id	sid	tid	token	lemma	pos
ap-7660	1	1	acta	acta	PROPN
ap-7660	1	2	polytechnica	polytechnica	PROPN
ap-7660	1	3	https://doi.org/10.14311/ap.2022.62.0197	https://doi.org/10.14311/ap.2022.62.0197	PROPN
ap-7660	1	4	acta	acta	PROPN
ap-7660	1	5	polytechnica	polytechnica	PROPN
ap-7660	1	6	62(1):197–207	62(1):197–207	NOUN
ap-7660	1	7	,	,	PUNCT
ap-7660	1	8	2022	2022	NUM
ap-7660	1	9	©	©	ADP
ap-7660	1	10	2022	2022	NUM
ap-7660	1	11	the	the	DET
ap-7660	1	12	author(s	author(s	NOUN
ap-7660	1	13	)	)	PUNCT
ap-7660	1	14	.	.	PUNCT
ap-7660	2	1	licensed	license	VERB
ap-7660	2	2	under	under	ADP
ap-7660	2	3	a	a	DET
ap-7660	2	4	cc	cc	NOUN
ap-7660	2	5	-	-	PUNCT
ap-7660	2	6	by	by	ADP
ap-7660	2	7	4.0	4.0	NUM
ap-7660	2	8	licence	licence	NOUN
ap-7660	2	9	published	publish	VERB
ap-7660	2	10	by	by	ADP
ap-7660	2	11	the	the	DET
ap-7660	2	12	czech	czech	PROPN
ap-7660	2	13	technical	technical	PROPN
ap-7660	2	14	university	university	PROPN
ap-7660	2	15	in	in	ADP
ap-7660	2	16	prague	prague	PROPN
ap-7660	2	17	complex	complex	ADJ
ap-7660	2	18	topological	topological	ADJ
ap-7660	2	19	soliton	soliton	NOUN
ap-7660	2	20	with	with	ADP
ap-7660	2	21	real	real	ADJ
ap-7660	2	22	energy	energy	NOUN
ap-7660	2	23	in	in	ADP
ap-7660	2	24	particle	particle	NOUN
ap-7660	2	25	physics	physics	PROPN
ap-7660	2	26	takanobu	takanobu	PROPN
ap-7660	2	27	taira	taira	PROPN
ap-7660	2	28	city	city	PROPN
ap-7660	2	29	,	,	PUNCT
ap-7660	2	30	university	university	PROPN
ap-7660	2	31	of	of	ADP
ap-7660	2	32	london	london	PROPN
ap-7660	2	33	,	,	PUNCT
ap-7660	2	34	department	department	NOUN
ap-7660	2	35	of	of	ADP
ap-7660	2	36	mathematics	mathematics	PROPN
ap-7660	2	37	,	,	PUNCT
ap-7660	2	38	northampton	northampton	PROPN
ap-7660	2	39	square	square	PROPN
ap-7660	2	40	,	,	PUNCT
ap-7660	2	41	london	london	PROPN
ap-7660	2	42	ec1v	ec1v	PROPN
ap-7660	2	43	0hb	0hb	NOUN
ap-7660	2	44	,	,	PUNCT
ap-7660	2	45	uk	uk	PROPN
ap-7660	2	46	correspondence	correspondence	NOUN
ap-7660	2	47	:	:	PUNCT
ap-7660	2	48	takanobu.taira@city.ac.uk	takanobu.taira@city.ac.uk	NUM
ap-7660	2	49	abstract	abstract	ADJ
ap-7660	2	50	.	.	PUNCT
ap-7660	3	1	we	we	PRON
ap-7660	3	2	summarise	summarise	VERB
ap-7660	3	3	the	the	DET
ap-7660	3	4	procedure	procedure	NOUN
ap-7660	3	5	used	use	VERB
ap-7660	3	6	to	to	PART
ap-7660	3	7	find	find	VERB
ap-7660	3	8	the	the	DET
ap-7660	3	9	classical	classical	ADJ
ap-7660	3	10	masses	masse	NOUN
ap-7660	3	11	of	of	ADP
ap-7660	3	12	higgs	higgs	PROPN
ap-7660	3	13	particle	particle	PROPN
ap-7660	3	14	,	,	PUNCT
ap-7660	3	15	massive	massive	ADJ
ap-7660	3	16	gauge	gauge	NOUN
ap-7660	3	17	boson	boson	NOUN
ap-7660	3	18	and	and	CCONJ
ap-7660	3	19	t’hooft	t’hooft	NOUN
ap-7660	3	20	-	-	PUNCT
ap-7660	3	21	polyakov	polyakov	NOUN
ap-7660	3	22	monopole	monopole	NOUN
ap-7660	3	23	in	in	ADP
ap-7660	3	24	non	non	ADJ
ap-7660	3	25	-	-	ADJ
ap-7660	3	26	hermitian	hermitian	ADJ
ap-7660	3	27	gauge	gauge	NOUN
ap-7660	3	28	field	field	NOUN
ap-7660	3	29	theory	theory	NOUN
ap-7660	3	30	.	.	PUNCT
ap-7660	4	1	their	their	PRON
ap-7660	4	2	physical	physical	ADJ
ap-7660	4	3	regions	region	NOUN
ap-7660	4	4	are	be	AUX
ap-7660	4	5	explored	explore	VERB
ap-7660	4	6	,	,	PUNCT
ap-7660	4	7	and	and	CCONJ
ap-7660	4	8	the	the	DET
ap-7660	4	9	mechanism	mechanism	NOUN
ap-7660	4	10	of	of	ADP
ap-7660	4	11	the	the	DET
ap-7660	4	12	real	real	ADJ
ap-7660	4	13	value	value	NOUN
ap-7660	4	14	of	of	ADP
ap-7660	4	15	the	the	DET
ap-7660	4	16	monopole	monopole	ADJ
ap-7660	4	17	solution	solution	NOUN
ap-7660	4	18	is	be	AUX
ap-7660	4	19	analysed	analyse	VERB
ap-7660	4	20	in	in	ADP
ap-7660	4	21	different	different	ADJ
ap-7660	4	22	physical	physical	ADJ
ap-7660	4	23	regions	region	NOUN
ap-7660	4	24	.	.	PUNCT
ap-7660	5	1	keywords	keyword	NOUN
ap-7660	5	2	:	:	PUNCT
ap-7660	5	3	t’hooft	t’hooft	NOUN
ap-7660	5	4	-	-	PUNCT
ap-7660	5	5	polyakov	polyakov	NOUN
ap-7660	5	6	monopole	monopole	NOUN
ap-7660	5	7	,	,	PUNCT
ap-7660	5	8	quantum	quantum	ADJ
ap-7660	5	9	field	field	NOUN
ap-7660	5	10	theory	theory	NOUN
ap-7660	5	11	,	,	PUNCT
ap-7660	5	12	non	non	ADJ
ap-7660	5	13	-	-	ADJ
ap-7660	5	14	hermitian	hermitian	ADJ
ap-7660	5	15	quantum	quantum	ADJ
ap-7660	5	16	field	field	NOUN
ap-7660	5	17	theory	theory	NOUN
ap-7660	5	18	.	.	PUNCT
ap-7660	6	1	1	1	X
ap-7660	6	2	.	.	X
ap-7660	6	3	introduction	introduction	NOUN
ap-7660	6	4	quantum	quantum	NOUN
ap-7660	6	5	field	field	NOUN
ap-7660	6	6	theory	theory	NOUN
ap-7660	6	7	is	be	AUX
ap-7660	6	8	a	a	DET
ap-7660	6	9	key	key	ADJ
ap-7660	6	10	tool	tool	NOUN
ap-7660	6	11	to	to	PART
ap-7660	6	12	analyse	analyse	VERB
ap-7660	6	13	particle	particle	NOUN
ap-7660	6	14	physics	physics	PROPN
ap-7660	6	15	.	.	PUNCT
ap-7660	7	1	the	the	DET
ap-7660	7	2	most	most	ADV
ap-7660	7	3	modern	modern	ADJ
ap-7660	7	4	physical	physical	ADJ
ap-7660	7	5	description	description	NOUN
ap-7660	7	6	of	of	ADP
ap-7660	7	7	the	the	DET
ap-7660	7	8	fundamental	fundamental	ADJ
ap-7660	7	9	particle	particle	NOUN
ap-7660	7	10	interaction	interaction	NOUN
ap-7660	7	11	is	be	AUX
ap-7660	7	12	described	describe	VERB
ap-7660	7	13	by	by	ADP
ap-7660	7	14	the	the	DET
ap-7660	7	15	model	model	NOUN
ap-7660	7	16	called	call	VERB
ap-7660	7	17	the	the	DET
ap-7660	7	18	standard	standard	ADJ
ap-7660	7	19	model	model	NOUN
ap-7660	7	20	.	.	PUNCT
ap-7660	8	1	however	however	ADV
ap-7660	8	2	,	,	PUNCT
ap-7660	8	3	the	the	DET
ap-7660	8	4	model	model	NOUN
ap-7660	8	5	possesses	possess	VERB
ap-7660	8	6	several	several	ADJ
ap-7660	8	7	problems	problem	NOUN
ap-7660	8	8	such	such	ADJ
ap-7660	8	9	as	as	ADP
ap-7660	8	10	incompatibility	incompatibility	NOUN
ap-7660	8	11	with	with	ADP
ap-7660	8	12	the	the	DET
ap-7660	8	13	general	general	ADJ
ap-7660	8	14	relativity	relativity	NOUN
ap-7660	8	15	,	,	PUNCT
ap-7660	8	16	hierarchy	hierarchy	NOUN
ap-7660	8	17	problem	problem	NOUN
ap-7660	8	18	,	,	PUNCT
ap-7660	8	19	etc	etc	X
ap-7660	8	20	.	.	X
ap-7660	8	21	therefore	therefore	ADV
ap-7660	8	22	,	,	PUNCT
ap-7660	8	23	it	it	PRON
ap-7660	8	24	is	be	AUX
ap-7660	8	25	an	an	DET
ap-7660	8	26	active	active	ADJ
ap-7660	8	27	area	area	NOUN
ap-7660	8	28	to	to	PART
ap-7660	8	29	extend	extend	VERB
ap-7660	8	30	the	the	DET
ap-7660	8	31	standard	standard	ADJ
ap-7660	8	32	model	model	NOUN
ap-7660	8	33	.	.	PUNCT
ap-7660	9	1	recently	recently	ADV
ap-7660	9	2	a	a	DET
ap-7660	9	3	growing	grow	VERB
ap-7660	9	4	number	number	NOUN
ap-7660	9	5	of	of	ADP
ap-7660	9	6	research	research	NOUN
ap-7660	9	7	papers	paper	NOUN
ap-7660	9	8	started	start	VERB
ap-7660	9	9	exploring	explore	VERB
ap-7660	9	10	the	the	DET
ap-7660	9	11	non	non	ADJ
ap-7660	9	12	-	-	ADJ
ap-7660	9	13	hermitian	hermitian	ADJ
ap-7660	9	14	extension	extension	NOUN
ap-7660	9	15	of	of	ADP
ap-7660	9	16	the	the	DET
ap-7660	9	17	standard	standard	ADJ
ap-7660	9	18	model	model	NOUN
ap-7660	9	19	[	[	X
ap-7660	9	20	1–14	1–14	X
ap-7660	9	21	]	]	X
ap-7660	9	22	.	.	PUNCT
ap-7660	10	1	we	we	PRON
ap-7660	10	2	have	have	AUX
ap-7660	10	3	contributed	contribute	VERB
ap-7660	10	4	to	to	ADP
ap-7660	10	5	this	this	DET
ap-7660	10	6	development	development	NOUN
ap-7660	10	7	by	by	ADP
ap-7660	10	8	analysing	analyse	VERB
ap-7660	10	9	the	the	DET
ap-7660	10	10	goldstone	goldstone	NOUN
ap-7660	10	11	theorem	theorem	NOUN
ap-7660	10	12	[	[	X
ap-7660	10	13	8	8	NUM
ap-7660	10	14	,	,	PUNCT
ap-7660	10	15	10	10	NUM
ap-7660	10	16	]	]	PUNCT
ap-7660	10	17	,	,	PUNCT
ap-7660	10	18	the	the	DET
ap-7660	10	19	higgs	higgs	NOUN
ap-7660	10	20	mechanism	mechanism	NOUN
ap-7660	10	21	[	[	X
ap-7660	10	22	9	9	NUM
ap-7660	10	23	]	]	PUNCT
ap-7660	10	24	and	and	CCONJ
ap-7660	10	25	t’hooftpolyakov	t’hooftpolyakov	PROPN
ap-7660	10	26	monopoles	monopole	NOUN
ap-7660	10	27	[	[	X
ap-7660	10	28	11	11	NUM
ap-7660	10	29	]	]	PUNCT
ap-7660	10	30	.	.	PUNCT
ap-7660	11	1	the	the	DET
ap-7660	11	2	classical	classical	ADJ
ap-7660	11	3	masses	masse	NOUN
ap-7660	11	4	of	of	ADP
ap-7660	11	5	higgs	higgs	NOUN
ap-7660	11	6	particles	particle	NOUN
ap-7660	11	7	,	,	PUNCT
ap-7660	11	8	massive	massive	ADJ
ap-7660	11	9	gauge	gauge	NOUN
ap-7660	11	10	boson	boson	NOUN
ap-7660	11	11	and	and	CCONJ
ap-7660	11	12	monopoles	monopole	NOUN
ap-7660	11	13	were	be	AUX
ap-7660	11	14	analysed	analyse	VERB
ap-7660	11	15	.	.	PUNCT
ap-7660	12	1	however	however	ADV
ap-7660	12	2	,	,	PUNCT
ap-7660	12	3	a	a	DET
ap-7660	12	4	detailed	detailed	ADJ
ap-7660	12	5	analysis	analysis	NOUN
ap-7660	12	6	of	of	ADP
ap-7660	12	7	their	their	PRON
ap-7660	12	8	intersecting	intersecting	ADJ
ap-7660	12	9	physical	physical	ADJ
ap-7660	12	10	regions	region	NOUN
ap-7660	12	11	and	and	CCONJ
ap-7660	12	12	the	the	DET
ap-7660	12	13	mechanism	mechanism	NOUN
ap-7660	12	14	of	of	ADP
ap-7660	12	15	the	the	DET
ap-7660	12	16	real	real	ADJ
ap-7660	12	17	value	value	NOUN
ap-7660	12	18	of	of	ADP
ap-7660	12	19	the	the	DET
ap-7660	12	20	energy	energy	NOUN
ap-7660	12	21	of	of	ADP
ap-7660	12	22	monopole	monopole	NOUN
ap-7660	12	23	was	be	AUX
ap-7660	12	24	not	not	PART
ap-7660	12	25	explored	explore	VERB
ap-7660	12	26	.	.	PUNCT
ap-7660	13	1	the	the	DET
ap-7660	13	2	main	main	ADJ
ap-7660	13	3	aim	aim	NOUN
ap-7660	13	4	of	of	ADP
ap-7660	13	5	this	this	DET
ap-7660	13	6	contribution	contribution	NOUN
ap-7660	13	7	is	be	AUX
ap-7660	13	8	to	to	PART
ap-7660	13	9	fill	fill	VERB
ap-7660	13	10	this	this	DET
ap-7660	13	11	gap	gap	NOUN
ap-7660	13	12	.	.	PUNCT
ap-7660	14	1	there	there	PRON
ap-7660	14	2	are	be	VERB
ap-7660	14	3	two	two	NUM
ap-7660	14	4	separate	separate	ADJ
ap-7660	14	5	mechanisms	mechanism	NOUN
ap-7660	14	6	that	that	PRON
ap-7660	14	7	guarantee	guarantee	VERB
ap-7660	14	8	the	the	DET
ap-7660	14	9	real	real	ADJ
ap-7660	14	10	value	value	NOUN
ap-7660	14	11	of	of	ADP
ap-7660	14	12	the	the	DET
ap-7660	14	13	particle	particle	NOUN
ap-7660	14	14	masses	masse	NOUN
ap-7660	14	15	in	in	ADP
ap-7660	14	16	question	question	NOUN
ap-7660	14	17	.	.	PUNCT
ap-7660	15	1	first	first	ADV
ap-7660	15	2	,	,	PUNCT
ap-7660	15	3	the	the	DET
ap-7660	15	4	masses	masse	NOUN
ap-7660	15	5	of	of	ADP
ap-7660	15	6	higgs	higgs	NOUN
ap-7660	15	7	particles	particle	NOUN
ap-7660	15	8	are	be	AUX
ap-7660	15	9	given	give	VERB
ap-7660	15	10	by	by	ADP
ap-7660	15	11	a	a	DET
ap-7660	15	12	nonhermitian	nonhermitian	ADJ
ap-7660	15	13	mass	mass	NOUN
ap-7660	15	14	matrix	matrix	NOUN
ap-7660	15	15	m	m	VERB
ap-7660	15	16	.	.	PUNCT
ap-7660	16	1	assume	assume	VERB
ap-7660	16	2	that	that	SCONJ
ap-7660	16	3	the	the	DET
ap-7660	16	4	matrix	matrix	NOUN
ap-7660	16	5	possess	possess	VERB
ap-7660	16	6	anti	anti	ADJ
ap-7660	16	7	-	-	ADJ
ap-7660	16	8	linear	linear	ADJ
ap-7660	16	9	symmetry	symmetry	NOUN
ap-7660	16	10	,	,	PUNCT
ap-7660	16	11	which	which	PRON
ap-7660	16	12	we	we	PRON
ap-7660	16	13	refer	refer	VERB
ap-7660	16	14	to	to	ADP
ap-7660	16	15	as	as	ADP
ap-7660	16	16	pt	pt	PROPN
ap-7660	16	17	symmetry	symmetry	NOUN
ap-7660	16	18	,	,	PUNCT
ap-7660	16	19	that	that	SCONJ
ap-7660	16	20	satisfies	satisfy	VERB
ap-7660	16	21	[	[	X
ap-7660	16	22	pt	pt	X
ap-7660	16	23	,	,	PUNCT
ap-7660	16	24	m	m	VERB
ap-7660	16	25	]	]	X
ap-7660	16	26	=	=	PUNCT
ap-7660	16	27	0	0	NUM
ap-7660	16	28	,	,	PUNCT
ap-7660	16	29	mv	mv	PROPN
ap-7660	16	30	=	=	SYM
ap-7660	16	31	λv	λv	PROPN
ap-7660	16	32	,	,	PUNCT
ap-7660	16	33	pt	pt	PROPN
ap-7660	16	34	v	v	NOUN
ap-7660	16	35	=	=	SYM
ap-7660	16	36	eiθv	eiθv	X
ap-7660	16	37	,	,	PUNCT
ap-7660	16	38	where	where	SCONJ
ap-7660	16	39	{	{	PUNCT
ap-7660	16	40	v	v	NOUN
ap-7660	16	41	,	,	PUNCT
ap-7660	16	42	λ	λ	NOUN
ap-7660	16	43	}	}	PUNCT
ap-7660	16	44	are	be	AUX
ap-7660	16	45	eigenvectors	eigenvector	NOUN
ap-7660	16	46	and	and	CCONJ
ap-7660	16	47	eigenvalues	eigenvalue	NOUN
ap-7660	16	48	of	of	ADP
ap-7660	16	49	the	the	DET
ap-7660	16	50	mass	mass	ADJ
ap-7660	16	51	matrix	matrix	NOUN
ap-7660	16	52	.	.	PUNCT
ap-7660	17	1	from	from	ADP
ap-7660	17	2	this	this	PRON
ap-7660	17	3	,	,	PUNCT
ap-7660	17	4	it	it	PRON
ap-7660	17	5	is	be	AUX
ap-7660	17	6	trivial	trivial	ADJ
ap-7660	17	7	to	to	PART
ap-7660	17	8	show	show	VERB
ap-7660	17	9	that	that	SCONJ
ap-7660	17	10	the	the	DET
ap-7660	17	11	eigenvalues	eigenvalue	NOUN
ap-7660	17	12	are	be	AUX
ap-7660	17	13	real	real	ADJ
ap-7660	17	14	pt	pt	X
ap-7660	17	15	mvi	mvi	NOUN
ap-7660	17	16	=	=	NOUN
ap-7660	17	17	pt	pt	X
ap-7660	17	18	λivi	λivi	NOUN
ap-7660	18	1	=	=	X
ap-7660	18	2	λ∗	λ∗	NOUN
ap-7660	19	1	i	i	PRON
ap-7660	19	2	pt	pt	VERB
ap-7660	19	3	vi	vi	PROPN
ap-7660	19	4	=	=	SYM
ap-7660	19	5	λ∗	λ∗	PROPN
ap-7660	19	6	i	i	PROPN
ap-7660	19	7	eiθivi	eiθivi	NOUN
ap-7660	19	8	,	,	PUNCT
ap-7660	19	9	pt	pt	X
ap-7660	19	10	mvi	mvi	PROPN
ap-7660	19	11	=	=	SYM
ap-7660	19	12	mpt	mpt	PROPN
ap-7660	19	13	vi	vi	NOUN
ap-7660	19	14	=	=	NOUN
ap-7660	19	15	meiθivi	meiθivi	NOUN
ap-7660	19	16	=	=	SYM
ap-7660	19	17	λie	λie	NOUN
ap-7660	19	18	iθivi	iθivi	NOUN
ap-7660	19	19	.	.	PUNCT
ap-7660	20	1	it	it	PRON
ap-7660	20	2	was	be	AUX
ap-7660	20	3	shown	show	VERB
ap-7660	20	4	in	in	ADP
ap-7660	20	5	[	[	X
ap-7660	20	6	8	8	NUM
ap-7660	20	7	]	]	PUNCT
ap-7660	20	8	that	that	SCONJ
ap-7660	20	9	this	this	DET
ap-7660	20	10	pt	pt	NOUN
ap-7660	20	11	symmetry	symmetry	NOUN
ap-7660	20	12	is	be	AUX
ap-7660	20	13	related	relate	VERB
ap-7660	20	14	to	to	ADP
ap-7660	20	15	the	the	DET
ap-7660	20	16	cpt	cpt	NOUN
ap-7660	20	17	symmetry	symmetry	NOUN
ap-7660	20	18	of	of	ADP
ap-7660	20	19	the	the	DET
ap-7660	20	20	field	field	NOUN
ap-7660	20	21	-	-	PUNCT
ap-7660	20	22	theoretic	theoretic	NOUN
ap-7660	20	23	action	action	NOUN
ap-7660	20	24	.	.	PUNCT
ap-7660	21	1	on	on	ADP
ap-7660	21	2	the	the	DET
ap-7660	21	3	other	other	ADJ
ap-7660	21	4	hand	hand	NOUN
ap-7660	21	5	,	,	PUNCT
ap-7660	21	6	the	the	DET
ap-7660	21	7	classical	classical	ADJ
ap-7660	21	8	energy	energy	NOUN
ap-7660	21	9	of	of	ADP
ap-7660	21	10	the	the	DET
ap-7660	21	11	soliton	soliton	NOUN
ap-7660	21	12	solution	solution	NOUN
ap-7660	21	13	is	be	AUX
ap-7660	21	14	found	find	VERB
ap-7660	21	15	by	by	ADP
ap-7660	21	16	inserting	insert	VERB
ap-7660	21	17	the	the	DET
ap-7660	21	18	solution	solution	NOUN
ap-7660	21	19	into	into	ADP
ap-7660	21	20	the	the	DET
ap-7660	21	21	hamiltonian	hamiltonian	ADJ
ap-7660	21	22	e	e	NOUN
ap-7660	21	23	=	=	SYM
ap-7660	21	24	h[ϕ	h[ϕ	X
ap-7660	21	25	]	]	X
ap-7660	21	26	=	=	SYM
ap-7660	21	27	∫	∫	PROPN
ap-7660	21	28	d3xh(ϕ	d3xh(ϕ	PROPN
ap-7660	21	29	)	)	PUNCT
ap-7660	21	30	.	.	PUNCT
ap-7660	22	1	therefore	therefore	ADV
ap-7660	22	2	,	,	PUNCT
ap-7660	22	3	the	the	DET
ap-7660	22	4	techniques	technique	NOUN
ap-7660	22	5	from	from	ADP
ap-7660	22	6	pt	pt	PRON
ap-7660	22	7	symmetric	symmetric	ADJ
ap-7660	22	8	quantum	quantum	ADJ
ap-7660	22	9	mechanics	mechanic	NOUN
ap-7660	22	10	shown	show	VERB
ap-7660	22	11	above	above	ADV
ap-7660	22	12	can	can	AUX
ap-7660	22	13	not	not	PART
ap-7660	22	14	be	be	AUX
ap-7660	22	15	applied	apply	VERB
ap-7660	22	16	.	.	PUNCT
ap-7660	23	1	we	we	PRON
ap-7660	23	2	will	will	AUX
ap-7660	23	3	show	show	VERB
ap-7660	23	4	below	below	ADP
ap-7660	23	5	that	that	PRON
ap-7660	23	6	the	the	DET
ap-7660	23	7	energy	energy	NOUN
ap-7660	23	8	of	of	ADP
ap-7660	23	9	the	the	DET
ap-7660	23	10	soliton	soliton	NOUN
ap-7660	23	11	solutions	solution	NOUN
ap-7660	23	12	are	be	AUX
ap-7660	23	13	real	real	ADJ
ap-7660	23	14	when	when	SCONJ
ap-7660	23	15	the	the	DET
ap-7660	23	16	three	three	NUM
ap-7660	23	17	conditions	condition	NOUN
ap-7660	23	18	stated	state	VERB
ap-7660	23	19	below	below	ADP
ap-7660	23	20	holds	hold	NOUN
ap-7660	23	21	.	.	PUNCT
ap-7660	24	1	therefore	therefore	ADV
ap-7660	24	2	they	they	PRON
ap-7660	24	3	are	be	AUX
ap-7660	24	4	sufficient	sufficient	ADJ
ap-7660	24	5	conditions	condition	NOUN
ap-7660	24	6	to	to	PART
ap-7660	24	7	guarantee	guarantee	VERB
ap-7660	24	8	the	the	DET
ap-7660	24	9	real	real	ADJ
ap-7660	24	10	value	value	NOUN
ap-7660	24	11	of	of	ADP
ap-7660	24	12	particles	particle	NOUN
ap-7660	24	13	in	in	ADP
ap-7660	24	14	the	the	DET
ap-7660	24	15	model	model	NOUN
ap-7660	24	16	.	.	PUNCT
ap-7660	25	1	however	however	ADV
ap-7660	25	2	,	,	PUNCT
ap-7660	25	3	we	we	PRON
ap-7660	25	4	do	do	AUX
ap-7660	25	5	not	not	PART
ap-7660	25	6	claim	claim	VERB
ap-7660	25	7	that	that	SCONJ
ap-7660	25	8	these	these	PRON
ap-7660	25	9	are	be	AUX
ap-7660	25	10	necessary	necessary	ADJ
ap-7660	25	11	conditions	condition	NOUN
ap-7660	25	12	.	.	PUNCT
ap-7660	26	1	let	let	VERB
ap-7660	26	2	{	{	PUNCT
ap-7660	26	3	ϕ1	ϕ1	VERB
ap-7660	26	4	,	,	PUNCT
ap-7660	26	5	ϕ2	ϕ2	ADV
ap-7660	26	6	}	}	PUNCT
ap-7660	26	7	be	be	AUX
ap-7660	26	8	a	a	DET
ap-7660	26	9	set	set	NOUN
ap-7660	26	10	of	of	ADP
ap-7660	26	11	distinct	distinct	ADJ
ap-7660	26	12	(	(	PUNCT
ap-7660	26	13	or	or	CCONJ
ap-7660	26	14	identical	identical	ADJ
ap-7660	26	15	)	)	PUNCT
ap-7660	26	16	solutions	solution	NOUN
ap-7660	26	17	to	to	ADP
ap-7660	26	18	the	the	DET
ap-7660	26	19	equations	equation	NOUN
ap-7660	26	20	of	of	ADP
ap-7660	26	21	motion	motion	NOUN
ap-7660	26	22	δl	δl	PROPN
ap-7660	26	23	/	/	SYM
ap-7660	26	24	δϕ	δϕ	PROPN
ap-7660	26	25	−	−	PROPN
ap-7660	26	26	∂µ(δl	∂µ(δl	PROPN
ap-7660	26	27	/	/	SYM
ap-7660	26	28	δ∂µϕ	δ∂µϕ	NOUN
ap-7660	26	29	)	)	PUNCT
ap-7660	26	30	=	=	SYM
ap-7660	27	1	0	0	NUM
ap-7660	27	2	,	,	PUNCT
ap-7660	27	3	where	where	SCONJ
ap-7660	27	4	l(ϕ	l(ϕ	NUM
ap-7660	27	5	)	)	PUNCT
ap-7660	27	6	is	be	AUX
ap-7660	27	7	the	the	DET
ap-7660	27	8	field	field	NOUN
ap-7660	27	9	-	-	PUNCT
ap-7660	27	10	theoretic	theoretic	NOUN
ap-7660	27	11	lagrangian	lagrangian	ADJ
ap-7660	27	12	density	density	NOUN
ap-7660	27	13	.	.	PUNCT
ap-7660	28	1	the	the	DET
ap-7660	28	2	classical	classical	ADJ
ap-7660	28	3	energies	energy	NOUN
ap-7660	28	4	of	of	ADP
ap-7660	28	5	the	the	DET
ap-7660	28	6	solution	solution	NOUN
ap-7660	28	7	are	be	AUX
ap-7660	28	8	given	give	VERB
ap-7660	28	9	by	by	ADP
ap-7660	28	10	inserting	insert	VERB
ap-7660	28	11	the	the	DET
ap-7660	28	12	solution	solution	NOUN
ap-7660	28	13	into	into	ADP
ap-7660	28	14	the	the	DET
ap-7660	28	15	hamiltonian	hamiltonian	NOUN
ap-7660	28	16	,	,	PUNCT
ap-7660	28	17	ei	ei	X
ap-7660	28	18	=	=	PUNCT
ap-7660	28	19	h[ϕi	h[ϕi	PROPN
ap-7660	28	20	]	]	X
ap-7660	28	21	=	=	SYM
ap-7660	28	22	∫	∫	X
ap-7660	28	23	d3xh(ϕi	d3xh(ϕi	PROPN
ap-7660	28	24	)	)	PUNCT
ap-7660	28	25	,	,	PUNCT
ap-7660	28	26	for	for	ADP
ap-7660	28	27	i	i	PRON
ap-7660	28	28	∈	∈	PROPN
ap-7660	28	29	{	{	PUNCT
ap-7660	28	30	1	1	NUM
ap-7660	28	31	,	,	PUNCT
ap-7660	28	32	2	2	NUM
ap-7660	28	33	}	}	PUNCT
ap-7660	28	34	.	.	PUNCT
ap-7660	29	1	the	the	DET
ap-7660	29	2	classical	classical	ADJ
ap-7660	29	3	mass	mass	NOUN
ap-7660	29	4	of	of	ADP
ap-7660	29	5	the	the	DET
ap-7660	29	6	solution	solution	NOUN
ap-7660	29	7	ϕ1	ϕ1	NOUN
ap-7660	29	8	and	and	CCONJ
ap-7660	29	9	ϕ2	ϕ2	ADV
ap-7660	29	10	are	be	AUX
ap-7660	29	11	real	real	ADJ
ap-7660	29	12	if	if	SCONJ
ap-7660	29	13	there	there	PRON
ap-7660	29	14	exist	exist	VERB
ap-7660	29	15	some	some	DET
ap-7660	29	16	anti	anti	ADJ
ap-7660	29	17	-	-	ADJ
ap-7660	29	18	linear	linear	ADJ
ap-7660	29	19	symmetry	symmetry	NOUN
ap-7660	29	20	cpt	cpt	PROPN
ap-7660	29	21	(	(	PUNCT
ap-7660	29	22	note	note	VERB
ap-7660	29	23	that	that	PRON
ap-7660	29	24	is	be	AUX
ap-7660	29	25	it	it	PRON
ap-7660	29	26	not	not	PART
ap-7660	29	27	the	the	DET
ap-7660	29	28	standard	standard	ADJ
ap-7660	29	29	cpt	cpt	PROPN
ap-7660	29	30	symmetry	symmetry	NOUN
ap-7660	29	31	in	in	ADP
ap-7660	29	32	quantum	quantum	ADJ
ap-7660	29	33	field	field	NOUN
ap-7660	29	34	theory	theory	NOUN
ap-7660	29	35	)	)	PUNCT
ap-7660	29	36	such	such	ADJ
ap-7660	29	37	that	that	SCONJ
ap-7660	29	38	three	three	NUM
ap-7660	29	39	conditions	condition	NOUN
ap-7660	29	40	are	be	AUX
ap-7660	29	41	satisfied	satisfied	ADJ
ap-7660	29	42	:	:	PUNCT
ap-7660	29	43	(	(	PUNCT
ap-7660	29	44	1	1	NUM
ap-7660	29	45	.	.	PUNCT
ap-7660	29	46	)	)	PUNCT
ap-7660	30	1	cpt	cpt	NOUN
ap-7660	30	2	:	:	PUNCT
ap-7660	30	3	h[ϕ(x	h[ϕ(x	X
ap-7660	30	4	)	)	PUNCT
ap-7660	30	5	]	]	PUNCT
ap-7660	31	1	→	→	PUNCT
ap-7660	31	2	h[cpt	h[cpt	NOUN
ap-7660	31	3	ϕ(x	ϕ(x	NOUN
ap-7660	31	4	)	)	PUNCT
ap-7660	31	5	]	]	PUNCT
ap-7660	32	1	=	=	SYM
ap-7660	32	2	h†[ϕ(−x	h†[ϕ(−x	NOUN
ap-7660	32	3	)	)	PUNCT
ap-7660	32	4	]	]	PUNCT
ap-7660	32	5	.	.	PUNCT
ap-7660	33	1	(	(	PUNCT
ap-7660	33	2	2	2	NUM
ap-7660	33	3	.	.	PUNCT
ap-7660	33	4	)	)	PUNCT
ap-7660	33	5	cpt	cpt	NOUN
ap-7660	33	6	:	:	PUNCT
ap-7660	33	7	ϕ1(x	ϕ1(x	NUM
ap-7660	33	8	)	)	PUNCT
ap-7660	33	9	→	→	SYM
ap-7660	33	10	ϕ2(−x	ϕ2(−x	NOUN
ap-7660	33	11	)	)	PUNCT
ap-7660	33	12	.	.	PUNCT
ap-7660	34	1	(	(	PUNCT
ap-7660	34	2	3	3	NUM
ap-7660	34	3	.	.	PUNCT
ap-7660	34	4	)	)	PUNCT
ap-7660	34	5	h[ϕ1	h[ϕ1	NOUN
ap-7660	34	6	]	]	X
ap-7660	35	1	=	=	SYM
ap-7660	35	2	h[ϕ2	h[ϕ2	NOUN
ap-7660	35	3	]	]	X
ap-7660	35	4	.	.	PUNCT
ap-7660	36	1	if	if	SCONJ
ap-7660	36	2	two	two	NUM
ap-7660	36	3	solutions	solution	NOUN
ap-7660	36	4	are	be	AUX
ap-7660	36	5	identical	identical	ADJ
ap-7660	36	6	ϕ1	ϕ1	NOUN
ap-7660	36	7	=	=	SYM
ap-7660	36	8	ϕ2	ϕ2	ADV
ap-7660	36	9	,	,	PUNCT
ap-7660	36	10	then	then	ADV
ap-7660	36	11	the	the	DET
ap-7660	36	12	above	above	ADJ
ap-7660	36	13	condition	condition	NOUN
ap-7660	36	14	reduces	reduce	VERB
ap-7660	36	15	to	to	ADP
ap-7660	36	16	the	the	DET
ap-7660	36	17	reality	reality	NOUN
ap-7660	36	18	condition	condition	NOUN
ap-7660	36	19	of	of	ADP
ap-7660	36	20	the	the	DET
ap-7660	36	21	soliton	soliton	NOUN
ap-7660	36	22	solution	solution	NOUN
ap-7660	36	23	already	already	ADV
ap-7660	36	24	derived	derive	VERB
ap-7660	36	25	in	in	ADP
ap-7660	36	26	[	[	X
ap-7660	36	27	15	15	NUM
ap-7660	36	28	]	]	PUNCT
ap-7660	36	29	.	.	PUNCT
ap-7660	37	1	using	use	VERB
ap-7660	37	2	the	the	DET
ap-7660	37	3	above	above	ADJ
ap-7660	37	4	three	three	NUM
ap-7660	37	5	conditions	condition	NOUN
ap-7660	37	6	,	,	PUNCT
ap-7660	37	7	the	the	DET
ap-7660	37	8	real	real	ADJ
ap-7660	37	9	value	value	NOUN
ap-7660	37	10	of	of	ADP
ap-7660	37	11	the	the	DET
ap-7660	37	12	classical	classical	ADJ
ap-7660	37	13	mass	mass	NOUN
ap-7660	37	14	can	can	AUX
ap-7660	37	15	easily	easily	ADV
ap-7660	37	16	be	be	AUX
ap-7660	37	17	shown	show	VERB
ap-7660	37	18	by	by	ADP
ap-7660	37	19	the	the	DET
ap-7660	37	20	following	follow	VERB
ap-7660	37	21	argument∫	argument∫	NOUN
ap-7660	37	22	d3xh[cpt	d3xh[cpt	PROPN
ap-7660	37	23	ϕ(x	ϕ(x	PROPN
ap-7660	37	24	)	)	PUNCT
ap-7660	37	25	]	]	PUNCT
ap-7660	38	1	(	(	PUNCT
ap-7660	38	2	1)=	1)=	NUM
ap-7660	38	3	∫	∫	PROPN
ap-7660	38	4	d3xh†[ϕ(−x	d3xh†[ϕ(−x	PROPN
ap-7660	38	5	)	)	PUNCT
ap-7660	38	6	]	]	PUNCT
ap-7660	39	1	=	=	PUNCT
ap-7660	40	1	m†	m†	ADJ
ap-7660	40	2	1	1	NUM
ap-7660	40	3	,	,	PUNCT
ap-7660	40	4	(	(	PUNCT
ap-7660	40	5	2)=	2)=	NUM
ap-7660	40	6	∫	∫	PROPN
ap-7660	40	7	d3xh[ϕ2(−x	d3xh[ϕ2(−x	PROPN
ap-7660	40	8	)	)	PUNCT
ap-7660	40	9	]	]	PUNCT
ap-7660	41	1	=	=	SYM
ap-7660	41	2	m2	m2	PROPN
ap-7660	41	3	,	,	PUNCT
ap-7660	41	4	=	=	PRON
ap-7660	41	5	⇒	⇒	VERB
ap-7660	41	6	m†	m†	ADV
ap-7660	41	7	1	1	NUM
ap-7660	41	8	=	=	SYM
ap-7660	41	9	m2	m2	PROPN
ap-7660	41	10	(	(	PUNCT
ap-7660	41	11	3)=⇒	3)=⇒	PROPN
ap-7660	41	12	m†	m†	ADJ
ap-7660	41	13	1	1	NUM
ap-7660	41	14	=	=	SYM
ap-7660	41	15	m1	m1	NOUN
ap-7660	41	16	,	,	PUNCT
ap-7660	41	17	where	where	SCONJ
ap-7660	41	18	numbers	number	NOUN
ap-7660	41	19	above	above	ADP
ap-7660	41	20	the	the	DET
ap-7660	41	21	equal	equal	ADJ
ap-7660	41	22	signs	sign	NOUN
ap-7660	41	23	indicate	indicate	VERB
ap-7660	41	24	the	the	DET
ap-7660	41	25	condition	condition	NOUN
ap-7660	41	26	number	number	NOUN
ap-7660	41	27	.	.	PUNCT
ap-7660	42	1	the	the	DET
ap-7660	42	2	above	above	ADJ
ap-7660	42	3	analysis	analysis	NOUN
ap-7660	42	4	can	can	AUX
ap-7660	42	5	be	be	AUX
ap-7660	42	6	performed	perform	VERB
ap-7660	42	7	directly	directly	ADV
ap-7660	42	8	on	on	ADP
ap-7660	42	9	the	the	DET
ap-7660	42	10	complex	complex	ADJ
ap-7660	42	11	model	model	NOUN
ap-7660	42	12	.	.	PUNCT
ap-7660	43	1	however	however	ADV
ap-7660	43	2	,	,	PUNCT
ap-7660	43	3	the	the	DET
ap-7660	43	4	non	non	ADJ
ap-7660	43	5	-	-	ADJ
ap-7660	43	6	hermitian	hermitian	ADJ
ap-7660	43	7	theory	theory	NOUN
ap-7660	43	8	is	be	AUX
ap-7660	43	9	only	only	ADV
ap-7660	43	10	well	well	ADV
ap-7660	43	11	-	-	PUNCT
ap-7660	43	12	defined	define	VERB
ap-7660	43	13	once	once	SCONJ
ap-7660	43	14	the	the	DET
ap-7660	43	15	inner	inner	ADJ
ap-7660	43	16	-	-	PUNCT
ap-7660	43	17	product	product	NOUN
ap-7660	43	18	is	be	AUX
ap-7660	43	19	identified	identify	VERB
ap-7660	43	20	.	.	PUNCT
ap-7660	44	1	the	the	DET
ap-7660	44	2	modern	modern	ADJ
ap-7660	44	3	way	way	NOUN
ap-7660	44	4	of	of	ADP
ap-7660	44	5	the	the	DET
ap-7660	44	6	well	well	ADV
ap-7660	44	7	-	-	PUNCT
ap-7660	44	8	defined	define	VERB
ap-7660	44	9	non	non	ADJ
ap-7660	44	10	-	-	ADJ
ap-7660	44	11	hermitian	hermitian	ADJ
ap-7660	44	12	quantum	quantum	ADJ
ap-7660	44	13	mechanics	mechanic	NOUN
ap-7660	44	14	was	be	AUX
ap-7660	44	15	first	first	ADV
ap-7660	44	16	realised	realise	VERB
ap-7660	44	17	by	by	ADP
ap-7660	44	18	frederik	frederik	PROPN
ap-7660	44	19	scholtz	scholtz	PROPN
ap-7660	44	20	,	,	PUNCT
ap-7660	44	21	hendrik	hendrik	PROPN
ap-7660	44	22	geyer	geyer	PROPN
ap-7660	44	23	,	,	PUNCT
ap-7660	44	24	and	and	CCONJ
ap-7660	44	25	fritz	fritz	PROPN
ap-7660	44	26	hahne	hahne	PROPN
ap-7660	44	27	in	in	ADP
ap-7660	44	28	1992	1992	NUM
ap-7660	44	29	,	,	PUNCT
ap-7660	44	30	[	[	X
ap-7660	44	31	16	16	NUM
ap-7660	44	32	]	]	PUNCT
ap-7660	44	33	.	.	PUNCT
ap-7660	45	1	the	the	DET
ap-7660	45	2	authors	author	NOUN
ap-7660	45	3	used	use	VERB
ap-7660	45	4	the	the	DET
ap-7660	45	5	mathematical	mathematical	ADJ
ap-7660	45	6	condition	condition	NOUN
ap-7660	45	7	on	on	ADP
ap-7660	45	8	the	the	DET
ap-7660	45	9	operator	operator	NOUN
ap-7660	45	10	called	call	VERB
ap-7660	45	11	the	the	DET
ap-7660	45	12	quasi	quasi	NOUN
ap-7660	45	13	-	-	NOUN
ap-7660	45	14	hermiticity	hermiticity	ADJ
ap-7660	45	15	(	(	PUNCT
ap-7660	45	16	the	the	DET
ap-7660	45	17	term	term	NOUN
ap-7660	45	18	was	be	AUX
ap-7660	45	19	first	first	ADV
ap-7660	45	20	coined	coin	VERB
ap-7660	45	21	in	in	ADP
ap-7660	45	22	[	[	X
ap-7660	45	23	17	17	NUM
ap-7660	45	24	]	]	PUNCT
ap-7660	45	25	,	,	PUNCT
ap-7660	45	26	but	but	CCONJ
ap-7660	45	27	the	the	DET
ap-7660	45	28	metric	metric	NOUN
ap-7660	45	29	was	be	AUX
ap-7660	45	30	197	197	NUM
ap-7660	45	31	https://doi.org/10.14311/ap.2022.62.0197	https://doi.org/10.14311/ap.2022.62.0197	PROPN
ap-7660	45	32	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-7660	45	33	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-7660	45	34	takanobu	takanobu	PROPN
ap-7660	45	35	taira	taira	PROPN
ap-7660	45	36	acta	acta	PROPN
ap-7660	45	37	polytechnica	polytechnica	PROPN
ap-7660	45	38	not	not	PART
ap-7660	45	39	given	give	VERB
ap-7660	45	40	)	)	PUNCT
ap-7660	45	41	to	to	PART
ap-7660	45	42	define	define	VERB
ap-7660	45	43	the	the	DET
ap-7660	45	44	positive	positive	ADJ
ap-7660	45	45	definite	definite	ADJ
ap-7660	45	46	inner	inner	ADJ
ap-7660	45	47	product	product	NOUN
ap-7660	45	48	.	.	PUNCT
ap-7660	46	1	the	the	DET
ap-7660	46	2	quasi	quasi	NOUN
ap-7660	46	3	-	-	NOUN
ap-7660	46	4	hermiticity	hermiticity	NOUN
ap-7660	46	5	is	be	AUX
ap-7660	46	6	defined	define	VERB
ap-7660	46	7	as	as	ADP
ap-7660	46	8	a	a	DET
ap-7660	46	9	condition	condition	NOUN
ap-7660	46	10	on	on	ADP
ap-7660	46	11	the	the	DET
ap-7660	46	12	bounded	bounded	ADJ
ap-7660	46	13	linear	linear	ADJ
ap-7660	46	14	operator	operator	NOUN
ap-7660	46	15	of	of	ADP
ap-7660	46	16	the	the	DET
ap-7660	46	17	hilbert	hilbert	PROPN
ap-7660	46	18	space	space	NOUN
ap-7660	46	19	a	a	DET
ap-7660	46	20	:	:	PUNCT
ap-7660	46	21	h	h	NOUN
ap-7660	46	22	→	→	SYM
ap-7660	46	23	h	h	NOUN
ap-7660	46	24	,	,	PUNCT
ap-7660	46	25	which	which	PRON
ap-7660	46	26	satisfies	satisfy	VERB
ap-7660	46	27	(	(	PUNCT
ap-7660	46	28	i)⟨v|ρv⟩	i)⟨v|ρv⟩	NOUN
ap-7660	46	29	>	>	X
ap-7660	46	30	0	0	PUNCT
ap-7660	46	31	for	for	ADP
ap-7660	46	32	all	all	DET
ap-7660	46	33	|v⟩	|v⟩	PROPN
ap-7660	46	34	∈	∈	PROPN
ap-7660	46	35	h	h	NOUN
ap-7660	46	36	and	and	CCONJ
ap-7660	46	37	|v⟩	|v⟩	NOUN
ap-7660	46	38	=	=	SYM
ap-7660	46	39	̸	̸	NUM
ap-7660	46	40	0	0	NUM
ap-7660	46	41	.	.	PUNCT
ap-7660	47	1	(	(	PUNCT
ap-7660	47	2	ii)ρa	ii)ρa	X
ap-7660	47	3	=	=	SYM
ap-7660	47	4	a†ρ	a†ρ	NUM
ap-7660	47	5	.	.	PUNCT
ap-7660	48	1	where	where	SCONJ
ap-7660	48	2	the	the	DET
ap-7660	48	3	bounded	bounded	ADJ
ap-7660	48	4	hermitian	hermitian	PROPN
ap-7660	48	5	linear	linear	PROPN
ap-7660	48	6	operator	operator	NOUN
ap-7660	48	7	ρ	ρ	NOUN
ap-7660	48	8	:	:	PUNCT
ap-7660	48	9	h	h	NOUN
ap-7660	48	10	→	→	SYM
ap-7660	48	11	h	h	NOUN
ap-7660	48	12	is	be	AUX
ap-7660	48	13	often	often	ADV
ap-7660	48	14	called	call	VERB
ap-7660	48	15	the	the	DET
ap-7660	48	16	metric	metric	ADJ
ap-7660	48	17	operator	operator	NOUN
ap-7660	48	18	because	because	SCONJ
ap-7660	48	19	the	the	DET
ap-7660	48	20	inner	inner	ADJ
ap-7660	48	21	product	product	NOUN
ap-7660	48	22	is	be	AUX
ap-7660	48	23	defined	define	VERB
ap-7660	48	24	by	by	ADP
ap-7660	48	25	the	the	DET
ap-7660	48	26	operator	operator	NOUN
ap-7660	48	27	⟨·|·⟩ρ	⟨·|·⟩ρ	PROPN
ap-7660	48	28	:	:	PUNCT
ap-7660	48	29	=	=	PUNCT
ap-7660	48	30	⟨·|ρ·⟩	⟨·|ρ·⟩	NOUN
ap-7660	48	31	restores	restore	VERB
ap-7660	48	32	the	the	DET
ap-7660	48	33	hermiticity	hermiticity	NOUN
ap-7660	48	34	of	of	ADP
ap-7660	48	35	the	the	DET
ap-7660	48	36	operator	operator	NOUN
ap-7660	48	37	.	.	PUNCT
ap-7660	49	1	this	this	DET
ap-7660	49	2	result	result	NOUN
ap-7660	49	3	can	can	AUX
ap-7660	49	4	be	be	AUX
ap-7660	49	5	shown	show	VERB
ap-7660	49	6	by	by	ADP
ap-7660	49	7	using	use	VERB
ap-7660	49	8	the	the	DET
ap-7660	49	9	condition(ii	condition(ii	PROPN
ap-7660	49	10	)	)	PUNCT
ap-7660	49	11	⟨v|aw⟩ρ	⟨v|aw⟩ρ	PROPN
ap-7660	49	12	≡	≡	PROPN
ap-7660	49	13	⟨v|ρaw⟩	⟨v|ρaw⟩	PROPN
ap-7660	49	14	=	=	PROPN
ap-7660	49	15	⟨v|a†ρw⟩	⟨v|a†ρw⟩	NOUN
ap-7660	49	16	=	=	PUNCT
ap-7660	49	17	⟨av|ρw⟩	⟨av|ρw⟩	X
ap-7660	50	1	=	=	PUNCT
ap-7660	50	2	⟨av|w⟩ρ	⟨av|w⟩ρ	PUNCT
ap-7660	50	3	,	,	PUNCT
ap-7660	50	4	for	for	ADP
ap-7660	50	5	all	all	DET
ap-7660	50	6	|v⟩	|v⟩	NOUN
ap-7660	50	7	,	,	PUNCT
ap-7660	50	8	|w⟩	|w⟩	NOUN
ap-7660	50	9	∈	∈	PROPN
ap-7660	50	10	h.	h.	NOUN
ap-7660	50	11	note	note	VERB
ap-7660	50	12	that	that	SCONJ
ap-7660	50	13	the	the	DET
ap-7660	50	14	quasi	quasi	NOUN
ap-7660	50	15	-	-	NOUN
ap-7660	50	16	hermiticity	hermiticity	NOUN
ap-7660	50	17	alone	alone	ADV
ap-7660	50	18	does	do	AUX
ap-7660	50	19	not	not	PART
ap-7660	50	20	guarantee	guarantee	VERB
ap-7660	50	21	the	the	DET
ap-7660	50	22	real	real	ADJ
ap-7660	50	23	energy	energy	NOUN
ap-7660	50	24	spectrum	spectrum	NOUN
ap-7660	50	25	of	of	ADP
ap-7660	50	26	the	the	DET
ap-7660	50	27	hamiltonian	hamiltonian	NOUN
ap-7660	50	28	.	.	PUNCT
ap-7660	51	1	in	in	ADP
ap-7660	51	2	fact	fact	NOUN
ap-7660	51	3	,	,	PUNCT
ap-7660	51	4	one	one	PRON
ap-7660	51	5	requires	require	VERB
ap-7660	51	6	two	two	NUM
ap-7660	51	7	extra	extra	ADJ
ap-7660	51	8	conditions	condition	NOUN
ap-7660	51	9	.	.	PUNCT
ap-7660	52	1	(	(	PUNCT
ap-7660	52	2	iii)the	iii)the	DET
ap-7660	52	3	metric	metric	ADJ
ap-7660	52	4	operator	operator	NOUN
ap-7660	52	5	is	be	AUX
ap-7660	52	6	invertible	invertible	ADJ
ap-7660	52	7	.	.	PUNCT
ap-7660	53	1	(	(	PUNCT
ap-7660	53	2	iv)ρ	iv)ρ	X
ap-7660	53	3	=	=	PUNCT
ap-7660	53	4	η†η	η†η	NUM
ap-7660	53	5	.	.	PUNCT
ap-7660	54	1	the	the	DET
ap-7660	54	2	operator	operator	NOUN
ap-7660	54	3	which	which	PRON
ap-7660	54	4	satisfies	satisfy	VERB
ap-7660	54	5	only	only	ADV
ap-7660	54	6	conditions	condition	NOUN
ap-7660	54	7	(	(	PUNCT
ap-7660	54	8	ii	ii	NOUN
ap-7660	54	9	)	)	PUNCT
ap-7660	54	10	and	and	CCONJ
ap-7660	54	11	(	(	PUNCT
ap-7660	54	12	iv	iv	X
ap-7660	54	13	)	)	PUNCT
ap-7660	54	14	is	be	AUX
ap-7660	54	15	referred	refer	VERB
ap-7660	54	16	to	to	ADP
ap-7660	54	17	as	as	ADP
ap-7660	54	18	the	the	DET
ap-7660	54	19	pseudo	pseudo	NOUN
ap-7660	54	20	-	-	ADJ
ap-7660	54	21	hermitian	hermitian	ADJ
ap-7660	54	22	operator	operator	NOUN
ap-7660	54	23	,	,	PUNCT
ap-7660	54	24	which	which	PRON
ap-7660	54	25	was	be	AUX
ap-7660	54	26	first	first	ADV
ap-7660	54	27	introduced	introduce	VERB
ap-7660	54	28	in	in	ADP
ap-7660	54	29	[	[	X
ap-7660	54	30	18	18	NUM
ap-7660	54	31	]	]	PUNCT
ap-7660	54	32	.	.	PUNCT
ap-7660	55	1	these	these	DET
ap-7660	55	2	extra	extra	ADJ
ap-7660	55	3	conditions	condition	NOUN
ap-7660	55	4	were	be	AUX
ap-7660	55	5	considered	consider	VERB
ap-7660	55	6	in	in	ADP
ap-7660	55	7	[	[	X
ap-7660	55	8	16	16	NUM
ap-7660	55	9	]	]	PUNCT
ap-7660	55	10	to	to	PART
ap-7660	55	11	prove	prove	VERB
ap-7660	55	12	that	that	SCONJ
ap-7660	55	13	,	,	PUNCT
ap-7660	55	14	given	give	VERB
ap-7660	55	15	a	a	DET
