	8	equation	equation	NOUN
ap-6650	463	9	in	in	ADP
ap-6650	463	10	noncommutative	noncommutative	ADJ
ap-6650	463	11	phase	phase	NOUN
ap-6650	463	12	-	-	PUNCT
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ap-6650	463	14	[	[	X
ap-6650	463	15	28	28	NUM
ap-6650	463	16	]	]	PUNCT
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ap-6650	463	19	,	,	PUNCT
ap-6650	463	20	d.	d.	PROPN
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ap-6650	463	22	.	.	PUNCT
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ap-6650	464	2	in	in	ADP
ap-6650	464	3	quantum	quantum	ADJ
ap-6650	464	4	field	field	NOUN
ap-6650	464	5	theory	theory	NOUN
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ap-6650	464	7	the	the	DET
ap-6650	464	8	riemann	riemann	PROPN
ap-6650	464	9	-	-	PUNCT
ap-6650	464	10	hilbert	hilbert	PROPN
ap-6650	464	11	problem	problem	NOUN
ap-6650	465	1	i	i	PRON
ap-6650	465	2	:	:	PUNCT
ap-6650	465	3	the	the	DET
ap-6650	465	4	hopf	hopf	ADJ
ap-6650	465	5	algebra	algebra	NOUN
ap-6650	465	6	structure	structure	NOUN
ap-6650	465	7	of	of	ADP
ap-6650	465	8	graphs	graph	NOUN
ap-6650	465	9	and	and	CCONJ
ap-6650	465	10	the	the	DET
ap-6650	465	11	main	main	ADJ
ap-6650	465	12	theorem	theorem	NOUN
ap-6650	465	13	.	.	PUNCT
ap-6650	466	1	communications	communication	NOUN
ap-6650	466	2	in	in	ADP
ap-6650	466	3	mathematical	mathematical	ADJ
ap-6650	466	4	physics	physics	NOUN
ap-6650	466	5	210(1):249	210(1):249	NUM
ap-6650	466	6	–	–	PUNCT
ap-6650	466	7	273	273	NUM
ap-6650	466	8	,	,	PUNCT
ap-6650	466	9	2000	2000	NUM
ap-6650	466	10	.	.	PUNCT
ap-6650	467	1	doi:10.1007	doi:10.1007	VERB
ap-6650	467	2	/	/	SYM
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ap-6650	467	4	.	.	PUNCT
ap-6650	468	1	[	[	X
ap-6650	468	2	29	29	NUM
ap-6650	468	3	]	]	PUNCT
ap-6650	468	4	a.	a.	NOUN
ap-6650	468	5	connes	conne	NOUN
ap-6650	468	6	,	,	PUNCT
ap-6650	468	7	d.	d.	PROPN
ap-6650	468	8	kreimer	kreimer	PROPN
ap-6650	468	9	.	.	PUNCT
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ap-6650	469	2	in	in	ADP
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ap-6650	469	4	field	field	NOUN
ap-6650	469	5	theory	theory	NOUN
ap-6650	469	6	and	and	CCONJ
ap-6650	469	7	the	the	DET
ap-6650	469	8	riemann	riemann	PROPN
ap-6650	469	9	-	-	PUNCT
ap-6650	469	10	hilbert	hilbert	PROPN
ap-6650	469	11	problem	problem	PROPN
ap-6650	469	12	ii	ii	PROPN
ap-6650	469	13	:	:	PUNCT
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ap-6650	469	16	-	-	NOUN
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ap-6650	469	21	the	the	DET
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ap-6650	469	23	group	group	NOUN
ap-6650	469	24	.	.	PUNCT
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ap-6650	470	2	in	in	ADP
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ap-6650	470	4	physics	physics	NOUN