ap-7660	55	16	set	set	NOUN
ap-7660	55	17	of	of	ADP
ap-7660	55	18	pseudo	pseudo	NOUN
ap-7660	55	19	-	-	ADJ
ap-7660	55	20	hermitian	hermitian	ADJ
ap-7660	55	21	operators	operator	NOUN
ap-7660	55	22	a	a	DET
ap-7660	55	23	=	=	X
ap-7660	55	24	{	{	PUNCT
ap-7660	55	25	ai	ai	NOUN
ap-7660	55	26	}	}	PUNCT
ap-7660	55	27	,	,	PUNCT
ap-7660	55	28	the	the	DET
ap-7660	55	29	metric	metric	ADJ
ap-7660	55	30	operator	operator	NOUN
ap-7660	55	31	ρa	ρa	PRON
ap-7660	55	32	which	which	PRON
ap-7660	55	33	satisfies	satisfy	VERB
ap-7660	55	34	conditions	condition	NOUN
ap-7660	55	35	(	(	PUNCT
ap-7660	55	36	i	i	NOUN
ap-7660	55	37	)	)	PUNCT
ap-7660	55	38	,	,	PUNCT
ap-7660	55	39	(	(	PUNCT
ap-7660	55	40	ii	ii	NOUN
ap-7660	55	41	)	)	PUNCT
ap-7660	55	42	,	,	PUNCT
ap-7660	55	43	(	(	PUNCT
ap-7660	55	44	iii	iii	NOUN
ap-7660	55	45	)	)	PUNCT
ap-7660	55	46	and	and	CCONJ
ap-7660	55	47	(	(	PUNCT
ap-7660	55	48	iv	iv	X
ap-7660	55	49	)	)	PUNCT
ap-7660	55	50	for	for	ADP
ap-7660	55	51	all	all	DET
ap-7660	55	52	operators	operator	NOUN
ap-7660	55	53	of	of	ADP
ap-7660	55	54	set	set	NOUN
ap-7660	55	55	a	a	PRON
ap-7660	55	56	is	be	AUX
ap-7660	55	57	uniquely	uniquely	ADV
ap-7660	55	58	determined	determined	ADJ
ap-7660	55	59	if	if	SCONJ
ap-7660	55	60	and	and	CCONJ
ap-7660	55	61	only	only	ADV
ap-7660	55	62	if	if	SCONJ
ap-7660	55	63	all	all	DET
ap-7660	55	64	operators	operator	NOUN
ap-7660	55	65	of	of	ADP
ap-7660	55	66	the	the	DET
ap-7660	55	67	set	set	NOUN
ap-7660	55	68	a	a	PRON
ap-7660	55	69	are	be	AUX
ap-7660	55	70	irreducible	irreducible	ADJ
ap-7660	55	71	on	on	ADP
ap-7660	55	72	the	the	DET
ap-7660	55	73	hilbert	hilbert	PROPN
ap-7660	55	74	space	space	PROPN
ap-7660	55	75	h.	h.	PROPN
ap-7660	55	76	this	this	DET
ap-7660	55	77	procedure	procedure	NOUN
ap-7660	55	78	is	be	AUX
ap-7660	55	79	analogous	analogous	ADJ
ap-7660	55	80	to	to	ADP
ap-7660	55	81	the	the	DET
ap-7660	55	82	dyson	dyson	NOUN
ap-7660	55	83	mapping	mapping	NOUN
ap-7660	55	84	first	first	ADV
ap-7660	55	85	introduced	introduce	VERB
ap-7660	55	86	by	by	ADP
ap-7660	55	87	freeman	freeman	PROPN
ap-7660	55	88	dyson	dyson	PROPN
ap-7660	56	1	[	[	X
ap-7660	56	2	19	19	NUM
ap-7660	56	3	]	]	PUNCT
ap-7660	56	4	used	use	VERB
ap-7660	56	5	in	in	ADP
ap-7660	56	6	the	the	DET
ap-7660	56	7	study	study	NOUN
ap-7660	56	8	of	of	ADP
ap-7660	56	9	nuclear	nuclear	ADJ
ap-7660	56	10	reaction	reaction	NOUN
ap-7660	56	11	[	[	X
ap-7660	56	12	20–22	20–22	NUM
ap-7660	56	13	]	]	X
ap-7660	56	14	,	,	PUNCT
ap-7660	56	15	which	which	PRON
ap-7660	56	16	maps	map	VERB
ap-7660	56	17	the	the	DET
ap-7660	56	18	non	non	ADJ
ap-7660	56	19	-	-	ADJ
ap-7660	56	20	hermitian	hermitian	ADJ
ap-7660	56	21	operator	operator	NOUN
ap-7660	56	22	a	a	PRON
ap-7660	56	23	to	to	ADP
ap-7660	56	24	hermitian	hermitian	ADJ
ap-7660	56	25	operator	operator	NOUN
ap-7660	56	26	η−1aη	η−1aη	NOUN
ap-7660	56	27	via	via	ADP
ap-7660	56	28	dyson	dyson	PROPN
ap-7660	56	29	map	map	PROPN
ap-7660	56	30	η	η	PROPN
ap-7660	56	31	.	.	PROPN
ap-7660	56	32	the	the	DET
ap-7660	56	33	relation	relation	NOUN
ap-7660	56	34	between	between	ADP
ap-7660	56	35	the	the	DET
ap-7660	56	36	metric	metric	ADJ
ap-7660	56	37	operator	operator	NOUN
ap-7660	56	38	and	and	CCONJ
ap-7660	56	39	the	the	DET
ap-7660	56	40	dyson	dyson	NOUN
ap-7660	56	41	map	map	NOUN
ap-7660	56	42	is	be	AUX
ap-7660	56	43	found	find	VERB
ap-7660	56	44	by	by	ADP
ap-7660	56	45	utilising	utilise	VERB
ap-7660	56	46	the	the	DET
ap-7660	56	47	hermiticity	hermiticity	NOUN
ap-7660	56	48	of	of	ADP
ap-7660	56	49	the	the	DET
ap-7660	56	50	expression	expression	NOUN
ap-7660	56	51	η−1aη	η−1aη	NOUN
ap-7660	56	52	in	in	ADP
ap-7660	56	53	the	the	DET
ap-7660	56	54	following	following	ADJ
ap-7660	56	55	way	way	NOUN
ap-7660	56	56	η−1aη	η−1aη	NOUN
ap-7660	56	57	=	=	PUNCT
ap-7660	56	58	(	(	PUNCT
ap-7660	56	59	η−1aη)†	η−1aη)†	NOUN
ap-7660	56	60	=	=	NOUN
ap-7660	56	61	⇒	⇒	VERB
ap-7660	56	62	aη†η	aη†η	PROPN
ap-7660	56	63	=	=	PUNCT
ap-7660	56	64	η†ηa†	η†ηa†	NOUN
ap-7660	56	65	=	=	AUX
ap-7660	56	66	⇒	⇒	VERB
ap-7660	56	67	η†η	η†η	NUM
ap-7660	56	68	=	=	SYM
ap-7660	56	69	ρ	ρ	PROPN
ap-7660	56	70	.	.	PUNCT
ap-7660	57	1	(	(	PUNCT
ap-7660	57	2	1	1	X
ap-7660	57	3	)	)	PUNCT
ap-7660	57	4	we	we	PRON
ap-7660	57	5	will	will	AUX
ap-7660	57	6	utilise	utilise	VERB
ap-7660	57	7	this	this	DET
ap-7660	57	8	mapping	mapping	NOUN
ap-7660	57	9	to	to	PART
ap-7660	57	10	transform	transform	VERB
ap-7660	57	11	the	the	DET
ap-7660	57	12	nonhermitian	nonhermitian	ADJ
ap-7660	57	13	field	field	NOUN
ap-7660	57	14	-	-	PUNCT
ap-7660	57	15	theoretic	theoretic	NOUN
ap-7660	57	16	hamiltonian	hamiltonian	NOUN
ap-7660	57	17	to	to	ADP
ap-7660	57	18	a	a	DET
ap-7660	57	19	hermitian	hermitian	ADJ
ap-7660	57	20	hamiltonian	hamiltonian	NOUN
ap-7660	57	21	.	.	PUNCT
ap-7660	58	1	this	this	DET
ap-7660	58	2	procedure	procedure	NOUN
ap-7660	58	3	will	will	AUX
ap-7660	58	4	resolve	resolve	VERB
ap-7660	58	5	the	the	DET
ap-7660	58	6	issue	issue	NOUN
ap-7660	58	7	of	of	ADP
ap-7660	58	8	complex	complex	ADJ
ap-7660	58	9	vacuum	vacuum	NOUN
ap-7660	58	10	solution	solution	NOUN
ap-7660	58	11	and	and	CCONJ
ap-7660	58	12	derrick	derrick	PROPN
ap-7660	58	13	’s	’s	PART
ap-7660	58	14	scaling	scale	VERB
ap-7660	58	15	argument	argument	NOUN
ap-7660	58	16	,	,	PUNCT
ap-7660	58	17	as	as	SCONJ
ap-7660	58	18	we	we	PRON
ap-7660	58	19	will	will	AUX
ap-7660	58	20	see	see	VERB
ap-7660	58	21	below	below	ADV
ap-7660	58	22	.	.	PUNCT
ap-7660	59	1	however	however	ADV
ap-7660	59	2	,	,	PUNCT
ap-7660	59	3	we	we	PRON
ap-7660	59	4	note	note	VERB
ap-7660	59	5	that	that	SCONJ
ap-7660	59	6	the	the	DET
ap-7660	59	7	dyson	dyson	NOUN
ap-7660	59	8	map	map	NOUN
ap-7660	59	9	used	use	VERB
ap-7660	59	10	here	here	ADV
ap-7660	59	11	introduces	introduce	VERB
ap-7660	59	12	a	a	DET
ap-7660	59	13	negative	negative	ADJ
ap-7660	59	14	kinetic	kinetic	ADJ
ap-7660	59	15	sign	sign	NOUN
ap-7660	59	16	in	in	ADP
ap-7660	59	17	the	the	DET
ap-7660	59	18	kinetic	kinetic	ADJ
ap-7660	59	19	term	term	NOUN
ap-7660	59	20	of	of	ADP
ap-7660	59	21	one	one	NUM
ap-7660	59	22	of	of	ADP
ap-7660	59	23	the	the	DET
ap-7660	59	24	fields	field	NOUN
ap-7660	59	25	,	,	PUNCT
ap-7660	59	26	indicating	indicate	VERB
ap-7660	59	27	the	the	DET
ap-7660	59	28	ghost	ghost	NOUN
ap-7660	59	29	field	field	NOUN
ap-7660	59	30	problem	problem	NOUN
ap-7660	59	31	.	.	PUNCT
ap-7660	60	1	this	this	DET
ap-7660	60	2	issue	issue	NOUN
ap-7660	60	3	is	be	AUX
ap-7660	60	4	removed	remove	VERB
ap-7660	60	5	if	if	SCONJ
ap-7660	60	6	one	one	NUM
ap-7660	60	7	further	far	ADV
ap-7660	60	8	diagonalise	diagonalise	VERB
ap-7660	60	9	the	the	DET
ap-7660	60	10	hamiltonian	hamiltonian	NOUN
ap-7660	60	11	.	.	PUNCT
ap-7660	61	1	such	such	ADJ
ap-7660	61	2	diagonalisation	diagonalisation	NOUN
ap-7660	61	3	can	can	AUX
ap-7660	61	4	be	be	AUX
ap-7660	61	5	realised	realise	VERB
ap-7660	61	6	via	via	ADP
ap-7660	61	7	field	field	NOUN
ap-7660	61	8	-	-	PUNCT
ap-7660	61	9	redefinition	redefinition	NOUN
ap-7660	61	10	or	or	CCONJ
ap-7660	61	11	via	via	ADP
ap-7660	61	12	another	another	DET
ap-7660	61	13	dyson	dyson	NOUN
ap-7660	61	14	map	map	NOUN
ap-7660	61	15	.	.	PUNCT
ap-7660	62	1	a	a	DET
ap-7660	62	2	more	more	ADV
ap-7660	62	3	detailed	detailed	ADJ
ap-7660	62	4	discussion	discussion	NOUN
ap-7660	62	5	of	of	ADP
ap-7660	62	6	this	this	PRON
ap-7660	62	7	is	be	AUX
ap-7660	62	8	found	find	VERB
ap-7660	62	9	in	in	ADP
ap-7660	62	10	[	[	X
ap-7660	62	11	23	23	NUM
ap-7660	62	12	]	]	PUNCT
ap-7660	62	13	,	,	PUNCT
ap-7660	62	14	and	and	CCONJ
ap-7660	62	15	a	a	DET
ap-7660	62	16	dyson	dyson	NOUN
ap-7660	62	17	map	map	NOUN
ap-7660	62	18	which	which	PRON
ap-7660	62	19	diagonalise	diagonalise	VERB
ap-7660	62	20	the	the	DET
ap-7660	62	21	free	free	ADJ
ap-7660	62	22	part	part	NOUN
ap-7660	62	23	of	of	ADP
ap-7660	62	24	the	the	DET
ap-7660	62	25	non	non	ADJ
ap-7660	62	26	-	-	ADJ
ap-7660	62	27	hermitian	hermitian	ADJ
ap-7660	62	28	hamiltonian	hamiltonian	NOUN
ap-7660	62	29	is	be	AUX
ap-7660	62	30	found	find	VERB
ap-7660	62	31	in	in	ADP
ap-7660	62	32	[	[	X
ap-7660	62	33	12	12	NUM
ap-7660	62	34	]	]	PUNCT
ap-7660	62	35	.	.	PUNCT
ap-7660	63	1	2	2	X
ap-7660	63	2	.	.	X
ap-7660	63	3	methods	method	NOUN
ap-7660	63	4	in	in	ADP
ap-7660	63	5	this	this	DET
ap-7660	63	6	section	section	NOUN
ap-7660	63	7	,	,	PUNCT
ap-7660	63	8	we	we	PRON
ap-7660	63	9	will	will	AUX
ap-7660	63	10	summarise	summarise	VERB
ap-7660	63	11	the	the	DET
ap-7660	63	12	method	method	NOUN
ap-7660	63	13	used	use	VERB
ap-7660	63	14	in	in	ADP
ap-7660	63	15	[	[	X
ap-7660	63	16	8–11	8–11	X
ap-7660	63	17	]	]	PUNCT
ap-7660	63	18	to	to	PART
ap-7660	63	19	find	find	VERB
ap-7660	63	20	the	the	DET
ap-7660	63	21	masses	masse	NOUN
ap-7660	63	22	of	of	ADP
ap-7660	63	23	the	the	DET
ap-7660	63	24	higgs	higgs	NOUN
ap-7660	63	25	particles	particle	NOUN
ap-7660	63	26	,	,	PUNCT
ap-7660	63	27	massive	massive	ADJ
ap-7660	63	28	gauge	gauge	NOUN
ap-7660	63	29	particles	particle	NOUN
ap-7660	63	30	and	and	CCONJ
ap-7660	63	31	t’hooft	t’hooft	NOUN
ap-7660	63	32	-	-	PUNCT
ap-7660	63	33	polyakov	polyakov	NOUN
ap-7660	63	34	monopoles	monopole	NOUN
ap-7660	63	35	in	in	ADP
ap-7660	63	36	non	non	ADJ
ap-7660	63	37	-	-	ADJ
ap-7660	63	38	hermitian	hermitian	ADJ
ap-7660	63	39	gauge	gauge	NOUN
ap-7660	63	40	field	field	NOUN
ap-7660	63	41	theory	theory	NOUN
ap-7660	63	42	.	.	PUNCT
ap-7660	64	1	we	we	PRON
ap-7660	64	2	note	note	VERB
ap-7660	64	3	that	that	SCONJ
ap-7660	64	4	the	the	DET
ap-7660	64	5	explicit	explicit	ADJ
ap-7660	64	6	forms	form	NOUN
ap-7660	64	7	of	of	ADP
ap-7660	64	8	the	the	DET
ap-7660	64	9	similarity	similarity	NOUN
ap-7660	64	10	transformation	transformation	NOUN
ap-7660	64	11	will	will	AUX
ap-7660	64	12	not	not	PART
ap-7660	64	13	be	be	AUX
ap-7660	64	14	discussed	discuss	VERB
ap-7660	64	15	in	in	ADP
ap-7660	64	16	this	this	DET
ap-7660	64	17	paper	paper	NOUN
ap-7660	64	18	as	as	SCONJ
ap-7660	64	19	non	non	ADJ
ap-7660	64	20	-	-	ADJ
ap-7660	64	21	hermitian	hermitian	ADJ
ap-7660	64	22	and	and	CCONJ
ap-7660	64	23	hermitian	hermitian	ADJ
ap-7660	64	24	theories	theory	NOUN
ap-7660	64	25	are	be	AUX
ap-7660	64	26	isospectral	isospectral	ADJ
ap-7660	64	27	as	as	ADV
ap-7660	64	28	long	long	ADV
ap-7660	64	29	as	as	SCONJ
ap-7660	64	30	the	the	DET
ap-7660	64	31	cpt	cpt	PROPN
ap-7660	64	32	symmetry	symmetry	NOUN
ap-7660	64	33	is	be	AUX
ap-7660	64	34	preserved	preserve	VERB
ap-7660	64	35	for	for	ADP
ap-7660	64	36	hamiltonian	hamiltonian	ADJ
ap-7660	64	37	,	,	PUNCT
ap-7660	64	38	higgs	higgs	NOUN
ap-7660	64	39	particles	particle	NOUN
ap-7660	64	40	and	and	CCONJ
ap-7660	64	41	monopole	monopole	ADJ
ap-7660	64	42	solution	solution	NOUN
ap-7660	64	43	.	.	PUNCT
ap-7660	65	1	we	we	PRON
ap-7660	65	2	begin	begin	VERB
ap-7660	65	3	with	with	ADP
ap-7660	65	4	the	the	DET
ap-7660	65	5	non	non	ADJ
ap-7660	65	6	-	-	ADJ
ap-7660	65	7	hermitian	hermitian	ADJ
ap-7660	65	8	local	local	ADJ
ap-7660	65	9	su(2	su(2	NOUN
ap-7660	65	10	)	)	PUNCT
ap-7660	65	11	gauge	gauge	NOUN
ap-7660	65	12	theory	theory	NOUN
ap-7660	65	13	with	with	ADP
ap-7660	65	14	matter	matter	NOUN
ap-7660	65	15	fields	field	NOUN
ap-7660	65	16	in	in	ADP
ap-7660	65	17	the	the	DET
ap-7660	65	18	adjoint	adjoint	PROPN
ap-7660	65	19	representation	representation	NOUN
ap-7660	65	20	lad	lad	NOUN
ap-7660	65	21	2	2	NUM
ap-7660	65	22	=	=	SYM
ap-7660	65	23	1	1	NUM
ap-7660	65	24	4tr	4tr	NOUN
ap-7660	65	25	(	(	PUNCT
ap-7660	65	26	dϕ1)2	dϕ1)2	PROPN
ap-7660	65	27	+	+	NUM
ap-7660	65	28	m2	m2	PROPN
ap-7660	65	29	1	1	NUM
ap-7660	65	30	4	4	NUM
ap-7660	65	31	tr(ϕ2	tr(ϕ2	NOUN
ap-7660	65	32	1	1	NUM
ap-7660	65	33	)	)	PUNCT
ap-7660	65	34	(	(	PUNCT
ap-7660	65	35	2	2	X
ap-7660	65	36	)	)	PUNCT
ap-7660	65	37	−i	−i	NOUN
ap-7660	65	38	µ2	µ2	PROPN
ap-7660	65	39	2	2	NUM
ap-7660	65	40	tr(ϕ1ϕ2	tr(ϕ1ϕ2	NOUN
ap-7660	65	41	)	)	PUNCT
ap-7660	65	42	−	−	NOUN
ap-7660	66	1	g	g	NOUN
ap-7660	66	2	64	64	NUM
ap-7660	66	3	[	[	PUNCT
ap-7660	66	4	tr(ϕ2	tr(ϕ2	NOUN
ap-7660	66	5	1	1	NUM
ap-7660	66	6	)	)	PUNCT
ap-7660	66	7	]	]	PUNCT
ap-7660	66	8	2	2	NUM
ap-7660	66	9	+1	+1	NOUN
ap-7660	66	10	4tr	4tr	NOUN
ap-7660	66	11	(	(	PUNCT
ap-7660	66	12	dϕ2)2	dϕ2)2	PROPN
ap-7660	66	13	+	+	NUM
ap-7660	66	14	m2	m2	PROPN
ap-7660	66	15	2	2	NUM
ap-7660	66	16	4	4	NUM
ap-7660	66	17	tr(ϕ2	tr(ϕ2	NOUN
ap-7660	66	18	2	2	NUM
ap-7660	66	19	)	)	PUNCT
ap-7660	66	20	−	−	PROPN
ap-7660	66	21	1	1	NUM
ap-7660	66	22	8tr	8tr	NOUN
ap-7660	66	23	(	(	PUNCT
ap-7660	66	24	f	f	PROPN
ap-7660	66	25	2	2	NUM
ap-7660	66	26	)	)	PUNCT
ap-7660	66	27	.	.	PUNCT
ap-7660	67	1	here	here	ADV
ap-7660	67	2	we	we	PRON
ap-7660	67	3	take	take	VERB
ap-7660	67	4	g	g	NOUN
ap-7660	67	5	,	,	PUNCT
ap-7660	67	6	µ	µ	X
ap-7660	67	7	∈	∈	PROPN
ap-7660	67	8	r	r	NOUN
ap-7660	67	9	,	,	PUNCT
ap-7660	67	10	mi	mi	PROPN
ap-7660	67	11	∈	∈	PROPN
ap-7660	67	12	r	r	NOUN
ap-7660	67	13	and	and	CCONJ
ap-7660	67	14	discrete	discrete	ADJ
ap-7660	67	15	values	value	NOUN
ap-7660	67	16	ci	ci	PROPN
ap-7660	67	17	∈	∈	PROPN
ap-7660	67	18	{	{	PUNCT
ap-7660	67	19	−1	−1	NOUN
ap-7660	67	20	,	,	PUNCT
ap-7660	67	21	1	1	NUM
ap-7660	67	22	}	}	PUNCT
ap-7660	67	23	.	.	PUNCT
ap-7660	68	1	the	the	DET
ap-7660	68	2	two	two	NUM
ap-7660	68	3	fields	field	NOUN
ap-7660	68	4	{	{	PUNCT
ap-7660	68	5	ϕi}i=1,2	ϕi}i=1,2	PROPN
ap-7660	68	6	are	be	AUX
ap-7660	68	7	hermitian	hermitian	ADJ
ap-7660	68	8	matrices	matrix	NOUN
ap-7660	68	9	ϕi(t	ϕi(t	NOUN
ap-7660	68	10	,	,	PUNCT
ap-7660	69	1	x⃗	x⃗	PROPN
ap-7660	69	2	)	)	PUNCT
ap-7660	69	3	≡	≡	PROPN
ap-7660	69	4	ϕa	ϕa	INTJ
ap-7660	70	1	i	i	PROPN
ap-7660	70	2	(	(	PUNCT
ap-7660	70	3	t	t	PROPN
ap-7660	70	4	,	,	PUNCT
ap-7660	70	5	x⃗)t	x⃗)t	PUNCT
ap-7660	71	1	a	a	X
ap-7660	71	2	,	,	PUNCT
ap-7660	71	3	where	where	SCONJ
ap-7660	71	4	ϕa	ϕa	ADP
ap-7660	71	5	i	i	PROPN
ap-7660	71	6	(	(	PUNCT
ap-7660	71	7	t	t	PROPN
ap-7660	71	8	,	,	PUNCT
ap-7660	71	9	x⃗	x⃗	PROPN
ap-7660	71	10	)	)	PUNCT
ap-7660	71	11	is	be	AUX
ap-7660	71	12	a	a	DET
ap-7660	71	13	real	real	ADV
ap-7660	71	14	-	-	PUNCT
ap-7660	71	15	valued	value	VERB
ap-7660	71	16	field	field	NOUN
ap-7660	71	17	.	.	PUNCT
ap-7660	72	1	the	the	DET
ap-7660	72	2	three	three	NUM
ap-7660	72	3	generators	generator	NOUN
ap-7660	72	4	{	{	PUNCT
ap-7660	72	5	t	t	PROPN
ap-7660	72	6	a}a=1,2,3	a}a=1,2,3	NOUN
ap-7660	72	7	of	of	ADP
ap-7660	72	8	su(2	su(2	NOUN
ap-7660	72	9	)	)	PUNCT
ap-7660	72	10	in	in	ADP
ap-7660	72	11	the	the	DET
ap-7660	72	12	adjoint	adjoint	NOUN
ap-7660	72	13	representation	representation	NOUN
ap-7660	72	14	are	be	AUX
ap-7660	72	15	defined	define	VERB
ap-7660	72	16	by	by	ADP
ap-7660	72	17	three	three	NUM
ap-7660	72	18	hermitian	hermitian	ADJ
ap-7660	72	19	matrices	matrix	NOUN
ap-7660	72	20	of	of	ADP
ap-7660	72	21	the	the	DET
ap-7660	72	22	form	form	NOUN
ap-7660	72	23	(	(	PUNCT
ap-7660	72	24	t	t	NOUN
ap-7660	72	25	a)bc	a)bc	PROPN
ap-7660	72	26	=	=	PUNCT
ap-7660	73	1	−iϵabc	−iϵabc	PROPN
ap-7660	73	2	,	,	PUNCT
ap-7660	73	3	satisfying	satisfy	VERB
ap-7660	73	4	the	the	DET
ap-7660	73	5	commutation	commutation	NOUN
ap-7660	73	6	relation	relation	NOUN
ap-7660	73	7	[	[	X
ap-7660	73	8	t	t	X
ap-7660	73	9	a	a	X
ap-7660	73	10	,	,	PUNCT
ap-7660	73	11	t	t	PROPN
ap-7660	73	12	b	b	X
ap-7660	73	13	]	]	X
ap-7660	73	14	=	=	SYM
ap-7660	73	15	iϵabct	iϵabct	NOUN
ap-7660	73	16	c.	c.	PROPN
ap-7660	73	17	one	one	PROPN
ap-7660	73	18	can	can	AUX
ap-7660	73	19	check	check	VERB
ap-7660	73	20	that	that	PRON
ap-7660	73	21	tr(t	tr(t	PUNCT
ap-7660	73	22	at	at	ADP
ap-7660	73	23	b	b	NOUN
ap-7660	73	24	)	)	PUNCT
ap-7660	73	25	=	=	PUNCT
ap-7660	73	26	2δab	2δab	NOUN
ap-7660	73	27	.	.	PUNCT
ap-7660	74	1	the	the	DET
ap-7660	74	2	field	field	NOUN
ap-7660	74	3	strength	strength	NOUN
ap-7660	74	4	tensor	tensor	NOUN
ap-7660	74	5	is	be	AUX
ap-7660	74	6	defined	define	VERB
ap-7660	74	7	as	as	ADP
ap-7660	74	8	fµν	fµν	ADJ
ap-7660	74	9	=	=	SYM
ap-7660	74	10	∂µaν	∂µaν	NOUN
ap-7660	74	11	−	−	PROPN
ap-7660	74	12	∂νaµ	∂νaµ	PUNCT
ap-7660	74	13	−	−	PROPN
ap-7660	74	14	ie[aµ	ie[aµ	SYM
ap-7660	74	15	,	,	PUNCT
ap-7660	74	16	aν	aν	NOUN
ap-7660	74	17	]	]	X
ap-7660	74	18	,	,	PUNCT
ap-7660	74	19	where	where	SCONJ
ap-7660	74	20	the	the	DET
ap-7660	74	21	gauge	gauge	NOUN
ap-7660	74	22	fields	field	NOUN
ap-7660	74	23	are	be	AUX
ap-7660	74	24	aµ	aµ	PROPN
ap-7660	74	25	=	=	NOUN
ap-7660	74	26	aa	aa	INTJ
ap-7660	75	1	µt	µt	X
ap-7660	75	2	a.	a.	NOUN
ap-7660	75	3	the	the	DET
ap-7660	75	4	partial	partial	ADJ
ap-7660	75	5	derivative	derivative	NOUN
ap-7660	75	6	is	be	AUX
ap-7660	75	7	replaced	replace	VERB
ap-7660	75	8	with	with	ADP
ap-7660	75	9	the	the	DET
ap-7660	75	10	covariant	covariant	ADJ
ap-7660	75	11	derivative	derivative	NOUN
ap-7660	75	12	(	(	PUNCT
ap-7660	75	13	dµϕi)a	dµϕi)a	NOUN
ap-7660	75	14	:	:	PUNCT
ap-7660	75	15	=	=	SYM
ap-7660	75	16	∂µϕa	∂µϕa	PUNCT
ap-7660	75	17	i	i	NOUN
ap-7660	75	18	+	+	NUM
ap-7660	75	19	eεabcab	eεabcab	NOUN
ap-7660	75	20	µϕc	µϕc	CCONJ
ap-7660	75	21	i	i	PRON
ap-7660	75	22	to	to	PART
ap-7660	75	23	compensate	compensate	VERB
ap-7660	75	24	for	for	ADP
ap-7660	75	25	the	the	DET
ap-7660	75	26	local	local	ADJ
ap-7660	75	27	symmetry	symmetry	NOUN
ap-7660	75	28	group	group	NOUN
ap-7660	75	29	su(2	su(2	PROPN
ap-7660	75	30	)	)	PUNCT
ap-7660	75	31	.	.	PUNCT
ap-7660	76	1	this	this	DET
ap-7660	76	2	action	action	NOUN
ap-7660	76	3	is	be	AUX
ap-7660	76	4	invariant	invariant	ADJ
ap-7660	76	5	under	under	ADP
ap-7660	76	6	the	the	DET
ap-7660	76	7	local	local	ADJ
ap-7660	76	8	su(2	su(2	NOUN
ap-7660	76	9	)	)	PUNCT
ap-7660	76	10	transformation	transformation	NOUN
ap-7660	76	11	of	of	ADP
ap-7660	76	12	the	the	DET
ap-7660	76	13	matter	matter	NOUN
ap-7660	76	14	fields	field	NOUN
ap-7660	76	15	ϕi	ϕi	ADP
ap-7660	76	16	→	→	X
ap-7660	76	17	eiαa(x)t	eiαa(x)t	VERB
ap-7660	76	18	a	a	DET
ap-7660	76	19	ϕie	ϕie	NOUN
ap-7660	76	20	−iαa(x)t	−iαa(x)t	NOUN
ap-7660	76	21	a	a	DET
ap-7660	76	22	and	and	CCONJ
ap-7660	76	23	gauge	gauge	NOUN
ap-7660	76	24	fields	field	NOUN
ap-7660	76	25	aµ	aµ	PROPN
ap-7660	76	26	→	→	SYM
ap-7660	76	27	eiαa(x)t	eiαa(x)t	VERB
ap-7660	76	28	a	a	DET
ap-7660	76	29	aµe−iαa(x)t	aµe−iαa(x)t	NOUN
ap-7660	76	30	a	a	DET
ap-7660	76	31	+	+	NUM
ap-7660	76	32	1	1	NUM
ap-7660	76	33	e	e	NOUN
ap-7660	76	34	∂µαa(x)t	∂µαa(x)t	NOUN
ap-7660	76	35	a.	a.	NOUN
ap-7660	76	36	it	it	PRON
ap-7660	76	37	is	be	AUX
ap-7660	76	38	also	also	ADV
ap-7660	76	39	symmetric	symmetric	ADJ
ap-7660	76	40	under	under	ADP
ap-7660	76	41	modified	modified	ADJ
ap-7660	76	42	cpt	cpt	NOUN
ap-7660	76	43	symmetry	symmetry	NOUN
ap-7660	76	44	,	,	PUNCT
ap-7660	76	45	which	which	PRON
ap-7660	76	46	transforms	transform	VERB
ap-7660	76	47	two	two	NUM
ap-7660	76	48	fields	field	NOUN
ap-7660	76	49	,	,	PUNCT
ap-7660	76	50	ϕ1	ϕ1	NOUN
ap-7660	76	51	and	and	CCONJ
ap-7660	76	52	ϕ2	ϕ2	ADV
ap-7660	76	53	as	as	ADP
ap-7660	76	54	cpt	cpt	PROPN
ap-7660	76	55	:	:	PUNCT
ap-7660	76	56	ϕ1(t	ϕ1(t	NUM
ap-7660	76	57	,	,	PUNCT
ap-7660	76	58	x⃗	x⃗	PROPN
ap-7660	76	59	)	)	PUNCT
ap-7660	76	60	→	→	SYM
ap-7660	76	61	ϕ1(−t	ϕ1(−t	PROPN
ap-7660	76	62	,	,	PUNCT
ap-7660	76	63	−x⃗	−x⃗	PROPN
ap-7660	76	64	)	)	PUNCT
ap-7660	76	65	(	(	PUNCT
ap-7660	76	66	3	3	NUM
ap-7660	76	67	)	)	PUNCT
ap-7660	76	68	:	:	PUNCT
ap-7660	76	69	ϕ2(t	ϕ2(t	PROPN
ap-7660	76	70	,	,	PUNCT
ap-7660	76	71	x⃗	x⃗	PROPN
ap-7660	76	72	)	)	PUNCT
ap-7660	76	73	→	→	SYM
ap-7660	76	74	−ϕ2(−t	−ϕ2(−t	NUM
ap-7660	76	75	,	,	PUNCT
ap-7660	76	76	−x⃗	−x⃗	NOUN
ap-7660	76	77	)	)	PUNCT
ap-7660	76	78	:	:	PUNCT
ap-7660	77	1	i	i	PRON
ap-7660	77	2	→	→	SYM
ap-7660	77	3	−i	−i	PROPN
ap-7660	77	4	.	.	PUNCT
ap-7660	78	1	the	the	DET
ap-7660	78	2	equations	equation	NOUN
ap-7660	78	3	of	of	ADP
ap-7660	78	4	motion	motion	NOUN
ap-7660	78	5	for	for	ADP
ap-7660	78	6	the	the	DET
ap-7660	78	7	fields	field	NOUN
ap-7660	78	8	ϕi	ϕi	ADP
ap-7660	78	9	and	and	CCONJ
ap-7660	78	10	aµ	aµ	PROPN
ap-7660	78	11	of	of	ADP
ap-7660	78	12	the	the	DET
ap-7660	78	13	lagrangian	lagrangian	ADJ
ap-7660	78	14	(	(	PUNCT
ap-7660	78	15	2	2	NUM
ap-7660	78	16	)	)	PUNCT
ap-7660	78	17	are	be	AUX
ap-7660	78	18	(	(	PUNCT
ap-7660	78	19	dµdµϕi)a	dµdµϕi)a	NOUN
ap-7660	78	20	+	+	SYM
ap-7660	78	21	δv	δv	ADV
ap-7660	78	22	δϕa	δϕa	NOUN
ap-7660	78	23	i	i	NOUN
ap-7660	78	24	=	=	NOUN
ap-7660	78	25	0	0	NUM
ap-7660	78	26	,	,	PUNCT
ap-7660	78	27	(	(	PUNCT
ap-7660	78	28	4	4	X
ap-7660	78	29	)	)	PUNCT
ap-7660	78	30	dνf	dνf	NOUN
ap-7660	78	31	νµ	νµ	VERB
ap-7660	78	32	a	a	DET
ap-7660	78	33	−	−	NOUN
ap-7660	78	34	eϵabcϕb	eϵabcϕb	ADV
ap-7660	78	35	1(dµϕ)c	1(dµϕ)c	PRON
ap-7660	79	1	+	+	CCONJ
ap-7660	79	2	eϵabcϕb	eϵabcϕb	ADV
ap-7660	79	3	2(dµϕ)c	2(dµϕ)c	PRON
ap-7660	79	4	=	=	SYM
ap-7660	79	5	0	0	NUM
ap-7660	79	6	,	,	PUNCT
ap-7660	79	7	where	where	SCONJ
ap-7660	79	8	repeated	repeat	VERB
ap-7660	79	9	indices	index	NOUN
ap-7660	79	10	are	be	AUX
ap-7660	79	11	summed	sum	VERB
ap-7660	79	12	over	over	ADP
ap-7660	79	13	.	.	PUNCT
ap-7660	80	1	we	we	PRON
ap-7660	80	2	perform	perform	VERB
ap-7660	80	3	the	the	DET
ap-7660	80	4	similarity	similarity	NOUN
ap-7660	80	5	transformation	transformation	NOUN
ap-7660	80	6	of	of	ADP
ap-7660	80	7	the	the	DET
ap-7660	80	8	complex	complex	ADJ
ap-7660	80	9	lagrangian	lagrangian	ADJ
ap-7660	80	10	(	(	PUNCT
ap-7660	80	11	2	2	NUM
ap-7660	80	12	)	)	PUNCT
ap-7660	80	13	by	by	ADP
ap-7660	80	14	momentary	momentary	NOUN
ap-7660	80	15	resorting	resort	VERB
ap-7660	80	16	to	to	ADP
ap-7660	80	17	a	a	DET
ap-7660	80	18	quantum	quantum	ADJ
ap-7660	80	19	theory	theory	NOUN
ap-7660	80	20	where	where	SCONJ
ap-7660	80	21	we	we	PRON
ap-7660	80	22	assume	assume	VERB
ap-7660	80	23	an	an	DET
ap-7660	80	24	equal	equal	ADJ
ap-7660	80	25	time	time	NOUN
ap-7660	80	26	commutation	commutation	NOUN
ap-7660	80	27	relation	relation	NOUN
ap-7660	80	28	between	between	ADP
ap-7660	80	29	the	the	DET
ap-7660	80	30	fields	field	NOUN
ap-7660	81	1	ϕa	ϕa	VERB
ap-7660	81	2	i	i	PRON
ap-7660	81	3	and	and	CCONJ
ap-7660	81	4	their	their	PRON
ap-7660	81	5	canonical	canonical	ADJ
ap-7660	81	6	momenta	momenta	NOUN
ap-7660	82	1	πa	πa	ADP
ap-7660	82	2	i	i	PRON
ap-7660	82	3	=	=	PUNCT
ap-7660	82	4	∂0ϕa	∂0ϕa	VERB
ap-7660	82	5	i	i	PRON
ap-7660	82	6	,	,	PUNCT
ap-7660	82	7	satisfying	satisfy	VERB
ap-7660	82	8	the	the	DET
ap-7660	82	9	commutation	commutation	NOUN
ap-7660	82	10	relation	relation	NOUN
ap-7660	83	1	[	[	X
ap-7660	83	2	ϕa	ϕa	X
ap-7660	83	3	i	i	PRON
ap-7660	83	4	(	(	PUNCT
ap-7660	83	5	t	t	PROPN
ap-7660	83	6	,	,	PUNCT
ap-7660	83	7	x⃗	x⃗	PROPN
ap-7660	83	8	)	)	PUNCT
ap-7660	83	9	,	,	PUNCT
ap-7660	83	10	πb	πb	ADP
ap-7660	83	11	j(t	j(t	PROPN
ap-7660	83	12	,	,	PUNCT
ap-7660	83	13	y⃗	y⃗	NOUN
ap-7660	83	14	)	)	PUNCT
ap-7660	83	15	]	]	PUNCT
ap-7660	84	1	=	=	SYM
ap-7660	84	2	δ(x⃗	δ(x⃗	VERB
ap-7660	84	3	−	−	PROPN
ap-7660	84	4	y⃗)δijδab	y⃗)δijδab	NOUN
ap-7660	84	5	.	.	PUNCT
ap-7660	85	1	using	use	VERB
ap-7660	85	2	this	this	DET
ap-7660	85	3	relation	relation	NOUN
ap-7660	85	4	,	,	PUNCT
ap-7660	85	5	we	we	PRON
ap-7660	85	6	can	can	AUX
ap-7660	85	7	transform	transform	VERB
ap-7660	85	8	the	the	DET
ap-7660	85	9	corresponding	corresponding	ADJ
ap-7660	85	10	complex	complex	ADJ
ap-7660	85	11	hamiltonian	hamiltonian	NOUN
ap-7660	85	12	of	of	ADP
ap-7660	85	13	the	the	DET
ap-7660	85	14	lagrangian	lagrangian	ADJ
ap-7660	85	15	(	(	PUNCT
ap-7660	85	16	2	2	NUM
ap-7660	85	17	)	)	PUNCT
ap-7660	85	18	by	by	ADP
ap-7660	85	19	h	h	PROPN
ap-7660	85	20	→	→	SYM
ap-7660	85	21	eη±he−η±	eη±he−η±	PROPN
ap-7660	85	22	,	,	PUNCT
ap-7660	85	23	(	(	PUNCT
ap-7660	85	24	5	5	X
ap-7660	85	25	)	)	PUNCT
ap-7660	85	26	η±	η±	NOUN
ap-7660	85	27	=	=	SYM
ap-7660	85	28	∏3	∏3	NOUN
ap-7660	85	29	a=1	a=1	X
ap-7660	85	30	exp	exp	NOUN
ap-7660	85	31	(	(	PUNCT
ap-7660	85	32	±	±	NUM
ap-7660	85	33	π	π	PROPN
ap-7660	85	34	2	2	NUM
ap-7660	85	35	∫	∫	NOUN
ap-7660	85	36	d3xπa	d3xπa	NOUN
ap-7660	86	1	2ϕa	2ϕa	ADJ
ap-7660	86	2	2	2	X
ap-7660	86	3	)	)	PUNCT
ap-7660	86	4	,	,	PUNCT
ap-7660	86	5	where	where	SCONJ
ap-7660	86	6	h	h	NOUN
ap-7660	86	7	is	be	AUX
ap-7660	86	8	the	the	DET
ap-7660	86	9	field	field	NOUN
ap-7660	86	10	-	-	PUNCT
ap-7660	86	11	theoretic	theoretic	NOUN
ap-7660	86	12	hamiltonian	hamiltonian	NOUN
ap-7660	86	13	of	of	ADP
ap-7660	86	14	our	our	PRON
ap-7660	86	15	model	model	NOUN
ap-7660	86	16	(	(	PUNCT
ap-7660	86	17	2	2	NUM
ap-7660	86	18	)	)	PUNCT
ap-7660	86	19	,	,	PUNCT
ap-7660	86	20	obtained	obtain	VERB
ap-7660	86	21	via	via	ADP
ap-7660	86	22	legendre	legendre	PROPN
ap-7660	86	23	transformation	transformation	PROPN
ap-7660	86	24	.	.	PUNCT
ap-7660	87	1	this	this	DET
ap-7660	87	2	non	non	ADJ
ap-7660	87	3	-	-	NOUN
ap-7660	87	4	uniqueness	uniqueness	NOUN
ap-7660	87	5	of	of	ADP
ap-7660	87	6	the	the	DET
ap-7660	87	7	metric	metric	NOUN
ap-7660	87	8	is	be	AUX
ap-7660	87	9	analogous	analogous	ADJ
ap-7660	87	10	to	to	ADP
ap-7660	87	11	198	198	NUM
ap-7660	87	12	vol	vol	NOUN
ap-7660	87	13	.	.	PUNCT
ap-7660	88	1	62	62	NUM
ap-7660	88	2	no	no	INTJ
ap-7660	88	3	.	.	PUNCT
ap-7660	89	1	1/2022	1/2022	NUM
ap-7660	89	2	complex	complex	ADJ
ap-7660	89	3	topological	topological	ADJ
ap-7660	89	4	soliton	soliton	NOUN
ap-7660	89	5	with	with	ADP
ap-7660	89	6	real	real	ADJ
ap-7660	89	7	energy	energy	NOUN
ap-7660	89	8	in	in	ADP
ap-7660	89	9	particle	particle	NOUN
ap-7660	89	10	physics	physics	PROPN
ap-7660	89	11	the	the	DET
ap-7660	89	12	non	non	NOUN
ap-7660	89	13	-	-	NOUN
ap-7660	89	14	uniqueness	uniqueness	NOUN
ap-7660	89	15	of	of	ADP
ap-7660	89	16	the	the	DET
ap-7660	89	17	metric	metric	NOUN
ap-7660	89	18	and	and	CCONJ
ap-7660	89	19	its	its	PRON
ap-7660	89	20	connection	connection	NOUN
ap-7660	89	21	to	to	ADP
ap-7660	89	22	the	the	DET
ap-7660	89	23	observables	observable	NOUN
ap-7660	89	24	in	in	ADP
ap-7660	89	25	the	the	DET
ap-7660	89	26	quantum	quantum	ADJ
ap-7660	89	27	mechanical	mechanical	ADJ
ap-7660	89	28	setting	setting	NOUN
ap-7660	89	29	discussed	discuss	VERB
ap-7660	89	30	in	in	ADP
ap-7660	89	31	[	[	X
ap-7660	89	32	16	16	NUM
ap-7660	89	33	,	,	PUNCT
ap-7660	89	34	24	24	NUM
ap-7660	89	35	]	]	PUNCT
ap-7660	89	36	.	.	PUNCT
ap-7660	90	1	the	the	DET
ap-7660	90	2	adjoint	adjoint	PROPN
ap-7660	90	3	action	action	NOUN
ap-7660	90	4	of	of	ADP
ap-7660	90	5	η±	η±	NOUN
ap-7660	90	6	maps	map	VERB
ap-7660	90	7	the	the	DET
ap-7660	90	8	complex	complex	ADJ
ap-7660	90	9	action	action	NOUN
ap-7660	90	10	in	in	ADP
ap-7660	90	11	the	the	DET
ap-7660	90	12	equation	equation	NOUN
ap-7660	90	13	(	(	PUNCT
ap-7660	90	14	2	2	NUM
ap-7660	90	15	)	)	PUNCT
ap-7660	90	16	into	into	ADP
ap-7660	90	17	the	the	DET
ap-7660	90	18	following	follow	VERB
ap-7660	90	19	real	real	ADJ
ap-7660	90	20	action	action	NOUN
ap-7660	90	21	s	s	PART
ap-7660	90	22	=	=	NOUN
ap-7660	90	23	∫	∫	PROPN
ap-7660	90	24	d4x	d4x	PROPN
ap-7660	90	25	1	1	NUM
ap-7660	90	26	4tr	4tr	NOUN
ap-7660	90	27	(	(	PUNCT
ap-7660	90	28	dϕ1)2	dϕ1)2	PROPN
ap-7660	90	29	−	−	PROPN
ap-7660	90	30	1	1	NUM
ap-7660	90	31	4tr	4tr	NOUN
ap-7660	90	32	(	(	PUNCT
ap-7660	90	33	dϕ2)2	dϕ2)2	PROPN
ap-7660	90	34	(	(	PUNCT
ap-7660	90	35	6	6	NUM
ap-7660	90	36	)	)	PUNCT
ap-7660	91	1	+	+	NOUN
ap-7660	91	2	c1	c1	NOUN
ap-7660	91	3	m2	m2	PROPN
ap-7660	91	4	1	1	NUM
ap-7660	91	5	4	4	NUM
ap-7660	91	6	tr(ϕ2	tr(ϕ2	NOUN
ap-7660	91	7	1	1	NUM
ap-7660	91	8	)	)	PUNCT
ap-7660	91	9	−	−	PROPN
ap-7660	92	1	c2	c2	PROPN
ap-7660	92	2	m2	m2	PROPN
ap-7660	92	3	2	2	NUM
ap-7660	92	4	4	4	NUM
ap-7660	92	5	tr(ϕ2	tr(ϕ2	NOUN
ap-7660	92	6	2	2	NUM
ap-7660	92	7	)	)	PUNCT
ap-7660	92	8	−c3	−c3	NOUN
ap-7660	92	9	µ2	µ2	PROPN
ap-7660	92	10	2	2	NUM
ap-7660	92	11	tr(ϕ1ϕ2	tr(ϕ1ϕ2	NOUN
ap-7660	92	12	)	)	PUNCT
ap-7660	92	13	−	−	PROPN
ap-7660	93	1	g	g	NOUN
ap-7660	93	2	64	64	NUM
ap-7660	93	3	(	(	PUNCT
ap-7660	93	4	tr(ϕ2	tr(ϕ2	NOUN
ap-7660	93	5	1	1	NUM
ap-7660	93	6	)	)	PUNCT
ap-7660	93	7	)	)	PUNCT
ap-7660	93	8	2	2	NUM
ap-7660	93	9	−	−	NOUN
ap-7660	93	10	1	1	NUM
ap-7660	93	11	8tr(f	8tr(f	NUM
ap-7660	93	12	2	2	NUM
ap-7660	93	13	)	)	PUNCT
ap-7660	93	14	≡	≡	PROPN
ap-7660	93	15	∫	∫	PROPN
ap-7660	93	16	d4x	d4x	PROPN
ap-7660	93	17	1	1	NUM
ap-7660	93	18	4tr	4tr	NOUN
ap-7660	93	19	(	(	PUNCT
ap-7660	93	20	dϕ1)2	dϕ1)2	PROPN
ap-7660	93	21	−	−	PROPN
ap-7660	93	22	1	1	NUM
ap-7660	93	23	4tr	4tr	NOUN
ap-7660	93	24	(	(	PUNCT
ap-7660	93	25	dϕ2)2	dϕ2)2	X
ap-7660	93	26	−v	−v	NOUN
ap-7660	93	27	−	−	NOUN
ap-7660	93	28	1	1	NUM
ap-7660	93	29	8tr(f	8tr(f	NUM
ap-7660	93	30	2	2	NUM
ap-7660	93	31	)	)	PUNCT
ap-7660	93	32	.	.	PUNCT
ap-7660	94	1	the	the	DET
ap-7660	94	2	parameter	parameter	PROPN
ap-7660	94	3	c3	c3	PROPN
ap-7660	94	4	indicates	indicate	VERB
ap-7660	94	5	the	the	DET
ap-7660	94	6	different	different	ADJ
ap-7660	94	7	similarity	similarity	NOUN
ap-7660	94	8	transformations	transformation	NOUN
ap-7660	94	9	by	by	ADP
ap-7660	94	10	taking	take	VERB
ap-7660	94	11	the	the	DET
ap-7660	94	12	values	value	NOUN
ap-7660	94	13	±1	±1	VERB
ap-7660	94	14	for	for	ADP
ap-7660	94	15	η±	η±	NOUN
ap-7660	94	16	,	,	PUNCT
ap-7660	94	17	respectively	respectively	ADV
ap-7660	94	18	.	.	PUNCT
ap-7660	95	1	for	for	ADP
ap-7660	95	2	convenience	convenience	NOUN
ap-7660	95	3	,	,	PUNCT
ap-7660	95	4	let	let	VERB
ap-7660	95	5	us	we	PRON
ap-7660	95	6	rewrite	rewrite	VERB
ap-7660	95	7	the	the	DET
ap-7660	95	8	above	above	ADJ
ap-7660	95	9	real	real	ADJ
ap-7660	95	10	action	action	NOUN
ap-7660	95	11	in	in	ADP
ap-7660	95	12	terms	term	NOUN
ap-7660	95	13	of	of	ADP
ap-7660	95	14	each	each	DET
ap-7660	95	15	component	component	NOUN
ap-7660	95	16	of	of	ADP
ap-7660	95	17	the	the	DET
ap-7660	95	18	fields	field	NOUN
ap-7660	95	19	ϕa	ϕa	VERB
ap-7660	95	20	i	i	PRON
ap-7660	95	21	as	as	ADV
ap-7660	95	22	lad	lad	NOUN
ap-7660	95	23	2	2	NUM
ap-7660	96	1	=	=	SYM
ap-7660	96	2	1	1	NUM
ap-7660	96	3	2(dµϕi)aiij(dµϕj)a	2(dµϕi)aiij(dµϕj)a	NUM
ap-7660	96	4	+	+	CCONJ
ap-7660	96	5	1	1	NUM
ap-7660	96	6	2ϕa	2ϕa	NOUN
ap-7660	96	7	i	i	PRON
ap-7660	96	8	hijϕa	hijϕa	VERB
ap-7660	96	9	j	j	PROPN
ap-7660	96	10	(	(	PUNCT
ap-7660	96	11	7	7	NUM
ap-7660	96	12	)	)	PUNCT
ap-7660	96	13	−	−	NOUN
ap-7660	96	14	g	g	NOUN
ap-7660	96	15	16	16	NUM
ap-7660	96	16	(	(	PUNCT
ap-7660	96	17	ϕa	ϕa	VERB
ap-7660	96	18	i	i	PRON
ap-7660	96	19	eijϕa	eijϕa	PROPN
ap-7660	96	20	j	j	PROPN
ap-7660	96	21	)	)	PUNCT
ap-7660	96	22	2	2	NUM
ap-7660	96	23	−	−	PROPN
ap-7660	96	24	1	1	NUM
ap-7660	96	25	4f	4f	NOUN
ap-7660	96	26	a	a	DET
ap-7660	96	27	µνf	µνf	NOUN
ap-7660	96	28	aµν	aµν	PROPN
ap-7660	96	29	,	,	PUNCT
ap-7660	96	30	where	where	SCONJ
ap-7660	96	31	the	the	DET
ap-7660	96	32	matrices	matrix	NOUN
ap-7660	96	33	h	h	VERB
ap-7660	96	34	,	,	PUNCT
ap-7660	97	1	i	i	PRON
ap-7660	97	2	and	and	CCONJ
ap-7660	97	3	e	e	PROPN
ap-7660	97	4	are	be	AUX
ap-7660	97	5	defined	define	VERB
ap-7660	97	6	as	as	ADP
ap-7660	97	7	h	h	NOUN
ap-7660	97	8	:	:	PUNCT
ap-7660	97	9	=	=	SYM
ap-7660	97	10	(	(	PUNCT
ap-7660	97	11	m2	m2	PROPN
ap-7660	97	12	1	1	PROPN
ap-7660	97	13	−µ2	−µ2	PROPN
ap-7660	97	14	−µ2	−µ2	PROPN
ap-7660	97	15	−m2	−m2	NOUN
ap-7660	97	16	2	2	NUM
ap-7660	97	17	)	)	PUNCT
ap-7660	98	1	,	,	PUNCT
ap-7660	98	2	i	i	PRON
ap-7660	98	3	:	:	PUNCT
ap-7660	98	4	=	=	PUNCT
ap-7660	98	5	(	(	PUNCT
ap-7660	98	6	1	1	NUM
ap-7660	98	7	0	0	NUM
ap-7660	98	8	0	0	NUM
ap-7660	98	9	−1	−1	NOUN
ap-7660	98	10	)	)	PUNCT
ap-7660	98	11	,	,	PUNCT
ap-7660	98	12	(	(	PUNCT
ap-7660	98	13	8)	8)	NUM
ap-7660	98	14	e	e	NOUN
ap-7660	98	15	:	:	PUNCT
ap-7660	98	16	=	=	SYM
ap-7660	98	17	(	(	PUNCT
ap-7660	98	18	1	1	NUM
ap-7660	98	19	0	0	NUM
ap-7660	98	20	0	0	NUM
ap-7660	98	21	0	0	NUM
ap-7660	98	22	)	)	PUNCT
ap-7660	98	23	.	.	PUNCT
ap-7660	99	1	2.1	2.1	NUM
ap-7660	99	2	.	.	PUNCT
ap-7660	100	1	higgs	higgs	NOUN
ap-7660	100	2	and	and	CCONJ
ap-7660	100	3	gauge	gauge	ADJ
ap-7660	100	4	masses	masse	NOUN
ap-7660	100	5	next	next	ADV
ap-7660	100	6	,	,	PUNCT
ap-7660	100	7	we	we	PRON
ap-7660	100	8	define	define	VERB
ap-7660	100	9	the	the	DET
ap-7660	100	10	trivial	trivial	ADJ
ap-7660	100	11	solution	solution	NOUN
ap-7660	100	12	of	of	ADP
ap-7660	100	13	the	the	DET
ap-7660	100	14	equations	equation	NOUN
ap-7660	100	15	of	of	ADP
ap-7660	100	16	motion	motion	NOUN
ap-7660	100	17	by	by	ADP
ap-7660	100	18	solving	solve	VERB
ap-7660	100	19	δv	δv	ADV
ap-7660	100	20	=	=	SYM
ap-7660	100	21	0	0	NUM
ap-7660	100	22	and	and	CCONJ
ap-7660	100	23	dµϕi	dµϕi	ADJ
ap-7660	100	24	=	=	PUNCT
ap-7660	100	25	0	0	X
ap-7660	100	26	.	.	PUNCT
ap-7660	101	1	such	such	ADJ
ap-7660	101	2	vacuum	vacuum	NOUN
ap-7660	101	3	is	be	AUX
ap-7660	101	4	often	often	ADV
ap-7660	101	5	referred	refer	VERB
ap-7660	101	6	to	to	ADP
ap-7660	101	7	as	as	ADP
ap-7660	101	8	higgs	higgs	PROPN
ap-7660	101	9	vacuum	vacuum	PROPN
ap-7660	101	10	.	.	PUNCT
ap-7660	102	1	the	the	DET
ap-7660	102	2	first	first	ADJ