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ap-6650	470	6	–	–	PUNCT
ap-6650	470	7	241	241	NUM
ap-6650	470	8	,	,	PUNCT
ap-6650	470	9	2001	2001	NUM
ap-6650	470	10	.	.	PUNCT
ap-6650	471	1	doi:10.1007	doi:10.1007	PROPN
ap-6650	471	2	/	/	SYM
ap-6650	471	3	pl00005547	pl00005547	PROPN
ap-6650	471	4	.	.	PUNCT
ap-6650	472	1	[	[	X
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ap-6650	472	3	]	]	PUNCT
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ap-6650	472	9	-	-	PUNCT
ap-6650	472	10	tourneret	tourneret	PROPN
ap-6650	472	11	.	.	PUNCT
ap-6650	473	1	hopf	hopf	ADJ
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ap-6650	473	3	of	of	ADP
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ap-6650	473	5	-	-	ADJ
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ap-6650	473	7	field	field	NOUN
ap-6650	473	8	theory	theory	NOUN
ap-6650	473	9	.	.	PUNCT
ap-6650	474	1	journal	journal	PROPN
ap-6650	474	2	of	of	ADP
ap-6650	474	3	noncommutative	noncommutative	ADJ
ap-6650	474	4	geometry	geometry	NOUN
ap-6650	474	5	2(1	2(1	NUM
ap-6650	474	6	)	)	PUNCT
ap-6650	474	7	,	,	PUNCT
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ap-6650	474	9	.	.	PUNCT
ap-6650	475	1	[	[	X
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ap-6650	475	3	]	]	PUNCT
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ap-6650	475	5	m.	m.	PROPN
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ap-6650	475	8	j.	j.	PROPN
ap-6650	475	9	a.	a.	PROPN
ap-6650	475	10	harvey	harvey	PROPN
ap-6650	475	11	,	,	PUNCT
ap-6650	475	12	v.	v.	ADP
ap-6650	475	13	a.	a.	PROPN
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ap-6650	475	19	noncommutative	noncommutative	ADJ
ap-6650	475	20	field	field	PROPN
ap-6650	475	21	theory	theory	NOUN
ap-6650	475	22	and	and	CCONJ
ap-6650	475	23	lorentz	lorentz	PROPN
ap-6650	475	24	violation	violation	NOUN
ap-6650	475	25	.	.	PUNCT
ap-6650	476	1	physical	physical	ADJ
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ap-6650	476	5	,	,	PUNCT
ap-6650	476	6	2001	2001	NUM
ap-6650	476	7	.	.	PUNCT
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ap-6650	477	2	/	/	SYM
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ap-6650	478	1	[	[	X
ap-6650	478	2	32	32	NUM
ap-6650	478	3	]	]	PUNCT
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ap-6650	478	10	theory	theory	NOUN
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ap-6650	478	13	spaces	space	NOUN
ap-6650	478	14	.	.	PUNCT
ap-6650	479	1	physics	physics	NOUN
ap-6650	479	2	reports	report	VERB
ap-6650	479	3	378(4):207	378(4):207	NUM
ap-6650	479	4	–	–	PUNCT
ap-6650	479	5	299	299	NUM
ap-6650	479	6	,	,	PUNCT
ap-6650	479	7	2003	2003	NUM
ap-6650	479	8	.	.	PUNCT
ap-6650	480	1	doi:10.1016	doi:10.1016	PROPN
ap-6650	480	2	/	/	SYM
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ap-6650	480	4	-	-	PUNCT
ap-6650	480	5	1573(03)00059	1573(03)00059	PROPN