ap-7660	102	3	equation	equation	NOUN
ap-7660	102	4	can	can	AUX
ap-7660	102	5	be	be	AUX
ap-7660	102	6	simplified	simplify	VERB
ap-7660	102	7	by	by	ADP
ap-7660	102	8	choosing	choose	VERB
ap-7660	102	9	an	an	DET
ap-7660	102	10	ansatz	ansatz	ADJ
ap-7660	102	11	(	(	PUNCT
ap-7660	102	12	ϕ0	ϕ0	NOUN
ap-7660	102	13	i	i	NOUN
ap-7660	102	14	)	)	PUNCT
ap-7660	102	15	a(t	a(t	PROPN
ap-7660	102	16	,	,	PUNCT
ap-7660	102	17	x⃗	x⃗	PROPN
ap-7660	102	18	)	)	PUNCT
ap-7660	103	1	=	=	SYM
ap-7660	103	2	h0	h0	NOUN
ap-7660	103	3	i	i	PRON
ap-7660	103	4	r̂a(x⃗	r̂a(x⃗	VERB
ap-7660	103	5	)	)	PUNCT
ap-7660	104	1	where	where	SCONJ
ap-7660	104	2	r̂	r̂	NOUN
ap-7660	104	3	=	=	SYM
ap-7660	104	4	(	(	PUNCT
ap-7660	104	5	x	x	X
ap-7660	104	6	,	,	PUNCT
ap-7660	104	7	y	y	PROPN
ap-7660	104	8	,	,	PUNCT
ap-7660	104	9	z)/	z)/	PROPN
ap-7660	104	10	√	√	NUM
ap-7660	105	1	x2	x2	NOUN
ap-7660	106	1	+	+	CCONJ
ap-7660	106	2	y2	y2	PROPN
ap-7660	106	3	+	+	CCONJ
ap-7660	106	4	z2	z2	PROPN
ap-7660	106	5	and	and	CCONJ
ap-7660	106	6	{	{	PUNCT
ap-7660	106	7	h0	h0	PROPN
ap-7660	106	8	i	i	PROPN
ap-7660	106	9	}	}	PUNCT
ap-7660	106	10	are	be	AUX
ap-7660	106	11	some	some	DET
ap-7660	106	12	constants	constant	NOUN
ap-7660	106	13	to	to	PART
ap-7660	106	14	be	be	AUX
ap-7660	106	15	determined	determine	VERB
ap-7660	106	16	.	.	PUNCT
ap-7660	107	1	note	note	VERB
ap-7660	107	2	that	that	SCONJ
ap-7660	107	3	the	the	DET
ap-7660	107	4	vacuum	vacuum	NOUN
ap-7660	107	5	solution	solution	NOUN
ap-7660	107	6	has	have	VERB
ap-7660	107	7	a	a	DET
ap-7660	107	8	rotational	rotational	ADJ
ap-7660	107	9	symmetry	symmetry	NOUN
ap-7660	107	10	so(3	so(3	NOUN
ap-7660	107	11	)	)	PUNCT
ap-7660	107	12	since	since	SCONJ
ap-7660	107	13	r̂ar̂a	r̂ar̂a	NOUN
ap-7660	107	14	=	=	NOUN
ap-7660	107	15	1	1	X
ap-7660	107	16	.	.	X
ap-7660	107	17	inserting	insert	VERB
ap-7660	107	18	this	this	DET
ap-7660	107	19	ansatz	ansatz	ADV
ap-7660	107	20	into	into	ADP
ap-7660	107	21	the	the	DET
ap-7660	107	22	equation	equation	NOUN
ap-7660	107	23	(	(	PUNCT
ap-7660	107	24	7	7	NUM
ap-7660	107	25	)	)	PUNCT
ap-7660	107	26	,	,	PUNCT
ap-7660	107	27	we	we	PRON
ap-7660	107	28	find	find	VERB
ap-7660	107	29	v	v	NOUN
ap-7660	107	30	=	=	SYM
ap-7660	107	31	−1	−1	NOUN
ap-7660	107	32	2hihijhj	2hihijhj	NUM
ap-7660	107	33	+	+	CCONJ
ap-7660	107	34	g	g	PROPN
ap-7660	107	35	16h4	16h4	NUM
ap-7660	107	36	1	1	NUM
ap-7660	107	37	.	.	PUNCT
ap-7660	108	1	(	(	PUNCT
ap-7660	108	2	9	9	NUM
ap-7660	108	3	)	)	PUNCT
ap-7660	108	4	then	then	ADV
ap-7660	108	5	the	the	DET
ap-7660	108	6	vacuum	vacuum	NOUN
ap-7660	108	7	equation	equation	NOUN
ap-7660	108	8	δv	δv	ADV
ap-7660	108	9	=	=	SYM
ap-7660	108	10	0	0	NUM
ap-7660	108	11	is	be	AUX
ap-7660	108	12	reduced	reduce	VERB
ap-7660	108	13	to	to	ADP
ap-7660	108	14	simple	simple	ADJ
ap-7660	108	15	coupled	couple	VERB
ap-7660	108	16	third	third	ADJ
ap-7660	108	17	order	order	NOUN
ap-7660	108	18	algebraic	algebraic	ADJ
ap-7660	108	19	equations	equation	NOUN
ap-7660	108	20	g	g	PROPN
ap-7660	108	21	4(h0	4(h0	PROPN
ap-7660	108	22	1)3	1)3	NUM
ap-7660	108	23	−	−	PROPN
ap-7660	108	24	c1m2	c1m2	PUNCT
ap-7660	108	25	1h0	1h0	NUM
ap-7660	108	26	1	1	NUM
ap-7660	108	27	+	+	CCONJ
ap-7660	108	28	c3µ2h0	c3µ2h0	PROPN
ap-7660	108	29	2	2	NUM
ap-7660	108	30	=	=	SYM
ap-7660	108	31	0	0	NUM
ap-7660	108	32	,	,	PUNCT
ap-7660	108	33	(	(	PUNCT
ap-7660	108	34	10	10	NUM
ap-7660	108	35	)	)	PUNCT
ap-7660	108	36	c2m2	c2m2	VERB
ap-7660	108	37	2h0	2h0	NUM
ap-7660	108	38	2	2	NUM
ap-7660	108	39	+	+	CCONJ
ap-7660	108	40	c3µ2h0	c3µ2h0	PROPN
ap-7660	108	41	1	1	NUM
ap-7660	108	42	=	=	SYM
ap-7660	108	43	0	0	NUM
ap-7660	108	44	,	,	PUNCT
ap-7660	108	45	dµϕα	dµϕα	NOUN
ap-7660	108	46	=	=	SYM
ap-7660	108	47	0	0	X
ap-7660	108	48	.	.	PUNCT
ap-7660	109	1	the	the	DET
ap-7660	109	2	resulting	result	VERB
ap-7660	109	3	vacuum	vacuum	NOUN
ap-7660	109	4	solutions	solution	NOUN
ap-7660	109	5	are	be	AUX
ap-7660	109	6	h0	h0	ADJ
ap-7660	109	7	2	2	NUM
ap-7660	110	1	=	=	SYM
ap-7660	110	2	−	−	PROPN
ap-7660	110	3	c2c3µ2	c2c3µ2	PROPN
ap-7660	110	4	m2	m2	PROPN
ap-7660	110	5	2	2	NUM
ap-7660	110	6	h0	h0	PROPN
ap-7660	110	7	1	1	NUM
ap-7660	110	8	,	,	PUNCT
ap-7660	110	9	(	(	PUNCT
ap-7660	110	10	h0	h0	NOUN
ap-7660	110	11	1)2	1)2	NUM
ap-7660	110	12	=	=	SYM
ap-7660	110	13	4	4	NUM
ap-7660	110	14	c2µ4+c1m2	c2µ4+c1m2	ADJ
ap-7660	110	15	1m2	1m2	NUM
ap-7660	110	16	2	2	NUM
ap-7660	110	17	gm2	gm2	NOUN
ap-7660	110	18	2	2	NUM
ap-7660	110	19	:	:	PUNCT
ap-7660	110	20	=	=	SYM
ap-7660	110	21	r2	r2	PROPN
ap-7660	110	22	,	,	PUNCT
ap-7660	110	23	(	(	PUNCT
ap-7660	110	24	11	11	NUM
ap-7660	110	25	)	)	PUNCT
ap-7660	110	26	(	(	PUNCT
ap-7660	110	27	a0	a0	PROPN
ap-7660	110	28	i	i	PRON
ap-7660	110	29	)	)	PUNCT
ap-7660	110	30	a	a	PRON
ap-7660	110	31	=	=	SYM
ap-7660	110	32	−	−	PROPN
ap-7660	110	33	1	1	NUM
ap-7660	110	34	er	er	INTJ
ap-7660	110	35	ϵiaj	ϵiaj	VERB
ap-7660	110	36	r̂j	r̂j	NOUN
ap-7660	110	37	+	+	CCONJ
ap-7660	110	38	r̂aai	r̂aai	PROPN
ap-7660	110	39	,	,	PUNCT
ap-7660	110	40	(	(	PUNCT
ap-7660	110	41	a0	a0	NOUN
ap-7660	110	42	0)a	0)a	PROPN
ap-7660	110	43	=	=	PUNCT
ap-7660	111	1	0	0	X
ap-7660	111	2	.	.	PUNCT
ap-7660	112	1	the	the	DET
ap-7660	112	2	ai	ai	NOUN
ap-7660	112	3	are	be	AUX
ap-7660	112	4	arbitrary	arbitrary	ADJ
ap-7660	112	5	functions	function	NOUN
ap-7660	112	6	of	of	ADP
ap-7660	112	7	space	space	NOUN
ap-7660	112	8	-	-	PUNCT
ap-7660	112	9	time	time	NOUN
ap-7660	112	10	.	.	PUNCT
ap-7660	113	1	the	the	DET
ap-7660	113	2	higgs	higgs	PROPN
ap-7660	113	3	particle	particle	NOUN
ap-7660	113	4	can	can	AUX
ap-7660	113	5	be	be	AUX
ap-7660	113	6	identified	identify	VERB
ap-7660	113	7	with	with	ADP
ap-7660	113	8	the	the	DET
ap-7660	113	9	fundamental	fundamental	ADJ
ap-7660	113	10	fields	field	NOUN
ap-7660	113	11	of	of	ADP
ap-7660	113	12	the	the	DET
ap-7660	113	13	theory	theory	NOUN
ap-7660	113	14	after	after	ADP
ap-7660	113	15	spontaneous	spontaneous	ADJ
ap-7660	113	16	symmetry	symmetry	NOUN
ap-7660	113	17	breaking	breaking	NOUN
ap-7660	113	18	of	of	ADP
ap-7660	113	19	the	the	DET
ap-7660	113	20	continuous	continuous	ADJ
ap-7660	113	21	symmetry	symmetry	NOUN
ap-7660	113	22	su(2	su(2	NOUN
ap-7660	113	23	)	)	PUNCT
ap-7660	113	24	by	by	ADP
ap-7660	113	25	taylor	taylor	NOUN
ap-7660	113	26	expanding	expand	VERB
ap-7660	113	27	around	around	ADP
ap-7660	113	28	the	the	DET
ap-7660	113	29	vacuum	vacuum	NOUN
ap-7660	113	30	solution	solution	NOUN
ap-7660	113	31	.	.	PUNCT
ap-7660	114	1	performing	perform	VERB
ap-7660	114	2	a	a	DET
ap-7660	114	3	taylor	taylor	NOUN
ap-7660	114	4	expansion	expansion	NOUN
ap-7660	114	5	around	around	ADP
ap-7660	114	6	the	the	DET
ap-7660	114	7	higgs	higgs	PROPN
ap-7660	114	8	vacuum	vacuum	PROPN
ap-7660	114	9	and	and	CCONJ
ap-7660	114	10	keeping	keep	VERB
ap-7660	114	11	a	a	DET
ap-7660	114	12	focus	focus	NOUN
ap-7660	114	13	on	on	ADP
ap-7660	114	14	the	the	DET
ap-7660	114	15	second	second	ADJ
ap-7660	114	16	-	-	PUNCT
ap-7660	114	17	order	order	NOUN
ap-7660	114	18	terms	term	NOUN
ap-7660	114	19	with	with	ADP
ap-7660	114	20	only	only	ADV
ap-7660	114	21	matter	matter	NOUN
ap-7660	114	22	fields	field	NOUN
ap-7660	114	23	ϕa	ϕa	ADP
ap-7660	114	24	i	i	PRON
ap-7660	114	25	,	,	PUNCT
ap-7660	114	26	the	the	DET
ap-7660	114	27	real	real	ADJ
ap-7660	114	28	lagrangian	lagrangian	ADJ
ap-7660	114	29	(	(	PUNCT
ap-7660	114	30	7	7	NUM
ap-7660	114	31	)	)	PUNCT
ap-7660	114	32	contains	contain	VERB
ap-7660	114	33	the	the	DET
ap-7660	114	34	following	follow	VERB
ap-7660	114	35	term	term	NOUN
ap-7660	114	36	s	s	PART
ap-7660	114	37	=	=	SYM
ap-7660	114	38	∫	∫	PROPN
ap-7660	114	39	d4x	d4x	PROPN
ap-7660	114	40	1	1	NUM
ap-7660	114	41	2ϕa	2ϕa	NOUN
ap-7660	114	42	i	i	PRON
ap-7660	114	43	(	(	PUNCT
ap-7660	114	44	−∂µ∂µiijδab	−∂µ∂µiijδab	X
ap-7660	114	45	−	−	PROPN
ap-7660	114	46	h̃ab	h̃ab	PROPN
ap-7660	114	47	ij	ij	NOUN
ap-7660	114	48	)	)	PUNCT
ap-7660	114	49	ϕb	ϕb	ADP
ap-7660	114	50	j	j	PROPN
ap-7660	115	1	+	+	PROPN
ap-7660	115	2	.	.	PUNCT
ap-7660	115	3	.	.	PUNCT
ap-7660	116	1	.	.	PUNCT
ap-7660	117	1	,	,	PUNCT
ap-7660	117	2	where	where	SCONJ
ap-7660	117	3	h̃	h̃	PROPN
ap-7660	117	4	is	be	AUX
ap-7660	117	5	a	a	DET
ap-7660	117	6	6	6	NUM
ap-7660	117	7	×	×	NOUN
ap-7660	117	8	6	6	NUM
ap-7660	117	9	block	block	NOUN
ap-7660	117	10	diagonal	diagonal	ADJ
ap-7660	117	11	hermitian	hermitian	ADJ
ap-7660	117	12	matrix	matrix	NOUN
ap-7660	117	13	.	.	PUNCT
ap-7660	118	1	after	after	ADP
ap-7660	118	2	diagonalising	diagonalise	VERB
ap-7660	118	3	the	the	DET
ap-7660	118	4	above	above	ADJ
ap-7660	118	5	term	term	NOUN
ap-7660	118	6	by	by	ADP
ap-7660	118	7	redefining	redefine	VERB
ap-7660	118	8	the	the	DET
ap-7660	118	9	fields	field	NOUN
ap-7660	118	10	with	with	ADP
ap-7660	118	11	the	the	DET
ap-7660	118	12	eigenvectors	eigenvector	NOUN
ap-7660	118	13	of	of	ADP
ap-7660	118	14	the	the	DET
ap-7660	118	15	non	non	ADJ
ap-7660	118	16	-	-	ADJ
ap-7660	118	17	hermitian	hermitian	ADJ
ap-7660	118	18	mass	mass	NOUN
ap-7660	118	19	matrix	matrix	NOUN
ap-7660	118	20	mab	mab	NOUN
ap-7660	118	21	ij	ij	NOUN
ap-7660	118	22	:	:	PUNCT
ap-7660	118	23	=	=	NOUN
ap-7660	118	24	iikδach̃cb	iikδach̃cb	PROPN
ap-7660	118	25	kj	kj	PROPN
ap-7660	118	26	,	,	PUNCT
ap-7660	118	27	we	we	PRON
ap-7660	118	28	find	find	VERB
ap-7660	118	29	that	that	SCONJ
ap-7660	118	30	the	the	DET
ap-7660	118	31	masses	masse	NOUN
ap-7660	118	32	of	of	ADP
ap-7660	118	33	the	the	DET
ap-7660	118	34	fundamental	fundamental	ADJ
ap-7660	118	35	fields	field	NOUN
ap-7660	118	36	after	after	SCONJ
ap-7660	118	37	the	the	DET
ap-7660	118	38	symmetry	symmetry	NOUN
ap-7660	118	39	breaking	break	VERB
ap-7660	118	40	to	to	PART
ap-7660	118	41	be	be	AUX
ap-7660	118	42	equal	equal	ADJ
ap-7660	118	43	to	to	ADP
ap-7660	118	44	the	the	DET
ap-7660	118	45	eigenvalues	eigenvalue	NOUN
ap-7660	118	46	of	of	ADP
ap-7660	118	47	mab	mab	NOUN
ap-7660	118	48	ij	ij	NOUN
ap-7660	118	49	given	give	VERB
ap-7660	118	50	as	as	ADP
ap-7660	118	51	m2	m2	PROPN
ap-7660	118	52	0	0	PROPN
ap-7660	118	53	=	=	PROPN
ap-7660	118	54	c2	c2	PROPN
ap-7660	118	55	µ4	µ4	PROPN
ap-7660	118	56	−	−	PROPN
ap-7660	118	57	m4	m4	PROPN
ap-7660	118	58	2	2	NUM
ap-7660	118	59	m2	m2	PROPN
ap-7660	118	60	2	2	NUM
ap-7660	118	61	,	,	PUNCT
ap-7660	118	62	m2	m2	PROPN
ap-7660	118	63	±	±	PROPN
ap-7660	118	64	=	=	SYM
ap-7660	118	65	k	k	PROPN
ap-7660	118	66	±	±	PROPN
ap-7660	118	67	√	√	PROPN
ap-7660	118	68	k2	k2	PROPN
ap-7660	118	69	+	+	CCONJ
ap-7660	118	70	2l	2l	NUM
ap-7660	118	71	,	,	PUNCT
ap-7660	118	72	(	(	PUNCT
ap-7660	118	73	12	12	NUM
ap-7660	118	74	)	)	PUNCT
ap-7660	118	75	where	where	SCONJ
ap-7660	118	76	k	k	NOUN
ap-7660	118	77	=	=	PUNCT
ap-7660	118	78	c1m2	c1m2	ADP
ap-7660	118	79	1	1	NUM
ap-7660	118	80	−	−	PROPN
ap-7660	118	81	c2	c2	PROPN
ap-7660	118	82	m2	m2	PROPN
ap-7660	118	83	2	2	NUM
ap-7660	118	84	2	2	NUM
ap-7660	118	85	+	+	NUM
ap-7660	118	86	3µ4	3µ4	NUM
ap-7660	118	87	2c2m2	2c2m2	NUM
ap-7660	118	88	2	2	NUM
ap-7660	118	89	and	and	CCONJ
ap-7660	118	90	l	l	NOUN
ap-7660	118	91	=	=	PUNCT
ap-7660	118	92	µ4	µ4	PROPN
ap-7660	118	93	+	+	NUM
ap-7660	118	94	c1c2m2	c1c2m2	PROPN
ap-7660	118	95	1m2	1m2	NUM
ap-7660	118	96	2	2	NUM
ap-7660	118	97	.	.	PUNCT
ap-7660	118	98	notice	notice	VERB
ap-7660	118	99	that	that	SCONJ
ap-7660	118	100	we	we	PRON
ap-7660	118	101	only	only	ADV
ap-7660	118	102	find	find	VERB
ap-7660	118	103	three	three	NUM
ap-7660	118	104	non	non	ADJ
ap-7660	118	105	-	-	ADJ
ap-7660	118	106	zero	zero	NUM
ap-7660	118	107	eigenvalues	eigenvalue	NOUN
ap-7660	118	108	.	.	PUNCT
ap-7660	119	1	the	the	DET
ap-7660	119	2	redefined	redefine	VERB
ap-7660	119	3	fields	field	NOUN
ap-7660	119	4	with	with	ADP
ap-7660	119	5	zero	zero	NUM
ap-7660	119	6	masses	masse	NOUN
ap-7660	119	7	(	(	PUNCT
ap-7660	119	8	eigenvalues	eigenvalue	NOUN
ap-7660	119	9	)	)	PUNCT
ap-7660	119	10	are	be	AUX
ap-7660	119	11	called	call	VERB
ap-7660	119	12	goldstone	goldstone	NOUN
ap-7660	119	13	fields	field	NOUN
ap-7660	119	14	,	,	PUNCT
ap-7660	119	15	which	which	PRON
ap-7660	119	16	can	can	AUX
ap-7660	119	17	be	be	AUX
ap-7660	119	18	absorbed	absorb	VERB
ap-7660	119	19	into	into	ADP
ap-7660	119	20	gauge	gauge	ADJ
ap-7660	119	21	fields	field	NOUN
ap-7660	119	22	aa	aa	PROPN
ap-7660	119	23	µ	µ	NOUN
ap-7660	119	24	by	by	ADP
ap-7660	119	25	defining	define	VERB
ap-7660	119	26	the	the	DET
ap-7660	119	27	new	new	ADJ
ap-7660	119	28	massive	massive	ADJ
ap-7660	119	29	gauge	gauge	NOUN
ap-7660	119	30	fields	field	NOUN
ap-7660	119	31	.	.	PUNCT
ap-7660	120	1	this	this	DET
ap-7660	120	2	process	process	NOUN
ap-7660	120	3	of	of	ADP
ap-7660	120	4	giving	give	VERB
ap-7660	120	5	mass	mass	NOUN
ap-7660	120	6	to	to	ADP
ap-7660	120	7	the	the	DET
ap-7660	120	8	previously	previously	ADV
ap-7660	120	9	massless	massless	ADJ
ap-7660	120	10	fields	field	NOUN
ap-7660	120	11	is	be	AUX
ap-7660	120	12	called	call	VERB
ap-7660	120	13	the	the	DET
ap-7660	120	14	higgs	higgs	NOUN
ap-7660	120	15	mechanism	mechanism	NOUN
ap-7660	120	16	.	.	PUNCT
ap-7660	121	1	the	the	DET
ap-7660	121	2	mass	mass	NOUN
ap-7660	121	3	of	of	ADP
ap-7660	121	4	the	the	DET
ap-7660	121	5	gauge	gauge	NOUN
ap-7660	121	6	fields	field	NOUN
ap-7660	121	7	can	can	AUX
ap-7660	121	8	be	be	AUX
ap-7660	121	9	found	find	VERB
ap-7660	121	10	by	by	ADP
ap-7660	121	11	expanding	expand	VERB
ap-7660	121	12	the	the	DET
ap-7660	121	13	kinetic	kinetic	ADJ
ap-7660	121	14	term	term	NOUN
ap-7660	121	15	of	of	ADP
ap-7660	121	16	ϕ	ϕ	NOUN
ap-7660	121	17	around	around	ADP
ap-7660	121	18	the	the	DET
ap-7660	121	19	higgs	higgs	PROPN
ap-7660	121	20	vacuum	vacuum	PROPN
ap-7660	121	21	ϕ0	ϕ0	PROPN
ap-7660	121	22	i	i	NOUN
ap-7660	121	23	=	=	SYM
ap-7660	121	24	h0	h0	PROPN
ap-7660	121	25	i	i	PROPN
ap-7660	121	26	r̂a	r̂a	NOUN
ap-7660	121	27	.	.	PUNCT
ap-7660	122	1	without	without	ADP
ap-7660	122	2	loss	loss	NOUN
ap-7660	122	3	of	of	ADP
ap-7660	122	4	generality	generality	NOUN
ap-7660	122	5	,	,	PUNCT
ap-7660	122	6	we	we	PRON
ap-7660	122	7	can	can	AUX
ap-7660	122	8	choose	choose	VERB
ap-7660	122	9	a	a	DET
ap-7660	122	10	particular	particular	ADJ
ap-7660	122	11	direction	direction	NOUN
ap-7660	122	12	of	of	ADP
ap-7660	122	13	the	the	DET
ap-7660	122	14	vacuum	vacuum	NOUN
ap-7660	122	15	by	by	ADP
ap-7660	122	16	taking	take	VERB
ap-7660	122	17	r̂	r̂	NOUN
ap-7660	122	18	=	=	SYM
ap-7660	122	19	(	(	PUNCT
ap-7660	122	20	0	0	NUM
ap-7660	122	21	,	,	PUNCT
ap-7660	122	22	0	0	NUM
ap-7660	122	23	,	,	PUNCT
ap-7660	122	24	1)t	1)t	PROPN
ap-7660	122	25	.	.	PUNCT
ap-7660	123	1	this	this	PRON
ap-7660	123	2	is	be	AUX
ap-7660	123	3	possible	possible	ADJ
ap-7660	123	4	due	due	ADP
ap-7660	123	5	to	to	ADP
ap-7660	123	6	the	the	DET
ap-7660	123	7	symmetry	symmetry	NOUN
ap-7660	123	8	of	of	ADP
ap-7660	123	9	the	the	DET
ap-7660	123	10	so(3	so(3	NOUN
ap-7660	123	11	)	)	PUNCT
ap-7660	123	12	vacuum	vacuum	NOUN
ap-7660	123	13	as	as	SCONJ
ap-7660	123	14	discussed	discuss	VERB
ap-7660	123	15	above	above	ADV
ap-7660	123	16	.	.	PUNCT
ap-7660	124	1	keeping	keep	VERB
ap-7660	124	2	the	the	DET
ap-7660	124	3	term	term	NOUN
ap-7660	124	4	only	only	ADV
ap-7660	124	5	quadratic	quadratic	ADJ
ap-7660	124	6	in	in	ADP
ap-7660	124	7	the	the	DET
ap-7660	124	8	gauge	gauge	ADJ
ap-7660	124	9	field	field	NOUN
ap-7660	124	10	,	,	PUNCT
ap-7660	124	11	we	we	PRON
ap-7660	124	12	find	find	VERB
ap-7660	124	13	1	1	NUM
ap-7660	124	14	2(dµϕi	2(dµϕi	NUM
ap-7660	124	15	+	+	CCONJ
ap-7660	124	16	dµϕ0	dµϕ0	PROPN
ap-7660	124	17	i	i	PRON
ap-7660	124	18	)	)	PUNCT
ap-7660	124	19	aiij(dµϕi	aiij(dµϕi	PROPN
ap-7660	125	1	+	+	CCONJ
ap-7660	125	2	dµϕ0	dµϕ0	PROPN
ap-7660	125	3	i	i	PRON
ap-7660	125	4	)	)	PUNCT
ap-7660	125	5	a	a	PRON
ap-7660	125	6	(	(	PUNCT
ap-7660	125	7	13	13	NUM
ap-7660	125	8	)	)	PUNCT
ap-7660	125	9	=	=	SYM
ap-7660	125	10	1	1	NUM
ap-7660	125	11	2	2	NUM
ap-7660	125	12	(	(	PUNCT
ap-7660	125	13	eaµ	eaµ	VERB
ap-7660	125	14	×	×	PROPN
ap-7660	125	15	ϕ0	ϕ0	NOUN
ap-7660	125	16	i	i	NOUN
ap-7660	125	17	)	)	PUNCT
ap-7660	125	18	a	a	DET
ap-7660	125	19	iij	iij	NOUN
ap-7660	125	20	(	(	PUNCT
ap-7660	125	21	eaµ	eaµ	VERB
ap-7660	125	22	×	×	PROPN
ap-7660	125	23	ϕ0	ϕ0	PROPN
ap-7660	125	24	j	j	PROPN
ap-7660	125	25	)	)	PUNCT
ap-7660	125	26	a	a	DET
ap-7660	125	27	+	+	NOUN
ap-7660	125	28	.	.	PUNCT
ap-7660	125	29	.	.	PUNCT
ap-7660	125	30	.	.	PUNCT
ap-7660	126	1	=	=	SYM
ap-7660	126	2	1	1	NUM
ap-7660	126	3	2e2h0	2e2h0	NUM
ap-7660	127	1	i	i	PROPN
ap-7660	127	2	iijh0	iijh0	NOUN
ap-7660	128	1	j	j	PROPN
ap-7660	128	2	(	(	PUNCT
ap-7660	128	3	a1	a1	NOUN
ap-7660	128	4	µa1µ	µa1µ	PROPN
ap-7660	128	5	+	+	NUM
ap-7660	128	6	a2	a2	PROPN
ap-7660	128	7	µa2µ	µa2µ	NOUN
ap-7660	128	8	)	)	PUNCT
ap-7660	128	9	+	+	CCONJ
ap-7660	128	10	.	.	PUNCT
ap-7660	128	11	.	.	PUNCT
ap-7660	128	12	.	.	PUNCT
ap-7660	129	1	=	=	SYM
ap-7660	129	2	1	1	NUM
ap-7660	129	3	2m2	2m2	NUM
ap-7660	129	4	g	g	NOUN
ap-7660	129	5	(	(	PUNCT
ap-7660	129	6	a1	a1	NOUN
ap-7660	129	7	µa1µ	µa1µ	PROPN
ap-7660	129	8	+	+	NUM
ap-7660	129	9	a2	a2	PROPN
ap-7660	129	10	µa2µ	µa2µ	NOUN
ap-7660	129	11	)	)	PUNCT
ap-7660	129	12	+	+	CCONJ
ap-7660	129	13	.	.	PUNCT
ap-7660	129	14	.	.	PUNCT
ap-7660	129	15	.	.	PUNCT
ap-7660	130	1	,	,	PUNCT
ap-7660	130	2	where	where	SCONJ
ap-7660	130	3	the	the	DET
ap-7660	130	4	mass	mass	NOUN
ap-7660	130	5	of	of	ADP
ap-7660	130	6	the	the	DET
ap-7660	130	7	gauge	gauge	NOUN
ap-7660	130	8	field	field	NOUN
ap-7660	130	9	is	be	AUX
ap-7660	130	10	identified	identify	VERB
ap-7660	130	11	to	to	PART
ap-7660	130	12	be	be	AUX
ap-7660	130	13	mg	mg	ADJ
ap-7660	130	14	:	:	PUNCT
ap-7660	130	15	=	=	SYM
ap-7660	130	16	√	√	PROPN
ap-7660	130	17	h0	h0	NOUN
ap-7660	130	18	i	i	PRON
ap-7660	130	19	iijh0	iijh0	NOUN
ap-7660	131	1	j	j	PROPN
ap-7660	131	2	=	=	SYM
ap-7660	131	3	e	e	PROPN
ap-7660	131	4	r	r	NOUN
ap-7660	131	5	√	√	PROPN
ap-7660	131	6	m4	m4	PROPN
ap-7660	131	7	2−µ4	2−µ4	NUM
ap-7660	131	8	m2	m2	PROPN
ap-7660	131	9	2	2	NUM
ap-7660	131	10	.	.	PUNCT
ap-7660	131	11	2.2	2.2	NUM
ap-7660	131	12	.	.	PUNCT
ap-7660	131	13	t’hooft	t’hooft	PROPN
ap-7660	131	14	-	-	PUNCT
ap-7660	131	15	polyakov	polyakov	PROPN
ap-7660	131	16	monopole	monopole	NOUN
ap-7660	131	17	to	to	PART
ap-7660	131	18	find	find	VERB
ap-7660	131	19	the	the	DET
ap-7660	131	20	monopole	monopole	ADJ
ap-7660	131	21	solutions	solution	NOUN
ap-7660	131	22	,	,	PUNCT
ap-7660	131	23	let	let	VERB
ap-7660	131	24	us	we	PRON
ap-7660	131	25	consider	consider	VERB
ap-7660	131	26	the	the	DET
ap-7660	131	27	following	follow	VERB
ap-7660	131	28	ansatz	ansatz	ADJ
ap-7660	131	29	(	(	PUNCT
ap-7660	131	30	ϕcl	ϕcl	ADV
ap-7660	131	31	i	i	PRON
ap-7660	131	32	)	)	PUNCT
ap-7660	131	33	a(x⃗	a(x⃗	VERB
ap-7660	131	34	)	)	PUNCT
ap-7660	132	1	=	=	SYM
ap-7660	132	2	hi(r)r̂a	hi(r)r̂a	PROPN
ap-7660	132	3	,	,	PUNCT
ap-7660	132	4	(	(	PUNCT
ap-7660	132	5	acl	acl	PROPN
ap-7660	132	6	i	i	PROPN
ap-7660	132	7	)	)	PUNCT
ap-7660	132	8	a	a	DET
ap-7660	132	9	=	=	NOUN
ap-7660	132	10	ϵiaj	ϵiaj	NOUN
ap-7660	132	11	r̂ja(r	r̂ja(r	NOUN
ap-7660	132	12	)	)	PUNCT
ap-7660	132	13	,	,	PUNCT
ap-7660	132	14	(	(	PUNCT
ap-7660	132	15	14	14	NUM
ap-7660	132	16	)	)	PUNCT
ap-7660	132	17	(	(	PUNCT
ap-7660	132	18	acl	acl	PROPN
ap-7660	132	19	0	0	NUM
ap-7660	132	20	)	)	PUNCT
ap-7660	132	21	a	a	DET
ap-7660	132	22	=	=	NOUN
ap-7660	132	23	0	0	NUM
ap-7660	132	24	,	,	PUNCT
ap-7660	132	25	where	where	SCONJ
ap-7660	132	26	the	the	DET
ap-7660	132	27	subscript	subscript	NOUN
ap-7660	132	28	cl	cl	NOUN
ap-7660	132	29	denotes	denote	VERB
ap-7660	132	30	the	the	DET
ap-7660	132	31	classical	classical	ADJ
ap-7660	132	32	solutions	solution	NOUN
ap-7660	132	33	to	to	ADP
ap-7660	132	34	the	the	DET
ap-7660	132	35	equations	equation	NOUN
ap-7660	132	36	of	of	ADP
ap-7660	132	37	motion	motion	NOUN
ap-7660	132	38	(	(	PUNCT
ap-7660	132	39	4	4	NUM
ap-7660	132	40	)	)	PUNCT
ap-7660	132	41	.	.	PUNCT
ap-7660	133	1	the	the	DET
ap-7660	133	2	difference	difference	NOUN
ap-7660	133	3	between	between	ADP
ap-7660	133	4	this	this	DET
ap-7660	133	5	ansatz	ansatz	ADJ
ap-7660	133	6	(	(	PUNCT
ap-7660	133	7	14	14	NUM
ap-7660	133	8	)	)	PUNCT
ap-7660	133	9	and	and	CCONJ
ap-7660	133	10	the	the	DET
ap-7660	133	11	higgs	higgs	PROPN
ap-7660	133	12	vacuum	vacuum	PROPN
ap-7660	133	13	(	(	PUNCT
ap-7660	133	14	11	11	NUM
ap-7660	133	15	)	)	PUNCT
ap-7660	133	16	199	199	NUM
ap-7660	133	17	takanobu	takanobu	PROPN
ap-7660	133	18	taira	taira	PROPN
ap-7660	133	19	acta	acta	PROPN
ap-7660	133	20	polytechnica	polytechnica	PROPN
ap-7660	133	21	is	be	AUX
ap-7660	133	22	that	that	SCONJ
ap-7660	133	23	the	the	DET
ap-7660	133	24	quantity	quantity	NOUN
ap-7660	133	25	hi	hi	INTJ
ap-7660	133	26	now	now	ADV
ap-7660	133	27	depends	depend	VERB
ap-7660	133	28	on	on	ADP
ap-7660	133	29	the	the	DET
ap-7660	133	30	spatial	spatial	ADJ
ap-7660	133	31	radius	radius	NOUN
ap-7660	133	32	hi	hi	INTJ
ap-7660	133	33	=	=	PUNCT
ap-7660	133	34	hi(r	hi(r	NOUN
ap-7660	133	35	)	)	PUNCT
ap-7660	133	36	.	.	PUNCT
ap-7660	134	1	here	here	ADV
ap-7660	134	2	we	we	PRON
ap-7660	134	3	are	be	AUX
ap-7660	134	4	only	only	ADV
ap-7660	134	5	considering	consider	VERB
ap-7660	134	6	the	the	DET
ap-7660	134	7	static	static	NOUN
ap-7660	134	8	ansatz	ansatz	ADV
ap-7660	134	9	to	to	PART
ap-7660	134	10	simplify	simplify	VERB
ap-7660	134	11	our	our	PRON
ap-7660	134	12	calculation	calculation	NOUN
ap-7660	134	13	,	,	PUNCT
ap-7660	134	14	but	but	CCONJ
ap-7660	134	15	one	one	NUM
ap-7660	134	16	may	may	AUX
ap-7660	134	17	,	,	PUNCT
ap-7660	134	18	of	of	ADP
ap-7660	134	19	course	course	NOUN
ap-7660	134	20	,	,	PUNCT
ap-7660	134	21	also	also	ADV
ap-7660	134	22	consider	consider	VERB
ap-7660	134	23	the	the	DET
ap-7660	134	24	time	time	NOUN
ap-7660	134	25	-	-	PUNCT
ap-7660	134	26	dependent	dependent	ADJ
ap-7660	134	27	solution	solution	NOUN
ap-7660	134	28	by	by	ADP
ap-7660	134	29	utilising	utilise	VERB
ap-7660	134	30	the	the	DET
ap-7660	134	31	lorentz	lorentz	PROPN
ap-7660	134	32	symmetry	symmetry	NOUN
ap-7660	134	33	of	of	ADP
ap-7660	134	34	the	the	DET
ap-7660	134	35	model	model	NOUN
ap-7660	134	36	and	and	CCONJ
ap-7660	134	37	performing	perform	VERB
ap-7660	134	38	a	a	DET
ap-7660	134	39	lorentz	lorentz	PROPN
ap-7660	134	40	boost	boost	NOUN
ap-7660	134	41	.	.	PUNCT
ap-7660	135	1	according	accord	VERB
ap-7660	135	2	to	to	ADP
ap-7660	135	3	derrick	derrick	PROPN
ap-7660	135	4	’s	’s	PART
ap-7660	135	5	scaling	scaling	ADJ
ap-7660	135	6	argument	argument	NOUN
ap-7660	135	7	[	[	X
ap-7660	135	8	25	25	NUM
ap-7660	135	9	]	]	PUNCT
ap-7660	135	10	,	,	PUNCT
ap-7660	135	11	for	for	ADP
ap-7660	135	12	the	the	DET
ap-7660	135	13	monopole	monopole	ADJ
ap-7660	135	14	solution	solution	NOUN
ap-7660	135	15	to	to	PART
ap-7660	135	16	have	have	VERB
ap-7660	135	17	finite	finite	ADJ
ap-7660	135	18	energy	energy	NOUN
ap-7660	135	19	,	,	PUNCT
ap-7660	135	20	we	we	PRON
ap-7660	135	21	require	require	VERB
ap-7660	135	22	the	the	DET
ap-7660	135	23	two	two	NUM
ap-7660	135	24	matter	matter	NOUN
ap-7660	135	25	fields	field	NOUN
ap-7660	135	26	of	of	ADP
ap-7660	135	27	the	the	DET
ap-7660	135	28	equation	equation	NOUN
ap-7660	135	29	(	(	PUNCT
ap-7660	135	30	14	14	NUM
ap-7660	135	31	)	)	PUNCT
ap-7660	135	32	to	to	PART
ap-7660	135	33	approach	approach	VERB
ap-7660	135	34	the	the	DET
ap-7660	135	35	vacuum	vacuum	NOUN
ap-7660	135	36	solutions	solution	NOUN
ap-7660	135	37	in	in	ADP
ap-7660	135	38	the	the	DET
ap-7660	135	39	equation	equation	NOUN
ap-7660	135	40	(	(	PUNCT
ap-7660	135	41	11	11	NUM
ap-7660	135	42	)	)	PUNCT
ap-7660	135	43	at	at	ADP
ap-7660	135	44	spatial	spatial	ADJ
ap-7660	135	45	infinity	infinity	NOUN
ap-7660	135	46	lim	lim	PROPN
ap-7660	135	47	r→∞	r→∞	PUNCT
ap-7660	135	48	h1(r	h1(r	PROPN
ap-7660	135	49	)	)	PUNCT
ap-7660	135	50	=	=	SYM
ap-7660	136	1	h0±	h0±	ADJ
ap-7660	136	2	1	1	NUM
ap-7660	136	3	=	=	SYM
ap-7660	136	4	±r	±r	PROPN
ap-7660	136	5	,	,	PUNCT
ap-7660	136	6	(	(	PUNCT
ap-7660	136	7	15	15	X
ap-7660	136	8	)	)	PUNCT
ap-7660	136	9	lim	lim	NOUN
ap-7660	136	10	r→∞	r→∞	PRON
ap-7660	136	11	h2(r	h2(r	PROPN
ap-7660	136	12	)	)	PUNCT
ap-7660	136	13	=	=	SYM
ap-7660	137	1	h0±	h0±	ADJ
ap-7660	137	2	2	2	NUM
ap-7660	137	3	=	=	SYM
ap-7660	137	4	∓c2c3µ2	∓c2c3µ2	PROPN
ap-7660	137	5	m2	m2	PROPN
ap-7660	137	6	2	2	PROPN
ap-7660	137	7	r.	r.	PROPN
ap-7660	137	8	also	also	ADV
ap-7660	137	9	,	,	PUNCT
ap-7660	137	10	notice	notice	VERB
ap-7660	137	11	that	that	SCONJ
ap-7660	137	12	at	at	ADP
ap-7660	137	13	some	some	DET
ap-7660	137	14	fixed	fix	VERB
ap-7660	137	15	value	value	NOUN
ap-7660	137	16	of	of	ADP
ap-7660	137	17	the	the	DET
ap-7660	137	18	radius	radius	NOUN
ap-7660	137	19	r	r	NOUN
ap-7660	137	20	,	,	PUNCT
ap-7660	137	21	the	the	DET
ap-7660	137	22	vacuum	vacuum	NOUN
ap-7660	137	23	solutions	solution	NOUN
ap-7660	137	24	ϕ0	ϕ0	NOUN
ap-7660	137	25	α	α	NOUN
ap-7660	137	26	and	and	CCONJ
ap-7660	137	27	monopole	monopole	ADJ
ap-7660	137	28	solutions	solution	NOUN
ap-7660	137	29	ϕcl	ϕcl	ADP
ap-7660	137	30	α	α	PROPN
ap-7660	137	31	both	both	PRON
ap-7660	137	32	belongs	belong	VERB
ap-7660	137	33	to	to	ADP
ap-7660	137	34	the	the	DET
ap-7660	137	35	2	2	NUM
ap-7660	137	36	-	-	PUNCT
ap-7660	137	37	sphere	sphere	NOUN
ap-7660	137	38	in	in	ADP
ap-7660	137	39	the	the	DET
ap-7660	137	40	field	field	NOUN
ap-7660	137	41	configuration	configuration	NOUN
ap-7660	137	42	space	space	NOUN
ap-7660	137	43	.	.	PUNCT
ap-7660	138	1	for	for	ADP
ap-7660	138	2	example	example	NOUN
ap-7660	138	3	,	,	PUNCT
ap-7660	138	4	ϕ0	ϕ0	NOUN
ap-7660	138	5	1	1	NUM
ap-7660	138	6	belongs	belong	VERB
ap-7660	138	7	to	to	ADP
ap-7660	138	8	the	the	DET
ap-7660	138	9	2	2	NUM
ap-7660	138	10	-	-	PUNCT
ap-7660	138	11	sphere	sphere	NOUN
ap-7660	138	12	with	with	ADP
ap-7660	138	13	radius	radius	NOUN
ap-7660	138	14	r	r	NOUN
ap-7660	138	15	because	because	SCONJ
ap-7660	138	16	(	(	PUNCT
ap-7660	138	17	ϕ0	ϕ0	NOUN
ap-7660	138	18	1)2	1)2	NUM
ap-7660	138	19	=	=	SYM
ap-7660	138	20	r2	r2	NOUN
ap-7660	138	21	.	.	PUNCT
ap-7660	139	1	therefore	therefore	ADV
ap-7660	139	2	,	,	PUNCT
ap-7660	139	3	solutions	solution	NOUN
ap-7660	139	4	ϕcl	ϕcl	ADV
ap-7660	139	5	i	i	PRON
ap-7660	139	6	can	can	AUX
ap-7660	139	7	be	be	AUX
ap-7660	139	8	seen	see	VERB
ap-7660	139	9	as	as	ADP
ap-7660	139	10	a	a	DET
ap-7660	139	11	mapping	mapping	NOUN
ap-7660	139	12	between	between	ADP
ap-7660	139	13	2	2	NUM
ap-7660	139	14	-	-	PUNCT
ap-7660	139	15	sphere	sphere	NOUN
ap-7660	139	16	in	in	ADP
ap-7660	139	17	spacetime	spacetime	NOUN
ap-7660	139	18	(	(	PUNCT
ap-7660	139	19	where	where	SCONJ
ap-7660	139	20	the	the	DET
ap-7660	139	21	radius	radius	NOUN
ap-7660	139	22	is	be	AUX
ap-7660	139	23	given	give	VERB
ap-7660	139	24	by	by	ADP
ap-7660	139	25	the	the	DET
ap-7660	139	26	profile	profile	NOUN
ap-7660	139	27	function	function	NOUN
ap-7660	139	28	hi	hi	INTJ
ap-7660	139	29	)	)	PUNCT
ap-7660	139	30	to	to	ADP
ap-7660	139	31	2	2	NUM
ap-7660	139	32	-	-	PUNCT
ap-7660	139	33	sphere	sphere	NOUN
ap-7660	139	34	in	in	ADP
ap-7660	139	35	field	field	NOUN
ap-7660	139	36	configuration	configuration	NOUN
ap-7660	139	37	space	space	NOUN
ap-7660	139	38	.	.	PUNCT
ap-7660	140	1	such	such	ADJ
ap-7660	140	2	mapping	mapping	NOUN
ap-7660	140	3	has	have	VERB
ap-7660	140	4	a	a	DET
ap-7660	140	5	topological	topological	ADJ
ap-7660	140	6	number	number	NOUN
ap-7660	140	7	called	call	VERB
ap-7660	140	8	the	the	DET
ap-7660	140	9	winding	wind	VERB
ap-7660	140	10	number	number	NOUN
ap-7660	140	11	n	n	CCONJ
ap-7660	140	12	∈	∈	PROPN
ap-7660	140	13	z	z	PROPN
ap-7660	140	14	,	,	PUNCT
ap-7660	140	15	which	which	PRON
ap-7660	140	16	can	can	AUX
ap-7660	140	17	be	be	AUX
ap-7660	140	18	explicitly	explicitly	ADV
ap-7660	140	19	realised	realise	VERB
ap-7660	140	20	by	by	ADP
ap-7660	140	21	redefining	redefine	VERB
ap-7660	140	22	the	the	DET
ap-7660	140	23	unit	unit	NOUN
ap-7660	140	24	vector	vector	NOUN
ap-7660	140	25	r̂a	r̂a	ADJ
ap-7660	140	26	as	as	ADP
ap-7660	140	27	r̂a	r̂a	NUM
ap-7660	140	28	n	n	NOUN
ap-7660	140	29	=	=	SYM
ap-7660	140	30			PROPN
ap-7660	140	31	sin(θ	sin(θ	PROPN
ap-7660	140	32	)	)	PUNCT
ap-7660	140	33	cos(nφ	cos(nφ	NOUN
ap-7660	140	34	)	)	PUNCT
ap-7660	140	35	sin(θ	sin(θ	PROPN
ap-7660	140	36	)	)	PUNCT
ap-7660	140	37	sin(nφ	sin(nφ	NOUN
ap-7660	140	38	)	)	PUNCT
ap-7660	140	39	cos(θ	cos(θ	PART
ap-7660	140	40	)	)	PUNCT
ap-7660	140	41			PROPN
ap-7660	140	42	.	.	PUNCT
ap-7660	141	1	(	(	PUNCT
ap-7660	141	2	16	16	NUM
ap-7660	141	3	)	)	PUNCT
ap-7660	141	4	therefore	therefore	ADV
ap-7660	141	5	different	different	ADJ
ap-7660	141	6	n	n	AUX
ap-7660	141	7	represent	represent	VERB
ap-7660	141	8	topologically	topologically	ADV
ap-7660	141	9	inequivalent	inequivalent	ADJ
ap-7660	141	10	solutions	solution	NOUN
ap-7660	141	11	.	.	PUNCT
ap-7660	142	1	since	since	SCONJ
ap-7660	142	2	we	we	PRON
ap-7660	142	3	require	require	VERB
ap-7660	142	4	the	the	DET
ap-7660	142	5	monopole	monopole	NOUN
ap-7660	142	6	and	and	CCONJ
ap-7660	142	7	vacuum	vacuum	NOUN
ap-7660	142	8	solutions	solution	NOUN
ap-7660	142	9	to	to	PART
ap-7660	142	10	smoothly	smoothly	ADV
ap-7660	142	11	deformed	deform	VERB
ap-7660	142	12	into	into	ADP
ap-7660	142	13	each	each	DET
ap-7660	142	14	other	other	ADJ
ap-7660	142	15	at	at	ADP
ap-7660	142	16	spacial	spacial	ADJ
ap-7660	142	17	infinity	infinity	NOUN
ap-7660	142	18	,	,	PUNCT
ap-7660	142	19	both	both	DET
ap-7660	142	20	solutions	solution	NOUN
ap-7660	142	21	need	need	VERB
ap-7660	142	22	to	to	PART
ap-7660	142	23	share	share	VERB
ap-7660	142	24	the	the	DET
ap-7660	142	25	same	same	ADJ
ap-7660	142	26	winding	wind	VERB
ap-7660	142	27	number	number	NOUN
ap-7660	142	28	.	.	PUNCT
ap-7660	143	1	it	it	PRON
ap-7660	143	2	is	be	AUX
ap-7660	143	3	important	important	ADJ
ap-7660	143	4	to	to	PART
ap-7660	143	5	note	note	VERB
ap-7660	143	6	that	that	SCONJ
ap-7660	143	7	winding	wind	VERB
ap-7660	143	8	numbers	number	NOUN
ap-7660	143	9	of	of	ADP
ap-7660	143	10	ϕ1	ϕ1	NOUN
ap-7660	143	11	and	and	CCONJ
ap-7660	143	12	ϕ2	ϕ2	ADV
ap-7660	143	13	need	need	VERB
ap-7660	143	14	to	to	PART
ap-7660	143	15	be	be	AUX
ap-7660	143	16	equal	equal	ADJ
ap-7660	143	17	to	to	PART
ap-7660	143	18	satisfy	satisfy	VERB
ap-7660	143	19	dϕ1	dϕ1	NOUN
ap-7660	143	20	=	=	PUNCT
ap-7660	143	21	dϕ2	dϕ2	PROPN
ap-7660	143	22	=	=	SYM
ap-7660	143	23	0	0	PROPN
ap-7660	143	24	,	,	PUNCT
ap-7660	143	25	and	and	CCONJ
ap-7660	143	26	therefore	therefore	ADV
ap-7660	143	27	we	we	PRON
ap-7660	143	28	will	will	AUX
ap-7660	143	29	denote	denote	VERB
ap-7660	143	30	the	the	DET
ap-7660	143	31	winding	wind	VERB
ap-7660	143	32	numbers	number	NOUN
ap-7660	143	33	of	of	ADP
ap-7660	143	34	ϕ1	ϕ1	NOUN
ap-7660	143	35	and	and	CCONJ
ap-7660	143	36	ϕ2	ϕ2	ADV
ap-7660	143	37	as	as	ADP
ap-7660	143	38	n	n	PRON
ap-7660	143	39	collectively	collectively	ADV
ap-7660	143	40	.	.	PUNCT
ap-7660	144	1	if	if	SCONJ
ap-7660	144	2	they	they	PRON
ap-7660	144	3	are	be	AUX
ap-7660	144	4	not	not	PART
ap-7660	144	5	equal	equal	ADJ
ap-7660	144	6	,	,	PUNCT
ap-7660	144	7	we	we	PRON
ap-7660	144	8	would	would	AUX
ap-7660	144	9	have	have	VERB
ap-7660	144	10	dϕ1	dϕ1	NOUN
ap-7660	144	11	=	=	SYM
ap-7660	144	12	0	0	PUNCT
ap-7660	144	13	but	but	CCONJ
ap-7660	144	14	dϕ2	dϕ2	PROPN
ap-7660	144	15	̸=	̸=	PROPN
ap-7660	144	16	0	0	NUM
ap-7660	144	17	.	.	PUNCT
ap-7660	145	1	next	next	ADJ
ap-7660	145	2	,	,	PUNCT
ap-7660	145	3	let	let	VERB
ap-7660	145	4	us	we	PRON
ap-7660	145	5	insert	insert	VERB
ap-7660	145	6	our	our	PRON
ap-7660	145	7	ansatz	ansatz	ADJ
ap-7660	145	8	equation	equation	NOUN
ap-7660	145	9	(	(	PUNCT
ap-7660	145	10	14	14	NUM
ap-7660	145	11	)	)	PUNCT
ap-7660	145	12	into	into	ADP
ap-7660	145	13	the	the	DET
ap-7660	145	14	equations	equation	NOUN
ap-7660	145	15	of	of	ADP
ap-7660	145	16	motion	motion	NOUN
ap-7660	145	17	equation	equation	NOUN
ap-7660	145	18	(	(	PUNCT
ap-7660	145	19	4	4	NUM
ap-7660	145	20	)	)	PUNCT
ap-7660	145	21	.	.	PUNCT
ap-7660	146	1	we	we	PRON
ap-7660	146	2	will	will	AUX
ap-7660	146	3	also	also	ADV
ap-7660	146	4	redefine	redefine	VERB
ap-7660	146	5	the	the	DET
ap-7660	146	6	ansatz	ansatz	NOUN
ap-7660	146	7	for	for	SCONJ
ap-7660	146	8	the	the	DET
ap-7660	146	9	gauge	gauge	NOUN
ap-7660	146	10	fields	field	NOUN
ap-7660	146	11	to	to	PART
ap-7660	146	12	be	be	AUX
ap-7660	146	13	aa	aa	NOUN
ap-7660	146	14	i	i	NOUN
ap-7660	146	15	=	=	PUNCT
ap-7660	147	1	ϵaibr̂b	ϵaibr̂b	X
ap-7660	147	2	(	(	PUNCT
ap-7660	147	3	1−u(r	1−u(r	NUM
ap-7660	147	4	)	)	PUNCT
ap-7660	147	5	er	er	INTJ
ap-7660	147	6	)	)	PUNCT
ap-7660	147	7	,	,	PUNCT
ap-7660	147	8	aa	aa	NOUN
ap-7660	147	9	0	0	NUM
ap-7660	147	10	=	=	SYM
ap-7660	147	11	0	0	PROPN
ap-7660	147	12	,	,	PUNCT
ap-7660	147	13	which	which	PRON