ap-6650	480	6	-	-	PUNCT
ap-6650	480	7	0	0	NUM
ap-6650	480	8	.	.	PUNCT
ap-6650	481	1	[	[	X
ap-6650	481	2	33	33	NUM
ap-6650	481	3	]	]	X
ap-6650	481	4	i.	i.	PROPN
ap-6650	481	5	haouam	haouam	PROPN
ap-6650	481	6	.	.	PUNCT
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ap-6650	482	2	the	the	DET
ap-6650	482	3	fisk	fisk	PROPN
ap-6650	482	4	-	-	PUNCT
ap-6650	482	5	tait	tait	PROPN
ap-6650	482	6	equation	equation	NOUN
ap-6650	482	7	for	for	ADP
ap-6650	482	8	spin-3/2	spin-3/2	NOUN
ap-6650	482	9	fermions	fermion	NOUN
ap-6650	482	10	interacting	interact	VERB
ap-6650	482	11	with	with	ADP
ap-6650	482	12	an	an	DET
ap-6650	482	13	external	external	ADJ
ap-6650	482	14	magnetic	magnetic	ADJ
ap-6650	482	15	field	field	NOUN
ap-6650	482	16	in	in	ADP
ap-6650	482	17	noncommutative	noncommutative	ADJ
ap-6650	482	18	space	space	NOUN
ap-6650	482	19	-	-	PUNCT
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ap-6650	482	21	.	.	PUNCT
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ap-6650	483	4	studies	study	NOUN
ap-6650	483	5	24(1):1801	24(1):1801	NUM
ap-6650	483	6	,	,	PUNCT
ap-6650	483	7	2020	2020	NUM
ap-6650	483	8	.	.	PUNCT
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ap-6650	484	2	/	/	SYM
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ap-6650	484	4	.	.	PUNCT
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ap-6650	485	2	34	34	NUM
ap-6650	485	3	]	]	X
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ap-6650	485	5	li	li	PROPN
ap-6650	485	6	,	,	PUNCT
ap-6650	485	7	j.	j.	PROPN
ap-6650	485	8	wang	wang	PROPN
ap-6650	485	9	,	,	PUNCT
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ap-6650	486	4	phase	phase	NOUN
ap-6650	486	5	space	space	NOUN
ap-6650	486	6	.	.	PUNCT
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ap-6650	487	2	physics	physics	NOUN
ap-6650	487	3	letters	letter	NOUN
ap-6650	487	4	a	a	DET
ap-6650	487	5	20(28):2165	20(28):2165	NUM
ap-6650	487	6	–	–	PUNCT
ap-6650	487	7	2174	2174	NUM
ap-6650	487	8	,	,	PUNCT
ap-6650	487	9	2005	2005	NUM
ap-6650	487	10	.	.	PUNCT
ap-6650	488	1	doi:10.1142	doi:10.1142	NOUN
ap-6650	488	2	/	/	SYM
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ap-6650	488	4	.	.	PUNCT
ap-6650	489	1	[	[	X
ap-6650	489	2	35	35	NUM
ap-6650	489	3	]	]	X
ap-6650	489	4	i.	i.	PROPN
ap-6650	489	5	haouam	haouam	PROPN
ap-6650	489	6	.	.	PUNCT
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ap-6650	490	2	solution	solution	NOUN
ap-6650	490	3	of	of	ADP
ap-6650	490	4	(	(	PUNCT
ap-6650	490	5	2	2	NUM
ap-6650	490	6	+	+	NOUN
ap-6650	490	7	1	1	NUM
ap-6650	490	8	)	)	PUNCT
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ap-6650	490	10	dirac	dirac	NOUN
ap-6650	490	11	equation	equation	NOUN
ap-6650	490	12	in	in	ADP
ap-6650	490	13	time	time	NOUN
ap-6650	490	14	-	-	PUNCT
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ap-6650	490	16	noncommutative	noncommutative	ADJ