ap-7660	147	14	are	be	AUX
ap-7660	147	15	more	more	ADV
ap-7660	147	16	in	in	ADP
ap-7660	147	17	line	line	NOUN
ap-7660	147	18	with	with	ADP
ap-7660	147	19	the	the	DET
ap-7660	147	20	original	original	ADJ
ap-7660	147	21	ansatz	ansatz	NOUN
ap-7660	147	22	given	give	VERB
ap-7660	147	23	in	in	ADP
ap-7660	147	24	[	[	X
ap-7660	147	25	26	26	NUM
ap-7660	147	26	,	,	PUNCT
ap-7660	147	27	27	27	NUM
ap-7660	147	28	]	]	PUNCT
ap-7660	147	29	,	,	PUNCT
ap-7660	147	30	compared	compare	VERB
ap-7660	147	31	to	to	ADP
ap-7660	147	32	equation	equation	NOUN
ap-7660	147	33	(	(	PUNCT
ap-7660	147	34	14	14	NUM
ap-7660	147	35	)	)	PUNCT
ap-7660	147	36	.	.	PUNCT
ap-7660	148	1	inserting	insert	VERB
ap-7660	148	2	these	these	DET
ap-7660	148	3	expressions	expression	NOUN
ap-7660	148	4	into	into	ADP
ap-7660	148	5	the	the	DET
ap-7660	148	6	equations	equation	NOUN
ap-7660	148	7	of	of	ADP
ap-7660	148	8	motion	motion	NOUN
ap-7660	148	9	equation	equation	NOUN
ap-7660	148	10	(	(	PUNCT
ap-7660	148	11	4	4	NUM
ap-7660	148	12	)	)	PUNCT
ap-7660	148	13	,	,	PUNCT
ap-7660	148	14	we	we	PRON
ap-7660	148	15	find	find	VERB
ap-7660	148	16	u	u	PRON
ap-7660	148	17	′′	′′	PROPN
ap-7660	148	18	(	(	PUNCT
ap-7660	148	19	r	r	NOUN
ap-7660	148	20	)	)	PUNCT
ap-7660	148	21	+	+	NOUN
ap-7660	148	22	u(r	u(r	NOUN
ap-7660	148	23	)	)	PUNCT
ap-7660	148	24	[	[	PUNCT
ap-7660	148	25	1	1	NUM
ap-7660	148	26	−	−	NUM
ap-7660	148	27	u2(r	u2(r	NUM
ap-7660	148	28	)	)	PUNCT
ap-7660	148	29	]	]	PUNCT
ap-7660	148	30	r2	r2	NOUN
ap-7660	148	31	(	(	PUNCT
ap-7660	148	32	17	17	NUM
ap-7660	148	33	)	)	PUNCT
ap-7660	149	1	+	+	NOUN
ap-7660	149	2	e2u(r	e2u(r	NOUN
ap-7660	149	3	)	)	PUNCT
ap-7660	149	4	2	2	NUM
ap-7660	149	5	{	{	PUNCT
ap-7660	149	6	h2	h2	NOUN
ap-7660	149	7	2(r	2(r	NUM
ap-7660	149	8	)	)	PUNCT
ap-7660	149	9	−	−	PROPN
ap-7660	149	10	h2	h2	NOUN
ap-7660	149	11	1(r	1(r	NUM
ap-7660	149	12	)	)	PUNCT
ap-7660	149	13	}	}	PUNCT
ap-7660	150	1	=	=	SYM
ap-7660	150	2	0	0	NUM
ap-7660	150	3	,	,	PUNCT
ap-7660	150	4	h	h	NOUN
ap-7660	150	5	′′	′′	NOUN
ap-7660	150	6	1	1	NUM
ap-7660	150	7	(	(	PUNCT
ap-7660	150	8	r	r	NOUN
ap-7660	150	9	)	)	PUNCT
ap-7660	150	10	+	+	NUM
ap-7660	150	11	2h	2h	NUM
ap-7660	150	12	′	′	NUM
ap-7660	150	13	1(r	1(r	NOUN
ap-7660	150	14	)	)	PUNCT
ap-7660	150	15	r	r	NOUN
ap-7660	150	16	−	−	NOUN
ap-7660	150	17	2h1(r)u2(r	2h1(r)u2(r	NOUN
ap-7660	150	18	)	)	PUNCT
ap-7660	150	19	r2	r2	NOUN
ap-7660	150	20	(	(	PUNCT
ap-7660	150	21	18	18	NUM
ap-7660	150	22	)	)	PUNCT
ap-7660	151	1	+	+	ADP
ap-7660	151	2	g	g	NOUN
ap-7660	151	3	{	{	PUNCT
ap-7660	151	4	−c1	−c1	PROPN
ap-7660	151	5	m2	m2	PROPN
ap-7660	151	6	1	1	NUM
ap-7660	151	7	g	g	NOUN
ap-7660	151	8	h1(r	h1(r	NOUN
ap-7660	151	9	)	)	PUNCT
ap-7660	151	10	+	+	CCONJ
ap-7660	152	1	c3	c3	PROPN
ap-7660	152	2	µ2	µ2	PROPN
ap-7660	152	3	g	g	PROPN
ap-7660	152	4	h2(r	h2(r	PROPN
ap-7660	152	5	)	)	PUNCT
ap-7660	152	6	+	+	CCONJ
ap-7660	152	7	1	1	NUM
ap-7660	152	8	4	4	NUM
ap-7660	152	9	h3	h3	NOUN
ap-7660	152	10	1(r	1(r	NUM
ap-7660	152	11	)	)	PUNCT
ap-7660	152	12	}	}	PUNCT
ap-7660	153	1	=	=	SYM
ap-7660	153	2	0	0	NUM
ap-7660	153	3	,	,	PUNCT
ap-7660	153	4	h	h	NOUN
ap-7660	153	5	′′	′′	NOUN
ap-7660	153	6	2	2	NUM
ap-7660	153	7	(	(	PUNCT
ap-7660	153	8	r	r	NOUN
ap-7660	153	9	)	)	PUNCT
ap-7660	153	10	+	+	NUM
ap-7660	153	11	2h	2h	NUM
ap-7660	153	12	′	′	NUM
ap-7660	153	13	2(r	2(r	NUM
ap-7660	153	14	)	)	PUNCT
ap-7660	153	15	r	r	NOUN
ap-7660	153	16	−	−	NOUN
ap-7660	153	17	2h2(r)u2(r	2h2(r)u2(r	NOUN
ap-7660	153	18	)	)	PUNCT
ap-7660	153	19	r2	r2	NOUN
ap-7660	153	20	(	(	PUNCT
ap-7660	153	21	19	19	NUM
ap-7660	153	22	)	)	PUNCT
ap-7660	154	1	+	+	NOUN
ap-7660	154	2	c2m2	c2m2	X
ap-7660	154	3	2	2	NUM
ap-7660	154	4	{	{	PUNCT
ap-7660	154	5	h2(r	h2(r	PROPN
ap-7660	154	6	)	)	PUNCT
ap-7660	154	7	+	+	CCONJ
ap-7660	154	8	c3	c3	PROPN
ap-7660	154	9	µ2	µ2	PROPN
ap-7660	154	10	m2	m2	PROPN
ap-7660	154	11	2	2	NUM
ap-7660	154	12	h1(r	h1(r	NOUN
ap-7660	154	13	)	)	PUNCT
ap-7660	154	14	}	}	PUNCT
ap-7660	154	15	=	=	SYM
ap-7660	154	16	0	0	X
ap-7660	154	17	.	.	PUNCT
ap-7660	154	18	notice	notice	VERB
ap-7660	154	19	that	that	SCONJ
ap-7660	154	20	these	these	DET
ap-7660	154	21	differential	differential	ADJ
ap-7660	154	22	equations	equation	NOUN
ap-7660	154	23	are	be	AUX
ap-7660	154	24	similar	similar	ADJ
ap-7660	154	25	to	to	ADP
ap-7660	154	26	the	the	DET
ap-7660	154	27	ones	one	NOUN
ap-7660	154	28	discussed	discuss	VERB
ap-7660	154	29	in	in	ADP
ap-7660	154	30	[	[	X
ap-7660	154	31	26	26	NUM
ap-7660	154	32	,	,	PUNCT
ap-7660	154	33	27	27	NUM
ap-7660	154	34	]	]	PUNCT
ap-7660	154	35	,	,	PUNCT
ap-7660	154	36	but	but	CCONJ
ap-7660	154	37	with	with	ADP
ap-7660	154	38	the	the	DET
ap-7660	154	39	extra	extra	ADJ
ap-7660	154	40	field	field	NOUN
ap-7660	154	41	h2	h2	NOUN
ap-7660	154	42	and	and	CCONJ
ap-7660	154	43	extra	extra	ADJ
ap-7660	154	44	differential	differential	ADJ
ap-7660	154	45	equation	equation	NOUN
ap-7660	154	46	(	(	PUNCT
ap-7660	154	47	19	19	NUM
ap-7660	154	48	)	)	PUNCT
ap-7660	154	49	.	.	PUNCT
ap-7660	155	1	in	in	ADP
ap-7660	155	2	the	the	DET
ap-7660	155	3	hermitian	hermitian	ADJ
ap-7660	155	4	model	model	NOUN
ap-7660	155	5	,	,	PUNCT
ap-7660	155	6	the	the	DET
ap-7660	155	7	exact	exact	ADJ
ap-7660	155	8	solutions	solution	NOUN
ap-7660	155	9	to	to	ADP
ap-7660	155	10	the	the	DET
ap-7660	155	11	differential	differential	ADJ
ap-7660	155	12	equations	equation	NOUN
ap-7660	155	13	were	be	AUX
ap-7660	155	14	found	find	VERB
ap-7660	155	15	by	by	ADP
ap-7660	155	16	taking	take	VERB
ap-7660	155	17	the	the	DET
ap-7660	155	18	parameter	parameter	NOUN
ap-7660	155	19	limit	limit	NOUN
ap-7660	155	20	called	call	VERB
ap-7660	155	21	the	the	DET
ap-7660	155	22	bps	bps	NOUN
ap-7660	155	23	limit	limit	NOUN
ap-7660	155	24	[	[	X
ap-7660	155	25	26	26	NUM
ap-7660	155	26	,	,	PUNCT
ap-7660	155	27	27	27	NUM
ap-7660	155	28	]	]	PUNCT
ap-7660	155	29	,	,	PUNCT
ap-7660	155	30	where	where	SCONJ
ap-7660	155	31	parameters	parameter	NOUN
ap-7660	155	32	in	in	ADP
ap-7660	155	33	the	the	DET
ap-7660	155	34	hermitian	hermitian	ADJ
ap-7660	155	35	model	model	NOUN
ap-7660	155	36	are	be	AUX
ap-7660	155	37	taken	take	VERB
ap-7660	155	38	to	to	ADP
ap-7660	155	39	zero	zero	NUM
ap-7660	155	40	while	while	SCONJ
ap-7660	155	41	keeping	keep	VERB
ap-7660	155	42	the	the	DET
ap-7660	155	43	vacuum	vacuum	NOUN
ap-7660	155	44	solution	solution	NOUN
ap-7660	155	45	finite	finite	NOUN
ap-7660	155	46	.	.	PUNCT
ap-7660	156	1	here	here	ADV
ap-7660	156	2	we	we	PRON
ap-7660	156	3	will	will	AUX
ap-7660	156	4	follow	follow	VERB
ap-7660	156	5	the	the	DET
ap-7660	156	6	same	same	ADJ
ap-7660	156	7	procedure	procedure	NOUN
ap-7660	156	8	and	and	CCONJ
ap-7660	156	9	take	take	VERB
ap-7660	156	10	the	the	DET
ap-7660	156	11	parameter	parameter	NOUN
ap-7660	156	12	limit	limit	NOUN
ap-7660	156	13	where	where	SCONJ
ap-7660	156	14	quantities	quantity	NOUN
ap-7660	156	15	in	in	ADP
ap-7660	156	16	the	the	DET
ap-7660	156	17	curly	curly	ADJ
ap-7660	156	18	brackets	bracket	NOUN
ap-7660	156	19	of	of	ADP
ap-7660	156	20	equations	equation	NOUN
ap-7660	156	21	(	(	PUNCT
ap-7660	156	22	18	18	NUM
ap-7660	156	23	)	)	PUNCT
ap-7660	156	24	and	and	CCONJ
ap-7660	156	25	(	(	PUNCT
ap-7660	156	26	19	19	NUM
ap-7660	156	27	)	)	PUNCT
ap-7660	156	28	vanish	vanish	VERB
ap-7660	156	29	but	but	CCONJ
ap-7660	156	30	keep	keep	VERB
ap-7660	156	31	the	the	DET
ap-7660	156	32	vacuum	vacuum	NOUN
ap-7660	156	33	solutions	solution	NOUN
ap-7660	156	34	equation	equation	NOUN
ap-7660	156	35	(	(	PUNCT
ap-7660	156	36	11	11	NUM
ap-7660	156	37	)	)	PUNCT
ap-7660	156	38	finite	finite	NOUN
ap-7660	156	39	.	.	PUNCT
ap-7660	157	1	we	we	PRON
ap-7660	157	2	will	will	AUX
ap-7660	157	3	see	see	VERB
ap-7660	157	4	in	in	ADP
ap-7660	157	5	section	section	NOUN
ap-7660	157	6	2.4	2.4	NUM
ap-7660	157	7	that	that	PRON
ap-7660	157	8	we	we	PRON
ap-7660	157	9	also	also	ADV
ap-7660	157	10	find	find	VERB
ap-7660	157	11	the	the	DET
ap-7660	157	12	approximate	approximate	ADJ
ap-7660	157	13	solutions	solution	NOUN
ap-7660	157	14	in	in	ADP
ap-7660	157	15	this	this	DET
ap-7660	157	16	limit	limit	NOUN
ap-7660	157	17	.	.	PUNCT
ap-7660	158	1	2.3	2.3	NUM
ap-7660	158	2	.	.	PUNCT
ap-7660	159	1	the	the	DET
ap-7660	159	2	energy	energy	NOUN
ap-7660	159	3	bound	bind	VERB
ap-7660	159	4	surprisingly	surprisingly	ADV
ap-7660	159	5	,	,	PUNCT
ap-7660	159	6	by	by	ADP
ap-7660	159	7	utilising	utilise	VERB
ap-7660	159	8	derrick	derrick	PROPN
ap-7660	159	9	’s	’s	PART
ap-7660	159	10	scaling	scale	VERB
ap-7660	159	11	argument	argument	NOUN
ap-7660	159	12	,	,	PUNCT
ap-7660	159	13	one	one	PRON
ap-7660	159	14	can	can	AUX
ap-7660	159	15	find	find	VERB
ap-7660	159	16	the	the	DET
ap-7660	159	17	lower	low	ADJ
ap-7660	159	18	bound	bind	VERB
ap-7660	159	19	of	of	ADP
ap-7660	159	20	the	the	DET
ap-7660	159	21	monopole	monopole	ADJ
ap-7660	159	22	energy	energy	NOUN
ap-7660	159	23	without	without	ADP
ap-7660	159	24	the	the	DET
ap-7660	159	25	explicit	explicit	ADJ
ap-7660	159	26	form	form	NOUN
ap-7660	159	27	of	of	ADP
ap-7660	159	28	the	the	DET
ap-7660	159	29	solution	solution	NOUN
ap-7660	159	30	.	.	PUNCT
ap-7660	160	1	the	the	DET
ap-7660	160	2	energy	energy	NOUN
ap-7660	160	3	of	of	ADP
ap-7660	160	4	the	the	DET
ap-7660	160	5	monopole	monopole	NOUN
ap-7660	160	6	can	can	AUX
ap-7660	160	7	be	be	AUX
ap-7660	160	8	found	find	VERB
ap-7660	160	9	by	by	ADP
ap-7660	160	10	inserting	insert	VERB
ap-7660	160	11	the	the	DET
ap-7660	160	12	monopole	monopole	ADJ
ap-7660	160	13	solution	solution	NOUN
ap-7660	160	14	into	into	ADP
ap-7660	160	15	the	the	DET
ap-7660	160	16	corresponding	corresponding	ADJ
ap-7660	160	17	hamiltonian	hamiltonian	NOUN
ap-7660	160	18	of	of	ADP
ap-7660	160	19	equation	equation	NOUN
ap-7660	160	20	(	(	PUNCT
ap-7660	160	21	6	6	NUM
ap-7660	160	22	)	)	PUNCT
ap-7660	160	23	.	.	PUNCT
ap-7660	161	1	h	h	NOUN
ap-7660	162	1	=	=	SYM
ap-7660	162	2	∫	∫	PROPN
ap-7660	162	3	d3x	d3x	ADV
ap-7660	162	4	tr	tr	PROPN
ap-7660	162	5	(	(	PUNCT
ap-7660	162	6	e2	e2	PROPN
ap-7660	162	7	)	)	PUNCT
ap-7660	162	8	+	+	CCONJ
ap-7660	162	9	tr	tr	VERB
ap-7660	162	10	(	(	PUNCT
ap-7660	162	11	b2	b2	NOUN
ap-7660	162	12	)	)	PUNCT
ap-7660	162	13	(	(	PUNCT
ap-7660	162	14	20	20	NUM
ap-7660	162	15	)	)	PUNCT
ap-7660	163	1	+	+	NOUN
ap-7660	163	2	tr	tr	VERB
ap-7660	163	3	{	{	PUNCT
ap-7660	163	4	(	(	PUNCT
ap-7660	163	5	d0ϕ1)2	d0ϕ1)2	PROPN
ap-7660	163	6	}	}	PUNCT
ap-7660	163	7	+	+	CCONJ
ap-7660	163	8	tr	tr	VERB
ap-7660	163	9	{	{	PUNCT
ap-7660	163	10	(	(	PUNCT
ap-7660	163	11	diϕ1)2	diϕ1)2	NOUN
ap-7660	163	12	}	}	PUNCT
ap-7660	163	13	−tr	−tr	NOUN
ap-7660	163	14	{	{	PUNCT
ap-7660	163	15	(	(	PUNCT
ap-7660	163	16	d0ϕ2)2	d0ϕ2)2	NOUN
ap-7660	163	17	}	}	PUNCT
ap-7660	163	18	−	−	NOUN
ap-7660	163	19	tr	tr	VERB
ap-7660	163	20	{	{	PUNCT
ap-7660	163	21	(	(	PUNCT
ap-7660	163	22	diϕ2)2	diϕ2)2	PROPN
ap-7660	163	23	}	}	PUNCT
ap-7660	163	24	+	+	CCONJ
ap-7660	163	25	v	v	NOUN
ap-7660	163	26	,	,	PUNCT
ap-7660	163	27	where	where	SCONJ
ap-7660	163	28	e	e	NOUN
ap-7660	163	29	,	,	PUNCT
ap-7660	163	30	b	b	NOUN
ap-7660	163	31	are	be	AUX
ap-7660	163	32	ei	ei	ADP
ap-7660	163	33	a	a	X
ap-7660	163	34	=	=	X
ap-7660	163	35	fa	fa	X
ap-7660	163	36	0i	0i	NOUN
ap-7660	163	37	,	,	PUNCT
ap-7660	163	38	bi	bi	NOUN
ap-7660	163	39	a	a	PRON
ap-7660	163	40	=	=	SYM
ap-7660	163	41	−	−	PROPN
ap-7660	163	42	1	1	NUM
ap-7660	163	43	2	2	NUM
ap-7660	163	44	ϵijkf	ϵijkf	NOUN
ap-7660	163	45	jk	jk	PROPN
ap-7660	163	46	a	a	PRON
ap-7660	163	47	,	,	PUNCT
ap-7660	163	48	i	i	PRON
ap-7660	163	49	,	,	PUNCT
ap-7660	163	50	j	j	PROPN
ap-7660	163	51	,	,	PUNCT
ap-7660	163	52	k	k	PROPN
ap-7660	163	53	∈	∈	PROPN
ap-7660	163	54	{	{	PUNCT
ap-7660	163	55	1	1	NUM
ap-7660	163	56	,	,	PUNCT
ap-7660	163	57	2	2	NUM
ap-7660	163	58	,	,	PUNCT
ap-7660	163	59	3	3	NUM
ap-7660	163	60	}	}	PUNCT
ap-7660	163	61	.	.	PUNCT
ap-7660	164	1	the	the	DET
ap-7660	164	2	gauge	gauge	NOUN
ap-7660	164	3	is	be	AUX
ap-7660	164	4	fixed	fix	VERB
ap-7660	164	5	to	to	PART
ap-7660	164	6	be	be	AUX
ap-7660	164	7	the	the	DET
ap-7660	164	8	radiation	radiation	NOUN
ap-7660	164	9	gauge	gauge	NOUN
ap-7660	164	10	(	(	PUNCT
ap-7660	164	11	i.e	i.e	INTJ
ap-7660	164	12	aa	aa	NOUN
ap-7660	164	13	0	0	NUM
ap-7660	164	14	=	=	SYM
ap-7660	164	15	0	0	NUM
ap-7660	164	16	,	,	PUNCT
ap-7660	164	17	∂iaa	∂iaa	X
ap-7660	164	18	i	i	NOUN
ap-7660	164	19	=	=	NOUN
ap-7660	164	20	0	0	NUM
ap-7660	164	21	)	)	PUNCT
ap-7660	164	22	.	.	PUNCT
ap-7660	165	1	notice	notice	VERB
ap-7660	165	2	that	that	SCONJ
ap-7660	165	3	our	our	PRON
ap-7660	165	4	monopole	monopole	ADJ
ap-7660	165	5	ansatz	ansatz	ADJ
ap-7660	165	6	equation	equation	NOUN
ap-7660	165	7	(	(	PUNCT
ap-7660	165	8	10	10	NUM
ap-7660	165	9	)	)	PUNCT
ap-7660	165	10	is	be	AUX
ap-7660	165	11	static	static	ADJ
ap-7660	165	12	with	with	ADP
ap-7660	165	13	no	no	DET
ap-7660	165	14	electric	electric	ADJ
ap-7660	165	15	charge	charge	NOUN
ap-7660	166	1	ea	ea	ADP
ap-7660	166	2	i	i	NOUN
ap-7660	166	3	=	=	NOUN
ap-7660	166	4	0	0	NUM
ap-7660	166	5	and	and	CCONJ
ap-7660	166	6	therefore	therefore	ADV
ap-7660	166	7	,	,	PUNCT
ap-7660	166	8	the	the	DET
ap-7660	166	9	above	above	ADJ
ap-7660	166	10	hamiltonian	hamiltonian	NOUN
ap-7660	166	11	reduces	reduce	VERB
ap-7660	166	12	to	to	ADP
ap-7660	166	13	e	e	NOUN
ap-7660	166	14	=	=	SYM
ap-7660	166	15	∫	∫	PROPN
ap-7660	166	16	d3x	d3x	PROPN
ap-7660	166	17	tr	tr	PUNCT
ap-7660	166	18	(	(	PUNCT
ap-7660	166	19	b2	b2	NOUN
ap-7660	166	20	)	)	PUNCT
ap-7660	167	1	+	+	CCONJ
ap-7660	167	2	tr	tr	VERB
ap-7660	167	3	{	{	PUNCT
ap-7660	167	4	(	(	PUNCT
ap-7660	167	5	diϕ1)2	diϕ1)2	NOUN
ap-7660	167	6	}	}	PUNCT
ap-7660	167	7	(	(	PUNCT
ap-7660	167	8	21	21	NUM
ap-7660	167	9	)	)	PUNCT
ap-7660	167	10	−tr	−tr	NOUN
ap-7660	167	11	{	{	PUNCT
ap-7660	167	12	(	(	PUNCT
ap-7660	167	13	diϕ2)2	diϕ2)2	PROPN
ap-7660	167	14	}	}	PUNCT
ap-7660	167	15	+	+	NOUN
ap-7660	167	16	v	v	NOUN
ap-7660	167	17	=	=	SYM
ap-7660	167	18	2	2	NUM
ap-7660	167	19	∫	∫	NOUN
ap-7660	167	20	d3x	d3x	PROPN
ap-7660	167	21	bi	bi	PROPN
ap-7660	167	22	abi	abi	PROPN
ap-7660	167	23	a	a	PROPN
ap-7660	167	24	+	+	X
ap-7660	167	25	(	(	PUNCT
ap-7660	167	26	diϕ1)a(diϕ1)a	diϕ1)a(diϕ1)a	NOUN
ap-7660	167	27	−(diϕ2)a(diϕ2)a	−(diϕ2)a(diϕ2)a	NOUN
ap-7660	167	28	+	+	CCONJ
ap-7660	167	29	1	1	NUM
ap-7660	167	30	2v	2v	NOUN
ap-7660	167	31	.	.	PUNCT
ap-7660	168	1	here	here	ADV
ap-7660	168	2	,	,	PUNCT
ap-7660	168	3	we	we	PRON
ap-7660	168	4	simplified	simplify	VERB
ap-7660	168	5	our	our	PRON
ap-7660	168	6	expression	expression	NOUN
ap-7660	168	7	by	by	ADP
ap-7660	168	8	dropping	drop	VERB
ap-7660	168	9	the	the	DET
ap-7660	168	10	superscripts	superscript	NOUN
ap-7660	168	11	acl	acl	PROPN
ap-7660	168	12	i	i	PRON
ap-7660	168	13	→	→	VERB
ap-7660	168	14	ai	ai	INTJ
ap-7660	168	15	,	,	PUNCT
ap-7660	168	16	ϕcl	ϕcl	ADV
ap-7660	168	17	α	α	PROPN
ap-7660	168	18	→	→	SYM
ap-7660	168	19	ϕα	ϕα	ADV
ap-7660	168	20	.	.	PUNCT
ap-7660	169	1	we	we	PRON
ap-7660	169	2	also	also	ADV
ap-7660	169	3	keep	keep	VERB
ap-7660	169	4	in	in	ADP
ap-7660	169	5	mind	mind	NOUN
ap-7660	169	6	that	that	SCONJ
ap-7660	169	7	these	these	DET
ap-7660	169	8	fields	field	NOUN
ap-7660	169	9	depend	depend	VERB
ap-7660	169	10	on	on	ADP
ap-7660	169	11	the	the	DET
ap-7660	169	12	winding	wind	VERB
ap-7660	169	13	numbers	number	NOUN
ap-7660	169	14	n	n	PRON
ap-7660	169	15	∈	∈	PROPN
ap-7660	169	16	z.	z.	PROPN
ap-7660	169	17	in	in	ADP
ap-7660	169	18	the	the	DET
ap-7660	169	19	hermitian	hermitian	ADJ
ap-7660	169	20	model	model	NOUN
ap-7660	169	21	(	(	PUNCT
ap-7660	169	22	i.e.	i.e.	X
ap-7660	169	23	when	when	SCONJ
ap-7660	169	24	ϕ2	ϕ2	ADV
ap-7660	169	25	=	=	SYM
ap-7660	169	26	0	0	NUM
ap-7660	169	27	)	)	PUNCT
ap-7660	169	28	,	,	PUNCT
ap-7660	169	29	one	one	PRON
ap-7660	169	30	can	can	AUX
ap-7660	169	31	rewrite	rewrite	VERB
ap-7660	169	32	the	the	DET
ap-7660	169	33	kinetic	kinetic	ADJ
ap-7660	169	34	term	term	NOUN
ap-7660	169	35	as	as	ADP
ap-7660	169	36	b2	b2	NOUN
ap-7660	169	37	+	+	CCONJ
ap-7660	169	38	dϕ2	dϕ2	PROPN
ap-7660	169	39	=	=	SYM
ap-7660	169	40	(	(	PUNCT
ap-7660	169	41	b	b	X
ap-7660	169	42	−	−	NOUN
ap-7660	169	43	dϕ)2	dϕ)2	NOUN
ap-7660	169	44	+	+	CCONJ
ap-7660	169	45	2bdϕ	2bdϕ	NUM
ap-7660	169	46	and	and	CCONJ
ap-7660	169	47	find	find	VERB
ap-7660	169	48	the	the	DET
ap-7660	169	49	lower	lower	ADV
ap-7660	169	50	bound	bind	VERB
ap-7660	169	51	to	to	ADP
ap-7660	169	52	be∫	be∫	PROPN
ap-7660	169	53	2bdϕ.	2bdϕ.	PROPN
ap-7660	169	54	here	here	ADV
ap-7660	169	55	we	we	PRON
ap-7660	169	56	will	will	AUX
ap-7660	169	57	follow	follow	VERB
ap-7660	169	58	a	a	DET
ap-7660	169	59	similar	similar	ADJ
ap-7660	169	60	procedure	procedure	NOUN
ap-7660	169	61	but	but	CCONJ
ap-7660	169	62	introduce	introduce	VERB
ap-7660	169	63	some	some	DET
ap-7660	169	64	arbitrary	arbitrary	ADJ
ap-7660	169	65	constant	constant	ADJ
ap-7660	169	66	α	α	NOUN
ap-7660	169	67	,	,	PUNCT
ap-7660	169	68	β	β	X
ap-7660	169	69	∈	∈	NOUN
ap-7660	169	70	r	r	NOUN
ap-7660	169	71	such	such	ADJ
ap-7660	169	72	that	that	DET
ap-7660	169	73	b2	b2	NOUN
ap-7660	169	74	=	=	SYM
ap-7660	169	75	α2b	α2b	NOUN
ap-7660	169	76	−	−	NOUN
ap-7660	169	77	β2b	β2b	PUNCT
ap-7660	169	78	where	where	SCONJ
ap-7660	169	79	α2	α2	ADJ
ap-7660	169	80	−	−	PROPN
ap-7660	169	81	β2	β2	NOUN
ap-7660	169	82	=	=	NOUN
ap-7660	169	83	1	1	X
ap-7660	169	84	.	.	PUNCT
ap-7660	170	1	this	this	PRON
ap-7660	170	2	will	will	AUX
ap-7660	170	3	allow	allow	VERB
ap-7660	170	4	200	200	NUM
ap-7660	170	5	vol	vol	NOUN
ap-7660	170	6	.	.	PUNCT
ap-7660	171	1	62	62	NUM
ap-7660	171	2	no	no	INTJ
ap-7660	171	3	.	.	PUNCT
ap-7660	172	1	1/2022	1/2022	NUM
ap-7660	172	2	complex	complex	ADJ
ap-7660	172	3	topological	topological	ADJ
ap-7660	172	4	soliton	soliton	NOUN
ap-7660	172	5	with	with	ADP
ap-7660	172	6	real	real	ADJ
ap-7660	172	7	energy	energy	NOUN
ap-7660	172	8	in	in	ADP
ap-7660	172	9	particle	particle	NOUN
ap-7660	172	10	physics	physics	PROPN
ap-7660	172	11	us	we	PRON
ap-7660	172	12	to	to	PART
ap-7660	172	13	rewrite	rewrite	VERB
ap-7660	172	14	the	the	DET
ap-7660	172	15	above	above	ADJ
ap-7660	172	16	energy	energy	NOUN
ap-7660	172	17	as	as	ADP
ap-7660	172	18	e	e	NOUN
ap-7660	172	19	=	=	SYM
ap-7660	172	20	2	2	NUM
ap-7660	172	21	∫	∫	NOUN
ap-7660	172	22	d3x	d3x	PROPN
ap-7660	172	23	α2	α2	PROPN
ap-7660	172	24	{	{	PUNCT
ap-7660	172	25	bi	bi	NOUN
ap-7660	172	26	a	a	PROPN
ap-7660	172	27	+	+	NUM
ap-7660	172	28	1	1	NUM
ap-7660	172	29	α	α	NOUN
ap-7660	172	30	(	(	PUNCT
ap-7660	172	31	diϕ1)a	diϕ1)a	PROPN
ap-7660	172	32	}	}	SYM
ap-7660	172	33	2	2	NUM
ap-7660	172	34	(	(	PUNCT
ap-7660	172	35	22	22	NUM
ap-7660	172	36	)	)	PUNCT
ap-7660	172	37	−β2	−β2	PROPN
ap-7660	172	38	{	{	PUNCT
ap-7660	172	39	bi	bi	NOUN
ap-7660	172	40	a	a	PRON
ap-7660	172	41	+	+	NUM
ap-7660	172	42	1	1	NUM
ap-7660	172	43	β	β	X
ap-7660	172	44	(	(	PUNCT
ap-7660	172	45	diϕ2)a	diϕ2)a	NOUN
ap-7660	172	46	}	}	PUNCT
ap-7660	172	47	2	2	NUM
ap-7660	172	48	+2	+2	PROPN
ap-7660	172	49	{	{	PUNCT
ap-7660	172	50	−αbi	−αbi	ADJ
ap-7660	172	51	a(diϕ1)a	a(diϕ1)a	VERB
ap-7660	173	1	+	+	NUM
ap-7660	173	2	βbi	βbi	NUM
ap-7660	173	3	a(diϕ2)a	a(diϕ2)a	ADJ
ap-7660	173	4	}	}	PUNCT
ap-7660	173	5	+	+	CCONJ
ap-7660	173	6	1	1	NUM
ap-7660	173	7	2v	2v	NOUN
ap-7660	173	8	.	.	PUNCT
ap-7660	174	1	to	to	PART
ap-7660	174	2	proceed	proceed	VERB
ap-7660	174	3	from	from	ADP
ap-7660	174	4	here	here	ADV
ap-7660	174	5	,	,	PUNCT
ap-7660	174	6	we	we	PRON
ap-7660	174	7	need	need	VERB
ap-7660	174	8	to	to	PART
ap-7660	174	9	assume	assume	VERB
ap-7660	174	10	extra	extra	ADJ
ap-7660	174	11	constraints	constraint	NOUN
ap-7660	174	12	on	on	ADP
ap-7660	174	13	α	α	NOUN
ap-7660	174	14	and	and	CCONJ
ap-7660	174	15	β	β	PRON
ap-7660	174	16	such	such	ADJ
ap-7660	174	17	that	that	SCONJ
ap-7660	174	18	the	the	DET
ap-7660	174	19	following	follow	VERB
ap-7660	174	20	inequalities	inequality	NOUN
ap-7660	174	21	are	be	AUX
ap-7660	174	22	true∫	true∫	VERB
ap-7660	174	23	d3x	d3x	ADV
ap-7660	174	24	α2	α2	PROPN
ap-7660	174	25	{	{	PUNCT
ap-7660	174	26	bi	bi	NOUN
ap-7660	174	27	a	a	PROPN
ap-7660	174	28	+	+	NUM
ap-7660	174	29	1	1	NUM
ap-7660	174	30	α	α	NOUN
ap-7660	174	31	(	(	PUNCT
ap-7660	174	32	diϕ1)a	diϕ1)a	PROPN
ap-7660	174	33	}	}	SYM
ap-7660	174	34	2	2	NUM
ap-7660	174	35	(	(	PUNCT
ap-7660	174	36	23	23	NUM
ap-7660	174	37	)	)	PUNCT
ap-7660	174	38	−β2	−β2	PROPN
ap-7660	174	39	{	{	PUNCT
ap-7660	174	40	bi	bi	NOUN
ap-7660	174	41	a	a	PRON
ap-7660	175	1	+	+	NUM
ap-7660	175	2	1	1	NUM
ap-7660	175	3	β	β	X
ap-7660	175	4	(	(	PUNCT
ap-7660	175	5	diϕ2)a	diϕ2)a	NOUN
ap-7660	175	6	}	}	PUNCT
ap-7660	175	7	2	2	NUM
ap-7660	175	8	≥	≥	NOUN
ap-7660	175	9	0,∫	0,∫	NUM
ap-7660	175	10	d3xv	d3xv	PRON
ap-7660	175	11	≥	≥	NOUN
ap-7660	175	12	0	0	NUM
ap-7660	175	13	.	.	PUNCT
ap-7660	175	14	with	with	ADP
ap-7660	175	15	these	these	DET
ap-7660	175	16	constraints	constraint	NOUN
ap-7660	175	17	we	we	PRON
ap-7660	175	18	can	can	AUX
ap-7660	175	19	now	now	ADV
ap-7660	175	20	write	write	VERB
ap-7660	175	21	down	down	ADP
ap-7660	175	22	the	the	DET
ap-7660	175	23	lower	low	ADJ
ap-7660	175	24	bound	bind	VERB
ap-7660	175	25	of	of	ADP
ap-7660	175	26	the	the	DET
ap-7660	175	27	monopole	monopole	NOUN
ap-7660	175	28	as	as	ADP
ap-7660	175	29	e	e	PROPN
ap-7660	175	30	≥	≥	NUM
ap-7660	175	31	2	2	NUM
ap-7660	175	32	∫	∫	NOUN
ap-7660	175	33	d3x	d3x	PROPN
ap-7660	175	34	{	{	PUNCT
ap-7660	175	35	−αbi	−αbi	ADJ
ap-7660	175	36	a(diϕ1)a	a(diϕ1)a	VERB
ap-7660	176	1	+	+	NUM
ap-7660	176	2	βbi	βbi	NUM
ap-7660	176	3	a(diϕ2)a	a(diϕ2)a	ADJ
ap-7660	176	4	}	}	PUNCT
ap-7660	176	5	(	(	PUNCT
ap-7660	176	6	24	24	NUM
ap-7660	176	7	)	)	PUNCT
ap-7660	176	8	=	=	SYM
ap-7660	176	9	2	2	NUM
ap-7660	176	10	∫	∫	NOUN
ap-7660	176	11	d3x	d3x	NOUN
ap-7660	176	12	−	−	PROPN
ap-7660	176	13	α	α	PROPN
ap-7660	176	14	{	{	PUNCT
ap-7660	176	15	bi	bi	NOUN
ap-7660	176	16	a∂iϕ	a∂iϕ	NOUN
ap-7660	176	17	a	a	DET
ap-7660	176	18	1	1	NUM
ap-7660	176	19	+	+	CCONJ
ap-7660	176	20	ebi	ebi	NOUN
ap-7660	176	21	aϵabcai	aϵabcai	NOUN
ap-7660	176	22	bϕc	bϕc	NOUN
ap-7660	176	23	1	1	NUM
ap-7660	176	24	}	}	PUNCT
ap-7660	176	25	+	+	PROPN
ap-7660	176	26	β	β	X
ap-7660	176	27	{	{	PUNCT
ap-7660	176	28	bi	bi	NOUN
ap-7660	176	29	a∂iϕ	a∂iϕ	NOUN
ap-7660	176	30	a	a	DET
ap-7660	176	31	2	2	NUM
ap-7660	176	32	+	+	CCONJ
ap-7660	176	33	ebi	ebi	NOUN
ap-7660	176	34	aϵabcai	aϵabcai	NOUN
ap-7660	176	35	bϕc	bϕc	NOUN
ap-7660	176	36	2	2	NUM
ap-7660	176	37	}	}	PUNCT
ap-7660	176	38	=	=	SYM
ap-7660	176	39	2	2	NUM
ap-7660	176	40	∫	∫	NOUN
ap-7660	176	41	d3x	d3x	NOUN
ap-7660	176	42	−	−	PROPN
ap-7660	176	43	α	α	PROPN
ap-7660	176	44	{	{	PUNCT
ap-7660	176	45	bi	bi	NOUN
ap-7660	176	46	a∂iϕ	a∂iϕ	NOUN
ap-7660	176	47	a	a	DET
ap-7660	176	48	1	1	NUM
ap-7660	176	49	+	+	CCONJ
ap-7660	176	50	(	(	PUNCT
ap-7660	176	51	−eϵabcai	−eϵabcai	NOUN
ap-7660	176	52	bbi	bbi	VERB
ap-7660	176	53	c	c	PROPN
ap-7660	176	54	)	)	PUNCT
ap-7660	176	55	ϕa	ϕa	ADP
ap-7660	176	56	1	1	NUM
ap-7660	176	57	}	}	PUNCT
ap-7660	176	58	+	+	PROPN
ap-7660	176	59	β	β	X
ap-7660	176	60	{	{	PUNCT
ap-7660	176	61	bi	bi	NOUN
ap-7660	176	62	a∂iϕ	a∂iϕ	NOUN
ap-7660	176	63	a	a	DET
ap-7660	176	64	2	2	NUM
ap-7660	176	65	+	+	CCONJ
ap-7660	176	66	(	(	PUNCT
ap-7660	176	67	−eϵabcai	−eϵabcai	NOUN
ap-7660	176	68	bbi	bbi	VERB
ap-7660	176	69	c	c	PROPN
ap-7660	176	70	)	)	PUNCT
ap-7660	177	1	ϕa	ϕa	ADP
ap-7660	177	2	1ϕc	1ϕc	NOUN
ap-7660	177	3	2	2	NUM
ap-7660	177	4	}	}	PUNCT
ap-7660	177	5	=	=	SYM
ap-7660	177	6	2	2	NUM
ap-7660	177	7	∫	∫	NOUN
ap-7660	177	8	d3x	d3x	NOUN
ap-7660	177	9	−	−	PROPN
ap-7660	177	10	α	α	PROPN
ap-7660	177	11	{	{	PUNCT
ap-7660	177	12	bi	bi	NOUN
ap-7660	177	13	a∂iϕ	a∂iϕ	NOUN
ap-7660	177	14	a	a	DET
ap-7660	177	15	1	1	NUM
ap-7660	177	16	+	+	CCONJ
ap-7660	177	17	∂ibi	∂ibi	NOUN
ap-7660	177	18	aϕa	aϕa	NOUN
ap-7660	177	19	1	1	NUM
ap-7660	177	20	}	}	PUNCT
ap-7660	177	21	+	+	PROPN
ap-7660	177	22	β	β	X
ap-7660	177	23	{	{	PUNCT
ap-7660	177	24	bi	bi	NOUN
ap-7660	177	25	a∂iϕ	a∂iϕ	NOUN
ap-7660	177	26	a	a	DET
ap-7660	177	27	2	2	NUM
ap-7660	177	28	+	+	CCONJ
ap-7660	177	29	∂ibi	∂ibi	PUNCT
ap-7660	177	30	aϕa	aϕa	NOUN
ap-7660	177	31	1	1	NUM
ap-7660	177	32	}	}	PUNCT
ap-7660	177	33	=	=	SYM
ap-7660	177	34	2	2	NUM
ap-7660	177	35	∫	∫	NOUN
ap-7660	177	36	d3x	d3x	NOUN
ap-7660	177	37	−	−	PROPN
ap-7660	177	38	α∂i	α∂i	NUM
ap-7660	177	39	(	(	PUNCT
ap-7660	177	40	bi	bi	NOUN
ap-7660	177	41	aϕ1	aϕ1	PROPN
ap-7660	177	42	a	a	X
ap-7660	177	43	)	)	PUNCT
ap-7660	178	1	+	+	NUM
ap-7660	178	2	β∂i	β∂i	X
ap-7660	178	3	(	(	PUNCT
ap-7660	178	4	bi	bi	NOUN
ap-7660	178	5	aϕ2	aϕ2	NOUN
ap-7660	178	6	a	a	X
ap-7660	178	7	)	)	PUNCT
ap-7660	178	8	=	=	SYM
ap-7660	178	9	lim	lim	PROPN
ap-7660	178	10	r→∞	r→∞	PRON
ap-7660	178	11	(	(	PUNCT
ap-7660	178	12	−2α	−2α	PROPN
ap-7660	178	13	∫	∫	PROPN
ap-7660	178	14	sr	sr	PROPN
ap-7660	178	15	dsibi	dsibi	PROPN
ap-7660	178	16	aϕ1	aϕ1	NOUN
ap-7660	178	17	a	a	PRON
ap-7660	178	18	+	+	NUM
ap-7660	178	19	2β	2β	NUM
ap-7660	178	20	∫	∫	NOUN
ap-7660	178	21	sr	sr	PROPN
ap-7660	178	22	dsibi	dsibi	VERB
ap-7660	178	23	aϕ2	aϕ2	NOUN
ap-7660	178	24	a	a	X
ap-7660	178	25	)	)	PUNCT
ap-7660	178	26	,	,	PUNCT
ap-7660	178	27	where	where	SCONJ
ap-7660	178	28	in	in	ADP
ap-7660	178	29	the	the	DET
ap-7660	178	30	fourth	fourth	ADJ
ap-7660	178	31	line	line	NOUN
ap-7660	178	32	,	,	PUNCT
ap-7660	178	33	we	we	PRON
ap-7660	178	34	used	use	VERB
ap-7660	178	35	dib	dib	PROPN
ap-7660	178	36	a	a	DET
ap-7660	178	37	i	i	NOUN
ap-7660	178	38	=	=	NOUN
ap-7660	178	39	0	0	PROPN
ap-7660	178	40	,	,	PUNCT
ap-7660	178	41	which	which	PRON
ap-7660	178	42	can	can	AUX
ap-7660	178	43	be	be	AUX
ap-7660	178	44	shown	show	VERB
ap-7660	178	45	from	from	ADP
ap-7660	178	46	the	the	DET
ap-7660	178	47	bianchi	bianchi	NOUN
ap-7660	178	48	identity	identity	NOUN
ap-7660	178	49	dµϵµνρσf	dµϵµνρσf	PROPN
ap-7660	178	50	a	a	DET
ap-7660	178	51	ρσ	ρσ	ADP
ap-7660	178	52	=	=	NOUN
ap-7660	178	53	0	0	PROPN
ap-7660	178	54	.	.	PUNCT
ap-7660	179	1	the	the	DET
ap-7660	179	2	last	last	ADJ
ap-7660	179	3	line	line	NOUN
ap-7660	179	4	is	be	AUX
ap-7660	179	5	obtained	obtain	VERB
ap-7660	179	6	by	by	ADP
ap-7660	179	7	using	use	VERB
ap-7660	179	8	the	the	DET
ap-7660	179	9	gauss	gauss	PROPN
ap-7660	179	10	theorem	theorem	NOUN
ap-7660	179	11	at	at	ADP
ap-7660	179	12	some	some	DET
ap-7660	179	13	fixed	fix	VERB
ap-7660	179	14	value	value	NOUN
ap-7660	179	15	of	of	ADP
ap-7660	179	16	the	the	DET
ap-7660	179	17	radius	radius	NOUN
ap-7660	179	18	r.	r.	PROPN
ap-7660	179	19	since	since	SCONJ
ap-7660	179	20	the	the	DET
ap-7660	179	21	ϕa	ϕa	X
ap-7660	179	22	i	i	PRON
ap-7660	179	23	in	in	ADP
ap-7660	179	24	the	the	DET
ap-7660	179	25	integrand	integrand	NOUN
ap-7660	179	26	is	be	AUX
ap-7660	179	27	only	only	ADV
ap-7660	179	28	defined	define	VERB
ap-7660	179	29	over	over	ADP
ap-7660	179	30	the	the	DET
ap-7660	179	31	2	2	NUM
ap-7660	179	32	-	-	PUNCT
ap-7660	179	33	sphere	sphere	NOUN
ap-7660	179	34	with	with	ADP
ap-7660	179	35	a	a	DET
ap-7660	179	36	large	large	ADJ
ap-7660	179	37	radius	radius	NOUN
ap-7660	179	38	,	,	PUNCT
ap-7660	179	39	we	we	PRON
ap-7660	179	40	can	can	AUX
ap-7660	179	41	use	use	VERB
ap-7660	179	42	the	the	DET
ap-7660	179	43	asymptotic	asymptotic	ADJ
ap-7660	179	44	conditions	condition	NOUN
ap-7660	179	45	(	(	PUNCT
ap-7660	179	46	15	15	NUM
ap-7660	179	47	)	)	PUNCT
ap-7660	179	48	and	and	CCONJ
ap-7660	179	49	replace	replace	VERB
ap-7660	179	50	the	the	DET
ap-7660	179	51	monopole	monopole	ADJ
ap-7660	179	52	solutions	solution	NOUN
ap-7660	179	53	{	{	PUNCT
ap-7660	179	54	ϕa	ϕa	NOUN
ap-7660	179	55	α	α	PROPN
ap-7660	179	56	,	,	PUNCT
ap-7660	179	57	ba	ba	PROPN
ap-7660	179	58	i	i	PRON
ap-7660	179	59	}	}	PUNCT
ap-7660	179	60	with	with	ADP
ap-7660	179	61	the	the	DET
ap-7660	179	62	higgs	higgs	PROPN
ap-7660	179	63	vacuum	vacuum	PROPN
ap-7660	179	64	{	{	PUNCT
ap-7660	179	65	(	(	PUNCT
ap-7660	179	66	ϕ0	ϕ0	NOUN
ap-7660	179	67	α)a	α)a	NOUN
ap-7660	179	68	,	,	PUNCT
ap-7660	179	69	(	(	PUNCT
ap-7660	179	70	b0	b0	NOUN
ap-7660	179	71	i	i	PRON
ap-7660	179	72	)	)	PUNCT
ap-7660	179	73	a	a	X
ap-7660	179	74	}	}	PUNCT
ap-7660	179	75	e	e	X
ap-7660	179	76	≥	≥	X
ap-7660	179	77	(	(	PUNCT
ap-7660	179	78	−2αϕ0	−2αϕ0	VERB
ap-7660	179	79	1	1	NUM
ap-7660	179	80	a	a	DET
ap-7660	179	81	+	+	CCONJ
ap-7660	179	82	2βϕ0	2βϕ0	NUM
ap-7660	179	83	2	2	NUM
ap-7660	179	84	a	a	NOUN
ap-7660	179	85	)	)	PUNCT
ap-7660	179	86	lim	lim	PROPN
ap-7660	179	87	r→∞	r→∞	PROPN
ap-7660	179	88	∫	∫	PROPN
ap-7660	179	89	sr	sr	PROPN
ap-7660	179	90	dsi(b0	dsi(b0	PROPN
ap-7660	179	91	i	i	PRON
ap-7660	179	92	)	)	PUNCT
ap-7660	179	93	a	a	DET
ap-7660	179	94	(	(	PUNCT
ap-7660	179	95	25	25	NUM
ap-7660	179	96	)	)	PUNCT
ap-7660	179	97	=	=	PRON
ap-7660	179	98	(	(	PUNCT
ap-7660	179	99	∓2αrr̂a	∓2αrr̂a	NOUN
ap-7660	179	100	n	n	NOUN
ap-7660	179	101	∓	∓	NOUN
ap-7660	179	102	2β	2β	NOUN
ap-7660	179	103	c2c3µ2	c2c3µ2	NOUN
ap-7660	179	104	m2	m2	PROPN
ap-7660	179	105	2	2	PROPN
ap-7660	179	106	rr̂a	rr̂a	PROPN
ap-7660	179	107	n	n	PROPN
ap-7660	179	108	)	)	PUNCT
ap-7660	179	109	lim	lim	PROPN
ap-7660	179	110	r→∞	r→∞	PROPN
ap-7660	179	111	∫	∫	PROPN
ap-7660	179	112	sr	sr	PROPN
ap-7660	179	113	dsi(b0	dsi(b0	PROPN
ap-7660	179	114	i	i	PRON
ap-7660	179	115	)	)	PUNCT
ap-7660	179	116	a	a	X
ap-7660	179	117	,	,	PUNCT
ap-7660	179	118	where	where	SCONJ
ap-7660	179	119	the	the	DET
ap-7660	179	120	upper	upper	ADJ
ap-7660	179	121	and	and	CCONJ
ap-7660	179	122	lower	low	ADJ
ap-7660	179	123	signs	sign	NOUN
ap-7660	179	124	of	of	ADP
ap-7660	179	125	the	the	DET
ap-7660	179	126	above	above	ADJ
ap-7660	179	127	energy	energy	NOUN
ap-7660	179	128	correspond	correspond	NOUN
ap-7660	179	129	to	to	ADP
ap-7660	179	130	the	the	DET
ap-7660	179	131	upper	upper	ADJ
ap-7660	179	132	and	and	CCONJ
ap-7660	179	133	lower	low	ADJ
ap-7660	179	134	signs	sign	NOUN
ap-7660	179	135	of	of	ADP
ap-7660	179	136	the	the	DET
ap-7660	179	137	vacuum	vacuum	NOUN
ap-7660	179	138	solutions	solution	NOUN
ap-7660	179	139	in	in	ADP
ap-7660	179	140	equation	equation	NOUN
ap-7660	179	141	(	(	PUNCT
ap-7660	179	142	11	11	NUM
ap-7660	179	143	)	)	PUNCT
ap-7660	179	144	.	.	PUNCT
ap-7660	180	1	the	the	DET
ap-7660	180	2	explicit	explicit	ADJ
ap-7660	180	3	value	value	NOUN
ap-7660	180	4	of	of	ADP
ap-7660	180	5	ba	ba	PROPN
ap-7660	180	6	0i	0i	PROPN
ap-7660	180	7	can	can	AUX
ap-7660	180	8	be	be	AUX
ap-7660	180	9	obtained	obtain	VERB
ap-7660	180	10	by	by	ADP
ap-7660	180	11	inserting	insert	VERB
ap-7660	180	12	the	the	DET
ap-7660	180	13	higgs	higgs	NOUN
ap-7660	180	14	vacuum	vacuum	NOUN
ap-7660	180	15	(	(	PUNCT
ap-7660	180	16	11	11	NUM
ap-7660	180	17	)	)	PUNCT
ap-7660	180	18	into	into	ADP
ap-7660	180	19	the	the	DET
ap-7660	180	20	definition	definition	NOUN
ap-7660	180	21	of	of	ADP
ap-7660	180	22	the	the	DET
ap-7660	180	23	magnetic	magnetic	ADJ
ap-7660	180	24	field	field	NOUN
ap-7660	181	1	ba	ba	NOUN
ap-7660	182	1	i	i	NOUN
ap-7660	182	2	=	=	PUNCT
ap-7660	182	3	−1	−1	PROPN
ap-7660	182	4	2ϵi	2ϵi	PROPN
ap-7660	182	5	jk	jk	PROPN
ap-7660	182	6	(	(	PUNCT
ap-7660	182	7	∂jak	∂jak	NUM
ap-7660	182	8	−	−	PROPN
ap-7660	182	9	∂kaj	∂kaj	PUNCT
ap-7660	182	10	+	+	NUM
ap-7660	182	11	eaj	eaj	PROPN
ap-7660	182	12	×	×	PROPN
ap-7660	182	13	ak)a	ak)a	PROPN
ap-7660	182	14	.	.	PUNCT
ap-7660	183	1	(	(	PUNCT
ap-7660	183	2	26	26	NUM
ap-7660	183	3	)	)	PUNCT
ap-7660	183	4	after	after	ADP
ap-7660	183	5	a	a	DET
ap-7660	183	6	lengthy	lengthy	ADJ
ap-7660	183	7	calculation	calculation	NOUN
ap-7660	183	8	,	,	PUNCT
ap-7660	183	9	this	this	DET
ap-7660	183	10	expression	expression	NOUN
ap-7660	183	11	can	can	AUX
ap-7660	183	12	be	be	AUX
ap-7660	183	13	simplified	simplify	VERB
ap-7660	183	14	to	to	ADP
ap-7660	183	15	ba	ba	PROPN
ap-7660	183	16	0i	0i	NOUN
ap-7660	183	17	=	=	PUNCT
ap-7660	184	1	ϕ̂0a	ϕ̂0a	ADJ
ap-7660	184	2	bi	bi	NOUN
ap-7660	184	3	=	=	NOUN
ap-7660	184	4	r̂a	r̂a	NUM
ap-7660	184	5	nbi	nbi	NOUN
ap-7660	184	6	,	,	PUNCT
ap-7660	184	7	where	where	SCONJ
ap-7660	184	8	ϕ̂0a	ϕ̂0a	ADV
ap-7660	184	9	is	be	AUX
ap-7660	184	10	a	a	DET
ap-7660	184	11	normalised	normalise	VERB
ap-7660	184	12	solution	solution	NOUN
ap-7660	184	13	∑	∑	PUNCT
ap-7660	184	14	a	a	DET
ap-7660	184	15	ϕ̂0a	ϕ̂0a	ADJ
ap-7660	184	16	ϕ̂0a	ϕ̂0a	NOUN
ap-7660	184	17	=	=	NOUN
ap-7660	184	18	1	1	X
ap-7660	184	19	.	.	PUNCT
ap-7660	185	1	the	the	DET
ap-7660	185	2	bi	bi	NOUN
ap-7660	185	3	is	be	AUX
ap-7660	185	4	defined	define	VERB
ap-7660	185	5	as	as	ADP
ap-7660	185	6	bi	bi	PROPN
ap-7660	185	7	≡	≡	PROPN
ap-7660	185	8	−1	−1	NOUN
ap-7660	185	9	2ϵijk	2ϵijk	NUM
ap-7660	185	10	{	{	PUNCT
ap-7660	185	11	∂jak	∂jak	NUM
ap-7660	185	12	−	−	PROPN
ap-7660	185	13	∂kaj	∂kaj	PUNCT
ap-7660	185	14	+	+	NUM
ap-7660	185	15	1	1	NUM
ap-7660	185	16	e	e	NOUN
ap-7660	185	17	r̂n	r̂n	NOUN
ap-7660	185	18	·	·	PUNCT
ap-7660	185	19	(	(	PUNCT
ap-7660	185	20	∂j	∂j	NOUN
ap-7660	185	21	r̂n	r̂n	NOUN
ap-7660	185	22	×	×	NOUN
ap-7660	185	23	∂kr̂n	∂kr̂n	PUNCT
ap-7660	185	24	)	)	PUNCT
ap-7660	185	25	}	}	PUNCT
ap-7660	185	26	.	.	PUNCT
ap-7660	186	1	(	(	PUNCT
ap-7660	186	2	27	27	NUM
ap-7660	186	3	)	)	PUNCT
ap-7660	186	4	where	where	SCONJ
ap-7660	186	5	a	a	PRON
ap-7660	186	6	was	be	AUX
ap-7660	186	7	defined	define	VERB
ap-7660	186	8	in	in	ADP
ap-7660	186	9	equation	equation	NOUN
ap-7660	186	10	(	(	PUNCT
ap-7660	186	11	11	11	NUM
ap-7660	186	12	)	)	PUNCT
ap-7660	186	13	.	.	PUNCT
ap-7660	187	1	notice	notice	VERB
ap-7660	187	2	that	that	SCONJ
ap-7660	187	3	integrating	integrate	VERB
ap-7660	187	4	the	the	DET
ap-7660	187	5	first	first	ADJ
ap-7660	187	6	term	term	NOUN
ap-7660	187	7	over	over	ADP
ap-7660	187	8	the	the	DET
ap-7660	187	9	2	2	NUM
ap-7660	187	10	-	-	PUNCT
ap-7660	187	11	sphere	sphere	NOUN
ap-7660	187	12	gives	give	VERB
ap-7660	187	13	zero	zero	NUM
ap-7660	187	14	by	by	ADP
ap-7660	187	15	stoke	stoke	PROPN
ap-7660	187	16	’s	’s	PART
ap-7660	187	17	theorem	theorem	PROPN
ap-7660	187	18	∫	∫	PROPN
ap-7660	187	19	s	s	PART
ap-7660	187	20	∂	∂	NUM
ap-7660	187	21	×	×	NOUN
ap-7660	188	1	a	a	PRON
ap-7660	188	2	=	=	X
ap-7660	188	3	∫	∫	PROPN
ap-7660	188	4	∂s	∂s	PROPN
ap-7660	188	5	a	a	PROPN
ap-7660	188	6	=	=	SYM
ap-7660	188	7	0	0	NUM
ap-7660	188	8	,	,	PUNCT
ap-7660	188	9	where	where	SCONJ
ap-7660	188	10	one	one	PRON
ap-7660	188	11	can	can	AUX
ap-7660	188	12	show	show	VERB
ap-7660	188	13	that	that	SCONJ
ap-7660	188	14	stoke	stoke	NOUN
ap-7660	188	15	’s	’s	PART
ap-7660	188	16	theorem	theorem	NOUN
ap-7660	188	17	on	on	ADP
ap-7660	188	18	the	the	DET
ap-7660	188	19	closed	closed	ADJ
ap-7660	188	20	surface	surface	NOUN
ap-7660	188	21	gives	give	VERB
ap-7660	188	22	zero	zero	NUM
ap-7660	188	23	by	by	ADP
ap-7660	188	24	dividing	divide	VERB
ap-7660	188	25	the	the	DET
ap-7660	188	26	sphere	sphere	NOUN
ap-7660	188	27	into	into	ADP
ap-7660	188	28	two	two	NUM
ap-7660	188	29	open	open	ADJ
ap-7660	188	30	surfaces	surface	NOUN
ap-7660	188	31	.	.	PUNCT
ap-7660	189	1	the	the	DET
ap-7660	189	2	second	second	ADJ
ap-7660	189	3	term	term	NOUN
ap-7660	189	4	is	be	AUX
ap-7660	189	5	a	a	DET
ap-7660	189	6	topological	topological	ADJ
ap-7660	189	7	term	term	NOUN
ap-7660	189	8	which	which	PRON
ap-7660	189	9	can	can	AUX
ap-7660	189	10	be	be	AUX
ap-7660	189	11	evaluated	evaluate	VERB
ap-7660	189	12	as∫	as∫	NOUN
ap-7660	189	13	dsibi	dsibi	NOUN
ap-7660	189	14	=	=	SYM
ap-7660	189	15	−4πn	−4πn	NOUN
ap-7660	189	16	e	e	NOUN
ap-7660	189	17	.	.	PUNCT
ap-7660	190	1	(	(	PUNCT
ap-7660	190	2	28	28	NUM
ap-7660	190	3	)	)	PUNCT
ap-7660	190	4	the	the	DET
ap-7660	190	5	explicit	explicit	ADJ
ap-7660	190	6	calculation	calculation	NOUN
ap-7660	190	7	is	be	AUX
ap-7660	190	8	in	in	ADP
ap-7660	190	9	[	[	X
ap-7660	190	10	28	28	NUM
ap-7660	190	11	]	]	PUNCT
ap-7660	190	12	.	.	PUNCT
ap-7660	191	1	this	this	PRON
ap-7660	191	2	is	be	AUX
ap-7660	191	3	the	the	DET
ap-7660	191	4	magnetic	magnetic	ADJ
ap-7660	191	5	charge	charge	NOUN
ap-7660	191	6	of	of	ADP
ap-7660	191	7	the	the	DET
ap-7660	191	8	monopole	monopole	ADJ
ap-7660	191	9	solutions	solution	NOUN
ap-7660	191	10	.	.	PUNCT
ap-7660	192	1	therefore	therefore	ADV
ap-7660	192	2	integer	integer	NOUN
ap-7660	192	3	n	n	CCONJ
ap-7660	192	4	,	,	PUNCT
ap-7660	192	5	which	which	PRON
ap-7660	192	6	corresponds	correspond	VERB
ap-7660	192	7	to	to	ADP
ap-7660	192	8	the	the	DET
ap-7660	192	9	winding	wind	VERB
ap-7660	192	10	number	number	NOUN
ap-7660	192	11	of	of	ADP
ap-7660	192	12	the	the	DET
ap-7660	192	13	solution	solution	NOUN
ap-7660	192	14	,	,	PUNCT
ap-7660	192	15	comes	come	VERB
ap-7660	192	16	from	from	ADP
ap-7660	192	17	the	the	DET
ap-7660	192	18	ansatz	ansatz	ADJ
ap-7660	192	19	ba	ba	NOUN
ap-7660	193	1	i	i	PRON
ap-7660	193	2	=	=	PUNCT
ap-7660	193	3	ϕ̂0a	ϕ̂0a	INTJ
ap-7660	193	4	bi	bi	NOUN
ap-7660	193	5	.	.	PUNCT
ap-7660	194	1	in	in	ADP
ap-7660	194	2	our	our	PRON
ap-7660	194	3	case	case	NOUN
ap-7660	194	4	,	,	PUNCT
ap-7660	194	5	there	there	PRON
ap-7660	194	6	is	be	VERB
ap-7660	194	7	an	an	DET
ap-7660	194	8	ambiguity	ambiguity	NOUN
ap-7660	194	9	of	of	ADP
ap-7660	194	10	whether	whether	SCONJ
ap-7660	194	11	to	to	PART
ap-7660	194	12	choose	choose	VERB
ap-7660	194	13	ba	ba	PROPN
ap-7660	195	1	i	i	NOUN
ap-7660	195	2	=	=	PUNCT
ap-7660	195	3	ϕ̂0	ϕ̂0	PROPN
ap-7660	196	1	1	1	NUM
ap-7660	196	2	a	a	DET
ap-7660	196	3	bi	bi	NOUN
ap-7660	196	4	or	or	CCONJ
ap-7660	196	5	ba	ba	NOUN
ap-7660	197	1	i	i	NOUN
ap-7660	197	2	=	=	PUNCT
ap-7660	197	3	ϕ̂0	ϕ̂0	PROPN
ap-7660	197	4	2	2	NUM
ap-7660	197	5	a	a	DET
ap-7660	197	6	bi	bi	NOUN
ap-7660	197	7	.	.	PUNCT
ap-7660	198	1	now	now	ADV
ap-7660	198	2	we	we	PRON
ap-7660	198	3	see	see	VERB
ap-7660	198	4	explicitly	explicitly	ADV
ap-7660	198	5	the	the	DET
ap-7660	198	6	reason	reason	NOUN
ap-7660	198	7	why	why	SCONJ
ap-7660	198	8	we	we	PRON
ap-7660	198	9	choose	choose	VERB
ap-7660	198	10	to	to	PART
ap-7660	198	11	keep	keep	VERB
ap-7660	198	12	the	the	DET
ap-7660	198	13	same	same	ADJ
ap-7660	198	14	integer	integer	NOUN
ap-7660	198	15	values	value	NOUN
ap-7660	198	16	for	for	ADP
ap-7660	198	17	solutions	solution	NOUN
ap-7660	198	18	ϕ0	ϕ0	NOUN
ap-7660	198	19	1	1	NUM
ap-7660	198	20	and	and	CCONJ
ap-7660	198	21	ϕ0	ϕ0	NOUN
ap-7660	198	22	2	2	NUM
ap-7660	198	23	.	.	PUNCT
ap-7660	199	1	if	if	SCONJ
ap-7660	199	2	the	the	DET
ap-7660	199	3	integer	integer	NOUN
ap-7660	199	4	values	value	NOUN
ap-7660	199	5	of	of	ADP
ap-7660	199	6	r̂a	r̂a	NUM
ap-7660	199	7	n	n	PROPN
ap-7660	199	8	in	in	ADP
ap-7660	199	9	solutions	solution	NOUN
ap-7660	199	10	ϕ0	ϕ0	NOUN
ap-7660	199	11	1	1	NUM
ap-7660	199	12	,	,	PUNCT
ap-7660	199	13	ϕ0	ϕ0	NOUN
ap-7660	199	14	2	2	NUM
ap-7660	199	15	are	be	AUX
ap-7660	199	16	different	different	ADJ
ap-7660	199	17	,	,	PUNCT
ap-7660	199	18	then	then	ADV
ap-7660	199	19	the	the	DET
ap-7660	199	20	integration∫	integration∫	NOUN
ap-7660	199	21	sr	sr	PROPN
ap-7660	199	22	dsi(b0	dsi(b0	PROPN
ap-7660	199	23	i	i	PRON
ap-7660	199	24	)	)	PUNCT
ap-7660	199	25	a	a	PRON
ap-7660	199	26	will	will	AUX
ap-7660	199	27	be	be	AUX
ap-7660	199	28	different	different	ADJ
ap-7660	199	29	,	,	PUNCT
ap-7660	199	30	leading	lead	VERB
ap-7660	199	31	to	to	ADP
ap-7660	199	32	inconsistent	inconsistent	ADJ
ap-7660	199	33	energy	energy	NOUN
ap-7660	199	34	.	.	PUNCT
ap-7660	200	1	finally	finally	ADV
ap-7660	200	2	,	,	PUNCT
ap-7660	200	3	we	we	PRON
ap-7660	200	4	find	find	VERB
ap-7660	200	5	our	our	PRON
ap-7660	200	6	lower	low	ADJ
ap-7660	200	7	bound	bind	VERB
ap-7660	200	8	of	of	ADP
ap-7660	200	9	the	the	DET
ap-7660	200	10	monopole	monopole	ADJ
ap-7660	200	11	energy	energy	NOUN
ap-7660	200	12	e	e	PROPN
ap-7660	200	13	≥	≥	PRON
ap-7660	200	14	∓2r	∓2r	PROPN
ap-7660	200	15	(	(	PUNCT
ap-7660	200	16	α	α	NOUN
ap-7660	200	17	+	+	X
ap-7660	200	18	β	β	X
ap-7660	200	19	c2c3µ2	c2c3µ2	NOUN
ap-7660	200	20	m2	m2	PROPN
ap-7660	200	21	2	2	NUM
ap-7660	200	22	)	)	PUNCT
ap-7660	200	23	r̂a	r̂a	PRON
ap-7660	200	24	nr̂a	nr̂a	PROPN
ap-7660	200	25	n	n	PROPN
ap-7660	200	26	(	(	PUNCT
ap-7660	200	27	−4πn	−4πn	NOUN
ap-7660	200	28	e	e	NOUN
ap-7660	200	29	)	)	PUNCT
ap-7660	200	30	(	(	PUNCT
ap-7660	200	31	29	29	NUM
ap-7660	200	32	)	)	PUNCT
ap-7660	200	33	=	=	SYM
ap-7660	200	34	±8πnr	±8πnr	PROPN
ap-7660	200	35	e	e	X
ap-7660	200	36	(	(	PUNCT
ap-7660	200	37	α	α	PROPN
ap-7660	200	38	+	+	X
ap-7660	200	39	β	β	X
ap-7660	200	40	c2c3µ2	c2c3µ2	NOUN
ap-7660	200	41	m2	m2	PROPN
ap-7660	200	42	2	2	NUM
ap-7660	200	43	)	)	PUNCT
ap-7660	200	44	.	.	PUNCT
ap-7660	201	1	notice	notice	VERB
ap-7660	201	2	that	that	SCONJ
ap-7660	201	3	we	we	PRON
ap-7660	201	4	have	have	VERB
ap-7660	201	5	some	some	DET
ap-7660	201	6	freedom	freedom	NOUN
ap-7660	201	7	to	to	PART
ap-7660	201	8	choose	choose	VERB
ap-7660	201	9	α	α	X
ap-7660	201	10	,	,	PUNCT
ap-7660	201	11	β	β	X
ap-7660	201	12	∈	∈	NOUN
ap-7660	201	13	r	r	NOUN
ap-7660	201	14	as	as	ADV
ap-7660	201	15	long	long	ADV
ap-7660	201	16	as	as	SCONJ
ap-7660	201	17	our	our	PRON
ap-7660	201	18	initial	initial	ADJ
ap-7660	201	19	assumptions	assumption	NOUN
ap-7660	201	20	(	(	PUNCT
ap-7660	201	21	23	23	NUM
ap-7660	201	22	)	)	PUNCT
ap-7660	201	23	are	be	AUX
ap-7660	201	24	satisfied	satisfied	ADJ
ap-7660	201	25	.	.	PUNCT
ap-7660	202	1	we	we	PRON
ap-7660	202	2	will	will	AUX
ap-7660	202	3	see	see	VERB
ap-7660	202	4	in	in	ADP
ap-7660	202	5	the	the	DET
ap-7660	202	6	next	next	ADJ
ap-7660	202	7	section	section	NOUN
ap-7660	202	8	that	that	SCONJ
ap-7660	202	9	we	we	PRON
ap-7660	202	10	can	can	AUX
ap-7660	202	11	take	take	VERB
ap-7660	202	12	a	a	DET
ap-7660	202	13	parameter	parameter	NOUN
ap-7660	202	14	limit	limit	NOUN
ap-7660	202	15	of	of	ADP
ap-7660	202	16	our	our	PRON
ap-7660	202	17	model	model	NOUN
ap-7660	202	18	,	,	PUNCT
ap-7660	202	19	which	which	PRON
ap-7660	202	20	saturates	saturate	VERB
ap-7660	202	21	the	the	DET
ap-7660	202	22	above	above	ADJ
ap-7660	202	23	inequality	inequality	NOUN
ap-7660	202	24	and	and	CCONJ
ap-7660	202	25	gives	give	VERB
ap-7660	202	26	exact	exact	ADJ
ap-7660	202	27	values	value	NOUN
ap-7660	202	28	to	to	ADP
ap-7660	202	29	α	α	PROPN
ap-7660	202	30	and	and	CCONJ
ap-7660	202	31	β	β	NOUN
ap-7660	202	32	.	.	PROPN
ap-7660	202	33	2.4	2.4	NUM
ap-7660	202	34	.	.	PUNCT
ap-7660	203	1	the	the	DET
ap-7660	203	2	fourfold	fourfold	ADJ
ap-7660	203	3	bps	bps	NOUN
ap-7660	203	4	scaling	scaling	NOUN
ap-7660	203	5	limit	limit	VERB
ap-7660	203	6	our	our	PRON
ap-7660	203	7	main	main	ADJ
ap-7660	203	8	goal	goal	NOUN
ap-7660	203	9	is	be	AUX
ap-7660	203	10	now	now	ADV
ap-7660	203	11	to	to	PART
ap-7660	203	12	solve	solve	VERB
ap-7660	203	13	the	the	DET
ap-7660	203	14	coupled	couple	VERB
ap-7660	203	15	differential	differential	ADJ
ap-7660	203	16	equations	equation	NOUN
ap-7660	203	17	(	(	PUNCT
ap-7660	203	18	17)-(19	17)-(19	NUM
ap-7660	203	19	)	)	PUNCT
ap-7660	203	20	.	.	PUNCT
ap-7660	204	1	prasad	prasad	PROPN
ap-7660	204	2	,	,	PUNCT
ap-7660	204	3	sommerfield	sommerfield	ADJ
ap-7660	204	4	,	,	PUNCT
ap-7660	204	5	and	and	CCONJ
ap-7660	204	6	bogomolny	bogomolny	VERB
ap-7660	204	7	[	[	PUNCT
ap-7660	204	8	26	26	NUM
ap-7660	204	9	,	,	PUNCT
ap-7660	204	10	27	27	NUM
ap-7660	204	11	]	]	PUNCT
ap-7660	204	12	managed	manage	VERB
ap-7660	204	13	to	to	PART
ap-7660	204	14	find	find	VERB
ap-7660	204	15	the	the	DET
ap-7660	204	16	exact	exact	ADJ
ap-7660	204	17	solution	solution	NOUN
ap-7660	204	18	by	by	ADP
ap-7660	204	19	taking	take	VERB
ap-7660	204	20	the	the	DET
ap-7660	204	21	parameter	parameter	NOUN
ap-7660	204	22	limit	limit	NOUN
ap-7660	204	23	,	,	PUNCT
ap-7660	204	24	which	which	PRON
ap-7660	204	25	simplifies	simplify	VERB
ap-7660	204	26	the	the	DET
ap-7660	204	27	differential	differential	ADJ
ap-7660	204	28	equations	equation	NOUN
ap-7660	204	29	.	.	PUNCT
ap-7660	205	1	the	the	DET
ap-7660	205	2	multiple	multiple	ADJ
ap-7660	205	3	scaling	scaling	NOUN
ap-7660	205	4	limit	limit	NOUN
ap-7660	205	5	is	be	AUX
ap-7660	205	6	taken	take	VERB
ap-7660	205	7	so	so	SCONJ
ap-7660	205	8	that	that	SCONJ
ap-7660	205	9	all	all	DET
ap-7660	205	10	the	the	DET
ap-7660	205	11	parameters	parameter	NOUN
ap-7660	205	12	of	of	ADP
ap-7660	205	13	the	the	DET
ap-7660	205	14	model	model	NOUN
ap-7660	205	15	tend	tend	VERB
ap-7660	205	16	to	to	ADP
ap-7660	205	17	zero	zero	NUM
ap-7660	205	18	with	with	ADP
ap-7660	205	19	some	some	DET
ap-7660	205	20	combinations	combination	NOUN
ap-7660	205	21	of	of	ADP
ap-7660	205	22	the	the	DET
ap-7660	205	23	parameter	parameter	NOUN
ap-7660	205	24	remaining	remain	VERB
ap-7660	205	25	finite	finite	NOUN
ap-7660	205	26	.	.	PUNCT
ap-7660	206	1	the	the	DET
ap-7660	206	2	combinations	combination	NOUN
ap-7660	206	3	are	be	AUX
ap-7660	206	4	taken	take	VERB
ap-7660	206	5	so	so	SCONJ
ap-7660	206	6	that	that	SCONJ
ap-7660	206	7	the	the	DET
ap-7660	206	8	vacuum	vacuum	NOUN
ap-7660	206	9	solutions	solution	NOUN
ap-7660	206	10	stay	stay	VERB
ap-7660	206	11	finite	finite	ADJ
ap-7660	206	12	in	in	ADP
ap-7660	206	13	this	this	DET
ap-7660	206	14	limit	limit	NOUN
ap-7660	206	15	.	.	PUNCT
ap-7660	207	1	inspired	inspire	VERB
ap-7660	207	2	by	by	ADP
ap-7660	207	3	this	this	PRON
ap-7660	207	4	,	,	PUNCT
ap-7660	207	5	we	we	PRON
ap-7660	207	6	will	will	AUX
ap-7660	207	7	take	take	VERB
ap-7660	207	8	here	here	ADV
ap-7660	207	9	a	a	DET
ap-7660	207	10	fourfold	fourfold	ADJ
ap-7660	207	11	scaling	scaling	NOUN
ap-7660	207	12	limit	limit	NOUN
ap-7660	207	13	g	g	NOUN
ap-7660	207	14	,	,	PUNCT
ap-7660	207	15	m1	m1	PROPN
ap-7660	207	16	,	,	PUNCT
ap-7660	207	17	m2	m2	PROPN
ap-7660	207	18	,	,	PUNCT
ap-7660	207	19	µ	µ	X
ap-7660	207	20	→	→	SYM
ap-7660	207	21	0	0	NUM
ap-7660	207	22	,	,	PUNCT
ap-7660	207	23	m2	m2	PROPN
ap-7660	207	24	1	1	NUM
ap-7660	207	25	g	g	NOUN
ap-7660	207	26	<	<	X
ap-7660	207	27	∞	∞	PROPN
ap-7660	207	28	,	,	PUNCT
ap-7660	207	29	µ2	µ2	PROPN
ap-7660	207	30	g	g	PROPN
ap-7660	207	31	<	<	X
ap-7660	207	32	∞	∞	PROPN
ap-7660	207	33	,	,	PUNCT
ap-7660	207	34	µ2	µ2	PROPN
ap-7660	207	35	m2	m2	PROPN
ap-7660	207	36	2	2	NUM
ap-7660	207	37	<	<	X
ap-7660	207	38	∞.	∞.	PROPN
ap-7660	207	39	(	(	PUNCT
ap-7660	207	40	30	30	NUM
ap-7660	207	41	)	)	PUNCT
ap-7660	207	42	this	this	PRON
ap-7660	207	43	will	will	AUX
ap-7660	207	44	ensure	ensure	VERB
ap-7660	207	45	that	that	SCONJ
ap-7660	207	46	the	the	DET
ap-7660	207	47	vacuum	vacuum	NOUN
ap-7660	207	48	solutions	solution	NOUN
ap-7660	207	49	equation	equation	NOUN
ap-7660	207	50	(	(	PUNCT
ap-7660	207	51	11	11	NUM
ap-7660	207	52	)	)	PUNCT
ap-7660	207	53	stays	stay	VERB
ap-7660	207	54	finite	finite	NOUN
ap-7660	207	55	,	,	PUNCT
ap-7660	207	56	but	but	CCONJ
ap-7660	207	57	crucially	crucially	ADV
ap-7660	207	58	the	the	DET
ap-7660	207	59	curly	curly	ADJ
ap-7660	207	60	bracket	bracket	NOUN
ap-7660	207	61	parts	part	NOUN
ap-7660	207	62	201	201	NUM
ap-7660	207	63	takanobu	takanobu	PROPN
ap-7660	207	64	taira	taira	PROPN
ap-7660	207	65	acta	acta	PROPN
ap-7660	207	66	polytechnica	polytechnica	PROPN
ap-7660	207	67	in	in	ADP
ap-7660	207	68	equations	equation	NOUN
ap-7660	207	69	(	(	PUNCT
ap-7660	207	70	18	18	NUM
ap-7660	207	71	)	)	PUNCT
ap-7660	207	72	and	and	CCONJ
ap-7660	207	73	(	(	PUNCT
ap-7660	207	74	19	19	NUM
ap-7660	207	75	)	)	PUNCT
ap-7660	207	76	vanish	vanish	VERB
ap-7660	207	77	.	.	PUNCT
ap-7660	208	1	there	there	PRON
ap-7660	208	2	is	be	VERB
ap-7660	208	3	a	a	DET
ap-7660	208	4	physical	physical	ADJ
ap-7660	208	5	motivation	motivation	NOUN
ap-7660	208	6	for	for	ADP
ap-7660	208	7	this	this	DET
ap-7660	208	8	limit	limit	NOUN
ap-7660	208	9	in	in	ADP
ap-7660	208	10	which	which	PRON
ap-7660	208	11	the	the	DET
ap-7660	208	12	mass	mass	ADJ
ap-7660	208	13	ratio	ratio	NOUN
ap-7660	208	14	of	of	ADP
ap-7660	208	15	the	the	DET
ap-7660	208	16	higgs	higgs	PROPN
ap-7660	208	17	and	and	CCONJ
ap-7660	208	18	gauge	gauge	NOUN
ap-7660	208	19	mass	mass	NOUN
ap-7660	208	20	are	be	AUX
ap-7660	208	21	taken	take	VERB
ap-7660	208	22	to	to	PART
ap-7660	208	23	be	be	AUX
ap-7660	208	24	zero	zero	NUM
ap-7660	208	25	(	(	PUNCT
ap-7660	208	26	i.e.	i.e.	X
ap-7660	208	27	mhiggs	mhigg	NOUN
ap-7660	208	28	<	<	X
ap-7660	208	29	<	<	X
ap-7660	208	30	mg	mg	PROPN
ap-7660	208	31	)	)	PUNCT
ap-7660	208	32	as	as	SCONJ
ap-7660	208	33	described	describe	VERB
ap-7660	208	34	in	in	ADP
ap-7660	208	35	[	[	X
ap-7660	208	36	29	29	NUM
ap-7660	208	37	]	]	PUNCT
ap-7660	208	38	.	.	PUNCT
ap-7660	209	1	we	we	PRON
ap-7660	209	2	will	will	AUX
ap-7660	209	3	see	see	VERB
ap-7660	209	4	in	in	ADP
ap-7660	209	5	the	the	DET
ap-7660	209	6	next	next	ADJ
ap-7660	209	7	section	section	NOUN
ap-7660	209	8	that	that	SCONJ
ap-7660	209	9	the	the	DET
ap-7660	209	10	same	same	ADJ
ap-7660	209	11	type	type	NOUN
ap-7660	209	12	of	of	ADP
ap-7660	209	13	behaviour	behaviour	NOUN
ap-7660	209	14	is	be	AUX
ap-7660	209	15	present	present	ADJ
ap-7660	209	16	in	in	ADP
ap-7660	209	17	our	our	PRON
ap-7660	209	18	model	model	NOUN
ap-7660	209	19	,	,	PUNCT
ap-7660	209	20	hence	hence	ADV
ap-7660	209	21	justifying	justify	VERB
ap-7660	209	22	equation	equation	NOUN
ap-7660	209	23	(	(	PUNCT
ap-7660	209	24	30	30	NUM
ap-7660	209	25	)	)	PUNCT
ap-7660	209	26	.	.	PUNCT
ap-7660	210	1	the	the	DET
ap-7660	210	2	resulting	result	VERB
ap-7660	210	3	set	set	NOUN
ap-7660	210	4	of	of	ADP
ap-7660	210	5	differential	differential	ADJ
ap-7660	210	6	equations	equation	NOUN
ap-7660	210	7	,	,	PUNCT
ap-7660	210	8	after	after	ADP
ap-7660	210	9	taking	take	VERB
ap-7660	210	10	the	the	DET
ap-7660	210	11	bps	bps	NOUN
ap-7660	210	12	limit	limit	NOUN
ap-7660	210	13	,	,	PUNCT
ap-7660	210	14	is	be	AUX
ap-7660	210	15	similar	similar	ADJ
ap-7660	210	16	to	to	ADP
ap-7660	210	17	the	the	DET
ap-7660	210	18	ones	one	NOUN
ap-7660	210	19	considered	consider	VERB
ap-7660	210	20	in	in	ADP
ap-7660	210	21	[	[	X
ap-7660	210	22	26	26	NUM
ap-7660	210	23	,	,	PUNCT
ap-7660	210	24	27	27	NUM
ap-7660	210	25	]	]	PUNCT
ap-7660	210	26	with	with	ADP
ap-7660	210	27	the	the	DET
ap-7660	210	28	slightly	slightly	ADV
ap-7660	210	29	different	different	ADJ
ap-7660	210	30	quadratic	quadratic	ADJ
ap-7660	210	31	term	term	NOUN
ap-7660	210	32	in	in	ADP
ap-7660	210	33	equation	equation	NOUN
ap-7660	210	34	(	(	PUNCT
ap-7660	210	35	17	17	NUM
ap-7660	210	36	)	)	PUNCT
ap-7660	210	37	.	.	PUNCT
ap-7660	211	1	it	it	PRON
ap-7660	211	2	is	be	AUX
ap-7660	211	3	natural	natural	ADJ
ap-7660	211	4	to	to	PART
ap-7660	211	5	consider	consider	VERB
ap-7660	211	6	a	a	DET
ap-7660	211	7	similar	similar	ADJ
ap-7660	211	8	ansatz	ansatz	NOUN
ap-7660	211	9	as	as	SCONJ
ap-7660	211	10	given	give	VERB
ap-7660	211	11	in	in	ADP
ap-7660	211	12	[	[	X
ap-7660	211	13	26	26	NUM
ap-7660	211	14	,	,	PUNCT
ap-7660	211	15	27	27	NUM
ap-7660	211	16	]	]	PUNCT
ap-7660	211	17	u(r	u(r	NOUN
ap-7660	211	18	)	)	PUNCT
ap-7660	212	1	=	=	PUNCT
ap-7660	212	2	evr	evr	PROPN
ap-7660	212	3	sinh	sinh	PROPN
ap-7660	212	4	(	(	PUNCT
ap-7660	212	5	evr	evr	PROPN
ap-7660	212	6	)	)	PUNCT
ap-7660	212	7	,	,	PUNCT
ap-7660	212	8	(	(	PUNCT
ap-7660	212	9	31	31	NUM
ap-7660	212	10	)	)	PUNCT
ap-7660	212	11	h1(r	h1(r	NOUN
ap-7660	212	12	)	)	PUNCT
ap-7660	212	13	=	=	SYM
ap-7660	212	14	−αf(r	−αf(r	NOUN
ap-7660	212	15	)	)	PUNCT
ap-7660	212	16	,	,	PUNCT
ap-7660	212	17	(	(	PUNCT
ap-7660	212	18	32	32	NUM
ap-7660	212	19	)	)	PUNCT
ap-7660	212	20	h2(r	h2(r	NOUN
ap-7660	212	21	)	)	PUNCT
ap-7660	212	22	=	=	SYM
ap-7660	212	23	−βf(r	−βf(r	NOUN
ap-7660	212	24	)	)	PUNCT
ap-7660	212	25	,	,	PUNCT
ap-7660	212	26	(	(	PUNCT
ap-7660	212	27	33	33	NUM
ap-7660	212	28	)	)	PUNCT
ap-7660	212	29	where	where	SCONJ
ap-7660	212	30	α	α	X
ap-7660	212	31	,	,	PUNCT
ap-7660	212	32	β	β	X
ap-7660	212	33	∈	∈	NOUN
ap-7660	212	34	r	r	NOUN
ap-7660	212	35	were	be	AUX
ap-7660	212	36	introduced	introduce	VERB
ap-7660	212	37	in	in	ADP
ap-7660	212	38	section	section	NOUN
ap-7660	212	39	2.3	2.3	NUM
ap-7660	212	40	and	and	CCONJ
ap-7660	212	41	f(r	f(r	NOUN
ap-7660	212	42	)	)	PUNCT
ap-7660	212	43	≡	≡	PROPN
ap-7660	212	44	{	{	PUNCT
ap-7660	212	45	v	v	NUM
ap-7660	212	46	coth	coth	NOUN
ap-7660	212	47	(	(	PUNCT
ap-7660	212	48	evr	evr	PROPN
ap-7660	212	49	)	)	PUNCT
ap-7660	212	50	−	−	PROPN
ap-7660	212	51	1	1	NUM
ap-7660	212	52	er	er	INTJ
ap-7660	212	53	}	}	PUNCT
ap-7660	212	54	.	.	PUNCT
ap-7660	213	1	one	one	PRON
ap-7660	213	2	can	can	AUX
ap-7660	213	3	check	check	VERB
ap-7660	213	4	that	that	SCONJ
ap-7660	213	5	this	this	PRON
ap-7660	213	6	ansatz	ansatz	ADJ
ap-7660	213	7	indeed	indeed	ADV
ap-7660	213	8	satisfies	satisfy	VERB
ap-7660	213	9	differential	differential	ADJ
ap-7660	213	10	equations	equation	NOUN
ap-7660	213	11	equation	equation	NOUN
ap-7660	213	12	(	(	PUNCT
ap-7660	213	13	17)-(19	17)-(19	NUM
ap-7660	213	14	)	)	PUNCT
ap-7660	213	15	in	in	ADP
ap-7660	213	16	the	the	DET
ap-7660	213	17	bps	bps	NOUN
ap-7660	213	18	limit	limit	NOUN
ap-7660	213	19	.	.	PUNCT
ap-7660	214	1	we	we	PRON
ap-7660	214	2	have	have	AUX
ap-7660	214	3	decided	decide	VERB
ap-7660	214	4	to	to	PART
ap-7660	214	5	put	put	VERB
ap-7660	214	6	a	a	DET
ap-7660	214	7	prefactor	prefactor	NOUN
ap-7660	214	8	α	α	NOUN
ap-7660	214	9	and	and	CCONJ
ap-7660	214	10	β	β	PROPN
ap-7660	214	11	in	in	ADP
ap-7660	214	12	front	front	NOUN
ap-7660	214	13	of	of	ADP
ap-7660	214	14	equations	equation	NOUN
ap-7660	214	15	(	(	PUNCT
ap-7660	214	16	32	32	NUM
ap-7660	214	17	)	)	PUNCT
ap-7660	214	18	and	and	CCONJ
ap-7660	214	19	(	(	PUNCT
ap-7660	214	20	33	33	NUM
ap-7660	214	21	)	)	PUNCT
ap-7660	214	22	to	to	PART
ap-7660	214	23	satisfy	satisfy	VERB
ap-7660	214	24	the	the	DET
ap-7660	214	25	differential	differential	ADJ
ap-7660	214	26	equation	equation	NOUN
ap-7660	214	27	(	(	PUNCT
ap-7660	214	28	17	17	NUM
ap-7660	214	29	)	)	PUNCT
ap-7660	214	30	.	.	PUNCT
ap-7660	215	1	note	note	VERB
ap-7660	215	2	that	that	SCONJ
ap-7660	215	3	if	if	SCONJ
ap-7660	215	4	we	we	PRON
ap-7660	215	5	take	take	VERB
ap-7660	215	6	α	α	NOUN
ap-7660	215	7	=	=	SYM
ap-7660	215	8	1	1	NUM
ap-7660	215	9	,	,	PUNCT
ap-7660	215	10	we	we	PRON
ap-7660	215	11	get	get	VERB
ap-7660	215	12	exactly	exactly	ADV
ap-7660	215	13	the	the	DET
ap-7660	215	14	same	same	ADJ
ap-7660	215	15	as	as	SCONJ
ap-7660	215	16	given	give	VERB
ap-7660	215	17	in	in	ADP
ap-7660	215	18	[	[	X
ap-7660	215	19	26	26	NUM
ap-7660	215	20	,	,	PUNCT
ap-7660	215	21	27	27	NUM
ap-7660	215	22	]	]	PUNCT
ap-7660	215	23	,	,	PUNCT
ap-7660	215	24	which	which	PRON
ap-7660	215	25	is	be	AUX
ap-7660	215	26	known	know	VERB
ap-7660	215	27	to	to	PART
ap-7660	215	28	satisfy	satisfy	VERB
ap-7660	215	29	the	the	DET
ap-7660	215	30	first	first	ADJ
ap-7660	215	31	-	-	PUNCT
ap-7660	215	32	order	order	NOUN
ap-7660	215	33	differential	differential	ADJ
ap-7660	215	34	equation	equation	NOUN
ap-7660	215	35	called	call	VERB
ap-7660	215	36	the	the	DET
ap-7660	215	37	bogomolny	bogomolny	ADJ
ap-7660	215	38	equation	equation	NOUN
ap-7660	215	39	bi	bi	NOUN
ap-7660	215	40	−	−	PROPN
ap-7660	215	41	diϕ	diϕ	PROPN
ap-7660	215	42	=	=	SYM
ap-7660	215	43	0	0	X
ap-7660	215	44	.	.	PUNCT
ap-7660	216	1	the	the	DET
ap-7660	216	2	ansatz	ansatz	ADJ
ap-7660	216	3	(	(	PUNCT
ap-7660	216	4	31)-(33	31)-(33	NUM
ap-7660	216	5	)	)	PUNCT
ap-7660	216	6	only	only	ADV
ap-7660	216	7	differs	differ	VERB
ap-7660	216	8	from	from	ADP
ap-7660	216	9	the	the	DET
ap-7660	216	10	ones	one	NOUN
ap-7660	216	11	given	give	VERB
ap-7660	216	12	in	in	ADP
ap-7660	216	13	[	[	X
ap-7660	216	14	26	26	NUM
ap-7660	216	15	,	,	PUNCT
ap-7660	216	16	27	27	NUM
ap-7660	216	17	]	]	PUNCT
ap-7660	216	18	by	by	ADP
ap-7660	216	19	the	the	DET
ap-7660	216	20	prefactors	prefactor	NOUN
ap-7660	216	21	α	α	NOUN
ap-7660	216	22	and	and	CCONJ
ap-7660	216	23	β	β	NOUN
ap-7660	216	24	,	,	PUNCT
ap-7660	216	25	and	and	CCONJ
ap-7660	216	26	therefore	therefore	ADV
ap-7660	216	27	our	our	PRON
ap-7660	216	28	ansatz	ansatz	NOUN
ap-7660	216	29	should	should	AUX
ap-7660	216	30	satisfy	satisfy	VERB
ap-7660	216	31	the	the	DET
ap-7660	216	32	bogomolny	bogomolny	ADJ
ap-7660	216	33	equation	equation	NOUN
ap-7660	216	34	with	with	ADP
ap-7660	216	35	the	the	DET
ap-7660	216	36	appropriate	appropriate	ADJ
ap-7660	216	37	scaling	scaling	NOUN
ap-7660	216	38	to	to	PART
ap-7660	216	39	cancel	cancel	VERB
ap-7660	216	40	the	the	DET
ap-7660	216	41	prefactor	prefactor	NOUN
ap-7660	216	42	in	in	ADP
ap-7660	216	43	equations	equation	NOUN
ap-7660	216	44	(	(	PUNCT
ap-7660	216	45	32	32	NUM
ap-7660	216	46	)	)	PUNCT
ap-7660	216	47	and	and	CCONJ
ap-7660	216	48	(	(	PUNCT
ap-7660	216	49	33	33	NUM
ap-7660	216	50	)	)	PUNCT
ap-7660	216	51	bb	bb	NOUN
ap-7660	217	1	i	i	NOUN
ap-7660	217	2	+	+	CCONJ
ap-7660	217	3	1	1	NUM
ap-7660	217	4	α	α	NOUN
ap-7660	217	5	(	(	PUNCT
ap-7660	217	6	diϕ1)b	diϕ1)b	PROPN
ap-7660	217	7	=	=	PROPN
ap-7660	217	8	0	0	PROPN
ap-7660	217	9	,	,	PUNCT
ap-7660	217	10	(	(	PUNCT
ap-7660	217	11	34	34	NUM
ap-7660	217	12	)	)	PUNCT
ap-7660	217	13	bb	bb	NOUN
ap-7660	218	1	i	i	PRON
ap-7660	218	2	+	+	NOUN
ap-7660	218	3	1	1	NUM
ap-7660	218	4	β	β	X
ap-7660	218	5	(	(	PUNCT
ap-7660	218	6	diϕ2)b	diϕ2)b	NOUN
ap-7660	218	7	=	=	SYM
ap-7660	218	8	0	0	NUM
ap-7660	218	9	,	,	PUNCT
ap-7660	218	10	(	(	PUNCT
ap-7660	218	11	35	35	NUM
ap-7660	218	12	)	)	PUNCT
ap-7660	218	13	where	where	SCONJ
ap-7660	218	14	ϕα	ϕα	ADV
ap-7660	218	15	≡	≡	PROPN
ap-7660	218	16	hα(r)r̂n	hα(r)r̂n	PROPN
ap-7660	218	17	.	.	PUNCT
ap-7660	219	1	if	if	SCONJ
ap-7660	219	2	we	we	PRON
ap-7660	219	3	compare	compare	VERB
ap-7660	219	4	these	these	DET
ap-7660	219	5	equations	equation	NOUN
ap-7660	219	6	to	to	ADP
ap-7660	219	7	the	the	DET
ap-7660	219	8	terms	term	NOUN
ap-7660	219	9	appearing	appear	VERB
ap-7660	219	10	in	in	ADP
ap-7660	219	11	the	the	DET
ap-7660	219	12	energy	energy	NOUN
ap-7660	219	13	of	of	ADP
ap-7660	219	14	the	the	DET
ap-7660	219	15	monopole	monopole	ADJ
ap-7660	219	16	equation	equation	NOUN
ap-7660	219	17	(	(	PUNCT
ap-7660	219	18	22	22	NUM
ap-7660	219	19	)	)	PUNCT
ap-7660	219	20	,	,	PUNCT
ap-7660	219	21	then	then	ADV
ap-7660	219	22	we	we	PRON
ap-7660	219	23	can	can	AUX
ap-7660	219	24	saturate	saturate	VERB
ap-7660	219	25	the	the	DET
ap-7660	219	26	inequality	inequality	NOUN
ap-7660	219	27	in	in	ADP
ap-7660	219	28	equation	equation	NOUN
ap-7660	219	29	(	(	PUNCT
ap-7660	219	30	29	29	NUM
ap-7660	219	31	)	)	PUNCT
ap-7660	219	32	by	by	ADP
ap-7660	219	33	e[ϕ1	e[ϕ1	NOUN
ap-7660	219	34	,	,	PUNCT
ap-7660	219	35	ϕ2	ϕ2	ADV
ap-7660	219	36	]	]	PUNCT
ap-7660	219	37	=	=	SYM
ap-7660	219	38	±8πnr	±8πnr	PROPN
ap-7660	219	39	e	e	PROPN
ap-7660	219	40	(	(	PUNCT
ap-7660	219	41	α	α	PROPN
ap-7660	219	42	+	+	X
ap-7660	219	43	β	β	X
ap-7660	219	44	c2c3µ2	c2c3µ2	NOUN
ap-7660	219	45	m2	m2	PROPN
ap-7660	219	46	2	2	NUM
ap-7660	219	47	)	)	PUNCT
ap-7660	219	48	,	,	PUNCT
ap-7660	219	49	(	(	PUNCT
ap-7660	219	50	36	36	NUM
ap-7660	219	51	)	)	PUNCT
ap-7660	219	52	where	where	SCONJ
ap-7660	219	53	upper	upper	ADJ
ap-7660	219	54	and	and	CCONJ
ap-7660	219	55	lower	low	ADJ
ap-7660	219	56	signs	sign	NOUN
ap-7660	219	57	correspond	correspond	VERB
ap-7660	219	58	to	to	ADP
ap-7660	219	59	the	the	DET
ap-7660	219	60	vacuum	vacuum	NOUN
ap-7660	219	61	solutions	solution	NOUN
ap-7660	219	62	equation	equation	NOUN
ap-7660	219	63	(	(	PUNCT
ap-7660	219	64	11	11	NUM
ap-7660	219	65	)	)	PUNCT
ap-7660	219	66	,	,	PUNCT
ap-7660	219	67	when	when	SCONJ
ap-7660	219	68	taking	take	VERB
ap-7660	219	69	the	the	DET
ap-7660	219	70	square	square	ADJ
ap-7660	219	71	root	root	NOUN
ap-7660	219	72	.	.	PUNCT
ap-7660	220	1	we	we	PRON
ap-7660	220	2	can	can	AUX
ap-7660	220	3	calculate	calculate	VERB
ap-7660	220	4	the	the	DET
ap-7660	220	5	explicit	explicit	ADJ
ap-7660	220	6	forms	form	NOUN
ap-7660	220	7	of	of	ADP
ap-7660	220	8	α	α	NOUN
ap-7660	220	9	and	and	CCONJ
ap-7660	220	10	β	β	X
ap-7660	220	11	by	by	ADP
ap-7660	220	12	comparing	compare	VERB
ap-7660	220	13	the	the	DET
ap-7660	220	14	asymptotic	asymptotic	ADJ
ap-7660	220	15	conditions	condition	NOUN
ap-7660	220	16	in	in	ADP
ap-7660	220	17	equation	equation	NOUN
ap-7660	220	18	(	(	PUNCT
ap-7660	220	19	15	15	NUM
ap-7660	220	20	)	)	PUNCT
ap-7660	220	21	lim	lim	NOUN
ap-7660	220	22	r→∞	r→∞	PRON
ap-7660	220	23	h±	h±	PROPN
ap-7660	220	24	1	1	NUM
ap-7660	220	25	=	=	SYM
ap-7660	220	26	h0±	h0±	ADJ
ap-7660	220	27	1	1	NUM
ap-7660	220	28	=	=	SYM
ap-7660	220	29	±r	±r	PROPN
ap-7660	220	30	,	,	PUNCT
ap-7660	220	31	(	(	PUNCT
ap-7660	220	32	37	37	NUM
ap-7660	220	33	)	)	PUNCT
ap-7660	220	34	lim	lim	NOUN
ap-7660	220	35	r→∞	r→∞	PRON
ap-7660	220	36	h±	h±	PROPN
ap-7660	220	37	2	2	NUM
ap-7660	220	38	=	=	SYM
ap-7660	220	39	h0±	h0±	ADJ
ap-7660	220	40	2	2	NUM
ap-7660	220	41	=	=	SYM
ap-7660	220	42	∓c2c3µ2	∓c2c3µ2	PROPN
ap-7660	220	43	m2	m2	PROPN
ap-7660	220	44	2	2	NUM
ap-7660	220	45	r	r	NOUN
ap-7660	220	46	,	,	PUNCT
ap-7660	220	47	with	with	ADP
ap-7660	220	48	the	the	DET
ap-7660	220	49	asymptotic	asymptotic	ADJ
ap-7660	220	50	values	value	NOUN
ap-7660	220	51	of	of	ADP
ap-7660	220	52	equations	equation	NOUN
ap-7660	220	53	(	(	PUNCT
ap-7660	220	54	31)-(33	31)-(33	NUM
ap-7660	220	55	)	)	PUNCT
ap-7660	220	56	limr→∞	limr→∞	PROPN
ap-7660	220	57	u(r	u(r	NOUN
ap-7660	220	58	)	)	PUNCT
ap-7660	221	1	=	=	SYM
ap-7660	221	2	0	0	NUM
ap-7660	221	3	,	,	PUNCT
ap-7660	221	4	limr→∞	limr→∞	PROPN
ap-7660	221	5	h±	h±	PROPN
ap-7660	221	6	1	1	NUM
ap-7660	221	7	(	(	PUNCT
ap-7660	221	8	r	r	NOUN
ap-7660	221	9	)	)	PUNCT
ap-7660	221	10	=	=	SYM
ap-7660	221	11	−αv	−αv	NOUN
ap-7660	221	12	,	,	PUNCT
ap-7660	221	13	(	(	PUNCT
ap-7660	221	14	38	38	NUM
ap-7660	221	15	)	)	PUNCT
ap-7660	221	16	limr→∞	limr→∞	PROPN
ap-7660	221	17	h±	h±	PROPN
ap-7660	221	18	2	2	NUM
ap-7660	221	19	(	(	PUNCT
ap-7660	221	20	r	r	NOUN
ap-7660	221	21	)	)	PUNCT
ap-7660	221	22	=	=	SYM
ap-7660	221	23	−βv	−βv	NOUN
ap-7660	221	24	.	.	PUNCT
ap-7660	222	1	by	by	ADP
ap-7660	222	2	derrick	derrick	PROPN
ap-7660	222	3	’s	’s	PART
ap-7660	222	4	scaling	scale	VERB
ap-7660	222	5	argument	argument	NOUN
ap-7660	222	6	,	,	PUNCT
ap-7660	222	7	the	the	DET
ap-7660	222	8	two	two	NUM
ap-7660	222	9	asymptotic	asymptotic	ADJ
ap-7660	222	10	values	value	NOUN
ap-7660	222	11	(	(	PUNCT
ap-7660	222	12	37	37	NUM
ap-7660	222	13	)	)	PUNCT
ap-7660	222	14	and	and	CCONJ
ap-7660	222	15	(	(	PUNCT
ap-7660	222	16	38	38	NUM
ap-7660	222	17	)	)	PUNCT
ap-7660	222	18	should	should	AUX
ap-7660	222	19	match	match	VERB
ap-7660	222	20	,	,	PUNCT
ap-7660	222	21	resulting	result	VERB
ap-7660	222	22	in	in	ADP
ap-7660	222	23	algebraic	algebraic	ADJ
ap-7660	222	24	equations	equation	NOUN
ap-7660	222	25	for	for	ADP
ap-7660	222	26	α	α	PROPN
ap-7660	222	27	and	and	CCONJ
ap-7660	222	28	β	β	NOUN
ap-7660	222	29	.	.	PUNCT
ap-7660	223	1	using	use	VERB
ap-7660	223	2	α2	α2	PROPN
ap-7660	223	3	−	−	PROPN
ap-7660	223	4	β2	β2	NOUN
ap-7660	223	5	=	=	NOUN
ap-7660	223	6	1	1	NUM
ap-7660	223	7	and	and	CCONJ
ap-7660	223	8	assuming	assume	VERB
ap-7660	223	9	m4	m4	PROPN
ap-7660	223	10	2	2	NUM
ap-7660	223	11	≥	≥	NOUN
ap-7660	223	12	µ4	µ4	PROPN
ap-7660	223	13	,	,	PUNCT
ap-7660	223	14	we	we	PRON
ap-7660	223	15	find	find	VERB
ap-7660	223	16	the	the	DET
ap-7660	223	17	four	four	NUM
ap-7660	223	18	set	set	NOUN
ap-7660	223	19	of	of	ADP
ap-7660	223	20	real	real	ADJ
ap-7660	223	21	solutions	solution	NOUN
ap-7660	224	1	α	α	NOUN
ap-7660	224	2	=	=	SYM
ap-7660	224	3	∓(±)m2	∓(±)m2	ADJ
ap-7660	224	4	2	2	NUM
ap-7660	224	5	l	l	NOUN
ap-7660	224	6	,	,	PUNCT
ap-7660	224	7	v	v	NOUN
ap-7660	224	8	=	=	SYM
ap-7660	224	9	(	(	PUNCT
ap-7660	224	10	±	±	NOUN
ap-7660	224	11	)	)	PUNCT
ap-7660	224	12	rl	rl	ADP
ap-7660	224	13	m2	m2	PROPN
ap-7660	224	14	2	2	NUM
ap-7660	224	15	,	,	PUNCT
ap-7660	224	16	β	β	NOUN
ap-7660	224	17	=	=	SYM
ap-7660	224	18	±(±)c2c3µ2	±(±)c2c3µ2	PROPN
ap-7660	224	19	l	l	NOUN
ap-7660	224	20	,	,	PUNCT
ap-7660	224	21	(	(	PUNCT
ap-7660	224	22	39	39	NUM
ap-7660	224	23	)	)	PUNCT
ap-7660	224	24	where	where	SCONJ
ap-7660	224	25	l	l	NOUN
ap-7660	224	26	=	=	PUNCT
ap-7660	224	27	√	√	PUNCT
ap-7660	224	28	m4	m4	PROPN
ap-7660	224	29	2	2	NUM
ap-7660	224	30	−	−	NOUN
ap-7660	224	31	µ4	µ4	PROPN
ap-7660	224	32	.	.	PUNCT
ap-7660	225	1	the	the	DET
ap-7660	225	2	plus	plus	CCONJ
ap-7660	225	3	-	-	PUNCT
ap-7660	225	4	minus	minus	NOUN
ap-7660	225	5	signs	sign	NOUN
ap-7660	225	6	in	in	ADP
ap-7660	225	7	the	the	DET
ap-7660	225	8	brackets	bracket	NOUN
ap-7660	225	9	correspond	correspond	VERB
ap-7660	225	10	to	to	ADP
ap-7660	225	11	the	the	DET
ap-7660	225	12	two	two	NUM
ap-7660	225	13	possible	possible	ADJ
ap-7660	225	14	solutions	solution	NOUN
ap-7660	225	15	to	to	ADP
ap-7660	225	16	the	the	DET
ap-7660	225	17	algebraic	algebraic	ADJ
ap-7660	225	18	equation	equation	NOUN
ap-7660	225	19	α2	α2	PROPN
ap-7660	225	20	−	−	PROPN
ap-7660	225	21	β2	β2	NOUN
ap-7660	225	22	=	=	NOUN
ap-7660	225	23	1	1	X
ap-7660	225	24	.	.	PUNCT
ap-7660	226	1	these	these	PRON
ap-7660	226	2	need	need	VERB
ap-7660	226	3	to	to	PART
ap-7660	226	4	be	be	AUX
ap-7660	226	5	distinguished	distinguish	VERB
ap-7660	226	6	from	from	ADP
ap-7660	226	7	the	the	DET
ap-7660	226	8	upper	upper	ADJ
ap-7660	226	9	and	and	CCONJ
ap-7660	226	10	lower	low	ADJ
ap-7660	226	11	signs	sign	NOUN
ap-7660	226	12	of	of	ADP
ap-7660	226	13	α	α	NOUN
ap-7660	226	14	and	and	CCONJ
ap-7660	226	15	β	β	NOUN
ap-7660	226	16	,	,	PUNCT
ap-7660	226	17	which	which	PRON
ap-7660	226	18	correspond	correspond	VERB
ap-7660	226	19	to	to	ADP
ap-7660	226	20	the	the	DET
ap-7660	226	21	vacuums	vacuum	NOUN
ap-7660	226	22	solutions	solution	NOUN
ap-7660	226	23	(	(	PUNCT
ap-7660	226	24	11	11	NUM
ap-7660	226	25	)	)	PUNCT