ap-6650	490	17	phase	phase	NOUN
ap-6650	490	18	-	-	PUNCT
ap-6650	490	19	space	space	NOUN
ap-6650	490	20	.	.	PUNCT
ap-6650	491	1	acta	acta	PROPN
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ap-6650	491	4	–	–	PUNCT
ap-6650	491	5	121	121	NUM
ap-6650	491	6	,	,	PUNCT
ap-6650	491	7	2020	2020	NUM
ap-6650	491	8	.	.	PUNCT
ap-6650	492	1	doi:10.14311	doi:10.14311	NOUN
ap-6650	492	2	/	/	SYM
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ap-6650	492	4	.	.	PUNCT
ap-6650	493	1	[	[	X
ap-6650	493	2	36	36	NUM
ap-6650	493	3	]	]	X
ap-6650	493	4	i.	i.	PROPN
ap-6650	493	5	haouam	haouam	PROPN
ap-6650	493	6	.	.	PUNCT
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ap-6650	494	2	the	the	DET
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ap-6650	494	4	geometry	geometry	NOUN
ap-6650	494	5	in	in	ADP
ap-6650	494	6	quantum	quantum	ADJ
ap-6650	494	7	mechanics	mechanic	NOUN
ap-6650	494	8	.	.	PUNCT
ap-6650	495	1	journal	journal	PROPN
ap-6650	495	2	of	of	ADP
ap-6650	495	3	physical	physical	ADJ
ap-6650	495	4	studies	study	NOUN
ap-6650	495	5	24(2):2002	24(2):2002	NUM
ap-6650	495	6	,	,	PUNCT
ap-6650	495	7	2020	2020	NUM
ap-6650	495	8	.	.	PUNCT
ap-6650	496	1	doi:10.30970	doi:10.30970	PROPN
ap-6650	496	2	/	/	SYM
ap-6650	496	3	jps.24.2002	jps.24.2002	NOUN
ap-6650	496	4	.	.	PUNCT
ap-6650	497	1	[	[	X
ap-6650	497	2	37	37	NUM
ap-6650	497	3	]	]	X
ap-6650	497	4	i.	i.	PROPN
ap-6650	497	5	haouam	haouam	PROPN
ap-6650	497	6	.	.	PUNCT
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ap-6650	498	2	non	non	ADJ
ap-6650	498	3	-	-	ADJ
ap-6650	498	4	relativistic	relativistic	ADJ
ap-6650	498	5	limit	limit	NOUN
ap-6650	498	6	of	of	ADP
ap-6650	498	7	the	the	DET
ap-6650	498	8	dkp	dkp	PROPN
ap-6650	498	9	equation	equation	NOUN
ap-6650	498	10	in	in	ADP
ap-6650	498	11	non	non	ADJ
ap-6650	498	12	-	-	ADJ
ap-6650	498	13	commutative	commutative	ADJ
ap-6650	498	14	phase	phase	NOUN
ap-6650	498	15	-	-	PUNCT
ap-6650	498	16	space	space	NOUN
ap-6650	498	17	.	.	PUNCT
ap-6650	499	1	symmetry	symmetry	NOUN
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ap-6650	499	3	,	,	PUNCT
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ap-6650	499	5	.	.	PUNCT
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ap-6650	500	2	/	/	SYM
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ap-6650	500	4	.	.	PUNCT
ap-6650	501	1	[	[	X
ap-6650	501	2	38	38	NUM
ap-6650	501	3	]	]	PUNCT
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ap-6650	501	5	haouam	haouam	PROPN
ap-6650	501	6	.	.	PUNCT
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ap-6650	501	8	equation	equation	NOUN
ap-6650	501	9	in	in	ADP
ap-6650	501	10	presence	presence	NOUN
ap-6650	501	11	of	of	ADP
ap-6650	501	12	a	a	DET
ap-6650	501	13	non	non	ADJ
ap-6650	501	14	-	-	ADJ
ap-6650	501	15	local	local	ADJ
ap-6650	501	16	potential	potential	NOUN