ap-7660	226	26	.	.	PUNCT
ap-7660	227	1	inserting	insert	VERB
ap-7660	227	2	the	the	DET
ap-7660	227	3	explicit	explicit	ADJ
ap-7660	227	4	values	value	NOUN
ap-7660	227	5	of	of	ADP
ap-7660	227	6	α	α	NOUN
ap-7660	227	7	and	and	CCONJ
ap-7660	227	8	β	β	X
ap-7660	227	9	to	to	ADP
ap-7660	227	10	the	the	DET
ap-7660	227	11	energy	energy	NOUN
ap-7660	227	12	equation	equation	NOUN
ap-7660	227	13	(	(	PUNCT
ap-7660	227	14	36	36	NUM
ap-7660	227	15	)	)	PUNCT
ap-7660	227	16	we	we	PRON
ap-7660	227	17	find	find	VERB
ap-7660	227	18	e[ϕ1	e[ϕ1	NOUN
ap-7660	227	19	,	,	PUNCT
ap-7660	227	20	ϕ2	ϕ2	ADV
ap-7660	227	21	]	]	X
ap-7660	227	22	≡	≡	PROPN
ap-7660	227	23	(	(	PUNCT
ap-7660	227	24	±)8πnr	±)8πnr	NUM
ap-7660	227	25	em2	em2	NOUN
ap-7660	227	26	2	2	NUM
ap-7660	227	27	(	(	PUNCT
ap-7660	227	28	−m4	−m4	PROPN
ap-7660	227	29	2	2	NUM
ap-7660	227	30	+	+	CCONJ
ap-7660	227	31	µ4	µ4	PROPN
ap-7660	227	32	l	l	NOUN
ap-7660	227	33	)	)	PUNCT
ap-7660	227	34	(	(	PUNCT
ap-7660	227	35	40	40	NUM
ap-7660	227	36	)	)	PUNCT
ap-7660	227	37	=	=	NOUN
ap-7660	227	38	(	(	PUNCT
ap-7660	227	39	±)−8πnr	±)−8πnr	PROPN
ap-7660	227	40	em2	em2	NOUN
ap-7660	227	41	2	2	NUM
ap-7660	227	42	l	l	NOUN
ap-7660	227	43	,	,	PUNCT
ap-7660	227	44	with	with	ADP
ap-7660	227	45	corresponding	correspond	VERB
ap-7660	227	46	solutions	solution	NOUN
ap-7660	227	47	h±	h±	PROPN
ap-7660	227	48	1	1	NUM
ap-7660	227	49	(	(	PUNCT
ap-7660	227	50	r	r	NOUN
ap-7660	227	51	)	)	PUNCT
ap-7660	227	52	=	=	SYM
ap-7660	227	53	±(±)m2	±(±)m2	NOUN
ap-7660	227	54	2	2	NUM
ap-7660	227	55	l	l	NOUN
ap-7660	227	56	[	[	PUNCT
ap-7660	227	57	rl	rl	X
ap-7660	227	58	m2	m2	PROPN
ap-7660	227	59	2	2	NUM
ap-7660	227	60	coth	coth	NOUN
ap-7660	227	61	(	(	PUNCT
ap-7660	227	62	erl	erl	NOUN
ap-7660	227	63	m2	m2	PROPN
ap-7660	227	64	2	2	NUM
ap-7660	227	65	r	r	NOUN
ap-7660	227	66	)	)	PUNCT
ap-7660	227	67	−	−	PROPN
ap-7660	228	1	1	1	NUM
ap-7660	229	1	er	er	INTJ
ap-7660	229	2	]	]	PUNCT
ap-7660	229	3	,	,	PUNCT
ap-7660	229	4	(	(	PUNCT
ap-7660	229	5	41	41	NUM
ap-7660	229	6	)	)	PUNCT
ap-7660	229	7	h±	h±	NOUN
ap-7660	229	8	2	2	NUM
ap-7660	229	9	(	(	PUNCT
ap-7660	229	10	r	r	NOUN
ap-7660	229	11	)	)	PUNCT
ap-7660	230	1	=	=	SYM
ap-7660	230	2	∓(±)c2c3µ2	∓(±)c2c3µ2	NUM
ap-7660	230	3	l	l	NOUN
ap-7660	230	4	[	[	PUNCT
ap-7660	230	5	rl	rl	X
ap-7660	230	6	m2	m2	PROPN
ap-7660	230	7	2	2	NUM
ap-7660	230	8	coth	coth	NOUN
ap-7660	230	9	(	(	PUNCT
ap-7660	230	10	erl	erl	NOUN
ap-7660	230	11	m2	m2	PROPN
ap-7660	230	12	2	2	NUM
ap-7660	230	13	r	r	NOUN
ap-7660	230	14	)	)	PUNCT
ap-7660	230	15	−	−	PROPN
ap-7660	231	1	1	1	NUM
ap-7660	231	2	er	er	INTJ
ap-7660	231	3	]	]	PUNCT
ap-7660	231	4	.	.	PUNCT
ap-7660	232	1	it	it	PRON
ap-7660	232	2	is	be	AUX
ap-7660	232	3	crucial	crucial	ADJ
ap-7660	232	4	to	to	PART
ap-7660	232	5	note	note	VERB
ap-7660	232	6	that	that	SCONJ
ap-7660	232	7	although	although	SCONJ
ap-7660	232	8	it	it	PRON
ap-7660	232	9	seems	seem	VERB
ap-7660	232	10	like	like	SCONJ
ap-7660	232	11	there	there	PRON
ap-7660	232	12	are	be	VERB
ap-7660	232	13	two	two	NUM
ap-7660	232	14	monopole	monopole	ADJ
ap-7660	232	15	solutions	solution	NOUN
ap-7660	232	16	{	{	PUNCT
ap-7660	232	17	h±	h±	NOUN
ap-7660	232	18	1	1	NUM
ap-7660	232	19	,	,	PUNCT
ap-7660	232	20	h±	h±	PROPN
ap-7660	232	21	2	2	NUM
ap-7660	232	22	}	}	PUNCT
ap-7660	232	23	,	,	PUNCT
ap-7660	232	24	the	the	DET
ap-7660	232	25	two	two	NUM
ap-7660	232	26	solutions	solution	NOUN
ap-7660	232	27	are	be	AUX
ap-7660	232	28	related	relate	VERB
ap-7660	232	29	non	non	ADJ
ap-7660	232	30	-	-	ADJ
ap-7660	232	31	trivially	trivially	ADV
ap-7660	232	32	in	in	ADP
ap-7660	232	33	their	their	PRON
ap-7660	232	34	asymptotic	asymptotic	ADJ
ap-7660	232	35	limit	limit	NOUN
ap-7660	232	36	by	by	ADP
ap-7660	232	37	the	the	DET
ap-7660	232	38	constraint	constraint	NOUN
ap-7660	232	39	limr→∞	limr→∞	PROPN
ap-7660	232	40	h±	h±	PROPN
ap-7660	232	41	2	2	NUM
ap-7660	232	42	=	=	SYM
ap-7660	232	43	(	(	PUNCT
ap-7660	232	44	−c2c3µ2	−c2c3µ2	NUM
ap-7660	232	45	/	/	SYM
ap-7660	232	46	m2	m2	PROPN
ap-7660	232	47	2	2	NUM
ap-7660	232	48	)	)	PUNCT
ap-7660	232	49	limr→∞	limr→∞	PROPN
ap-7660	232	50	h±	h±	NOUN
ap-7660	232	51	1	1	NUM
ap-7660	232	52	given	give	VERB
ap-7660	232	53	in	in	ADP
ap-7660	232	54	equation	equation	NOUN
ap-7660	232	55	(	(	PUNCT
ap-7660	232	56	10	10	NUM
ap-7660	232	57	)	)	PUNCT
ap-7660	232	58	.	.	PUNCT
ap-7660	233	1	for	for	ADP
ap-7660	233	2	example	example	NOUN
ap-7660	233	3	,	,	PUNCT
ap-7660	233	4	one	one	PRON
ap-7660	233	5	can	can	AUX
ap-7660	233	6	not	not	PART
ap-7660	233	7	choose	choose	VERB
ap-7660	233	8	{	{	PUNCT
ap-7660	233	9	h+	h+	PROPN
ap-7660	233	10	1	1	NUM
ap-7660	233	11	,	,	PUNCT
ap-7660	233	12	h−	h−	PROPN
ap-7660	233	13	2	2	NUM
ap-7660	233	14	}	}	PUNCT
ap-7660	233	15	as	as	ADP
ap-7660	233	16	a	a	DET
ap-7660	233	17	solution	solution	NOUN
ap-7660	233	18	as	as	SCONJ
ap-7660	233	19	this	this	PRON
ap-7660	233	20	will	will	AUX
ap-7660	233	21	break	break	VERB
ap-7660	233	22	the	the	DET
ap-7660	233	23	asymptotic	asymptotic	ADJ
ap-7660	233	24	constraint	constraint	NOUN
ap-7660	233	25	.	.	PUNCT
ap-7660	234	1	the	the	DET
ap-7660	234	2	solution	solution	NOUN
ap-7660	234	3	(	(	PUNCT
ap-7660	234	4	41	41	NUM
ap-7660	234	5	)	)	PUNCT
ap-7660	234	6	can	can	AUX
ap-7660	234	7	be	be	AUX
ap-7660	234	8	constrained	constrain	VERB
ap-7660	234	9	further	far	ADV
ap-7660	234	10	by	by	ADP
ap-7660	234	11	imposing	impose	VERB
ap-7660	234	12	that	that	SCONJ
ap-7660	234	13	the	the	DET
ap-7660	234	14	energy	energy	NOUN
ap-7660	234	15	(	(	PUNCT
ap-7660	234	16	40	40	NUM
ap-7660	234	17	)	)	PUNCT
ap-7660	234	18	is	be	AUX
ap-7660	234	19	real	real	ADJ
ap-7660	234	20	and	and	CCONJ
ap-7660	234	21	positive	positive	ADJ
ap-7660	234	22	.	.	PUNCT
ap-7660	235	1	e[ϕ1	e[ϕ1	NOUN
ap-7660	235	2	,	,	PUNCT
ap-7660	235	3	ϕ2	ϕ2	ADV
ap-7660	235	4	]	]	PUNCT
ap-7660	235	5	>	>	X
ap-7660	235	6	0	0	PUNCT
ap-7660	236	1	=	=	AUX
ap-7660	236	2	⇒	⇒	X
ap-7660	236	3	−(±)8πnr	−(±)8πnr	PUNCT
ap-7660	236	4	em2	em2	NOUN
ap-7660	236	5	2	2	NUM
ap-7660	236	6	l	l	NOUN
ap-7660	236	7	=	=	NOUN
ap-7660	236	8	⇒	⇒	NOUN
ap-7660	236	9	−(±)n	−(±)n	PROPN
ap-7660	236	10	>	>	X
ap-7660	236	11	0	0	NUM
ap-7660	236	12	.	.	PUNCT
ap-7660	237	1	(	(	PUNCT
ap-7660	237	2	42	42	NUM
ap-7660	237	3	)	)	PUNCT
ap-7660	237	4	therefore	therefore	ADV
ap-7660	237	5	we	we	PRON
ap-7660	237	6	can	can	AUX
ap-7660	237	7	ensure	ensure	VERB
ap-7660	237	8	positive	positive	ADJ
ap-7660	237	9	energy	energy	NOUN
ap-7660	237	10	if	if	SCONJ
ap-7660	237	11	(	(	PUNCT
ap-7660	237	12	±	±	NUM
ap-7660	237	13	)	)	PUNCT
ap-7660	237	14	=	=	SYM
ap-7660	237	15	sign(n	sign(n	NOUN
ap-7660	237	16	)	)	PUNCT
ap-7660	237	17	.	.	PUNCT
ap-7660	238	1	the	the	DET
ap-7660	238	2	final	final	ADJ
ap-7660	238	3	form	form	NOUN
ap-7660	238	4	of	of	ADP
ap-7660	238	5	the	the	DET
ap-7660	238	6	monopole	monopole	ADJ
ap-7660	238	7	solution	solution	NOUN
ap-7660	238	8	with	with	ADP
ap-7660	238	9	positive	positive	ADJ
ap-7660	238	10	energy	energy	NOUN
ap-7660	238	11	are	be	AUX
ap-7660	238	12	h±	h±	PROPN
ap-7660	238	13	1	1	NUM
ap-7660	238	14	(	(	PUNCT
ap-7660	238	15	r	r	NOUN
ap-7660	238	16	)	)	PUNCT
ap-7660	238	17	=	=	NOUN
ap-7660	238	18	±sign(n)m2	±sign(n)m2	NOUN
ap-7660	238	19	2	2	NUM
ap-7660	238	20	l	l	NOUN
ap-7660	238	21	[	[	PUNCT
ap-7660	238	22	rl	rl	X
ap-7660	238	23	m2	m2	PROPN
ap-7660	238	24	2	2	NUM
ap-7660	238	25	coth	coth	NOUN
ap-7660	238	26	(	(	PUNCT
ap-7660	238	27	erl	erl	NOUN
ap-7660	238	28	m2	m2	PROPN
ap-7660	238	29	2	2	NUM
ap-7660	238	30	r	r	NOUN
ap-7660	238	31	)	)	PUNCT
ap-7660	238	32	−	−	PROPN
ap-7660	239	1	1	1	NUM
ap-7660	239	2	er	er	INTJ
ap-7660	239	3	]	]	PUNCT
ap-7660	239	4	,	,	PUNCT
ap-7660	239	5	(	(	PUNCT
ap-7660	239	6	43	43	NUM
ap-7660	239	7	)	)	PUNCT
ap-7660	239	8	h±	h±	NOUN
ap-7660	239	9	2	2	NUM
ap-7660	239	10	(	(	PUNCT
ap-7660	239	11	r	r	NOUN
ap-7660	239	12	)	)	PUNCT
ap-7660	239	13	=	=	NOUN
ap-7660	240	1	∓sign(n)c2c3µ2	∓sign(n)c2c3µ2	PRON
ap-7660	240	2	l	l	NOUN
ap-7660	240	3	[	[	PUNCT
ap-7660	240	4	rl	rl	X
ap-7660	240	5	m2	m2	PROPN
ap-7660	240	6	2	2	NUM
ap-7660	240	7	coth	coth	NOUN
ap-7660	240	8	(	(	PUNCT
ap-7660	240	9	erl	erl	NOUN
ap-7660	240	10	m2	m2	PROPN
ap-7660	240	11	2	2	NUM
ap-7660	240	12	r	r	NOUN
ap-7660	240	13	)	)	PUNCT
ap-7660	240	14	−	−	PROPN
ap-7660	241	1	1	1	NUM
ap-7660	241	2	er	er	INTJ
ap-7660	241	3	]	]	PUNCT
ap-7660	241	4	.	.	PUNCT
ap-7660	242	1	with	with	ADP
ap-7660	242	2	energy	energy	NOUN
ap-7660	242	3	e	e	NOUN
ap-7660	242	4	=	=	PUNCT
ap-7660	242	5	8|n|πlr	8|n|πlr	NUM
ap-7660	242	6	/	/	SYM
ap-7660	242	7	em2	em2	NOUN
ap-7660	242	8	2	2	NUM
ap-7660	242	9	.	.	PUNCT
ap-7660	242	10	we	we	PRON
ap-7660	242	11	conclude	conclude	VERB
ap-7660	242	12	this	this	DET
ap-7660	242	13	subsection	subsection	NOUN
ap-7660	242	14	by	by	ADP
ap-7660	242	15	observing	observe	VERB
ap-7660	242	16	that	that	SCONJ
ap-7660	242	17	the	the	DET
ap-7660	242	18	above	above	ADJ
ap-7660	242	19	solution	solution	NOUN
ap-7660	242	20	depends	depend	VERB
ap-7660	242	21	on	on	ADP
ap-7660	242	22	the	the	DET
ap-7660	242	23	parameter	parameter	NOUN
ap-7660	242	24	c3	c3	PROPN
ap-7660	242	25	,	,	PUNCT
ap-7660	242	26	which	which	PRON
ap-7660	242	27	takes	take	VERB
ap-7660	242	28	value	value	NOUN
ap-7660	242	29	{	{	PUNCT
ap-7660	242	30	−1	−1	NOUN
ap-7660	242	31	,	,	PUNCT
ap-7660	242	32	1	1	NUM
ap-7660	242	33	}	}	PUNCT
ap-7660	242	34	depending	depend	VERB
ap-7660	242	35	on	on	ADP
ap-7660	242	36	the	the	DET
ap-7660	242	37	choice	choice	NOUN
ap-7660	242	38	of	of	ADP
ap-7660	242	39	the	the	DET
ap-7660	242	40	similarity	similarity	NOUN
ap-7660	242	41	transformation	transformation	NOUN
ap-7660	242	42	.	.	PUNCT
ap-7660	243	1	choosing	choose	VERB
ap-7660	243	2	a	a	DET
ap-7660	243	3	different	different	ADJ
ap-7660	243	4	values	value	NOUN
ap-7660	243	5	of	of	ADP
ap-7660	243	6	c3	c3	PROPN
ap-7660	243	7	also	also	ADV
ap-7660	243	8	result	result	VERB
ap-7660	243	9	in	in	ADP
ap-7660	243	10	a	a	DET
ap-7660	243	11	different	different	ADJ
ap-7660	243	12	asymptotic	asymptotic	ADJ
ap-7660	243	13	values	value	NOUN
ap-7660	243	14	(	(	PUNCT
ap-7660	243	15	37	37	NUM
ap-7660	243	16	)	)	PUNCT
ap-7660	243	17	,	,	PUNCT
ap-7660	243	18	meaning	mean	VERB
ap-7660	243	19	solutions	solution	NOUN
ap-7660	243	20	for	for	ADP
ap-7660	243	21	c3	c3	PROPN
ap-7660	243	22	=	=	SYM
ap-7660	243	23	1	1	NUM
ap-7660	243	24	and	and	CCONJ
ap-7660	243	25	c3	c3	NOUN
ap-7660	243	26	=	=	PUNCT
ap-7660	243	27	−1	−1	NOUN
ap-7660	243	28	are	be	AUX
ap-7660	243	29	topologically	topologically	ADV
ap-7660	243	30	different	different	ADJ
ap-7660	243	31	.	.	PUNCT
ap-7660	244	1	since	since	SCONJ
ap-7660	244	2	the	the	DET
ap-7660	244	3	energy	energy	NOUN
ap-7660	244	4	is	be	AUX
ap-7660	244	5	independent	independent	ADJ
ap-7660	244	6	of	of	ADP
ap-7660	244	7	c3	c3	PROPN
ap-7660	244	8	,	,	PUNCT
ap-7660	244	9	two	two	NUM
ap-7660	244	10	distinct	distinct	ADJ
ap-7660	244	11	solutions	solution	NOUN
ap-7660	244	12	share	share	VERB
ap-7660	244	13	the	the	DET
ap-7660	244	14	same	same	ADJ
ap-7660	244	15	energy	energy	NOUN
ap-7660	244	16	.	.	PUNCT
ap-7660	245	1	respecting	respect	VERB
ap-7660	245	2	one	one	NUM
ap-7660	245	3	of	of	ADP
ap-7660	245	4	the	the	DET
ap-7660	245	5	main	main	ADJ
ap-7660	245	6	features	feature	NOUN
ap-7660	245	7	of	of	ADP
ap-7660	245	8	similarity	similarity	NOUN
ap-7660	245	9	transformation	transformation	NOUN
ap-7660	245	10	,	,	PUNCT
ap-7660	245	11	which	which	PRON
ap-7660	245	12	is	be	AUX
ap-7660	245	13	to	to	PART
ap-7660	245	14	preserve	preserve	VERB
ap-7660	245	15	the	the	DET
ap-7660	245	16	energy	energy	NOUN
ap-7660	245	17	of	of	ADP
ap-7660	245	18	the	the	DET
ap-7660	245	19	transformed	transform	VERB
ap-7660	245	20	hamiltonian	hamiltonian	NOUN
ap-7660	245	21	.	.	PUNCT
ap-7660	246	1	in	in	ADP
ap-7660	246	2	the	the	DET
ap-7660	246	3	next	next	ADJ
ap-7660	246	4	section	section	NOUN
ap-7660	246	5	,	,	PUNCT
ap-7660	246	6	we	we	PRON
ap-7660	246	7	will	will	AUX
ap-7660	246	8	investigate	investigate	VERB
ap-7660	246	9	in	in	ADP
ap-7660	246	10	detail	detail	NOUN
ap-7660	246	11	how	how	SCONJ
ap-7660	246	12	the	the	DET
ap-7660	246	13	solution	solution	NOUN
ap-7660	246	14	changes	change	VERB
ap-7660	246	15	and	and	CCONJ
ap-7660	246	16	a	a	DET
ap-7660	246	17	new	new	ADJ
ap-7660	246	18	cpt	cpt	NOUN
ap-7660	246	19	symmetry	symmetry	NOUN
ap-7660	246	20	emerges	emerge	VERB
ap-7660	246	21	by	by	ADP
ap-7660	246	22	changing	change	VERB
ap-7660	246	23	the	the	DET
ap-7660	246	24	parameter	parameter	NOUN
ap-7660	246	25	values	value	NOUN
ap-7660	246	26	.	.	PUNCT
ap-7660	247	1	202	202	NUM
ap-7660	247	2	vol	vol	NOUN
ap-7660	247	3	.	.	PUNCT
ap-7660	248	1	62	62	NUM
ap-7660	248	2	no	no	INTJ
ap-7660	248	3	.	.	PUNCT
ap-7660	249	1	1/2022	1/2022	NUM
ap-7660	249	2	complex	complex	ADJ
ap-7660	249	3	topological	topological	ADJ
ap-7660	249	4	soliton	soliton	NOUN
ap-7660	249	5	with	with	ADP
ap-7660	249	6	real	real	ADJ
ap-7660	249	7	energy	energy	NOUN
ap-7660	249	8	in	in	ADP
ap-7660	249	9	particle	particle	NOUN
ap-7660	249	10	physics	physics	NOUN
ap-7660	249	11	figure	figure	NOUN
ap-7660	249	12	1	1	NUM
ap-7660	249	13	.	.	PUNCT
ap-7660	249	14	monopole	monopole	NOUN
ap-7660	249	15	,	,	PUNCT
ap-7660	249	16	gauge	gauge	NOUN
ap-7660	249	17	and	and	CCONJ
ap-7660	249	18	higgs	higgs	PROPN
ap-7660	249	19	masses	masse	NOUN
ap-7660	249	20	plotted	plot	VERB
ap-7660	249	21	for	for	ADP
ap-7660	249	22	m2	m2	PROPN
ap-7660	249	23	1	1	NUM
ap-7660	249	24	/	/	SYM
ap-7660	249	25	g	g	NOUN
ap-7660	249	26	=	=	SYM
ap-7660	249	27	−0.44	−0.44	NOUN
ap-7660	249	28	,	,	PUNCT
ap-7660	249	29	µ/g	µ/g	PROPN
ap-7660	249	30	=	=	SYM
ap-7660	249	31	−0.14	−0.14	PROPN
ap-7660	249	32	,	,	PUNCT
ap-7660	249	33	e	e	X
ap-7660	249	34	=	=	SYM
ap-7660	249	35	2	2	NUM
ap-7660	249	36	,	,	PUNCT
ap-7660	249	37	c1	c1	NOUN
ap-7660	249	38	=	=	PROPN
ap-7660	249	39	−c2	−c2	PROPN
ap-7660	249	40	=	=	PUNCT
ap-7660	249	41	−1	−1	NOUN
ap-7660	249	42	.	.	PUNCT
ap-7660	250	1	the	the	DET
ap-7660	250	2	solid	solid	ADJ
ap-7660	250	3	line	line	NOUN
ap-7660	250	4	represents	represent	VERB
ap-7660	250	5	the	the	DET
ap-7660	250	6	real	real	ADJ
ap-7660	250	7	part	part	NOUN
ap-7660	250	8	,	,	PUNCT
ap-7660	250	9	and	and	CCONJ
ap-7660	250	10	the	the	DET
ap-7660	250	11	dotted	dotted	ADJ
ap-7660	250	12	line	line	NOUN
ap-7660	250	13	represents	represent	VERB
ap-7660	250	14	the	the	DET
ap-7660	250	15	imaginary	imaginary	ADJ
ap-7660	250	16	part	part	NOUN
ap-7660	250	17	of	of	ADP
ap-7660	250	18	the	the	DET
ap-7660	250	19	masses	masse	NOUN
ap-7660	250	20	.	.	PUNCT
ap-7660	251	1	the	the	DET
ap-7660	251	2	dotted	dotted	ADJ
ap-7660	251	3	vertical	vertical	ADJ
ap-7660	251	4	lines	line	NOUN
ap-7660	251	5	indicate	indicate	VERB
ap-7660	251	6	the	the	DET
ap-7660	251	7	boundaries	boundary	NOUN
ap-7660	251	8	of	of	ADP
ap-7660	251	9	the	the	DET
ap-7660	251	10	physical	physical	ADJ
ap-7660	251	11	regions	region	NOUN
ap-7660	251	12	where	where	SCONJ
ap-7660	251	13	all	all	DET
ap-7660	251	14	the	the	DET
ap-7660	251	15	masses	masse	NOUN
ap-7660	251	16	acquire	acquire	VERB
ap-7660	251	17	real	real	ADJ
ap-7660	251	18	positive	positive	ADJ
ap-7660	251	19	values	value	NOUN
ap-7660	251	20	.	.	PUNCT
ap-7660	252	1	3	3	X
ap-7660	252	2	.	.	NOUN
ap-7660	252	3	results	result	NOUN
ap-7660	252	4	and	and	CCONJ
ap-7660	252	5	discussion	discussion	NOUN
ap-7660	252	6	this	this	DET
ap-7660	252	7	section	section	NOUN
ap-7660	252	8	will	will	AUX
ap-7660	252	9	investigate	investigate	VERB
ap-7660	252	10	the	the	DET
ap-7660	252	11	behaviour	behaviour	NOUN
ap-7660	252	12	of	of	ADP
ap-7660	252	13	solution	solution	NOUN
ap-7660	252	14	(	(	PUNCT
ap-7660	252	15	43	43	NUM
ap-7660	252	16	)	)	PUNCT
ap-7660	252	17	in	in	ADP
ap-7660	252	18	different	different	ADJ
ap-7660	252	19	regimes	regime	NOUN
ap-7660	252	20	of	of	ADP
ap-7660	252	21	the	the	DET
ap-7660	252	22	parameter	parameter	NOUN
ap-7660	252	23	spaces	space	VERB
ap-7660	252	24	.	.	PUNCT
ap-7660	253	1	we	we	PRON
ap-7660	253	2	will	will	AUX
ap-7660	253	3	compare	compare	VERB
ap-7660	253	4	the	the	DET
ap-7660	253	5	physical	physical	ADJ
ap-7660	253	6	regions	region	NOUN
ap-7660	253	7	of	of	ADP
ap-7660	253	8	gauge	gauge	ADJ
ap-7660	253	9	particles	particle	NOUN
ap-7660	253	10	,	,	PUNCT
ap-7660	253	11	higgs	higgs	NOUN
ap-7660	253	12	particles	particle	NOUN
ap-7660	253	13	and	and	CCONJ
ap-7660	253	14	monopoles	monopole	NOUN
ap-7660	253	15	found	find	VERB
ap-7660	253	16	in	in	ADP
ap-7660	253	17	the	the	DET
ap-7660	253	18	previous	previous	ADJ
ap-7660	253	19	section	section	NOUN
ap-7660	253	20	.	.	PUNCT
ap-7660	254	1	we	we	PRON
ap-7660	254	2	will	will	AUX
ap-7660	254	3	see	see	VERB
ap-7660	254	4	that	that	SCONJ
ap-7660	254	5	the	the	DET
ap-7660	254	6	two	two	NUM
ap-7660	254	7	regions	region	NOUN
ap-7660	254	8	coincide	coincide	NOUN
ap-7660	254	9	,	,	PUNCT
ap-7660	254	10	but	but	CCONJ
ap-7660	254	11	the	the	DET
ap-7660	254	12	solutions	solution	NOUN
ap-7660	254	13	in	in	ADP
ap-7660	254	14	different	different	ADJ
ap-7660	254	15	regions	region	NOUN
ap-7660	254	16	possess	possess	VERB
ap-7660	254	17	different	different	ADJ
ap-7660	254	18	cpt	cpt	NOUN
ap-7660	254	19	symmetries	symmetry	NOUN
ap-7660	254	20	.	.	PUNCT
ap-7660	255	1	different	different	ADJ
ap-7660	255	2	symmetries	symmetry	NOUN
ap-7660	255	3	of	of	ADP
ap-7660	255	4	solutions	solution	NOUN
ap-7660	255	5	in	in	ADP
ap-7660	255	6	different	different	ADJ
ap-7660	255	7	regions	region	NOUN
ap-7660	255	8	are	be	AUX
ap-7660	255	9	not	not	PART
ap-7660	255	10	coincident	coincident	ADJ
ap-7660	255	11	,	,	PUNCT
ap-7660	255	12	but	but	CCONJ
ap-7660	255	13	the	the	DET
ap-7660	255	14	consequence	consequence	NOUN
ap-7660	255	15	of	of	ADP
ap-7660	255	16	the	the	DET
ap-7660	255	17	three	three	NUM
ap-7660	255	18	reality	reality	NOUN
ap-7660	255	19	conditions	condition	NOUN
ap-7660	255	20	stated	state	VERB
ap-7660	255	21	in	in	ADP
ap-7660	255	22	the	the	DET
ap-7660	255	23	introduction	introduction	NOUN
ap-7660	255	24	.	.	PUNCT
ap-7660	256	1	in	in	ADP
ap-7660	256	2	fact	fact	NOUN
ap-7660	256	3	,	,	PUNCT
ap-7660	256	4	it	it	PRON
ap-7660	256	5	is	be	AUX
ap-7660	256	6	deeply	deeply	ADV
ap-7660	256	7	related	relate	VERB
ap-7660	256	8	to	to	ADP
ap-7660	256	9	the	the	DET
ap-7660	256	10	real	real	ADJ
ap-7660	256	11	value	value	NOUN
ap-7660	256	12	of	of	ADP
ap-7660	256	13	energy	energy	NOUN
ap-7660	256	14	,	,	PUNCT
ap-7660	256	15	which	which	PRON
ap-7660	256	16	will	will	AUX
ap-7660	256	17	be	be	AUX
ap-7660	256	18	discussed	discuss	VERB
ap-7660	256	19	extensively	extensively	ADV
ap-7660	256	20	in	in	ADP
ap-7660	256	21	[	[	X
ap-7660	256	22	30	30	NUM
ap-7660	256	23	]	]	SYM
ap-7660	256	24	.	.	PUNCT
ap-7660	257	1	3.1	3.1	NUM
ap-7660	257	2	.	.	PUNCT
ap-7660	257	3	higgs	higgs	PROPN
ap-7660	257	4	mass	mass	PROPN
ap-7660	257	5	and	and	CCONJ
ap-7660	257	6	exceptional	exceptional	ADJ
ap-7660	257	7	points	point	NOUN
ap-7660	257	8	let	let	VERB
ap-7660	257	9	us	we	PRON
ap-7660	257	10	recall	recall	VERB
ap-7660	257	11	the	the	DET
ap-7660	257	12	masses	masse	NOUN
ap-7660	257	13	of	of	ADP
ap-7660	257	14	the	the	DET
ap-7660	257	15	particles	particle	NOUN
ap-7660	257	16	and	and	CCONJ
ap-7660	257	17	monopole	monopole	NOUN
ap-7660	257	18	m2	m2	PROPN
ap-7660	257	19	0	0	PUNCT
ap-7660	258	1	=	=	PROPN
ap-7660	258	2	c2	c2	PROPN
ap-7660	258	3	µ4−m4	µ4−m4	NUM
ap-7660	258	4	2	2	NUM
ap-7660	258	5	m2	m2	PROPN
ap-7660	258	6	2	2	NUM
ap-7660	258	7	,	,	PUNCT
ap-7660	258	8	m2	m2	PROPN
ap-7660	258	9	±	±	PROPN
ap-7660	258	10	=	=	SYM
ap-7660	258	11	k	k	PROPN
ap-7660	258	12	±	±	PROPN
ap-7660	258	13	√	√	PROPN
ap-7660	258	14	k2	k2	PROPN
ap-7660	258	15	+	+	CCONJ
ap-7660	258	16	2l	2l	NUM
ap-7660	258	17	,	,	PUNCT
ap-7660	258	18	(	(	PUNCT
ap-7660	258	19	44	44	NUM
ap-7660	258	20	)	)	PUNCT
ap-7660	258	21	mg	mg	PROPN
ap-7660	259	1	=	=	SYM
ap-7660	259	2	e	e	X
ap-7660	259	3	rl	rl	PROPN
ap-7660	259	4	m2	m2	PROPN
ap-7660	259	5	2	2	NUM
ap-7660	259	6	,	,	PUNCT
ap-7660	259	7	mmono	mmono	NOUN
ap-7660	259	8	=	=	SYM
ap-7660	259	9	8|n|πlr	8|n|πlr	NUM
ap-7660	259	10	em2	em2	NOUN
ap-7660	259	11	2	2	NUM
ap-7660	259	12	.	.	PUNCT
ap-7660	260	1	where	where	SCONJ
ap-7660	260	2	k	k	NOUN
ap-7660	260	3	=	=	PUNCT
ap-7660	260	4	c1m2	c1m2	ADP
ap-7660	260	5	1	1	NUM
ap-7660	260	6	−	−	PROPN
ap-7660	260	7	c2	c2	PROPN
ap-7660	260	8	m2	m2	PROPN
ap-7660	260	9	2	2	NUM
ap-7660	260	10	2	2	NUM
ap-7660	260	11	+	+	NUM
ap-7660	260	12	3µ4	3µ4	NUM
ap-7660	260	13	2c2m2	2c2m2	NUM
ap-7660	260	14	2	2	NUM
ap-7660	260	15	and	and	CCONJ
ap-7660	260	16	l	l	NOUN
ap-7660	260	17	=	=	PUNCT
ap-7660	260	18	µ4	µ4	PROPN
ap-7660	260	19	+	+	NUM
ap-7660	260	20	c1c2m2	c1c2m2	PROPN
ap-7660	260	21	1m2	1m2	NUM
ap-7660	260	22	2	2	NUM
ap-7660	260	23	.	.	PUNCT
ap-7660	260	24	notice	notice	VERB
ap-7660	260	25	that	that	SCONJ
ap-7660	260	26	the	the	DET
ap-7660	260	27	masses	masse	NOUN
ap-7660	260	28	do	do	AUX
ap-7660	260	29	not	not	PART
ap-7660	260	30	depend	depend	VERB
ap-7660	260	31	on	on	ADP
ap-7660	260	32	c3	c3	PROPN
ap-7660	260	33	,	,	PUNCT
ap-7660	260	34	meaning	mean	VERB
ap-7660	260	35	they	they	PRON
ap-7660	260	36	do	do	AUX
ap-7660	260	37	not	not	PART
ap-7660	260	38	depend	depend	VERB
ap-7660	260	39	on	on	ADP
ap-7660	260	40	the	the	DET
ap-7660	260	41	similarity	similarity	NOUN
ap-7660	260	42	transformation	transformation	NOUN
ap-7660	260	43	as	as	SCONJ
ap-7660	260	44	expected	expect	VERB
ap-7660	260	45	.	.	PUNCT
ap-7660	261	1	we	we	PRON
ap-7660	261	2	also	also	ADV
ap-7660	261	3	comment	comment	VERB
ap-7660	261	4	that	that	SCONJ
ap-7660	261	5	in	in	ADP
ap-7660	261	6	the	the	DET
ap-7660	261	7	bps	bps	NOUN
ap-7660	261	8	limit	limit	NOUN
ap-7660	261	9	,	,	PUNCT
ap-7660	261	10	we	we	PRON
ap-7660	261	11	have	have	VERB
ap-7660	261	12	m0	m0	NOUN
ap-7660	261	13	=	=	SYM
ap-7660	261	14	m±	m±	PROPN
ap-7660	261	15	=	=	SYM
ap-7660	261	16	0	0	NUM
ap-7660	261	17	,	,	PUNCT
ap-7660	261	18	but	but	CCONJ
ap-7660	261	19	mg	mg	PROPN
ap-7660	261	20	and	and	CCONJ
ap-7660	261	21	m±	m±	PROPN
ap-7660	261	22	stays	stay	NOUN
ap-7660	261	23	finite	finite	PROPN
ap-7660	261	24	,	,	PUNCT
ap-7660	261	25	such	such	ADJ
ap-7660	261	26	that	that	SCONJ
ap-7660	261	27	the	the	DET
ap-7660	261	28	ratios	ratio	NOUN
ap-7660	261	29	mhiggs	mhiggs	PROPN
ap-7660	261	30	/	/	SYM
ap-7660	261	31	mg	mg	PROPN
ap-7660	261	32	vanish	vanish	VERB
ap-7660	261	33	in	in	ADP
ap-7660	261	34	the	the	DET
ap-7660	261	35	bps	bps	NOUN
ap-7660	261	36	limit	limit	NOUN
ap-7660	261	37	.	.	PUNCT
ap-7660	262	1	this	this	PRON
ap-7660	262	2	is	be	AUX
ap-7660	262	3	in	in	ADP
ap-7660	262	4	line	line	NOUN
ap-7660	262	5	with	with	ADP
ap-7660	262	6	the	the	DET
ap-7660	262	7	hermitian	hermitian	ADJ
ap-7660	262	8	case	case	NOUN
ap-7660	262	9	[	[	X
ap-7660	262	10	29	29	NUM
ap-7660	262	11	]	]	PUNCT
ap-7660	262	12	,	,	PUNCT
ap-7660	262	13	providing	provide	VERB
ap-7660	262	14	the	the	DET
ap-7660	262	15	physical	physical	ADJ
ap-7660	262	16	interpretation	interpretation	NOUN
ap-7660	262	17	with	with	ADP
ap-7660	262	18	mhiggs	mhigg	NOUN
ap-7660	262	19	<	<	X
ap-7660	262	20	<	<	X
ap-7660	262	21	mg	mg	PROPN
ap-7660	262	22	for	for	ADP
ap-7660	262	23	the	the	DET
ap-7660	262	24	bps	bps	NOUN
ap-7660	262	25	limit	limit	NOUN
ap-7660	262	26	.	.	PUNCT
ap-7660	263	1	one	one	PRON
ap-7660	263	2	may	may	AUX
ap-7660	263	3	notice	notice	VERB
ap-7660	263	4	that	that	SCONJ
ap-7660	263	5	when	when	SCONJ
ap-7660	263	6	c2	c2	PROPN
ap-7660	263	7	=	=	SYM
ap-7660	263	8	1	1	NUM
ap-7660	263	9	,	,	PUNCT
ap-7660	263	10	requiring	require	VERB
ap-7660	263	11	positive	positive	ADJ
ap-7660	263	12	mass	mass	NOUN
ap-7660	263	13	m2	m2	PROPN
ap-7660	263	14	0	0	PUNCT
ap-7660	263	15	>	>	X
ap-7660	263	16	0	0	PROPN
ap-7660	263	17	,	,	PUNCT
ap-7660	263	18	implies	imply	VERB
ap-7660	263	19	that	that	SCONJ
ap-7660	263	20	µ4	µ4	PROPN
ap-7660	263	21	−	−	PROPN
ap-7660	263	22	m4	m4	PROPN
ap-7660	263	23	2	2	NUM
ap-7660	263	24	>	>	X
ap-7660	263	25	0	0	NUM
ap-7660	263	26	.	.	PUNCT
ap-7660	264	1	this	this	PRON
ap-7660	264	2	means	mean	VERB
ap-7660	264	3	the	the	DET
ap-7660	264	4	quantity	quantity	NOUN
ap-7660	264	5	l	l	NOUN
ap-7660	264	6	=	=	PUNCT
ap-7660	264	7	√	√	PUNCT
ap-7660	264	8	m4	m4	PROPN
ap-7660	264	9	2	2	NUM
ap-7660	264	10	−	−	PROPN
ap-7660	264	11	µ4	µ4	PROPN
ap-7660	264	12	is	be	AUX
ap-7660	264	13	purely	purely	ADV
ap-7660	264	14	imaginary	imaginary	ADJ
ap-7660	264	15	.	.	PUNCT
ap-7660	265	1	one	one	PRON
ap-7660	265	2	may	may	AUX
ap-7660	265	3	then	then	ADV
ap-7660	265	4	discard	discard	VERB
ap-7660	265	5	this	this	DET
ap-7660	265	6	region	region	NOUN
ap-7660	265	7	as	as	ADP
ap-7660	265	8	unphysical	unphysical	ADJ
ap-7660	265	9	.	.	PUNCT
ap-7660	266	1	however	however	ADV
ap-7660	266	2	,	,	PUNCT
ap-7660	266	3	we	we	PRON
ap-7660	266	4	will	will	AUX
ap-7660	266	5	see	see	VERB
ap-7660	266	6	in	in	ADP
ap-7660	266	7	the	the	DET
ap-7660	266	8	next	next	ADJ
ap-7660	266	9	section	section	NOUN
ap-7660	266	10	that	that	SCONJ
ap-7660	266	11	there	there	PRON
ap-7660	266	12	is	be	VERB
ap-7660	266	13	a	a	DET
ap-7660	266	14	disconnected	disconnected	ADJ
ap-7660	266	15	region	region	NOUN
ap-7660	266	16	beyond	beyond	ADP
ap-7660	266	17	µ4	µ4	PROPN
ap-7660	266	18	−	−	PROPN
ap-7660	266	19	m4	m4	PROPN
ap-7660	266	20	2	2	NUM
ap-7660	266	21	>	>	SYM
ap-7660	266	22	0	0	NUM
ap-7660	266	23	,	,	PUNCT
ap-7660	266	24	which	which	PRON
ap-7660	266	25	admit	admit	VERB
ap-7660	266	26	real	real	ADJ
ap-7660	266	27	energy	energy	NOUN
ap-7660	266	28	because	because	SCONJ
ap-7660	266	29	r	r	NOUN
ap-7660	266	30	also	also	ADV
ap-7660	266	31	becomes	become	VERB
ap-7660	266	32	purely	purely	ADV
ap-7660	266	33	complex	complex	ADJ
ap-7660	266	34	.	.	PUNCT
ap-7660	267	1	this	this	PRON
ap-7660	267	2	is	be	AUX
ap-7660	267	3	not	not	PART
ap-7660	267	4	coincident	coincident	ADJ
ap-7660	267	5	,	,	PUNCT
ap-7660	267	6	and	and	CCONJ
ap-7660	267	7	in	in	ADP
ap-7660	267	8	fact	fact	NOUN
ap-7660	267	9	,	,	PUNCT
ap-7660	267	10	we	we	PRON
ap-7660	267	11	will	will	AUX
ap-7660	267	12	see	see	VERB
ap-7660	267	13	an	an	DET
ap-7660	267	14	emerging	emerge	VERB
ap-7660	267	15	new	new	ADJ
ap-7660	267	16	cpt	cpt	NOUN
ap-7660	267	17	symmetry	symmetry	NOUN
ap-7660	267	18	for	for	ADP
ap-7660	267	19	the	the	DET
ap-7660	267	20	monopoles	monopole	NOUN
ap-7660	267	21	.	.	PUNCT
ap-7660	268	1	in	in	ADP
ap-7660	268	2	the	the	DET
ap-7660	268	3	rest	rest	NOUN
ap-7660	268	4	of	of	ADP
ap-7660	268	5	the	the	DET
ap-7660	268	6	section	section	NOUN
ap-7660	268	7	,	,	PUNCT
ap-7660	268	8	we	we	PRON
ap-7660	268	9	will	will	AUX
ap-7660	268	10	exclusively	exclusively	ADV
ap-7660	268	11	focus	focus	VERB
ap-7660	268	12	on	on	ADP
ap-7660	268	13	the	the	DET
ap-7660	268	14	monopole	monopole	NOUN
ap-7660	268	15	and	and	CCONJ
ap-7660	268	16	gauge	gauge	ADJ
ap-7660	268	17	masses	masse	NOUN
ap-7660	268	18	.	.	PUNCT
ap-7660	269	1	the	the	DET
ap-7660	269	2	main	main	ADJ
ap-7660	269	3	message	message	NOUN
ap-7660	269	4	of	of	ADP
ap-7660	269	5	this	this	DET
ap-7660	269	6	section	section	NOUN
ap-7660	269	7	is	be	AUX
ap-7660	269	8	the	the	DET
ap-7660	269	9	emerging	emerge	VERB
ap-7660	269	10	symmetry	symmetry	NOUN
ap-7660	269	11	responsible	responsible	ADJ
ap-7660	269	12	for	for	ADP
ap-7660	269	13	the	the	DET
ap-7660	269	14	real	real	ADJ
ap-7660	269	15	value	value	NOUN
ap-7660	269	16	of	of	ADP
ap-7660	269	17	the	the	DET
ap-7660	269	18	monopole	monopole	ADJ
ap-7660	269	19	masses	masse	NOUN
ap-7660	269	20	.	.	PUNCT
ap-7660	270	1	the	the	DET
ap-7660	270	2	requirement	requirement	NOUN
ap-7660	270	3	to	to	PART
ap-7660	270	4	make	make	VERB
ap-7660	270	5	the	the	DET
ap-7660	270	6	whole	whole	ADJ
ap-7660	270	7	theory	theory	NOUN
ap-7660	270	8	physical	physical	ADJ
ap-7660	270	9	demands	demand	NOUN
ap-7660	270	10	also	also	ADV
ap-7660	270	11	to	to	PART
ap-7660	270	12	consider	consider	VERB
ap-7660	270	13	the	the	DET
ap-7660	270	14	intersection	intersection	NOUN
ap-7660	270	15	of	of	ADP
ap-7660	270	16	the	the	DET
ap-7660	270	17	physical	physical	ADJ
ap-7660	270	18	regions	region	NOUN
ap-7660	270	19	between	between	ADP
ap-7660	270	20	monopole	monopole	ADJ
ap-7660	270	21	masses	masse	NOUN
ap-7660	270	22	and	and	CCONJ
ap-7660	270	23	higgs	higgs	NOUN
ap-7660	270	24	masses	masse	NOUN
ap-7660	270	25	.	.	PUNCT
ap-7660	271	1	as	as	ADP
ap-7660	271	2	an	an	DET
ap-7660	271	3	example	example	NOUN
ap-7660	271	4	,	,	PUNCT
ap-7660	271	5	we	we	PRON
ap-7660	271	6	plot	plot	VERB
ap-7660	271	7	all	all	DET
ap-7660	271	8	the	the	DET
ap-7660	271	9	masses	masse	NOUN
ap-7660	271	10	of	of	ADP
ap-7660	271	11	the	the	DET
ap-7660	271	12	theory	theory	NOUN
ap-7660	271	13	in	in	ADP
ap-7660	271	14	figure	figure	NOUN
ap-7660	271	15	1	1	NUM
ap-7660	271	16	.	.	PUNCT
ap-7660	272	1	as	as	SCONJ
ap-7660	272	2	one	one	PRON
ap-7660	272	3	can	can	AUX
ap-7660	272	4	see	see	VERB
ap-7660	272	5	,	,	PUNCT
ap-7660	272	6	intersection	intersection	NOUN
ap-7660	272	7	points	point	NOUN
ap-7660	272	8	of	of	ADP
ap-7660	272	9	the	the	DET
ap-7660	272	10	physical	physical	ADJ
ap-7660	272	11	regions	region	NOUN
ap-7660	272	12	of	of	ADP
ap-7660	272	13	higgs	higgs	NOUN
ap-7660	272	14	masses	masse	NOUN
ap-7660	272	15	and	and	CCONJ
ap-7660	272	16	monopole	monopole	NOUN
ap-7660	272	17	/	/	SYM
ap-7660	272	18	gauge	gauge	NOUN
ap-7660	272	19	masses	masse	NOUN
ap-7660	272	20	are	be	AUX
ap-7660	272	21	non	non	ADJ
ap-7660	272	22	-	-	ADJ
ap-7660	272	23	trivial	trivial	ADJ
ap-7660	272	24	.	.	PUNCT
ap-7660	273	1	in	in	ADP
ap-7660	273	2	fact	fact	NOUN
ap-7660	273	3	,	,	PUNCT
ap-7660	273	4	they	they	PRON
ap-7660	273	5	are	be	AUX
ap-7660	273	6	bounded	bound	VERB
ap-7660	273	7	by	by	ADP
ap-7660	273	8	two	two	NUM
ap-7660	273	9	types	type	NOUN
ap-7660	273	10	of	of	ADP
ap-7660	273	11	exceptional	exceptional	ADJ
ap-7660	273	12	points	point	NOUN
ap-7660	273	13	.	.	PUNCT
ap-7660	274	1	the	the	DET
ap-7660	274	2	first	first	ADJ
ap-7660	274	3	type	type	NOUN
ap-7660	274	4	is	be	AUX
ap-7660	274	5	when	when	SCONJ
ap-7660	274	6	two	two	NUM
ap-7660	274	7	masses	masse	NOUN
ap-7660	274	8	of	of	ADP
ap-7660	274	9	higgs	higgs	NOUN
ap-7660	274	10	particles	particle	NOUN
ap-7660	274	11	coincide	coincide	VERB
ap-7660	274	12	and	and	CCONJ
ap-7660	274	13	form	form	VERB
ap-7660	274	14	a	a	DET
ap-7660	274	15	complex	complex	ADJ
ap-7660	274	16	conjugate	conjugate	ADJ
ap-7660	274	17	pair	pair	NOUN
ap-7660	274	18	.	.	PUNCT
ap-7660	275	1	such	such	DET
ap-7660	275	2	a	a	DET
ap-7660	275	3	point	point	NOUN
ap-7660	275	4	is	be	AUX
ap-7660	275	5	known	know	VERB
ap-7660	275	6	as	as	ADP
ap-7660	275	7	an	an	DET
ap-7660	275	8	exceptional	exceptional	ADJ
ap-7660	275	9	point	point	NOUN
ap-7660	275	10	where	where	SCONJ
ap-7660	275	11	the	the	DET
ap-7660	275	12	mass	mass	ADJ
ap-7660	275	13	matrix	matrix	NOUN
ap-7660	275	14	is	be	AUX
ap-7660	275	15	non	non	ADJ
ap-7660	275	16	-	-	ADJ
ap-7660	275	17	diagonalisable	diagonalisable	ADJ
ap-7660	275	18	,	,	PUNCT
ap-7660	275	19	and	and	CCONJ
ap-7660	275	20	the	the	DET
ap-7660	275	21	corresponding	corresponding	ADJ
ap-7660	275	22	eigenvectors	eigenvector	NOUN
ap-7660	275	23	coincide	coincide	VERB
ap-7660	275	24	.	.	PUNCT
ap-7660	276	1	the	the	DET
ap-7660	276	2	second	second	ADJ
ap-7660	276	3	type	type	NOUN
ap-7660	276	4	is	be	AUX
ap-7660	276	5	when	when	SCONJ
ap-7660	276	6	the	the	DET
ap-7660	276	7	gauge	gauge	NOUN
ap-7660	276	8	and	and	CCONJ
ap-7660	276	9	the	the	DET
ap-7660	276	10	monopole	monopole	ADJ
ap-7660	276	11	masses	masse	NOUN
ap-7660	276	12	vanishes	vanish	VERB
ap-7660	276	13	.	.	PUNCT
ap-7660	277	1	interestingly	interestingly	ADV
ap-7660	277	2	,	,	PUNCT
ap-7660	277	3	this	this	PRON
ap-7660	277	4	is	be	AUX
ap-7660	277	5	where	where	SCONJ
ap-7660	277	6	one	one	NUM
ap-7660	277	7	of	of	ADP
ap-7660	277	8	the	the	DET
ap-7660	277	9	higgs	higgs	NOUN
ap-7660	277	10	masses	masse	NOUN
ap-7660	277	11	also	also	ADV
ap-7660	277	12	vanish	vanish	VERB
ap-7660	277	13	.	.	PUNCT
ap-7660	278	1	since	since	SCONJ
ap-7660	278	2	the	the	DET
ap-7660	278	3	mass	mass	ADJ
ap-7660	278	4	matrix	matrix	NOUN
ap-7660	278	5	already	already	ADV
ap-7660	278	6	has	have	VERB
ap-7660	278	7	a	a	DET
ap-7660	278	8	zero	zero	NUM
ap-7660	278	9	eigenvalue	eigenvalue	NOUN
ap-7660	278	10	,	,	PUNCT
ap-7660	278	11	as	as	ADP
ap-7660	278	12	the	the	DET
ap-7660	278	13	result	result	NOUN
ap-7660	278	14	of	of	ADP
ap-7660	278	15	the	the	DET
ap-7660	278	16	spontaneous	spontaneous	ADJ
ap-7660	278	17	symmetry	symmetry	NOUN
ap-7660	278	18	breaking	breaking	NOUN
ap-7660	278	19	,	,	PUNCT
ap-7660	278	20	it	it	PRON
ap-7660	278	21	seems	seem	VERB
ap-7660	278	22	the	the	DET
ap-7660	278	23	number	number	NOUN
ap-7660	278	24	of	of	ADP
ap-7660	278	25	massless	massless	NOUN
ap-7660	278	26	fields	field	NOUN
ap-7660	278	27	is	be	AUX
ap-7660	278	28	increased	increase	VERB
ap-7660	278	29	.	.	PUNCT
ap-7660	279	1	however	however	ADV
ap-7660	279	2	,	,	PUNCT
ap-7660	279	3	at	at	ADP
ap-7660	279	4	this	this	DET
ap-7660	279	5	point	point	NOUN
ap-7660	279	6	,	,	PUNCT
ap-7660	279	7	the	the	DET
ap-7660	279	8	mass	mass	ADJ
ap-7660	279	9	matrix	matrix	NOUN
ap-7660	279	10	is	be	AUX
ap-7660	279	11	also	also	ADV
ap-7660	279	12	non	non	ADJ
ap-7660	279	13	-	-	ADJ
ap-7660	279	14	diagonalisable	diagonalisable	ADJ
ap-7660	279	15	.	.	PUNCT
ap-7660	280	1	therefore	therefore	ADV
ap-7660	280	2	one	one	PRON
ap-7660	280	3	can	can	AUX
ap-7660	280	4	not	not	PART
ap-7660	280	5	diagonalise	diagonalise	VERB
ap-7660	280	6	the	the	DET
ap-7660	280	7	hamiltonian	hamiltonian	NOUN
ap-7660	280	8	to	to	PART
ap-7660	280	9	identify	identify	VERB
ap-7660	280	10	the	the	DET
ap-7660	280	11	field	field	NOUN
ap-7660	280	12	which	which	PRON
ap-7660	280	13	corresponds	correspond	VERB
ap-7660	280	14	to	to	ADP
ap-7660	280	15	the	the	DET
ap-7660	280	16	extra	extra	ADJ
ap-7660	280	17	massless	massless	ADJ
ap-7660	280	18	fundamental	fundamental	ADJ
ap-7660	280	19	field	field	NOUN
ap-7660	280	20	.	.	PUNCT
ap-7660	281	1	therefore	therefore	ADV
ap-7660	281	2	this	this	DET
ap-7660	281	3	point	point	NOUN
ap-7660	281	4	is	be	AUX
ap-7660	281	5	also	also	ADV
ap-7660	281	6	an	an	DET
ap-7660	281	7	exceptional	exceptional	ADJ
ap-7660	281	8	point	point	NOUN
ap-7660	281	9	.	.	PUNCT
ap-7660	282	1	however	however	ADV
ap-7660	282	2	,	,	PUNCT
ap-7660	282	3	the	the	DET
ap-7660	282	4	eigenvalues	eigenvalue	NOUN
ap-7660	282	5	do	do	AUX
ap-7660	282	6	not	not	PART
ap-7660	282	7	become	become	VERB
ap-7660	282	8	complex	complex	ADJ
ap-7660	282	9	conjugate	conjugate	ADJ
ap-7660	282	10	pairs	pair	NOUN
ap-7660	282	11	beyond	beyond	ADP
ap-7660	282	12	this	this	DET
ap-7660	282	13	point	point	NOUN
ap-7660	282	14	,	,	PUNCT
ap-7660	282	15	and	and	CCONJ
ap-7660	282	16	as	as	SCONJ
ap-7660	282	17	one	one	PRON
ap-7660	282	18	can	can	AUX
ap-7660	282	19	see	see	VERB
ap-7660	282	20	from	from	ADP
ap-7660	282	21	figure	figure	NOUN
ap-7660	282	22	1	1	NUM
ap-7660	282	23	that	that	SCONJ
ap-7660	282	24	one	one	NUM
ap-7660	282	25	of	of	ADP
ap-7660	282	26	the	the	DET
ap-7660	282	27	mass	mass	PROPN
ap-7660	282	28	square	square	PROPN
ap-7660	282	29	m2	m2	PROPN
ap-7660	282	30	0	0	NUM
ap-7660	282	31	become	become	VERB
ap-7660	282	32	negative	negative	ADJ
ap-7660	282	33	,	,	PUNCT
ap-7660	282	34	and	and	CCONJ
ap-7660	282	35	gauge	gauge	NOUN
ap-7660	282	36	and	and	CCONJ
ap-7660	282	37	monopole	monopole	ADJ
ap-7660	282	38	masses	masse	NOUN
ap-7660	282	39	become	become	VERB
ap-7660	282	40	complex	complex	ADJ
ap-7660	282	41	but	but	CCONJ
ap-7660	282	42	with	with	ADP
ap-7660	282	43	no	no	DET
ap-7660	282	44	conjugate	conjugate	ADJ
ap-7660	282	45	pair	pair	NOUN
ap-7660	282	46	.	.	PUNCT
ap-7660	283	1	we	we	PRON
ap-7660	283	2	dub	dub	VERB
ap-7660	283	3	such	such	DET
ap-7660	283	4	a	a	DET
ap-7660	283	5	point	point	NOUN
ap-7660	283	6	as	as	ADP
ap-7660	283	7	zero	zero	NUM
ap-7660	283	8	exceptional	exceptional	ADJ
ap-7660	283	9	point	point	NOUN
ap-7660	283	10	to	to	PART
ap-7660	283	11	distinguish	distinguish	VERB
ap-7660	283	12	from	from	ADP
ap-7660	283	13	the	the	DET
ap-7660	283	14	standard	standard	ADJ
ap-7660	283	15	exceptional	exceptional	ADJ
ap-7660	283	16	point	point	NOUN
ap-7660	283	17	.	.	PUNCT
ap-7660	284	1	3.2	3.2	NUM
ap-7660	284	2	.	.	PUNCT
ap-7660	285	1	change	change	NOUN
ap-7660	285	2	in	in	ADP
ap-7660	285	3	cpt	cpt	PROPN
ap-7660	285	4	symmetry	symmetry	NOUN
ap-7660	285	5	and	and	CCONJ
ap-7660	285	6	complex	complex	ADJ
ap-7660	285	7	monopole	monopole	ADJ
ap-7660	285	8	solution	solution	NOUN
ap-7660	285	9	we	we	PRON
ap-7660	285	10	begin	begin	VERB
ap-7660	285	11	by	by	ADP
ap-7660	285	12	introducing	introduce	VERB
ap-7660	285	13	the	the	DET
ap-7660	285	14	useful	useful	ADJ
ap-7660	285	15	quantities	quantity	NOUN
ap-7660	285	16	m2	m2	PROPN
ap-7660	285	17	1	1	NUM
ap-7660	285	18	/	/	SYM
ap-7660	285	19	g	g	PROPN
ap-7660	285	20	≡	≡	PROPN
ap-7660	285	21	x	x	PROPN
ap-7660	285	22	,	,	PUNCT
ap-7660	285	23	µ2	µ2	PROPN
ap-7660	285	24	/	/	SYM
ap-7660	285	25	g	g	PROPN
ap-7660	285	26	≡	≡	PROPN
ap-7660	285	27	y	y	PROPN
ap-7660	285	28	,	,	PUNCT
ap-7660	285	29	µ2	µ2	PROPN
ap-7660	285	30	/	/	SYM
ap-7660	285	31	m2	m2	PROPN
ap-7660	285	32	2	2	NUM
ap-7660	285	33	≡	≡	PROPN
ap-7660	285	34	z.	z.	PROPN
ap-7660	286	1	the	the	DET
ap-7660	286	2	gauge	gauge	PROPN
ap-7660	286	3	mass	mass	PROPN
ap-7660	286	4	,	,	PUNCT
ap-7660	286	5	monopole	monopole	ADJ
ap-7660	286	6	mass	mass	NOUN
ap-7660	286	7	and	and	CCONJ
ap-7660	286	8	monopole	monopole	ADJ
ap-7660	286	9	solutions	solution	NOUN
ap-7660	286	10	can	can	AUX
ap-7660	286	11	be	be	AUX
ap-7660	286	12	rewritten	rewrite	VERB
ap-7660	286	13	in	in	ADP
ap-7660	286	14	terms	term	NOUN
ap-7660	286	15	of	of	ADP
ap-7660	286	16	these	these	DET
ap-7660	286	17	quantities	quantity	NOUN
ap-7660	286	18	mg	mg	NOUN
ap-7660	287	1	=	=	SYM
ap-7660	288	1	er	er	INTJ
ap-7660	288	2	√	√	NUM
ap-7660	288	3	1	1	NUM
ap-7660	288	4	−	−	PROPN
ap-7660	288	5	z2	z2	PROPN
ap-7660	288	6	,	,	PUNCT
ap-7660	288	7	mmono	mmono	NOUN
ap-7660	288	8	=	=	SYM
ap-7660	288	9	8|n|πr	8|n|πr	NUM
ap-7660	288	10	e	e	NOUN
ap-7660	288	11	√	√	ADP
ap-7660	288	12	1	1	NUM
ap-7660	288	13	−	−	PROPN
ap-7660	288	14	z2	z2	PROPN
ap-7660	288	15	,	,	PUNCT
ap-7660	288	16	(	(	PUNCT
ap-7660	288	17	45	45	NUM
ap-7660	288	18	)	)	PUNCT
ap-7660	288	19	203	203	NUM
ap-7660	288	20	takanobu	takanobu	PROPN
ap-7660	288	21	taira	taira	PROPN
ap-7660	288	22	acta	acta	PROPN
ap-7660	288	23	polytechnica	polytechnica	PROPN
ap-7660	288	24	figure	figure	NOUN
ap-7660	288	25	2	2	NUM
ap-7660	288	26	.	.	PUNCT
ap-7660	288	27	monopole	monopole	NOUN
ap-7660	288	28	and	and	CCONJ
ap-7660	288	29	gauge	gauge	ADJ
ap-7660	288	30	masses	masse	NOUN
ap-7660	288	31	plotted	plot	VERB
ap-7660	288	32	for	for	ADP
ap-7660	288	33	x	x	SYM
ap-7660	288	34	=	=	SYM
ap-7660	288	35	1	1	NUM
ap-7660	288	36	,	,	PUNCT
ap-7660	288	37	y	y	NOUN
ap-7660	288	38	=	=	NUM
ap-7660	288	39	0.8	0.8	NUM
ap-7660	288	40	,	,	PUNCT
ap-7660	288	41	e	e	X
ap-7660	288	42	=	=	SYM
ap-7660	288	43	2	2	NUM
ap-7660	288	44	,	,	PUNCT
ap-7660	288	45	c1	c1	NOUN
ap-7660	288	46	=	=	PROPN
ap-7660	288	47	−c2	−c2	PROPN
ap-7660	288	48	=	=	PUNCT
ap-7660	289	1	1	1	X
ap-7660	289	2	.	.	PUNCT
ap-7660	290	1	the	the	DET
ap-7660	290	2	solid	solid	ADJ
ap-7660	290	3	line	line	NOUN
ap-7660	290	4	represents	represent	VERB
ap-7660	290	5	the	the	DET
ap-7660	290	6	real	real	ADJ
ap-7660	290	7	part	part	NOUN
ap-7660	290	8	,	,	PUNCT
ap-7660	290	9	and	and	CCONJ
ap-7660	290	10	the	the	DET
ap-7660	290	11	dotted	dotted	ADJ
ap-7660	290	12	line	line	NOUN
ap-7660	290	13	represents	represent	VERB
ap-7660	290	14	the	the	DET
ap-7660	290	15	imaginary	imaginary	ADJ
ap-7660	290	16	part	part	NOUN
ap-7660	290	17	of	of	ADP
ap-7660	290	18	the	the	DET
ap-7660	290	19	masses	masse	NOUN
ap-7660	290	20	.	.	PUNCT
ap-7660	291	1	figure	figure	VERB
ap-7660	291	2	3	3	NUM
ap-7660	291	3	.	.	PUNCT
ap-7660	292	1	both	both	DET
ap-7660	292	2	panels	panel	NOUN
ap-7660	292	3	are	be	AUX
ap-7660	292	4	plotted	plot	VERB
ap-7660	292	5	for	for	ADP
ap-7660	292	6	x	x	SYM
ap-7660	292	7	=	=	SYM
ap-7660	292	8	1	1	NUM
ap-7660	292	9	,	,	PUNCT
ap-7660	292	10	y	y	NOUN
ap-7660	292	11	=	=	PUNCT
ap-7660	292	12	0.8	0.8	NUM
ap-7660	292	13	,	,	PUNCT
ap-7660	292	14	n	n	NOUN
ap-7660	292	15	=	=	SYM
ap-7660	292	16	1	1	NUM
ap-7660	292	17	,	,	PUNCT
ap-7660	293	1	e	e	NOUN
ap-7660	293	2	=	=	SYM
ap-7660	293	3	2	2	X
ap-7660	293	4	.	.	PUNCT
ap-7660	294	1	the	the	DET
ap-7660	294	2	solid	solid	ADJ
ap-7660	294	3	line	line	NOUN
ap-7660	294	4	represents	represent	VERB
ap-7660	294	5	the	the	DET
ap-7660	294	6	real	real	ADJ
ap-7660	294	7	part	part	NOUN
ap-7660	294	8	,	,	PUNCT
ap-7660	294	9	and	and	CCONJ
ap-7660	294	10	the	the	DET
ap-7660	294	11	dotted	dotted	ADJ
ap-7660	294	12	line	line	NOUN
ap-7660	294	13	represents	represent	VERB
ap-7660	294	14	the	the	DET
ap-7660	294	15	imaginary	imaginary	ADJ
ap-7660	294	16	part	part	NOUN
ap-7660	294	17	of	of	ADP
ap-7660	294	18	the	the	DET
ap-7660	294	19	masses	masse	NOUN
ap-7660	294	20	.	.	PUNCT
ap-7660	295	1	panel	panel	NOUN
ap-7660	295	2	(	(	PUNCT
ap-7660	295	3	a	a	X
ap-7660	295	4	)	)	PUNCT
ap-7660	295	5	shows	show	VERB
ap-7660	295	6	the	the	DET
ap-7660	295	7	monopole	monopole	NOUN
ap-7660	295	8	and	and	CCONJ
ap-7660	295	9	gauge	gauge	ADJ
ap-7660	295	10	masses	masse	NOUN
ap-7660	295	11	against	against	ADP
ap-7660	295	12	z	z	PROPN
ap-7660	295	13	≥	≥	NUM
ap-7660	295	14	0	0	NUM
ap-7660	295	15	,	,	PUNCT
ap-7660	295	16	with	with	ADP
ap-7660	295	17	vertical	vertical	ADJ
ap-7660	295	18	lines	line	NOUN
ap-7660	295	19	indicating	indicate	VERB
ap-7660	295	20	the	the	DET
ap-7660	295	21	location	location	NOUN
ap-7660	295	22	of	of	ADP
ap-7660	295	23	the	the	DET
ap-7660	295	24	boundaries	boundary	NOUN
ap-7660	295	25	of	of	ADP
ap-7660	295	26	three	three	NUM
ap-7660	295	27	regions	region	NOUN
ap-7660	295	28	.	.	PUNCT
ap-7660	296	1	panel	panel	NOUN
ap-7660	296	2	(	(	PUNCT
ap-7660	296	3	b	b	NOUN
ap-7660	296	4	)	)	PUNCT
ap-7660	296	5	shows	show	VERB
ap-7660	296	6	three	three	NUM
ap-7660	296	7	profile	profile	NOUN
ap-7660	296	8	function	function	NOUN
ap-7660	296	9	h1(r	h1(r	NOUN
ap-7660	296	10	)	)	PUNCT
ap-7660	296	11	defined	define	VERB
ap-7660	296	12	on	on	ADP
ap-7660	296	13	each	each	DET
ap-7660	296	14	region	region	NOUN
ap-7660	296	15	indicated	indicate	VERB
ap-7660	296	16	in	in	ADP
ap-7660	296	17	panel	panel	NOUN
ap-7660	296	18	(	(	PUNCT
ap-7660	296	19	a	a	NOUN
ap-7660	296	20	)	)	PUNCT
ap-7660	296	21	.	.	PUNCT
ap-7660	297	1	h±	h±	NOUN
ap-7660	297	2	1	1	NUM
ap-7660	297	3	(	(	PUNCT
ap-7660	297	4	r	r	NOUN
ap-7660	297	5	)	)	PUNCT
ap-7660	297	6	=	=	SYM
ap-7660	297	7	±	±	NUM
ap-7660	297	8	sign(n)√	sign(n)√	NOUN
ap-7660	297	9	1	1	NUM
ap-7660	297	10	−	−	PROPN
ap-7660	297	11	z2	z2	NOUN
ap-7660	297	12	[	[	PUNCT
ap-7660	297	13	r	r	NOUN
ap-7660	297	14	√	√	NUM
ap-7660	297	15	1	1	NUM
ap-7660	297	16	−	−	NOUN
ap-7660	297	17	z2coth(r̂	z2coth(r̂	NUM
ap-7660	297	18	)	)	PUNCT
ap-7660	297	19	−	−	PROPN
ap-7660	297	20	1	1	NUM
ap-7660	297	21	er	er	INTJ
ap-7660	297	22	]	]	PUNCT
ap-7660	297	23	,	,	PUNCT
ap-7660	297	24	(	(	PUNCT
ap-7660	297	25	46	46	X
ap-7660	297	26	)	)	PUNCT
ap-7660	297	27	h±	h±	NOUN
ap-7660	297	28	2	2	NUM
ap-7660	297	29	(	(	PUNCT
ap-7660	297	30	r	r	NOUN
ap-7660	297	31	)	)	PUNCT
ap-7660	297	32	=	=	VERB
ap-7660	298	1	∓	∓	PROPN
ap-7660	298	2	sign(n)c2c3z√	sign(n)c2c3z√	PROPN
ap-7660	298	3	1	1	NUM
ap-7660	298	4	−	−	PROPN
ap-7660	298	5	z2	z2	NOUN
ap-7660	298	6	[	[	PUNCT
ap-7660	298	7	r	r	NOUN
ap-7660	298	8	√	√	NUM
ap-7660	298	9	1	1	NUM
ap-7660	298	10	−	−	NOUN
ap-7660	298	11	z2coth(r̂	z2coth(r̂	NUM
ap-7660	298	12	)	)	PUNCT
ap-7660	298	13	−	−	PROPN
ap-7660	298	14	1	1	NUM
ap-7660	298	15	er	er	INTJ
ap-7660	298	16	]	]	PUNCT
ap-7660	298	17	,	,	PUNCT
ap-7660	298	18	(	(	PUNCT
ap-7660	298	19	47	47	NUM
ap-7660	298	20	)	)	PUNCT
ap-7660	298	21	where	where	SCONJ
ap-7660	298	22	r2	r2	NOUN
ap-7660	298	23	=	=	SYM
ap-7660	298	24	4(c2zy	4(c2zy	PROPN
ap-7660	298	25	+	+	CCONJ
ap-7660	298	26	c1x	c1x	NOUN
ap-7660	298	27	)	)	PUNCT
ap-7660	298	28	and	and	CCONJ
ap-7660	298	29	r̂	r̂	NOUN
ap-7660	298	30	=	=	SYM
ap-7660	298	31	er	er	INTJ
ap-7660	298	32	√	√	INTJ
ap-7660	298	33	1	1	NUM
ap-7660	298	34	−	−	PROPN
ap-7660	298	35	z2r	z2r	NOUN
ap-7660	298	36	.	.	PUNCT
ap-7660	299	1	the	the	DET
ap-7660	299	2	monopole	monopole	ADJ
ap-7660	299	3	masses	masse	NOUN
ap-7660	299	4	are	be	AUX
ap-7660	299	5	plotted	plot	VERB
ap-7660	299	6	against	against	ADP
ap-7660	299	7	the	the	DET
ap-7660	299	8	gauge	gauge	NOUN
ap-7660	299	9	mass	mass	NOUN
ap-7660	299	10	for	for	ADP
ap-7660	299	11	fixed	fix	VERB
ap-7660	299	12	parameters	parameter	NOUN
ap-7660	299	13	with	with	ADP
ap-7660	299	14	n	n	PRON
ap-7660	299	15	∈	∈	NOUN
ap-7660	299	16	{	{	PUNCT
ap-7660	299	17	1	1	NUM
ap-7660	299	18	,	,	PUNCT
ap-7660	299	19	2	2	NUM
ap-7660	299	20	,	,	PUNCT
ap-7660	299	21	3	3	NUM
ap-7660	299	22	,	,	PUNCT
ap-7660	299	23	4	4	NUM
ap-7660	299	24	}	}	PUNCT
ap-7660	299	25	in	in	ADP
ap-7660	299	26	figure	figure	NOUN
ap-7660	299	27	2	2	NUM
ap-7660	299	28	with	with	ADP
ap-7660	299	29	weak	weak	ADJ
ap-7660	299	30	and	and	CCONJ
ap-7660	299	31	strong	strong	ADJ
ap-7660	299	32	couplings	coupling	NOUN
ap-7660	299	33	e	e	NOUN
ap-7660	299	34	=	=	SYM
ap-7660	299	35	2	2	NUM
ap-7660	299	36	,	,	PUNCT
ap-7660	299	37	e	e	NOUN
ap-7660	299	38	=	=	SYM
ap-7660	299	39	10	10	NUM
ap-7660	299	40	.	.	PUNCT
ap-7660	300	1	notice	notice	VERB
ap-7660	300	2	that	that	SCONJ
ap-7660	300	3	the	the	DET
ap-7660	300	4	gauge	gauge	NOUN
ap-7660	300	5	mass	mass	NOUN
ap-7660	300	6	is	be	AUX
ap-7660	300	7	smaller	small	ADJ
ap-7660	300	8	than	than	ADP
ap-7660	300	9	any	any	PRON
ap-7660	300	10	of	of	ADP
ap-7660	300	11	the	the	DET
ap-7660	300	12	monopole	monopole	ADJ
ap-7660	300	13	masses	masse	NOUN
ap-7660	300	14	for	for	ADP
ap-7660	300	15	weak	weak	ADJ
ap-7660	300	16	coupling	coupling	NOUN
ap-7660	300	17	,	,	PUNCT
ap-7660	300	18	but	but	CCONJ
ap-7660	300	19	when	when	SCONJ
ap-7660	300	20	e	e	NOUN
ap-7660	300	21	is	be	AUX
ap-7660	300	22	large	large	ADJ
ap-7660	300	23	enough	enough	ADV
ap-7660	300	24	,	,	PUNCT
ap-7660	300	25	some	some	PRON
ap-7660	300	26	of	of	ADP
ap-7660	300	27	the	the	DET
ap-7660	300	28	monopole	monopole	ADJ
ap-7660	300	29	masses	masse	NOUN
ap-7660	300	30	can	can	AUX
ap-7660	300	31	become	become	VERB
ap-7660	300	32	smaller	small	ADJ
ap-7660	300	33	than	than	ADP
ap-7660	300	34	the	the	DET
ap-7660	300	35	gauge	gauge	NOUN
ap-7660	300	36	mass	mass	PROPN
ap-7660	300	37	.	.	PUNCT
ap-7660	301	1	this	this	PRON
ap-7660	301	2	is	be	AUX
ap-7660	301	3	clear	clear	ADJ
ap-7660	301	4	by	by	ADP
ap-7660	301	5	inspecting	inspect	VERB
ap-7660	301	6	the	the	DET
ap-7660	301	7	monopole	monopole	NOUN
ap-7660	301	8	,	,	PUNCT
ap-7660	301	9	and	and	CCONJ
ap-7660	301	10	gauge	gauge	VERB
ap-7660	301	11	mass	mass	NOUN
ap-7660	301	12	in	in	ADP
ap-7660	301	13	equation	equation	NOUN
ap-7660	301	14	(	(	PUNCT
ap-7660	301	15	45	45	NUM
ap-7660	301	16	)	)	PUNCT
ap-7660	301	17	and	and	CCONJ
ap-7660	301	18	two	two	NUM
ap-7660	301	19	masses	masse	NOUN
ap-7660	301	20	coincide	coincide	VERB
ap-7660	301	21	when	when	SCONJ
ap-7660	301	22	e	e	NOUN
ap-7660	301	23	=	=	NOUN
ap-7660	301	24	√	√	NUM
ap-7660	301	25	8|n|π	8|n|π	NUM
ap-7660	301	26	.	.	PUNCT
ap-7660	302	1	note	note	VERB
ap-7660	302	2	that	that	SCONJ
ap-7660	302	3	n	n	NOUN
ap-7660	302	4	=	=	SYM
ap-7660	302	5	0	0	NUM
ap-7660	302	6	is	be	AUX
ap-7660	302	7	not	not	PART
ap-7660	302	8	a	a	DET
ap-7660	302	9	monopole	monopole	NOUN
ap-7660	302	10	mass	mass	NOUN
ap-7660	302	11	as	as	SCONJ
ap-7660	302	12	it	it	PRON
ap-7660	302	13	corresponds	correspond	VERB
ap-7660	302	14	to	to	ADP
ap-7660	302	15	the	the	DET
ap-7660	302	16	solution	solution	NOUN
ap-7660	302	17	with	with	ADP
ap-7660	302	18	zero	zero	NUM
ap-7660	302	19	winding	wind	VERB
ap-7660	302	20	number	number	NOUN
ap-7660	302	21	,	,	PUNCT
ap-7660	302	22	which	which	PRON
ap-7660	302	23	is	be	AUX
ap-7660	302	24	topologically	topologically	ADV
ap-7660	302	25	equivalent	equivalent	ADJ
ap-7660	302	26	to	to	ADP
ap-7660	302	27	the	the	DET
ap-7660	302	28	trivial	trivial	ADJ
ap-7660	302	29	solution	solution	NOUN
ap-7660	302	30	.	.	PUNCT
ap-7660	303	1	from	from	ADP
ap-7660	303	2	figure	figure	NOUN
ap-7660	303	3	2	2	NUM
ap-7660	303	4	,	,	PUNCT
ap-7660	303	5	we	we	PRON
ap-7660	303	6	also	also	ADV
ap-7660	303	7	observe	observe	VERB
ap-7660	303	8	disconnected	disconnected	ADJ
ap-7660	303	9	regions	region	NOUN
ap-7660	303	10	where	where	SCONJ
ap-7660	303	11	both	both	PRON
ap-7660	303	12	monopole	monopole	NOUN
ap-7660	303	13	and	and	CCONJ
ap-7660	303	14	gauge	gauge	ADJ
ap-7660	303	15	masses	masse	NOUN
ap-7660	303	16	become	become	VERB
ap-7660	303	17	real	real	ADJ
ap-7660	303	18	to	to	ADP
ap-7660	303	19	purely	purely	ADV
ap-7660	303	20	complex	complex	ADJ
ap-7660	303	21	.	.	PUNCT
ap-7660	304	1	a	a	DET
ap-7660	304	2	more	more	ADV
ap-7660	304	3	detailed	detailed	ADJ
ap-7660	304	4	plot	plot	NOUN
ap-7660	304	5	of	of	ADP
ap-7660	304	6	this	this	PRON
ap-7660	304	7	is	be	AUX
ap-7660	304	8	shown	show	VERB
ap-7660	304	9	in	in	ADP
ap-7660	304	10	figure	figure	NOUN
ap-7660	304	11	3	3	NUM
ap-7660	304	12	.	.	PUNCT
ap-7660	304	13	region	region	NOUN
ap-7660	304	14	2	2	NUM
ap-7660	304	15	is	be	AUX
ap-7660	304	16	bounded	bound	VERB
ap-7660	304	17	by	by	ADP
ap-7660	304	18	two	two	NUM
ap-7660	304	19	points	point	NOUN
ap-7660	304	20	with	with	ADP
ap-7660	304	21	lower	low	ADJ
ap-7660	304	22	bound	bind	VERB
ap-7660	304	23	µ2	µ2	PROPN
ap-7660	304	24	/	/	SYM
ap-7660	304	25	m2	m2	PROPN
ap-7660	304	26	2	2	NUM
ap-7660	304	27	=	=	SYM
ap-7660	304	28	1	1	NUM
ap-7660	304	29	corresponding	correspond	VERB
ap-7660	304	30	to	to	ADP
ap-7660	304	31	the	the	DET
ap-7660	304	32	zero	zero	NUM
ap-7660	304	33	exceptional	exceptional	ADJ
ap-7660	304	34	point	point	NOUN
ap-7660	304	35	where	where	SCONJ
ap-7660	304	36	the	the	DET
ap-7660	304	37	vacuum	vacuum	NOUN
ap-7660	304	38	manifolds	manifold	NOUN
ap-7660	304	39	stay	stay	VERB
ap-7660	304	40	finite	finite	ADJ
ap-7660	304	41	(	(	PUNCT
ap-7660	304	42	i.e.	i.e.	X
ap-7660	304	43	spontaneous	spontaneous	ADJ
ap-7660	304	44	symmetry	symmetry	NOUN
ap-7660	304	45	breaking	breaking	NOUN
ap-7660	304	46	occur	occur	VERB
ap-7660	304	47	)	)	PUNCT
ap-7660	304	48	.	.	PUNCT
ap-7660	305	1	however	however	ADV
ap-7660	305	2	,	,	PUNCT
ap-7660	305	3	the	the	DET
ap-7660	305	4	higgs	higgs	NOUN
ap-7660	305	5	mechanism	mechanism	NOUN
ap-7660	305	6	fails	fail	VERB
ap-7660	305	7	because	because	SCONJ
ap-7660	305	8	the	the	DET
ap-7660	305	9	hamiltonian	hamiltonian	NOUN
ap-7660	305	10	is	be	AUX
ap-7660	305	11	non	non	ADJ
ap-7660	305	12	-	-	ADJ
ap-7660	305	13	diagonalisable	diagonalisable	ADJ
ap-7660	305	14	,	,	PUNCT
ap-7660	305	15	as	as	SCONJ
ap-7660	305	16	discussed	discuss	VERB
ap-7660	305	17	in	in	ADP
ap-7660	305	18	the	the	DET
ap-7660	305	19	previous	previous	ADJ
ap-7660	305	20	section	section	NOUN
ap-7660	305	21	.	.	PUNCT
ap-7660	306	1	the	the	DET
ap-7660	306	2	upper	upper	ADJ
ap-7660	306	3	bounds	bound	NOUN
ap-7660	306	4	correspond	correspond	VERB
ap-7660	306	5	to	to	ADP
ap-7660	306	6	the	the	DET
ap-7660	306	7	point	point	NOUN
ap-7660	306	8	where	where	SCONJ
ap-7660	306	9	the	the	DET
ap-7660	306	10	vacuum	vacuum	NOUN
ap-7660	306	11	manifold	manifold	NOUN
ap-7660	306	12	vanishes	vanish	VERB
ap-7660	306	13	.	.	PUNCT
ap-7660	307	1	therefore	therefore	ADV
ap-7660	307	2	,	,	PUNCT
ap-7660	307	3	the	the	DET
ap-7660	307	4	spontaneous	spontaneous	ADJ
ap-7660	307	5	symmetry	symmetry	NOUN
ap-7660	307	6	breaking	breaking	NOUN
ap-7660	307	7	does	do	AUX
ap-7660	307	8	not	not	PART
ap-7660	307	9	occur	occur	VERB
ap-7660	307	10	,	,	PUNCT
ap-7660	307	11	implying	imply	VERB
ap-7660	307	12	that	that	SCONJ
ap-7660	307	13	the	the	DET
ap-7660	307	14	gauge	gauge	NOUN
ap-7660	307	15	fields	field	NOUN
ap-7660	307	16	do	do	AUX
ap-7660	307	17	not	not	PART
ap-7660	307	18	acquire	acquire	VERB
ap-7660	307	19	a	a	DET
ap-7660	307	20	mass	mass	NOUN
ap-7660	307	21	through	through	ADP
ap-7660	307	22	the	the	DET
ap-7660	307	23	higgs	higgs	NOUN
ap-7660	307	24	mechanism	mechanism	NOUN
ap-7660	307	25	,	,	PUNCT
ap-7660	307	26	resulting	result	VERB
ap-7660	307	27	in	in	ADP
ap-7660	307	28	a	a	DET
ap-7660	307	29	massless	massless	ADJ
ap-7660	307	30	gauge	gauge	NOUN
ap-7660	307	31	field	field	NOUN
ap-7660	307	32	.	.	PUNCT
ap-7660	308	1	most	most	ADV
ap-7660	308	2	crucially	crucially	ADV
ap-7660	308	3	,	,	PUNCT
ap-7660	308	4	an	an	DET
ap-7660	308	5	interesting	interesting	ADJ
ap-7660	308	6	region	region	NOUN
ap-7660	308	7	(	(	PUNCT
ap-7660	308	8	denoted	denote	VERB
ap-7660	308	9	by	by	ADP
ap-7660	308	10	region	region	NOUN
ap-7660	308	11	3	3	NUM
ap-7660	308	12	in	in	ADP
ap-7660	308	13	figure	figure	NOUN
ap-7660	308	14	4	4	NUM
ap-7660	308	15	)	)	PUNCT
ap-7660	308	16	reappears	reappear	VERB
ap-7660	308	17	as	as	SCONJ
ap-7660	308	18	one	one	NUM
ap-7660	308	19	increases	increase	VERB
ap-7660	308	20	the	the	DET
ap-7660	308	21	value	value	NOUN
ap-7660	308	22	of	of	ADP
ap-7660	308	23	z.	z.	PROPN
ap-7660	308	24	the	the	DET
ap-7660	308	25	profile	profile	NOUN
ap-7660	308	26	function	function	NOUN
ap-7660	308	27	in	in	ADP
ap-7660	308	28	region	region	NOUN
ap-7660	308	29	3	3	NUM
ap-7660	308	30	is	be	AUX
ap-7660	308	31	purely	purely	ADV
ap-7660	308	32	complex	complex	ADJ
ap-7660	308	33	,	,	PUNCT
ap-7660	308	34	which	which	PRON
ap-7660	308	35	signals	signal	VERB
ap-7660	308	36	that	that	SCONJ
ap-7660	308	37	this	this	PRON
ap-7660	308	38	may	may	AUX
ap-7660	308	39	lead	lead	VERB
ap-7660	308	40	to	to	ADP
ap-7660	308	41	complex	complex	ADJ
ap-7660	308	42	energies	energy	NOUN
ap-7660	308	43	.	.	PUNCT
ap-7660	309	1	however	however	ADV
ap-7660	309	2	,	,	PUNCT
ap-7660	309	3	as	as	SCONJ
ap-7660	309	4	one	one	PRON
ap-7660	309	5	can	can	AUX
ap-7660	309	6	see	see	VERB
ap-7660	309	7	from	from	ADP
ap-7660	309	8	figure	figure	NOUN
ap-7660	309	9	3	3	NUM
ap-7660	309	10	,	,	PUNCT
ap-7660	309	11	the	the	DET
ap-7660	309	12	energy	energy	NOUN
ap-7660	309	13	is	be	AUX
ap-7660	309	14	real	real	ADJ
ap-7660	309	15	.	.	PUNCT
ap-7660	310	1	the	the	DET
ap-7660	310	2	reason	reason	NOUN
ap-7660	310	3	for	for	ADP
ap-7660	310	4	the	the	DET
ap-7660	310	5	real	real	ADJ
ap-7660	310	6	energy	energy	NOUN
ap-7660	310	7	is	be	AUX
ap-7660	310	8	that	that	SCONJ
ap-7660	310	9	the	the	DET
ap-7660	310	10	conditions	condition	NOUN
ap-7660	310	11	stated	state	VERB
ap-7660	310	12	in	in	ADP
ap-7660	310	13	the	the	DET
ap-7660	310	14	introduction	introduction	NOUN
ap-7660	310	15	hold	hold	NOUN
ap-7660	310	16	.	.	PUNCT
ap-7660	311	1	we	we	PRON
ap-7660	311	2	will	will	AUX
ap-7660	311	3	specify	specify	VERB
ap-7660	311	4	below	below	ADP
ap-7660	311	5	the	the	DET
ap-7660	311	6	cpt	cpt	PROPN
ap-7660	311	7	symmetry	symmetry	NOUN
ap-7660	311	8	responsible	responsible	ADJ
ap-7660	311	9	for	for	ADP
ap-7660	311	10	the	the	DET
ap-7660	311	11	real	real	ADJ
ap-7660	311	12	value	value	NOUN
ap-7660	311	13	of	of	ADP
ap-7660	311	14	the	the	DET
ap-7660	311	15	energy	energy	NOUN
ap-7660	311	16	.	.	PUNCT
ap-7660	312	1	note	note	VERB
ap-7660	312	2	that	that	SCONJ
ap-7660	312	3	the	the	DET
ap-7660	312	4	profile	profile	NOUN
ap-7660	312	5	function	function	NOUN
ap-7660	312	6	h2	h2	PROPN
ap-7660	312	7	only	only	ADV
ap-7660	312	8	differ	differ	VERB
ap-7660	312	9	from	from	ADP
ap-7660	312	10	h1	h1	NOUN
ap-7660	312	11	by	by	ADP
ap-7660	312	12	some	some	DET
ap-7660	312	13	factor	factor	NOUN
ap-7660	312	14	in	in	ADP
ap-7660	312	15	front	front	NOUN
ap-7660	312	16	.	.	PUNCT
ap-7660	313	1	therefore	therefore	ADV
ap-7660	313	2	we	we	PRON
ap-7660	313	3	omitted	omit	VERB
ap-7660	313	4	it	it	PRON
ap-7660	313	5	from	from	ADP
ap-7660	313	6	the	the	DET
ap-7660	313	7	plot	plot	NOUN
ap-7660	313	8	.	.	PUNCT
ap-7660	314	1	another	another	DET
ap-7660	314	2	physical	physical	ADJ
ap-7660	314	3	region	region	NOUN
ap-7660	314	4	is	be	AUX
ap-7660	314	5	when	when	SCONJ
ap-7660	314	6	c1	c1	PROPN
ap-7660	314	7	=	=	PROPN
ap-7660	314	8	−c2	−c2	PROPN
ap-7660	314	9	=	=	PUNCT
ap-7660	314	10	−1	−1	NOUN
ap-7660	314	11	.	.	PUNCT
ap-7660	315	1	the	the	DET
ap-7660	315	2	monopole	monopole	NOUN
ap-7660	315	3	and	and	CCONJ
ap-7660	315	4	gauge	gauge	ADJ
ap-7660	315	5	masses	masse	NOUN
ap-7660	315	6	for	for	ADP
ap-7660	315	7	this	this	DET
ap-7660	315	8	case	case	NOUN
ap-7660	315	9	is	be	AUX
ap-7660	315	10	plotted	plot	VERB
ap-7660	315	11	in	in	ADP
ap-7660	315	12	figure	figure	NOUN
ap-7660	315	13	4	4	NUM
ap-7660	315	14	.	.	PUNCT
ap-7660	316	1	we	we	PRON
ap-7660	316	2	observe	observe	VERB
ap-7660	316	3	almost	almost	ADV
ap-7660	316	4	an	an	DET
ap-7660	316	5	identical	identical	ADJ
ap-7660	316	6	plot	plot	NOUN
ap-7660	316	7	from	from	ADP
ap-7660	316	8	the	the	DET
ap-7660	316	9	figure	figure	NOUN
ap-7660	316	10	3	3	NUM
ap-7660	316	11	but	but	CCONJ
ap-7660	316	12	with	with	ADP
ap-7660	316	13	real	real	ADJ
ap-7660	316	14	and	and	CCONJ
ap-7660	316	15	imaginary	imaginary	ADJ
ap-7660	316	16	parts	part	NOUN
ap-7660	316	17	swapped	swap	VERB
ap-7660	316	18	.	.	PUNCT
ap-7660	317	1	the	the	DET
ap-7660	317	2	profile	profile	NOUN
ap-7660	317	3	functions	function	NOUN
ap-7660	317	4	also	also	ADV
ap-7660	317	5	respect	respect	VERB
ap-7660	317	6	these	these	DET
ap-7660	317	7	changes	change	NOUN
ap-7660	317	8	as	as	ADP
ap-7660	317	9	regions	region	NOUN
ap-7660	317	10	1	1	NUM
ap-7660	317	11	and	and	CCONJ
ap-7660	317	12	3	3	NUM
ap-7660	317	13	no	no	ADV
ap-7660	317	14	longer	long	ADV
ap-7660	317	15	have	have	VERB
ap-7660	317	16	a	a	DET
ap-7660	317	17	definite	definite	ADJ
ap-7660	317	18	asymptotic	asymptotic	ADJ
ap-7660	317	19	value	value	NOUN
ap-7660	317	20	.	.	PUNCT
ap-7660	318	1	the	the	DET
ap-7660	318	2	boundaries	boundary	NOUN
ap-7660	318	3	are	be	AUX
ap-7660	318	4	unchanged	unchanged	ADJ
ap-7660	318	5	,	,	PUNCT
ap-7660	318	6	as	as	SCONJ
ap-7660	318	7	one	one	PRON
ap-7660	318	8	can	can	AUX
ap-7660	318	9	see	see	VERB
ap-7660	318	10	from	from	ADP
ap-7660	318	11	the	the	DET
ap-7660	318	12	figure	figure	NOUN
ap-7660	318	13	4	4	NUM
ap-7660	318	14	.	.	PUNCT
ap-7660	319	1	finally	finally	ADV
ap-7660	319	2	,	,	PUNCT
ap-7660	319	3	there	there	PRON
ap-7660	319	4	is	be	VERB
ap-7660	319	5	an	an	DET
ap-7660	319	6	interesting	interesting	ADJ
ap-7660	319	7	parameter	parameter	NOUN
ap-7660	319	8	point	point	NOUN
ap-7660	319	9	x	x	PUNCT
ap-7660	319	10	=	=	PUNCT
ap-7660	319	11	y	y	PROPN
ap-7660	319	12	where	where	SCONJ
ap-7660	319	13	region	region	NOUN
ap-7660	319	14	2	2	NUM
ap-7660	319	15	vanishes	vanish	VERB
ap-7660	319	16	(	(	PUNCT
ap-7660	319	17	see	see	VERB
ap-7660	319	18	figure	figure	NOUN
ap-7660	319	19	5	5	NUM
ap-7660	319	20	)	)	PUNCT
ap-7660	319	21	.	.	PUNCT
ap-7660	320	1	the	the	DET
ap-7660	320	2	two	two	NUM
ap-7660	320	3	boundaries	boundary	NOUN
ap-7660	320	4	z2	z2	NOUN
ap-7660	320	5	=	=	SYM
ap-7660	320	6	1	1	NUM
ap-7660	320	7	and	and	CCONJ
ap-7660	320	8	c2zy	c2zy	PRON
ap-7660	320	9	+	+	CCONJ
ap-7660	320	10	c1x	c1x	X
ap-7660	320	11	=	=	SYM
ap-7660	320	12	0	0	NUM
ap-7660	320	13	coincide	coincide	NOUN
ap-7660	320	14	when	when	SCONJ
ap-7660	320	15	x	x	PROPN
ap-7660	320	16	=	=	SYM
ap-7660	320	17	y	y	PROPN
ap-7660	320	18	and	and	CCONJ
ap-7660	320	19	the	the	DET
ap-7660	320	20	zero	zero	NUM
ap-7660	320	21	exceptional	exceptional	ADJ
ap-7660	320	22	point	point	NOUN
ap-7660	320	23	no	no	ADV
ap-7660	320	24	longer	long	ADV
ap-7660	320	25	exists	exist	VERB
ap-7660	320	26	because	because	SCONJ
ap-7660	320	27	the	the	DET
ap-7660	320	28	spontaneous	spontaneous	ADJ
ap-7660	320	29	symmetry	symmetry	NOUN
ap-7660	320	30	breaking	breaking	NOUN
ap-7660	320	31	does	do	AUX
ap-7660	320	32	not	not	PART
ap-7660	320	33	occur	occur	VERB
ap-7660	320	34	in	in	ADP
ap-7660	320	35	this	this	DET
ap-7660	320	36	case	case	NOUN
ap-7660	320	37	.	.	PUNCT
ap-7660	321	1	next	next	ADV
ap-7660	321	2	,	,	PUNCT
ap-7660	321	3	let	let	VERB
ap-7660	321	4	us	we	PRON
ap-7660	321	5	explain	explain	VERB
ap-7660	321	6	the	the	DET
ap-7660	321	7	real	real	ADJ
ap-7660	321	8	value	value	NOUN
ap-7660	321	9	of	of	ADP
ap-7660	321	10	the	the	DET
ap-7660	321	11	energies	energy	NOUN
ap-7660	321	12	in	in	ADP
ap-7660	321	13	different	different	ADJ
ap-7660	321	14	regions	region	NOUN
ap-7660	321	15	.	.	PUNCT
ap-7660	322	1	first	first	ADV
ap-7660	322	2	,	,	PUNCT
ap-7660	322	3	to	to	PART
ap-7660	322	4	realise	realise	VERB
ap-7660	322	5	the	the	DET
ap-7660	322	6	conditions	condition	NOUN
ap-7660	322	7	1	1	NUM
ap-7660	322	8	-	-	SYM
ap-7660	322	9	3	3	NUM
ap-7660	322	10	,	,	PUNCT
ap-7660	322	11	stated	state	VERB
ap-7660	322	12	in	in	ADP
ap-7660	322	13	the	the	DET
ap-7660	322	14	introduction	introduction	NOUN
ap-7660	322	15	,	,	PUNCT
ap-7660	322	16	we	we	PRON
ap-7660	322	17	require	require	VERB
ap-7660	322	18	the	the	DET
ap-7660	322	19	following	follow	VERB
ap-7660	322	20	204	204	NUM
ap-7660	322	21	vol	vol	NOUN
ap-7660	322	22	.	.	PUNCT
ap-7660	323	1	62	62	NUM
ap-7660	323	2	no	no	INTJ
ap-7660	323	3	.	.	PUNCT
ap-7660	324	1	1/2022	1/2022	NUM
ap-7660	324	2	complex	complex	ADJ
ap-7660	324	3	topological	topological	ADJ
ap-7660	324	4	soliton	soliton	NOUN
ap-7660	324	5	with	with	ADP
ap-7660	324	6	real	real	ADJ
ap-7660	324	7	energy	energy	NOUN
ap-7660	324	8	in	in	ADP
ap-7660	324	9	particle	particle	NOUN
ap-7660	324	10	physics	physics	NOUN
ap-7660	324	11	figure	figure	NOUN
ap-7660	324	12	4	4	NUM
ap-7660	324	13	.	.	PUNCT
ap-7660	325	1	both	both	DET
ap-7660	325	2	panels	panel	NOUN
ap-7660	325	3	are	be	AUX
ap-7660	325	4	plotted	plot	VERB
ap-7660	325	5	for	for	ADP
ap-7660	325	6	x	x	SYM
ap-7660	325	7	=	=	SYM
ap-7660	325	8	1	1	NUM
ap-7660	325	9	,	,	PUNCT
ap-7660	325	10	y	y	PROPN
ap-7660	325	11	=	=	SYM
ap-7660	325	12	1	1	NUM
ap-7660	325	13	,	,	PUNCT
ap-7660	325	14	n	n	NOUN
ap-7660	325	15	=	=	SYM
ap-7660	325	16	1	1	NUM
ap-7660	325	17	,	,	PUNCT
ap-7660	326	1	e	e	NOUN
ap-7660	326	2	=	=	SYM
ap-7660	326	3	2	2	X
ap-7660	326	4	.	.	PUNCT
ap-7660	327	1	the	the	DET
ap-7660	327	2	solid	solid	ADJ
ap-7660	327	3	line	line	NOUN
ap-7660	327	4	represents	represent	VERB
ap-7660	327	5	the	the	DET
ap-7660	327	6	real	real	ADJ
ap-7660	327	7	part	part	NOUN
ap-7660	327	8	,	,	PUNCT
ap-7660	327	9	and	and	CCONJ
ap-7660	327	10	the	the	DET
ap-7660	327	11	dotted	dotted	ADJ
ap-7660	327	12	line	line	NOUN
ap-7660	327	13	represents	represent	VERB
ap-7660	327	14	the	the	DET
ap-7660	327	15	imaginary	imaginary	ADJ
ap-7660	327	16	part	part	NOUN
ap-7660	327	17	of	of	ADP
ap-7660	327	18	the	the	DET
ap-7660	327	19	masses	masse	NOUN
ap-7660	327	20	.	.	PUNCT
ap-7660	328	1	figure	figure	VERB
ap-7660	328	2	5	5	NUM
ap-7660	328	3	.	.	PUNCT
ap-7660	329	1	both	both	DET
ap-7660	329	2	panels	panel	NOUN
ap-7660	329	3	are	be	AUX
ap-7660	329	4	plotted	plot	VERB
ap-7660	329	5	for	for	ADP
ap-7660	329	6	x	x	SYM
ap-7660	329	7	=	=	SYM
ap-7660	329	8	1	1	NUM
ap-7660	329	9	,	,	PUNCT
ap-7660	329	10	y	y	PROPN
ap-7660	329	11	=	=	SYM
ap-7660	329	12	1	1	NUM
ap-7660	329	13	,	,	PUNCT
ap-7660	329	14	n	n	NOUN
ap-7660	329	15	=	=	SYM
ap-7660	329	16	1	1	NUM
ap-7660	329	17	,	,	PUNCT
ap-7660	330	1	e	e	NOUN
ap-7660	330	2	=	=	SYM
ap-7660	330	3	2	2	X
ap-7660	330	4	.	.	PUNCT
ap-7660	331	1	the	the	DET
ap-7660	331	2	solid	solid	ADJ
ap-7660	331	3	line	line	NOUN
ap-7660	331	4	represents	represent	VERB
ap-7660	331	5	the	the	DET
ap-7660	331	6	real	real	ADJ
ap-7660	331	7	part	part	NOUN
ap-7660	331	8	,	,	PUNCT
ap-7660	331	9	and	and	CCONJ
ap-7660	331	10	the	the	DET
ap-7660	331	11	dotted	dotted	ADJ
ap-7660	331	12	line	line	NOUN
ap-7660	331	13	represents	represent	VERB
ap-7660	331	14	the	the	DET
ap-7660	331	15	imaginary	imaginary	ADJ
ap-7660	331	16	part	part	NOUN
ap-7660	331	17	of	of	ADP
ap-7660	331	18	the	the	DET
ap-7660	331	19	masses	masse	NOUN
ap-7660	331	20	.	.	PUNCT
ap-7660	332	1	transformations	transformation	NOUN
ap-7660	332	2	h±	h±	PROPN
ap-7660	332	3	2	2	NUM
ap-7660	332	4	(	(	PUNCT
ap-7660	332	5	r	r	NOUN
ap-7660	332	6	)	)	PUNCT
ap-7660	332	7	→	→	SYM
ap-7660	332	8	−h±	−h±	NUM
ap-7660	332	9	2	2	NUM
ap-7660	332	10	(	(	PUNCT
ap-7660	332	11	r	r	NOUN
ap-7660	332	12	)	)	PUNCT
ap-7660	332	13	,	,	PUNCT
ap-7660	332	14	h±	h±	PROPN
ap-7660	332	15	1	1	NUM
ap-7660	332	16	(	(	PUNCT
ap-7660	332	17	r	r	NOUN
ap-7660	332	18	)	)	PUNCT
ap-7660	332	19	→	→	SYM
ap-7660	332	20	h±	h±	PROPN
ap-7660	332	21	1	1	NUM
ap-7660	332	22	(	(	PUNCT
ap-7660	332	23	r	r	NOUN
ap-7660	332	24	)	)	PUNCT
ap-7660	332	25	in	in	ADP
ap-7660	332	26	region	region	NOUN
ap-7660	332	27	1	1	NUM
ap-7660	332	28	no	no	DET
ap-7660	332	29	symmetry	symmetry	NOUN
ap-7660	332	30	in	in	ADP
ap-7660	332	31	region	region	NOUN
ap-7660	332	32	2	2	NUM
ap-7660	332	33	h±	h±	PROPN
ap-7660	332	34	2	2	NUM
ap-7660	332	35	(	(	PUNCT
ap-7660	332	36	r	r	NOUN
ap-7660	332	37	)	)	PUNCT
ap-7660	332	38	→	→	SYM
ap-7660	332	39	−	−	PROPN
ap-7660	332	40	(	(	PUNCT
ap-7660	332	41	h±	h±	PROPN
ap-7660	332	42	2	2	NUM
ap-7660	332	43	(	(	PUNCT
ap-7660	332	44	r	r	NOUN
ap-7660	332	45	)	)	PUNCT
ap-7660	332	46	)	)	PUNCT
ap-7660	332	47	∗	∗	NOUN
ap-7660	332	48	,	,	PUNCT