ap-6650	501	17	in	in	ADP
ap-6650	501	18	non	non	ADJ
ap-6650	501	19	-	-	ADJ
ap-6650	501	20	commutative	commutative	ADJ
ap-6650	501	21	phase	phase	NOUN
ap-6650	501	22	-	-	PUNCT
ap-6650	501	23	space	space	NOUN
ap-6650	501	24	.	.	PUNCT
ap-6650	502	1	open	open	ADJ
ap-6650	502	2	journal	journal	PROPN
ap-6650	502	3	of	of	ADP
ap-6650	502	4	microphysics	microphysic	NOUN
ap-6650	502	5	9(3):15	9(3):15	NUM
ap-6650	502	6	–	–	PUNCT
ap-6650	502	7	28	28	NUM
ap-6650	502	8	,	,	PUNCT
ap-6650	502	9	2019	2019	NUM
ap-6650	502	10	.	.	PUNCT
ap-6650	503	1	doi:10.4236	doi:10.4236	PROPN
ap-6650	503	2	/	/	SYM
ap-6650	503	3	ojm.2019.93003	ojm.2019.93003	PROPN
ap-6650	503	4	.	.	PUNCT
ap-6650	504	1	[	[	X
ap-6650	504	2	39	39	NUM
ap-6650	504	3	]	]	PUNCT
ap-6650	504	4	j.	j.	PROPN
ap-6650	504	5	m.	m.	PROPN
ap-6650	504	6	wilkes	wilkes	PROPN
ap-6650	504	7	.	.	PUNCT
ap-6650	505	1	the	the	DET
ap-6650	505	2	pauli	pauli	PROPN
ap-6650	505	3	and	and	CCONJ
ap-6650	505	4	lévy	lévy	ADJ
ap-6650	505	5	-	-	PUNCT
ap-6650	505	6	leblond	leblond	NOUN
ap-6650	505	7	equations	equation	NOUN
ap-6650	505	8	,	,	PUNCT
ap-6650	505	9	and	and	CCONJ
ap-6650	505	10	the	the	DET
ap-6650	505	11	spin	spin	NOUN
ap-6650	505	12	current	current	ADJ
ap-6650	505	13	density	density	NOUN
ap-6650	505	14	.	.	PUNCT
ap-6650	506	1	european	european	PROPN
ap-6650	506	2	journal	journal	PROPN
ap-6650	506	3	of	of	ADP
ap-6650	506	4	physics	physics	PROPN
ap-6650	506	5	41(3):035402	41(3):035402	PROPN
ap-6650	506	6	,	,	PUNCT
ap-6650	506	7	2020	2020	NUM
ap-6650	506	8	.	.	PUNCT
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ap-6650	507	2	-	-	PUNCT
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ap-6650	507	4	/	/	SYM
ap-6650	507	5	ab7495	ab7495	NOUN
ap-6650	507	6	.	.	PUNCT
ap-6650	508	1	[	[	X
ap-6650	508	2	40	40	NUM
ap-6650	508	3	]	]	PUNCT
ap-6650	508	4	m.	m.	PROPN
ap-6650	508	5	e.	e.	PROPN
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ap-6650	508	7	,	,	PUNCT
ap-6650	508	8	d.	d.	PROPN
ap-6650	508	9	v.	v.	PROPN
ap-6650	508	10	schroeder	schroeder	PROPN
ap-6650	508	11	.	.	PUNCT
ap-6650	509	1	an	an	DET
ap-6650	509	2	introduction	introduction	NOUN
ap-6650	509	3	to	to	ADP
ap-6650	509	4	quantum	quantum	ADJ
ap-6650	509	5	field	field	NOUN
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ap-6650	509	7	.	.	PUNCT
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ap-6650	510	2	,	,	PUNCT
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ap-6650	510	4	.	.	PUNCT
ap-6650	510	5	:	:	PUNCT
ap-6650	511	1	addison	addison	PROPN
ap-6650	511	2	-	-	PUNCT
ap-6650	511	3	wesley	wesley	PROPN
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ap-6650	511	5	.	.	PUNCT
ap-6650	512	1	co.	co.	PROPN
ap-6650	512	2	,	,	PUNCT
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ap-6650	512	5	,	,	PUNCT
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ap-6650	512	7	.	.	PUNCT
ap-6650	513	1	[	[	X
ap-6650	513	2	41	41	NUM
ap-6650	513	3	]	]	PUNCT
ap-6650	513	4	m.	m.	NOUN
ap-6650	513	5	najafizadeh	najafizadeh	NOUN
ap-6650	513	6	,	,	PUNCT
ap-6650	513	7	m.	m.	NOUN
ap-6650	513	8	saadat	saadat	NOUN
ap-6650	513	9	.	.	PUNCT
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ap-6650	514	2	of	of	ADP
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ap-6650	514	4	systems	system	NOUN
ap-6650	514	5	on	on	ADP
ap-6650	514	6	noncommutative	noncommutative	ADJ
ap-6650	514	7	phase	phase	NOUN
ap-6650	514	8	space	space	NOUN
ap-6650	514	9	.	.	PUNCT
ap-6650	515	1	chinese	chinese	ADJ
ap-6650	515	2	journal	journal	PROPN
ap-6650	515	3	of	of	ADP
ap-6650	515	4	physics	physics	PROPN
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ap-6650	515	6	–	–	PUNCT
ap-6650	515	7	102	102	NUM
ap-6650	515	8	,	,	PUNCT
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ap-6650	515	10	.	.	PUNCT
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ap-6650	516	2	/	/	SYM
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ap-6650	516	4	.	.	PUNCT
ap-6650	517	1	[	[	X
ap-6650	517	2	42	42	NUM
ap-6650	517	3	]	]	PUNCT
ap-6650	517	4	w.	w.	PROPN
ap-6650	517	5	gao	gao	PROPN
ap-6650	517	6	-	-	PUNCT
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ap-6650	517	8	,	,	PUNCT
ap-6650	517	9	l.	l.	PROPN
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ap-6650	517	11	-	-	PUNCT
ap-6650	517	12	yun	yun	PROPN
ap-6650	517	13	,	,	PUNCT
ap-6650	517	14	l.	l.	PROPN
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ap-6650	517	16	-	-	PUNCT
ap-6650	517	17	wen	wen	PROPN
ap-6650	517	18	,	,	PUNCT
ap-6650	517	19	et	et	PROPN
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ap-6650	517	23	mechanics	mechanic	NOUN
ap-6650	517	24	in	in	ADP
ap-6650	517	25	non	non	ADJ
ap-6650	517	26	-	-	ADJ
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ap-6650	517	28	phase	phase	NOUN
ap-6650	517	29	space	space	NOUN
ap-6650	517	30	.	.	PUNCT
ap-6650	518	1	chinese	chinese	ADJ
ap-6650	518	2	physics	physics	PROPN
ap-6650	518	3	c	c	PROPN
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ap-6650	518	5	,	,	PUNCT
ap-6650	518	6	2008	2008	NUM
ap-6650	518	7	.	.	PUNCT
ap-6650	519	1	doi:10.1088/1674	doi:10.1088/1674	NOUN
ap-6650	519	2	-	-	PUNCT
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ap-6650	519	4	.	.	PUNCT
ap-6650	520	1	[	[	X
ap-6650	520	2	43	43	NUM
ap-6650	520	3	]	]	PUNCT
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ap-6650	520	5	e.	e.	PROPN
ap-6650	520	6	f.	f.	PROPN
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ap-6650	520	8	,	,	PUNCT
ap-6650	520	9	h.	h.	PROPN
ap-6650	520	10	smail	smail	NOUN
ap-6650	520	11	.	.	PUNCT
ap-6650	521	1	on	on	ADP
ap-6650	521	2	quantum	quantum	ADJ
ap-6650	521	3	mechanics	mechanic	NOUN
ap-6650	521	4	on	on	ADP
ap-6650	521	5	noncommutative	noncommutative	ADJ
ap-6650	521	6	quantum	quantum	NOUN
ap-6650	521	7	phase	phase	NOUN
ap-6650	521	8	space	space	NOUN
ap-6650	521	9	.	.	PUNCT
ap-6650	522	1	communications	communication	NOUN
ap-6650	522	2	in	in	ADP
ap-6650	522	3	theoretical	theoretical	ADJ
ap-6650	522	4	physics	physics	NOUN
ap-6650	522	5	41(6):837	41(6):837	PROPN
ap-6650	522	6	,	,	PUNCT
ap-6650	522	7	2004	2004	NUM
ap-6650	522	8	.	.	PUNCT
ap-6650	523	1	doi:10.1088/0253	doi:10.1088/0253	NOUN
ap-6650	523	2	-	-	PUNCT
ap-6650	523	3	6102/41/6/837	6102/41/6/837	NUM
ap-6650	523	4	.	.	PUNCT
ap-6650	524	1	[	[	X
ap-6650	524	2	44	44	NUM
ap-6650	524	3	]	]	PUNCT
ap-6650	524	4	m.	m.	NOUN
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ap-6650	524	8	m.	m.	NOUN
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ap-6650	524	10	-	-	PUNCT
ap-6650	524	11	jabbari	jabbari	NOUN
ap-6650	524	12	,	,	PUNCT
ap-6650	524	13	a.	a.	NOUN
ap-6650	524	14	tureanu	tureanu	NOUN
ap-6650	524	15	.	.	PUNCT
ap-6650	525	1	hydrogen	hydrogen	NOUN
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ap-6650	525	6	lamb	lamb	PROPN
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ap-6650	525	8	in	in	ADP
ap-6650	525	9	noncommutative	noncommutative	PROPN
ap-6650	525	10	qed	qed	PROPN
ap-6650	525	11	.	.	PUNCT
ap-6650	526	1	physical	physical	PROPN
ap-6650	526	2	review	review	NOUN
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ap-6650	526	4	86(13):2716	86(13):2716	NUM
ap-6650	526	5	–	–	PUNCT
ap-6650	526	6	2719	2719	NUM
ap-6650	526	7	,	,	PUNCT
ap-6650	526	8	2001	2001	NUM
ap-6650	526	9	.	.	PUNCT
ap-6650	527	1	[	[	X
ap-6650	527	2	45	45	NUM
ap-6650	527	3	]	]	X
ap-6650	527	4	s.	s.	PROPN
ap-6650	527	5	biswas	biswas	PROPN
ap-6650	527	6	.	.	PUNCT
ap-6650	528	1	bohr	bohr	PROPN
ap-6650	528	2	-	-	PUNCT
ap-6650	528	3	van	van	PROPN
ap-6650	528	4	leeuwen	leeuwen	PROPN
ap-6650	528	5	theorem	theorem	PROPN
ap-6650	528	6	in	in	ADP
ap-6650	528	7	non	non	ADJ
ap-6650	528	8	-	-	ADJ
ap-6650	528	9	commutative	commutative	ADJ
ap-6650	528	10	space	space	NOUN
ap-6650	528	11	.	.	PUNCT
ap-6650	529	1	physics	physics	NOUN
ap-6650	529	2	letters	letter	NOUN
ap-6650	529	3	a	a	DET
ap-6650	529	4	381(44):3723	381(44):3723	PROPN
ap-6650	529	5	–	–	PUNCT
ap-6650	529	6	3725	3725	NUM
ap-6650	529	7	,	,	PUNCT
ap-6650	529	8	2017	2017	NUM
ap-6650	529	9	.	.	PUNCT
ap-6650	530	1	doi:10.1016	doi:10.1016	PROPN
ap-6650	530	2	/	/	SYM
ap-6650	530	3	j.physleta.2017.10.003	j.physleta.2017.10.003	PROPN
ap-6650	530	4	.	.	PROPN
ap-6650	530	5	241	241	NUM
ap-6650	531	1	http://dx.doi.org/10.1007/s002200050779	http://dx.doi.org/10.1007/s002200050779	NOUN
ap-6650	531	2	http://dx.doi.org/10.1007/pl00005547	http://dx.doi.org/10.1007/pl00005547	NOUN
ap-6650	531	3	http://dx.doi.org/10.1103/physrevlett.87.141601	http://dx.doi.org/10.1103/physrevlett.87.141601	NOUN
ap-6650	531	4	http://dx.doi.org/10.1016/s0370-1573(03)00059-0	http://dx.doi.org/10.1016/s0370-1573(03)00059-0	PROPN
ap-6650	531	5	http://dx.doi.org/10.30970/jps.24.1801	http://dx.doi.org/10.30970/jps.24.1801	VERB
ap-6650	531	6	http://dx.doi.org/10.1142/s0217732305017421	http://dx.doi.org/10.1142/s0217732305017421	PRON
ap-6650	531	7	http://dx.doi.org/10.14311/ap.2020.60.0111	http://dx.doi.org/10.14311/ap.2020.60.0111	X
ap-6650	531	8	http://dx.doi.org/10.30970/jps.24.2002	http://dx.doi.org/10.30970/jps.24.2002	PROPN
ap-6650	531	9	http://dx.doi.org/10.3390/sym11020223	http://dx.doi.org/10.3390/sym11020223	PROPN
ap-6650	531	10	http://dx.doi.org/10.4236/ojm.2019.93003	http://dx.doi.org/10.4236/ojm.2019.93003	PROPN
ap-6650	531	11	http://dx.doi.org/10.1088/1361-6404/ab7495	http://dx.doi.org/10.1088/1361-6404/ab7495	PROPN
ap-6650	531	12	http://dx.doi.org/10.6122/cjp.51.94	http://dx.doi.org/10.6122/cjp.51.94	PROPN
ap-6650	531	13	http://dx.doi.org/10.1088/1674-1137/32/5/002	http://dx.doi.org/10.1088/1674-1137/32/5/002	PROPN
ap-6650	531	14	http://dx.doi.org/10.1088/0253-6102/41/6/837	http://dx.doi.org/10.1088/0253-6102/41/6/837	PROPN
ap-6650	531	15	http://dx.doi.org/10.1016/j.physleta.2017.10.003	http://dx.doi.org/10.1016/j.physleta.2017.10.003	PROPN
ap-6650	531	16	acta	acta	PROPN
ap-6650	531	17	polytechnica	polytechnica	PROPN
ap-6650	531	18	61(1):230–241	61(1):230–241	PROPN
ap-6650	531	19	,	,	PUNCT
ap-6650	531	20	2021	2021	NUM
ap-6650	531	21	1	1	NUM
ap-6650	531	22	introduction	introduction	NOUN
ap-6650	531	23	2	2	NUM
ap-6650	531	24	review	review	NOUN
ap-6650	531	25	of	of	ADP
ap-6650	531	26	noncommutative	noncommutative	ADJ
ap-6650	531	27	algebra	algebra	PROPN
ap-6650	531	28	3	3	NUM
ap-6650	531	29	pauli	pauli	PROPN
ap-6650	531	30	equation	equation	NOUN
ap-6650	531	31	in	in	ADP
ap-6650	531	32	noncommutative	noncommutative	ADJ
ap-6650	531	33	phase	phase	NOUN
ap-6650	531	34	-	-	PUNCT
ap-6650	531	35	space	space	NOUN
ap-6650	531	36	3.1	3.1	NUM
ap-6650	531	37	formulation	formulation	NOUN
ap-6650	531	38	of	of	ADP
ap-6650	531	39	noncommutative	noncommutative	PROPN
ap-6650	531	40	pauli	pauli	PROPN
ap-6650	531	41	equation	equation	NOUN
ap-6650	531	42	3.2	3.2	NUM
ap-6650	531	43	deformed	deform	VERB
ap-6650	531	44	continuity	continuity	NOUN
ap-6650	531	45	equation	equation	NOUN
ap-6650	531	46	3.3	3.3	NUM
ap-6650	531	47	derivation	derivation	NOUN
ap-6650	531	48	of	of	ADP
ap-6650	531	49	the	the	DET
ap-6650	531	50	magnetization	magnetization	NOUN
ap-6650	531	51	current	current	ADJ
ap-6650	531	52	4	4	NUM
ap-6650	531	53	noncommutative	noncommutative	ADJ
ap-6650	531	54	semi	semi	ADJ
ap-6650	531	55	-	-	ADJ
ap-6650	531	56	classical	classical	ADJ
ap-6650	531	57	partition	partition	NOUN
ap-6650	531	58	function	function	NOUN
ap-6650	531	59	5	5	NUM
ap-6650	531	60	conclusion	conclusion	NOUN
ap-6650	531	61	acknowledgements	acknowledgement	NOUN
ap-6650	531	62	references	reference	NOUN