ap-7660	332	49	h±	h±	PROPN
ap-7660	332	50	1	1	NUM
ap-7660	332	51	(	(	PUNCT
ap-7660	332	52	r	r	NOUN
ap-7660	332	53	)	)	PUNCT
ap-7660	332	54	→	→	SYM
ap-7660	332	55	(	(	PUNCT
ap-7660	332	56	h±	h±	NUM
ap-7660	332	57	1	1	NUM
ap-7660	332	58	(	(	PUNCT
ap-7660	332	59	r	r	NOUN
ap-7660	332	60	)	)	PUNCT
ap-7660	332	61	)	)	PUNCT
ap-7660	332	62	∗	∗	NOUN
ap-7660	332	63	in	in	ADP
ap-7660	332	64	region	region	NOUN
ap-7660	332	65	3	3	NUM
ap-7660	332	66	.	.	PUNCT
ap-7660	333	1	by	by	ADP
ap-7660	333	2	using	use	VERB
ap-7660	333	3	the	the	DET
ap-7660	333	4	explicit	explicit	ADJ
ap-7660	333	5	forms	form	NOUN
ap-7660	333	6	of	of	ADP
ap-7660	333	7	the	the	DET
ap-7660	333	8	solutions	solution	NOUN
ap-7660	333	9	(	(	PUNCT
ap-7660	333	10	46	46	NUM
ap-7660	333	11	)	)	PUNCT
ap-7660	333	12	and	and	CCONJ
ap-7660	333	13	(	(	PUNCT
ap-7660	333	14	47	47	NUM
ap-7660	333	15	)	)	PUNCT
ap-7660	333	16	.	.	PUNCT
ap-7660	334	1	we	we	PRON
ap-7660	334	2	can	can	AUX
ap-7660	334	3	show	show	VERB
ap-7660	334	4	that	that	SCONJ
ap-7660	334	5	the	the	DET
ap-7660	334	6	above	above	ADJ
ap-7660	334	7	transformations	transformation	NOUN
ap-7660	334	8	satisfy	satisfy	NOUN
ap-7660	334	9	condition	condition	NOUN
ap-7660	334	10	2	2	NUM
ap-7660	334	11	stated	state	VERB
ap-7660	334	12	in	in	ADP
ap-7660	334	13	the	the	DET
ap-7660	334	14	introduction	introduction	NOUN
ap-7660	334	15	,	,	PUNCT
ap-7660	334	16	in	in	ADP
ap-7660	334	17	regions	region	NOUN
ap-7660	334	18	1	1	NUM
ap-7660	334	19	h±	h±	NOUN
ap-7660	334	20	2	2	NUM
ap-7660	334	21	(	(	PUNCT
ap-7660	334	22	r	r	NOUN
ap-7660	334	23	)	)	PUNCT
ap-7660	334	24	→	→	SYM
ap-7660	334	25	−h±	−h±	NUM
ap-7660	334	26	2	2	NUM
ap-7660	334	27	(	(	PUNCT
ap-7660	334	28	r	r	NOUN
ap-7660	334	29	)	)	PUNCT
ap-7660	334	30	=	=	PUNCT
ap-7660	334	31	h∓	h∓	NOUN
ap-7660	334	32	2	2	NUM
ap-7660	334	33	(	(	PUNCT
ap-7660	334	34	r	r	NOUN
ap-7660	334	35	)	)	PUNCT
ap-7660	334	36	,	,	PUNCT
ap-7660	334	37	h±	h±	PROPN
ap-7660	334	38	1	1	NUM
ap-7660	334	39	(	(	PUNCT
ap-7660	334	40	r	r	NOUN
ap-7660	334	41	)	)	PUNCT
ap-7660	334	42	→	→	SYM
ap-7660	334	43	h±	h±	PROPN
ap-7660	334	44	1	1	NUM
ap-7660	334	45	(	(	PUNCT
ap-7660	334	46	r	r	NOUN
ap-7660	334	47	)	)	PUNCT
ap-7660	334	48	,	,	PUNCT
ap-7660	334	49	(	(	PUNCT
ap-7660	334	50	48	48	NUM
ap-7660	334	51	)	)	PUNCT
ap-7660	334	52	and	and	CCONJ
ap-7660	334	53	in	in	ADP
ap-7660	334	54	region	region	NOUN
ap-7660	334	55	3	3	NUM
ap-7660	334	56	h±	h±	PROPN
ap-7660	334	57	2	2	NUM
ap-7660	334	58	(	(	PUNCT
ap-7660	334	59	r	r	NOUN
ap-7660	334	60	)	)	PUNCT
ap-7660	334	61	→	→	SYM
ap-7660	334	62	−	−	PROPN
ap-7660	334	63	(	(	PUNCT
ap-7660	334	64	h±	h±	PROPN
ap-7660	334	65	2	2	NUM
ap-7660	334	66	(	(	PUNCT
ap-7660	334	67	r	r	NOUN
ap-7660	334	68	)	)	PUNCT
ap-7660	334	69	)	)	PUNCT
ap-7660	334	70	∗	∗	NOUN
ap-7660	334	71	=	=	PUNCT
ap-7660	335	1	h±	h±	PROPN
ap-7660	335	2	2	2	NUM
ap-7660	335	3	,	,	PUNCT
ap-7660	335	4	(	(	PUNCT
ap-7660	335	5	49	49	NUM
ap-7660	335	6	)	)	PUNCT
ap-7660	335	7	h±	h±	NOUN
ap-7660	335	8	1	1	NUM
ap-7660	335	9	(	(	PUNCT
ap-7660	335	10	r	r	NOUN
ap-7660	335	11	)	)	PUNCT
ap-7660	335	12	→	→	SYM
ap-7660	335	13	(	(	PUNCT
ap-7660	335	14	h±	h±	NUM
ap-7660	335	15	1	1	NUM
ap-7660	335	16	(	(	PUNCT
ap-7660	335	17	r	r	NOUN
ap-7660	335	18	)	)	PUNCT
ap-7660	335	19	)	)	PUNCT
ap-7660	335	20	∗	∗	NOUN
ap-7660	335	21	=	=	PUNCT
ap-7660	336	1	h∓	h∓	NOUN
ap-7660	336	2	1	1	NUM
ap-7660	336	3	.	.	PUNCT
ap-7660	336	4	notice	notice	VERB
ap-7660	336	5	that	that	SCONJ
ap-7660	336	6	in	in	ADP
ap-7660	336	7	regions	region	NOUN
ap-7660	336	8	1	1	NUM
ap-7660	336	9	and	and	CCONJ
ap-7660	336	10	3	3	NUM
ap-7660	336	11	,	,	PUNCT
ap-7660	336	12	the	the	DET
ap-7660	336	13	cpt	cpt	NOUN
ap-7660	336	14	relates	relate	VERB
ap-7660	336	15	two	two	NUM
ap-7660	336	16	distinct	distinct	ADJ
ap-7660	336	17	solutions	solution	NOUN
ap-7660	336	18	in	in	ADP
ap-7660	336	19	two	two	NUM
ap-7660	336	20	different	different	ADJ
ap-7660	336	21	ways	way	NOUN
ap-7660	336	22	.	.	PUNCT
ap-7660	337	1	for	for	ADP
ap-7660	337	2	example	example	NOUN
ap-7660	337	3	,	,	PUNCT
ap-7660	337	4	h±	h±	PROPN
ap-7660	337	5	2	2	NUM
ap-7660	337	6	is	be	AUX
ap-7660	337	7	mapped	map	VERB
ap-7660	337	8	to	to	ADP
ap-7660	337	9	h∓	h∓	PROPN
ap-7660	337	10	2	2	NUM
ap-7660	337	11	in	in	ADP
ap-7660	337	12	region	region	NOUN
ap-7660	337	13	1	1	NUM
ap-7660	337	14	,	,	PUNCT
ap-7660	337	15	but	but	CCONJ
ap-7660	337	16	it	it	PRON
ap-7660	337	17	is	be	AUX
ap-7660	337	18	mapped	map	VERB
ap-7660	337	19	to	to	ADP
ap-7660	337	20	itself	itself	PRON
ap-7660	337	21	in	in	ADP
ap-7660	337	22	region	region	NOUN
ap-7660	337	23	3	3	X
ap-7660	337	24	.	.	PUNCT
ap-7660	338	1	finally	finally	ADV
ap-7660	338	2	,	,	PUNCT
ap-7660	338	3	the	the	DET
ap-7660	338	4	condition	condition	NOUN
ap-7660	338	5	3	3	NUM
ap-7660	338	6	stated	state	VERB
ap-7660	338	7	in	in	ADP
ap-7660	338	8	the	the	DET
ap-7660	338	9	introduction	introduction	NOUN
ap-7660	338	10	is	be	AUX
ap-7660	338	11	satisfied	satisfied	ADJ
ap-7660	338	12	because	because	SCONJ
ap-7660	338	13	the	the	DET
ap-7660	338	14	energy	energy	NOUN
ap-7660	338	15	does	do	AUX
ap-7660	338	16	not	not	PART
ap-7660	338	17	depend	depend	VERB
ap-7660	338	18	on	on	ADP
ap-7660	338	19	the	the	DET
ap-7660	338	20	±	±	NOUN
ap-7660	338	21	signs	sign	NOUN
ap-7660	338	22	of	of	ADP
ap-7660	338	23	the	the	DET
ap-7660	338	24	solutions	solution	NOUN
ap-7660	338	25	.	.	PUNCT
ap-7660	339	1	this	this	PRON
ap-7660	339	2	explains	explain	VERB
ap-7660	339	3	the	the	DET
ap-7660	339	4	real	real	ADJ
ap-7660	339	5	energies	energy	NOUN
ap-7660	339	6	of	of	ADP
ap-7660	339	7	complex	complex	ADJ
ap-7660	339	8	monopoles	monopole	NOUN
ap-7660	339	9	in	in	ADP
ap-7660	339	10	region	region	NOUN
ap-7660	339	11	3	3	NUM
ap-7660	339	12	and	and	CCONJ
ap-7660	339	13	complex	complex	ADJ
ap-7660	339	14	energy	energy	NOUN
ap-7660	339	15	in	in	ADP
ap-7660	339	16	region	region	NOUN
ap-7660	339	17	2	2	NUM
ap-7660	339	18	.	.	PUNCT
ap-7660	340	1	indeed	indeed	ADV
ap-7660	340	2	,	,	PUNCT
ap-7660	340	3	we	we	PRON
ap-7660	340	4	observe	observe	VERB
ap-7660	340	5	the	the	DET
ap-7660	340	6	predicted	predict	VERB
ap-7660	340	7	behaviour	behaviour	NOUN
ap-7660	340	8	in	in	ADP
ap-7660	340	9	figure	figure	NOUN
ap-7660	340	10	3	3	NUM
ap-7660	340	11	.	.	PUNCT
ap-7660	340	12	region	region	NOUN
ap-7660	340	13	2	2	NUM
ap-7660	340	14	is	be	AUX
ap-7660	340	15	a	a	DET
ap-7660	340	16	hard	hard	ADJ
ap-7660	340	17	barrier	barrier	NOUN
ap-7660	340	18	between	between	ADP
ap-7660	340	19	two	two	NUM
ap-7660	340	20	cpt	cpt	NOUN
ap-7660	340	21	symmetric	symmetric	ADJ
ap-7660	340	22	regions	region	NOUN
ap-7660	340	23	where	where	SCONJ
ap-7660	340	24	solutions	solution	NOUN
ap-7660	340	25	are	be	AUX
ap-7660	340	26	either	either	CCONJ
ap-7660	340	27	real	real	ADJ
ap-7660	340	28	or	or	CCONJ
ap-7660	340	29	purely	purely	ADV
ap-7660	340	30	imaginary	imaginary	ADJ
ap-7660	340	31	.	.	PUNCT
ap-7660	341	1	the	the	DET
ap-7660	341	2	same	same	ADJ
ap-7660	341	3	analysis	analysis	NOUN
ap-7660	341	4	can	can	AUX
ap-7660	341	5	be	be	AUX
ap-7660	341	6	carried	carry	VERB
ap-7660	341	7	out	out	ADP
ap-7660	341	8	in	in	ADP
ap-7660	341	9	the	the	DET
ap-7660	341	10	other	other	ADJ
ap-7660	341	11	physical	physical	ADJ
ap-7660	341	12	region	region	NOUN
ap-7660	341	13	c1	c1	PROPN
ap-7660	341	14	=	=	PROPN
ap-7660	342	1	−c2	−c2	PROPN
ap-7660	342	2	=	=	PUNCT
ap-7660	342	3	−1	−1	NOUN
ap-7660	342	4	where	where	SCONJ
ap-7660	342	5	the	the	DET
ap-7660	342	6	symmetry	symmetry	NOUN
ap-7660	342	7	is	be	AUX
ap-7660	342	8	now	now	ADV
ap-7660	342	9	no	no	DET
ap-7660	342	10	symmetry	symmetry	NOUN
ap-7660	342	11	in	in	ADP
ap-7660	342	12	region	region	NOUN
ap-7660	342	13	1	1	NUM
ap-7660	342	14	h±	h±	PROPN
ap-7660	342	15	2	2	NUM
ap-7660	342	16	(	(	PUNCT
ap-7660	342	17	r)→−(h±	r)→−(h±	PROPN
ap-7660	342	18	2	2	NUM
ap-7660	342	19	(	(	PUNCT
ap-7660	342	20	r))∗	r))∗	VERB
ap-7660	342	21	h±	h±	PROPN
ap-7660	342	22	1	1	NUM
ap-7660	342	23	(	(	PUNCT
ap-7660	342	24	r)→(h±	r)→(h±	NOUN
ap-7660	342	25	1	1	NUM
ap-7660	342	26	(	(	PUNCT
ap-7660	342	27	r))∗	r))∗	VERB
ap-7660	342	28	in	in	ADP
ap-7660	342	29	region	region	NOUN
ap-7660	342	30	2	2	NUM
ap-7660	342	31	no	no	DET
ap-7660	342	32	symmetry	symmetry	NOUN
ap-7660	342	33	in	in	ADP
ap-7660	342	34	region	region	NOUN
ap-7660	342	35	3	3	NUM
ap-7660	342	36	.	.	PUNCT
ap-7660	343	1	(	(	PUNCT
ap-7660	343	2	50	50	NUM
ap-7660	343	3	)	)	PUNCT
ap-7660	343	4	we	we	PRON
ap-7660	343	5	have	have	AUX
ap-7660	343	6	observed	observe	VERB
ap-7660	343	7	that	that	SCONJ
ap-7660	343	8	one	one	PRON
ap-7660	343	9	can	can	AUX
ap-7660	343	10	find	find	VERB
ap-7660	343	11	a	a	DET
ap-7660	343	12	well	well	ADV
ap-7660	343	13	-	-	PUNCT
ap-7660	343	14	defined	define	VERB
ap-7660	343	15	monopole	monopole	ADJ
ap-7660	343	16	solution	solution	NOUN
ap-7660	343	17	in	in	ADP
ap-7660	343	18	two	two	NUM
ap-7660	343	19	disconnected	disconnected	ADJ
ap-7660	343	20	regions	region	NOUN
ap-7660	343	21	.	.	PUNCT
ap-7660	344	1	however	however	ADV
ap-7660	344	2	,	,	PUNCT
ap-7660	344	3	in	in	ADP
ap-7660	344	4	the	the	DET
ap-7660	344	5	full	full	ADJ
ap-7660	344	6	theory	theory	NOUN
ap-7660	344	7	where	where	SCONJ
ap-7660	344	8	we	we	PRON
ap-7660	344	9	include	include	VERB
ap-7660	344	10	the	the	DET
ap-7660	344	11	higgs	higgs	NOUN
ap-7660	344	12	particles	particle	NOUN
ap-7660	344	13	,	,	PUNCT
ap-7660	344	14	it	it	PRON
ap-7660	344	15	is	be	AUX
ap-7660	344	16	only	only	ADV
ap-7660	344	17	one	one	NUM
ap-7660	344	18	of	of	ADP
ap-7660	344	19	the	the	DET
ap-7660	344	20	regions	region	NOUN
ap-7660	344	21	which	which	PRON
ap-7660	344	22	are	be	AUX
ap-7660	344	23	considered	consider	VERB
ap-7660	344	24	physical	physical	ADJ
ap-7660	344	25	.	.	PUNCT
ap-7660	345	1	this	this	PRON
ap-7660	345	2	is	be	AUX
ap-7660	345	3	because	because	SCONJ
ap-7660	345	4	the	the	DET
ap-7660	345	5	higgs	higgs	PROPN
ap-7660	345	6	mass	mass	PROPN
ap-7660	345	7	m2	m2	PROPN
ap-7660	345	8	0	0	PROPN
ap-7660	345	9	is	be	AUX
ap-7660	345	10	either	either	CCONJ
ap-7660	345	11	positive	positive	ADJ
ap-7660	345	12	or	or	CCONJ
ap-7660	345	13	negative	negative	ADJ
ap-7660	345	14	depending	depend	VERB
ap-7660	345	15	on	on	ADP
ap-7660	345	16	which	which	DET
ap-7660	345	17	side	side	NOUN
ap-7660	345	18	of	of	ADP
ap-7660	345	19	z2	z2	NOUN
ap-7660	345	20	=	=	SYM
ap-7660	345	21	1	1	NUM
ap-7660	345	22	it	it	PRON
ap-7660	345	23	is	be	AUX
ap-7660	345	24	defined	define	VERB
ap-7660	345	25	.	.	PUNCT
ap-7660	346	1	because	because	SCONJ
ap-7660	346	2	two	two	NUM
ap-7660	346	3	disconnected	disconnected	ADJ
ap-7660	346	4	regions	region	NOUN
ap-7660	346	5	are	be	AUX
ap-7660	346	6	defined	define	VERB
ap-7660	346	7	on	on	ADP
ap-7660	346	8	either	either	DET
ap-7660	346	9	side	side	NOUN
ap-7660	346	10	of	of	ADP
ap-7660	346	11	the	the	DET
ap-7660	346	12	zero	zero	NUM
ap-7660	346	13	exceptional	exceptional	ADJ
ap-7660	346	14	point	point	NOUN
ap-7660	346	15	z2	z2	NOUN
ap-7660	346	16	=	=	SYM
ap-7660	346	17	1	1	NUM
ap-7660	346	18	,	,	PUNCT
ap-7660	346	19	the	the	DET
ap-7660	346	20	full	full	ADJ
ap-7660	346	21	physical	physical	ADJ
ap-7660	346	22	region	region	NOUN
ap-7660	346	23	restricts	restrict	VERB
ap-7660	346	24	one	one	NUM
ap-7660	346	25	from	from	ADP
ap-7660	346	26	moving	move	VERB
ap-7660	346	27	region	region	NOUN
ap-7660	346	28	1	1	NUM
ap-7660	346	29	to	to	PART
ap-7660	346	30	region	region	NOUN
ap-7660	346	31	3	3	NUM
ap-7660	346	32	by	by	ADP
ap-7660	346	33	changing	change	VERB
ap-7660	346	34	z.	z.	PROPN
ap-7660	346	35	this	this	PRON
ap-7660	346	36	is	be	AUX
ap-7660	346	37	most	most	ADV
ap-7660	346	38	clearly	clearly	ADV
ap-7660	346	39	seen	see	VERB
ap-7660	346	40	in	in	ADP
ap-7660	346	41	figure	figure	NOUN
ap-7660	346	42	1	1	NUM
ap-7660	346	43	where	where	SCONJ
ap-7660	346	44	the	the	DET
ap-7660	346	45	plot	plot	NOUN
ap-7660	346	46	of	of	ADP
ap-7660	346	47	m2	m2	PROPN
ap-7660	346	48	0	0	PROPN
ap-7660	346	49	(	(	PUNCT
ap-7660	346	50	green	green	ADJ
ap-7660	346	51	line	line	NOUN
ap-7660	346	52	)	)	PUNCT
ap-7660	346	53	becomes	become	VERB
ap-7660	346	54	negative	negative	ADJ
ap-7660	346	55	beyond	beyond	ADP
ap-7660	346	56	the	the	DET
ap-7660	346	57	zero	zero	NUM
ap-7660	346	58	exceptional	exceptional	ADJ
ap-7660	346	59	point	point	NOUN
ap-7660	346	60	.	.	PUNCT
ap-7660	347	1	this	this	PRON
ap-7660	347	2	may	may	AUX
ap-7660	347	3	imply	imply	VERB
ap-7660	347	4	that	that	SCONJ
ap-7660	347	5	the	the	DET
ap-7660	347	6	purely	purely	ADV
ap-7660	347	7	complex	complex	ADJ
ap-7660	347	8	monopole	monopole	NOUN
ap-7660	347	9	solution	solution	NOUN
ap-7660	347	10	we	we	PRON
ap-7660	347	11	observed	observe	VERB
ap-7660	347	12	is	be	AUX
ap-7660	347	13	not	not	PART
ap-7660	347	14	a	a	DET
ap-7660	347	15	possible	possible	ADJ
ap-7660	347	16	solution	solution	NOUN
ap-7660	347	17	of	of	ADP
ap-7660	347	18	the	the	DET
ap-7660	347	19	theory	theory	NOUN
ap-7660	347	20	.	.	PUNCT
ap-7660	348	1	however	however	ADV
ap-7660	348	2	,	,	PUNCT
ap-7660	348	3	the	the	DET
ap-7660	348	4	purely	purely	ADV
ap-7660	348	5	complex	complex	ADJ
ap-7660	348	6	solution	solution	NOUN
ap-7660	348	7	can	can	AUX
ap-7660	348	8	exist	exist	VERB
ap-7660	348	9	in	in	ADP
ap-7660	348	10	the	the	DET
ap-7660	348	11	full	full	ADJ
ap-7660	348	12	physical	physical	ADJ
ap-7660	348	13	region	region	NOUN
ap-7660	348	14	.	.	PUNCT
ap-7660	349	1	an	an	DET
ap-7660	349	2	example	example	NOUN
ap-7660	349	3	of	of	ADP
ap-7660	349	4	this	this	PRON
ap-7660	349	5	is	be	AUX
ap-7660	349	6	shown	show	VERB
ap-7660	349	7	in	in	ADP
ap-7660	349	8	the	the	DET
ap-7660	349	9	figure	figure	NOUN
ap-7660	349	10	6	6	NUM
ap-7660	349	11	where	where	SCONJ
ap-7660	349	12	we	we	PRON
ap-7660	349	13	observe	observe	VERB
ap-7660	349	14	that	that	SCONJ
ap-7660	349	15	the	the	DET
ap-7660	349	16	profile	profile	NOUN
ap-7660	349	17	function	function	VERB
ap-7660	349	18	h1	h1	NOUN
ap-7660	349	19	(	(	PUNCT
ap-7660	349	20	therefore	therefore	ADV
ap-7660	349	21	h2	h2	NOUN
ap-7660	349	22	)	)	PUNCT
ap-7660	349	23	is	be	AUX
ap-7660	349	24	purely	purely	ADV
ap-7660	349	25	complex	complex	ADJ
ap-7660	349	26	,	,	PUNCT
ap-7660	349	27	and	and	CCONJ
ap-7660	349	28	the	the	DET
ap-7660	349	29	higgs	higgs	NOUN
ap-7660	349	30	masses	masse	NOUN
ap-7660	349	31	,	,	PUNCT
ap-7660	349	32	gauge	gauge	ADJ
ap-7660	349	33	mass	mass	NOUN
ap-7660	349	34	are	be	AUX
ap-7660	349	35	all	all	ADV
ap-7660	349	36	real	real	ADJ
ap-7660	349	37	and	and	CCONJ
ap-7660	349	38	positive	positive	ADJ
ap-7660	349	39	.	.	PUNCT
ap-7660	350	1	4	4	X
ap-7660	350	2	.	.	X
ap-7660	350	3	conclusions	conclusion	NOUN
ap-7660	350	4	we	we	PRON
ap-7660	350	5	have	have	AUX
ap-7660	350	6	found	find	VERB
ap-7660	350	7	the	the	DET
ap-7660	350	8	t’hooft	t’hooft	NOUN
ap-7660	350	9	-	-	PUNCT
ap-7660	350	10	polyakov	polyakov	NOUN
ap-7660	350	11	monopole	monopole	NOUN
ap-7660	350	12	solution	solution	NOUN
ap-7660	350	13	(	(	PUNCT
ap-7660	350	14	43	43	NUM
ap-7660	350	15	)	)	PUNCT
ap-7660	350	16	in	in	ADP
ap-7660	350	17	the	the	DET
ap-7660	350	18	non	non	ADJ
ap-7660	350	19	-	-	ADJ
ap-7660	350	20	hermitian	hermitian	ADJ
ap-7660	350	21	theory	theory	NOUN
ap-7660	350	22	by	by	ADP
ap-7660	350	23	drawing	draw	VERB
ap-7660	350	24	an	an	DET
ap-7660	350	25	205	205	NUM
ap-7660	350	26	takanobu	takanobu	NOUN
ap-7660	350	27	taira	taira	PROPN
ap-7660	350	28	acta	acta	PROPN
ap-7660	350	29	polytechnica	polytechnica	PROPN
ap-7660	350	30	figure	figure	NOUN
ap-7660	350	31	6	6	NUM
ap-7660	350	32	.	.	PUNCT
ap-7660	351	1	both	both	DET
ap-7660	351	2	panels	panel	NOUN
ap-7660	351	3	are	be	AUX
ap-7660	351	4	plotted	plot	VERB
ap-7660	351	5	for	for	ADP
ap-7660	351	6	x	x	SYM
ap-7660	351	7	=	=	SYM
ap-7660	351	8	−2	−2	NOUN
ap-7660	351	9	,	,	PUNCT
ap-7660	351	10	y	y	PROPN
ap-7660	351	11	=	=	SYM
ap-7660	351	12	−0.6	−0.6	PROPN
ap-7660	351	13	,	,	PUNCT
ap-7660	351	14	c1	c1	NOUN
ap-7660	351	15	=	=	PROPN
ap-7660	352	1	−c2	−c2	PROPN
ap-7660	352	2	=	=	SYM
ap-7660	352	3	1	1	NUM
ap-7660	352	4	,	,	PUNCT
ap-7660	352	5	n	n	NOUN
ap-7660	352	6	=	=	SYM
ap-7660	352	7	1	1	NUM
ap-7660	352	8	,	,	PUNCT
ap-7660	352	9	e	e	NOUN
ap-7660	352	10	=	=	SYM
ap-7660	352	11	2	2	X
ap-7660	352	12	.	.	PUNCT
ap-7660	353	1	the	the	DET
ap-7660	353	2	solid	solid	ADJ
ap-7660	353	3	line	line	NOUN
ap-7660	353	4	represents	represent	VERB
ap-7660	353	5	the	the	DET
ap-7660	353	6	real	real	ADJ
ap-7660	353	7	part	part	NOUN
ap-7660	353	8	,	,	PUNCT
ap-7660	353	9	and	and	CCONJ
ap-7660	353	10	the	the	DET
ap-7660	353	11	dotted	dotted	ADJ
ap-7660	353	12	line	line	NOUN
ap-7660	353	13	represents	represent	VERB
ap-7660	353	14	the	the	DET
ap-7660	353	15	imaginary	imaginary	ADJ
ap-7660	353	16	part	part	NOUN
ap-7660	353	17	of	of	ADP
ap-7660	353	18	the	the	DET
ap-7660	353	19	masses	masse	NOUN
ap-7660	353	20	.	.	PUNCT
ap-7660	354	1	analogue	analogue	NOUN
ap-7660	354	2	from	from	ADP
ap-7660	354	3	the	the	DET
ap-7660	354	4	standard	standard	ADJ
ap-7660	354	5	procedure	procedure	NOUN
ap-7660	354	6	in	in	ADP
ap-7660	354	7	the	the	DET
ap-7660	354	8	hermitian	hermitian	ADJ
ap-7660	354	9	theory	theory	NOUN
ap-7660	354	10	.	.	PUNCT
ap-7660	355	1	the	the	DET
ap-7660	355	2	monopole	monopole	ADJ
ap-7660	355	3	masses	masse	NOUN
ap-7660	355	4	were	be	AUX
ap-7660	355	5	plotted	plot	VERB
ap-7660	355	6	with	with	ADP
ap-7660	355	7	the	the	DET
ap-7660	355	8	massive	massive	ADJ
ap-7660	355	9	gauge	gauge	NOUN
ap-7660	355	10	and	and	CCONJ
ap-7660	355	11	higgs	higgs	NOUN
ap-7660	355	12	masses	masse	NOUN
ap-7660	355	13	,	,	PUNCT
ap-7660	355	14	where	where	SCONJ
ap-7660	355	15	the	the	DET
ap-7660	355	16	physical	physical	ADJ
ap-7660	355	17	region	region	NOUN
ap-7660	355	18	of	of	ADP
ap-7660	355	19	the	the	DET
ap-7660	355	20	monopole	monopole	ADJ
ap-7660	355	21	masses	masse	NOUN
ap-7660	355	22	coincided	coincide	VERB
ap-7660	355	23	with	with	ADP
ap-7660	355	24	that	that	PRON
ap-7660	355	25	of	of	ADP
ap-7660	355	26	the	the	DET
ap-7660	355	27	gauge	gauge	NOUN
ap-7660	355	28	mass	mass	PROPN
ap-7660	355	29	.	.	PUNCT
ap-7660	356	1	it	it	PRON
ap-7660	356	2	was	be	AUX
ap-7660	356	3	also	also	ADV
ap-7660	356	4	observed	observe	VERB
ap-7660	356	5	that	that	SCONJ
ap-7660	356	6	there	there	PRON
ap-7660	356	7	are	be	VERB
ap-7660	356	8	two	two	NUM
ap-7660	356	9	distinct	distinct	ADJ
ap-7660	356	10	physical	physical	ADJ
ap-7660	356	11	regions	region	NOUN
ap-7660	356	12	bounded	bound	VERB
ap-7660	356	13	by	by	ADP
ap-7660	356	14	the	the	DET
ap-7660	356	15	zero	zero	NUM
ap-7660	356	16	exceptional	exceptional	ADJ
ap-7660	356	17	point	point	NOUN
ap-7660	356	18	and	and	CCONJ
ap-7660	356	19	the	the	DET
ap-7660	356	20	parameter	parameter	NOUN
ap-7660	356	21	limit	limit	NOUN
ap-7660	356	22	where	where	SCONJ
ap-7660	356	23	the	the	DET
ap-7660	356	24	vacuum	vacuum	NOUN
ap-7660	356	25	manifold	manifold	NOUN
ap-7660	356	26	becomes	become	VERB
ap-7660	356	27	trivial	trivial	ADJ
ap-7660	356	28	.	.	PUNCT
ap-7660	357	1	the	the	DET
ap-7660	357	2	profile	profile	NOUN
ap-7660	357	3	function	function	NOUN
ap-7660	357	4	(	(	PUNCT
ap-7660	357	5	radial	radial	ADJ
ap-7660	357	6	part	part	NOUN
ap-7660	357	7	of	of	ADP
ap-7660	357	8	the	the	DET
ap-7660	357	9	monopole	monopole	ADJ
ap-7660	357	10	solution	solution	NOUN
ap-7660	357	11	)	)	PUNCT
ap-7660	357	12	is	be	AUX
ap-7660	357	13	plotted	plot	VERB
ap-7660	357	14	in	in	ADP
ap-7660	357	15	figures	figure	NOUN
ap-7660	357	16	3	3	NUM
ap-7660	357	17	,	,	PUNCT
ap-7660	357	18	4	4	NUM
ap-7660	357	19	,	,	PUNCT
ap-7660	357	20	5	5	NUM
ap-7660	357	21	,	,	PUNCT
ap-7660	357	22	where	where	SCONJ
ap-7660	357	23	it	it	PRON
ap-7660	357	24	is	be	AUX
ap-7660	357	25	real	real	ADJ
ap-7660	357	26	and	and	CCONJ
ap-7660	357	27	purely	purely	ADV
ap-7660	357	28	complex	complex	ADJ
ap-7660	357	29	in	in	ADP
ap-7660	357	30	regions	region	NOUN
ap-7660	357	31	1	1	NUM
ap-7660	357	32	and	and	CCONJ
ap-7660	357	33	3	3	NUM
ap-7660	357	34	,	,	PUNCT
ap-7660	357	35	respectively	respectively	ADV
ap-7660	357	36	.	.	PUNCT
ap-7660	358	1	incidentally	incidentally	ADV
ap-7660	358	2	,	,	PUNCT
ap-7660	358	3	the	the	DET
ap-7660	358	4	cpt	cpt	PROPN
ap-7660	358	5	symmetries	symmetry	NOUN
ap-7660	358	6	of	of	ADP
ap-7660	358	7	the	the	DET
ap-7660	358	8	solution	solution	NOUN
ap-7660	358	9	are	be	AUX
ap-7660	358	10	different	different	ADJ
ap-7660	358	11	in	in	ADP
ap-7660	358	12	regions	region	NOUN
ap-7660	358	13	1	1	NUM
ap-7660	358	14	and	and	CCONJ
ap-7660	358	15	3	3	NUM
ap-7660	358	16	.	.	X
ap-7660	359	1	acknowledgements	acknowledgement	NOUN
ap-7660	359	2	tt	tt	PROPN
ap-7660	359	3	is	be	AUX
ap-7660	359	4	supported	support	VERB
ap-7660	359	5	by	by	ADP
ap-7660	359	6	epsrc	epsrc	PROPN
ap-7660	359	7	grant	grant	PROPN
ap-7660	359	8	ep	ep	PROPN
ap-7660	359	9	/	/	SYM
ap-7660	359	10	w522351/1	w522351/1	NOUN
ap-7660	359	11	.	.	PUNCT
ap-7660	360	1	references	reference	NOUN
ap-7660	360	2	[	[	X
ap-7660	360	3	1	1	X
ap-7660	360	4	]	]	PUNCT
ap-7660	360	5	j.	j.	PROPN
ap-7660	360	6	alexandre	alexandre	PROPN
ap-7660	360	7	,	,	PUNCT
ap-7660	360	8	p.	p.	PROPN
ap-7660	360	9	millington	millington	PROPN
ap-7660	360	10	,	,	PUNCT
ap-7660	360	11	d.	d.	PROPN
ap-7660	360	12	seynaeve	seynaeve	PROPN
ap-7660	360	13	.	.	PUNCT
ap-7660	361	1	symmetries	symmetry	NOUN
ap-7660	361	2	and	and	CCONJ
ap-7660	361	3	conservation	conservation	NOUN
ap-7660	361	4	laws	law	NOUN
ap-7660	361	5	in	in	ADP
ap-7660	361	6	non	non	ADJ
ap-7660	361	7	-	-	ADJ
ap-7660	361	8	hermitian	hermitian	ADJ
ap-7660	361	9	field	field	NOUN
ap-7660	361	10	theories	theory	NOUN
ap-7660	361	11	.	.	PUNCT
ap-7660	362	1	physical	physical	ADJ
ap-7660	362	2	review	review	PROPN
ap-7660	362	3	d	d	PROPN
ap-7660	362	4	96(6):065027	96(6):065027	NUM
ap-7660	362	5	,	,	PUNCT
ap-7660	362	6	2017	2017	NUM
ap-7660	362	7	.	.	PUNCT
ap-7660	363	1	https://doi.org/10.1103/physrevd.96.065027	https://doi.org/10.1103/physrevd.96.065027	PROPN
ap-7660	363	2	.	.	PUNCT
ap-7660	364	1	[	[	X
ap-7660	364	2	2	2	X
ap-7660	364	3	]	]	PUNCT
ap-7660	364	4	j.	j.	PROPN
ap-7660	364	5	alexandre	alexandre	PROPN
ap-7660	364	6	,	,	PUNCT
ap-7660	364	7	j.	j.	PROPN
ap-7660	364	8	ellis	ellis	PROPN
ap-7660	364	9	,	,	PUNCT
ap-7660	364	10	p.	p.	PROPN
ap-7660	364	11	millington	millington	PROPN
ap-7660	364	12	,	,	PUNCT
ap-7660	364	13	d.	d.	PROPN
ap-7660	364	14	seynaeve	seynaeve	PROPN
ap-7660	364	15	.	.	PUNCT
ap-7660	365	1	spontaneous	spontaneous	ADJ
ap-7660	365	2	symmetry	symmetry	NOUN
ap-7660	365	3	breaking	breaking	NOUN
ap-7660	365	4	and	and	CCONJ
ap-7660	365	5	the	the	DET
ap-7660	365	6	goldstone	goldstone	NOUN
ap-7660	365	7	theorem	theorem	NOUN
ap-7660	365	8	in	in	ADP
ap-7660	365	9	non	non	ADJ
ap-7660	365	10	-	-	ADJ
ap-7660	365	11	hermitian	hermitian	ADJ
ap-7660	365	12	field	field	NOUN
ap-7660	365	13	theories	theory	NOUN
ap-7660	365	14	.	.	PUNCT
ap-7660	366	1	physical	physical	ADJ
ap-7660	366	2	review	review	PROPN
ap-7660	366	3	d	d	PROPN
ap-7660	366	4	98(4):045001	98(4):045001	PROPN
ap-7660	366	5	,	,	PUNCT
ap-7660	366	6	2018	2018	NUM
ap-7660	366	7	.	.	PUNCT
ap-7660	367	1	https://doi.org/10.1103/physrevd.98.045001	https://doi.org/10.1103/physrevd.98.045001	NOUN
ap-7660	367	2	.	.	PUNCT
ap-7660	368	1	[	[	X
ap-7660	368	2	3	3	X
ap-7660	368	3	]	]	X
ap-7660	368	4	p.	p.	PROPN
ap-7660	368	5	d.	d.	PROPN
ap-7660	368	6	mannheim	mannheim	PROPN
ap-7660	368	7	.	.	PUNCT
ap-7660	369	1	goldstone	goldstone	NOUN
ap-7660	369	2	bosons	boson	NOUN
ap-7660	369	3	and	and	CCONJ
ap-7660	369	4	the	the	DET
ap-7660	369	5	englert	englert	PROPN
ap-7660	369	6	-	-	PUNCT
ap-7660	369	7	brout	brout	NOUN
ap-7660	369	8	-	-	PUNCT
ap-7660	369	9	higgs	higgs	NOUN
ap-7660	369	10	mechanism	mechanism	NOUN
ap-7660	369	11	in	in	ADP
ap-7660	369	12	non	non	ADJ
ap-7660	369	13	-	-	ADJ
ap-7660	369	14	hermitian	hermitian	ADJ
ap-7660	369	15	theories	theory	NOUN
ap-7660	369	16	.	.	PUNCT
ap-7660	370	1	physical	physical	ADJ
ap-7660	370	2	review	review	PROPN
ap-7660	370	3	d	d	PROPN
ap-7660	370	4	99(4):045006	99(4):045006	PROPN
ap-7660	370	5	,	,	PUNCT
ap-7660	370	6	2019	2019	NUM
ap-7660	370	7	.	.	PUNCT
ap-7660	371	1	https://doi.org/10.1103/physrevd.99.045006	https://doi.org/10.1103/physrevd.99.045006	NOUN
ap-7660	371	2	.	.	PUNCT
ap-7660	372	1	[	[	X
ap-7660	372	2	4	4	X
ap-7660	372	3	]	]	PUNCT
ap-7660	372	4	p.	p.	PROPN
ap-7660	372	5	millington	millington	PROPN
ap-7660	372	6	.	.	PUNCT
ap-7660	373	1	symmetry	symmetry	NOUN
ap-7660	373	2	properties	property	NOUN
ap-7660	373	3	of	of	ADP
ap-7660	373	4	non	non	ADJ
ap-7660	373	5	-	-	ADJ
ap-7660	373	6	hermitian	hermitian	ADJ
ap-7660	373	7	pt	pt	ADJ
ap-7660	373	8	-symmetric	-symmetric	ADJ
ap-7660	373	9	quantum	quantum	ADJ
ap-7660	373	10	field	field	NOUN
ap-7660	373	11	theories	theory	NOUN
ap-7660	373	12	.	.	PUNCT
ap-7660	374	1	journal	journal	PROPN
ap-7660	374	2	of	of	ADP
ap-7660	374	3	physics	physics	PROPN
ap-7660	374	4	:	:	PUNCT
ap-7660	374	5	conference	conference	NOUN
ap-7660	374	6	series	series	PROPN
ap-7660	374	7	1586(1):012001	1586(1):012001	PROPN
ap-7660	374	8	,	,	PUNCT
ap-7660	374	9	2020	2020	NUM
ap-7660	374	10	.	.	PUNCT
ap-7660	375	1	https://doi.org/10.1088/1742-6596/1586/1/012001	https://doi.org/10.1088/1742-6596/1586/1/012001	X
ap-7660	375	2	.	.	PUNCT
ap-7660	376	1	[	[	X
ap-7660	376	2	5	5	X
ap-7660	376	3	]	]	PUNCT
ap-7660	376	4	j.	j.	PROPN
ap-7660	376	5	alexandre	alexandre	PROPN
ap-7660	376	6	,	,	PUNCT
ap-7660	376	7	j.	j.	PROPN
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ap-7660	376	9	,	,	PUNCT
ap-7660	376	10	p.	p.	PROPN
ap-7660	376	11	millington	millington	PROPN
ap-7660	376	12	,	,	PUNCT
ap-7660	376	13	d.	d.	PROPN
ap-7660	376	14	seynaeve	seynaeve	PROPN
ap-7660	376	15	.	.	PUNCT
ap-7660	377	1	spontaneously	spontaneously	ADV
ap-7660	377	2	breaking	break	VERB
ap-7660	377	3	non	non	ADJ
ap-7660	377	4	-	-	ADJ
ap-7660	377	5	abelian	abelian	ADJ
ap-7660	377	6	gauge	gauge	NOUN
ap-7660	377	7	symmetry	symmetry	NOUN
ap-7660	377	8	in	in	ADP
ap-7660	377	9	non	non	ADJ
ap-7660	377	10	-	-	ADJ
ap-7660	377	11	hermitian	hermitian	ADJ
ap-7660	377	12	field	field	NOUN
ap-7660	377	13	theories	theory	NOUN
ap-7660	377	14	.	.	PUNCT
ap-7660	378	1	physical	physical	ADJ
ap-7660	378	2	review	review	PROPN
ap-7660	378	3	d	d	PROPN
ap-7660	378	4	101(3):035008	101(3):035008	PROPN
ap-7660	378	5	,	,	PUNCT
ap-7660	378	6	2019	2019	NUM
ap-7660	378	7	.	.	PUNCT
ap-7660	379	1	https://doi.org/10.1103/physrevd.101.035008	https://doi.org/10.1103/physrevd.101.035008	NOUN
ap-7660	379	2	.	.	PUNCT
ap-7660	380	1	[	[	X
ap-7660	380	2	6	6	NUM
ap-7660	380	3	]	]	PUNCT
ap-7660	380	4	j.	j.	PROPN
ap-7660	380	5	alexandre	alexandre	PROPN
ap-7660	380	6	,	,	PUNCT
ap-7660	380	7	j.	j.	PROPN
ap-7660	380	8	ellis	ellis	PROPN
ap-7660	380	9	,	,	PUNCT
ap-7660	380	10	p.	p.	PROPN
ap-7660	380	11	millington	millington	PROPN
ap-7660	380	12	,	,	PUNCT
ap-7660	380	13	d.	d.	PROPN
ap-7660	380	14	seynaeve	seynaeve	PROPN
ap-7660	380	15	.	.	PUNCT
ap-7660	381	1	gauge	gauge	NOUN
ap-7660	381	2	invariance	invariance	NOUN
ap-7660	381	3	and	and	CCONJ
ap-7660	381	4	the	the	DET
ap-7660	381	5	englert	englert	PROPN
ap-7660	381	6	-	-	PUNCT
ap-7660	381	7	brout	brout	NOUN
ap-7660	381	8	-	-	PUNCT
ap-7660	381	9	higgs	higgs	NOUN
ap-7660	381	10	mechanism	mechanism	NOUN
ap-7660	381	11	in	in	ADP
ap-7660	381	12	non	non	ADJ
ap-7660	381	13	-	-	ADJ
ap-7660	381	14	hermitian	hermitian	ADJ
ap-7660	381	15	field	field	NOUN
ap-7660	381	16	theories	theory	NOUN
ap-7660	381	17	.	.	PUNCT
ap-7660	382	1	physical	physical	ADJ
ap-7660	382	2	review	review	PROPN
ap-7660	382	3	d	d	PROPN
ap-7660	382	4	99(7):075024	99(7):075024	NUM
ap-7660	382	5	,	,	PUNCT
ap-7660	382	6	2019	2019	NUM
ap-7660	382	7	.	.	PUNCT
ap-7660	383	1	https://doi.org/10.1103/physrevd.99.075024	https://doi.org/10.1103/physrevd.99.075024	NOUN
ap-7660	383	2	.	.	PUNCT
ap-7660	384	1	[	[	X
ap-7660	384	2	7	7	X
ap-7660	384	3	]	]	PUNCT
ap-7660	384	4	j.	j.	PROPN
ap-7660	384	5	alexandre	alexandre	PROPN
ap-7660	384	6	,	,	PUNCT
ap-7660	384	7	j.	j.	PROPN
ap-7660	384	8	ellis	ellis	PROPN
ap-7660	384	9	,	,	PUNCT
ap-7660	384	10	p.	p.	PROPN
ap-7660	384	11	millington	millington	PROPN
ap-7660	384	12	.	.	PUNCT
ap-7660	385	1	discrete	discrete	ADJ
ap-7660	385	2	spacetime	spacetime	NOUN
ap-7660	385	3	symmetries	symmetry	NOUN
ap-7660	385	4	and	and	CCONJ
ap-7660	385	5	particle	particle	NOUN
ap-7660	385	6	mixing	mixing	NOUN
ap-7660	385	7	in	in	ADP
ap-7660	385	8	non	non	ADJ
ap-7660	385	9	-	-	ADJ
ap-7660	385	10	hermitian	hermitian	ADJ
ap-7660	385	11	scalar	scalar	ADJ
ap-7660	385	12	quantum	quantum	ADJ
ap-7660	385	13	field	field	NOUN
ap-7660	385	14	theories	theory	NOUN
ap-7660	385	15	.	.	PUNCT
ap-7660	386	1	physical	physical	ADJ
ap-7660	386	2	review	review	PROPN
ap-7660	386	3	d	d	PROPN
ap-7660	386	4	102(12):125030	102(12):125030	PROPN
ap-7660	386	5	,	,	PUNCT
ap-7660	386	6	2020	2020	NUM
ap-7660	386	7	.	.	PUNCT
ap-7660	387	1	https://doi.org/10.1103/physrevd.102.125030	https://doi.org/10.1103/physrevd.102.125030	NOUN
ap-7660	387	2	.	.	PUNCT
ap-7660	388	1	[	[	X
ap-7660	388	2	8	8	NUM
ap-7660	388	3	]	]	X
ap-7660	388	4	a.	a.	NOUN
ap-7660	388	5	fring	fring	NOUN
ap-7660	388	6	,	,	PUNCT
ap-7660	388	7	t.	t.	PROPN
ap-7660	388	8	taira	taira	PROPN
ap-7660	388	9	.	.	PUNCT
ap-7660	389	1	goldstone	goldstone	NOUN
ap-7660	389	2	bosons	boson	NOUN
ap-7660	389	3	in	in	ADP
ap-7660	389	4	different	different	ADJ
ap-7660	389	5	pt	pt	NOUN
ap-7660	389	6	-regimes	-regime	NOUN
ap-7660	389	7	of	of	ADP
ap-7660	389	8	non	non	ADJ
ap-7660	389	9	-	-	ADJ
ap-7660	389	10	hermitian	hermitian	ADJ
ap-7660	389	11	scalar	scalar	ADJ
ap-7660	389	12	quantum	quantum	ADJ
ap-7660	389	13	field	field	NOUN
ap-7660	389	14	theories	theory	NOUN
ap-7660	389	15	.	.	PUNCT
ap-7660	390	1	nuclear	nuclear	ADJ
ap-7660	390	2	physics	physics	PROPN
ap-7660	390	3	b	b	PROPN
ap-7660	390	4	950:114834	950:114834	NUM
ap-7660	390	5	,	,	PUNCT
ap-7660	390	6	2020	2020	NUM
ap-7660	390	7	.	.	PUNCT
ap-7660	391	1	https://doi.org/10.1016/j.nuclphysb.2019.114834	https://doi.org/10.1016/j.nuclphysb.2019.114834	NOUN
ap-7660	391	2	.	.	PUNCT
ap-7660	392	1	[	[	X
ap-7660	392	2	9	9	NUM
ap-7660	392	3	]	]	PUNCT
ap-7660	392	4	a.	a.	NOUN
ap-7660	392	5	fring	fring	NOUN
ap-7660	392	6	,	,	PUNCT
ap-7660	392	7	t.	t.	PROPN
ap-7660	392	8	taira	taira	PROPN
ap-7660	392	9	.	.	PUNCT
ap-7660	393	1	massive	massive	ADJ
ap-7660	393	2	gauge	gauge	ADJ
ap-7660	393	3	particles	particle	NOUN
ap-7660	393	4	versus	versus	ADP
ap-7660	393	5	goldstone	goldstone	NOUN
ap-7660	393	6	bosons	boson	NOUN
ap-7660	393	7	in	in	ADP
ap-7660	393	8	non	non	ADJ
ap-7660	393	9	-	-	ADJ
ap-7660	393	10	hermitian	hermitian	ADJ
ap-7660	393	11	non	non	ADJ
ap-7660	393	12	-	-	ADJ
ap-7660	393	13	abelian	abelian	ADJ
ap-7660	393	14	gauge	gauge	NOUN
ap-7660	393	15	theory	theory	NOUN
ap-7660	393	16	,	,	PUNCT
ap-7660	393	17	2020	2020	NUM
ap-7660	393	18	.	.	PUNCT
ap-7660	394	1	arxiv:2004.00723	arxiv:2004.00723	ADJ
ap-7660	394	2	.	.	PUNCT
ap-7660	395	1	[	[	X
ap-7660	395	2	10	10	NUM
ap-7660	395	3	]	]	X
ap-7660	395	4	a.	a.	NOUN
ap-7660	395	5	fring	fring	NOUN
ap-7660	395	6	,	,	PUNCT
ap-7660	395	7	t.	t.	PROPN
ap-7660	395	8	taira	taira	PROPN
ap-7660	395	9	.	.	PUNCT
ap-7660	396	1	pseudo	pseudo	NOUN
ap-7660	396	2	-	-	ADJ
ap-7660	396	3	hermitian	hermitian	ADJ
ap-7660	396	4	approach	approach	NOUN
ap-7660	396	5	to	to	ADP
ap-7660	396	6	goldstone	goldstone	NOUN
ap-7660	396	7	’s	’s	PART
ap-7660	396	8	theorem	theorem	NOUN
ap-7660	396	9	in	in	ADP
ap-7660	396	10	non	non	ADJ
ap-7660	396	11	-	-	ADJ
ap-7660	396	12	abelian	abelian	ADJ
ap-7660	396	13	non	non	ADJ
ap-7660	396	14	-	-	ADJ
ap-7660	396	15	hermitian	hermitian	ADJ
ap-7660	396	16	quantum	quantum	ADJ
ap-7660	396	17	field	field	NOUN
ap-7660	396	18	theories	theory	NOUN
ap-7660	396	19	.	.	PUNCT
ap-7660	397	1	physical	physical	ADJ
ap-7660	397	2	review	review	PROPN
ap-7660	397	3	d	d	PROPN
ap-7660	397	4	101(4):045014	101(4):045014	PROPN
ap-7660	397	5	,	,	PUNCT
ap-7660	397	6	2020	2020	NUM
ap-7660	397	7	.	.	PUNCT
ap-7660	398	1	https://doi.org/10.1103/physrevd.101.045014	https://doi.org/10.1103/physrevd.101.045014	NOUN
ap-7660	398	2	.	.	PUNCT
ap-7660	399	1	[	[	X
ap-7660	399	2	11	11	NUM
ap-7660	399	3	]	]	X
ap-7660	399	4	a.	a.	NOUN
ap-7660	399	5	fring	fring	NOUN
ap-7660	399	6	,	,	PUNCT
ap-7660	399	7	t.	t.	PROPN
ap-7660	399	8	taira	taira	PROPN
ap-7660	399	9	.	.	PUNCT
ap-7660	399	10	’	'	PUNCT
ap-7660	400	1	t	t	PROPN
ap-7660	400	2	hooft	hooft	NOUN
ap-7660	400	3	-	-	PUNCT
ap-7660	400	4	polyakov	polyakov	NOUN
ap-7660	400	5	monopoles	monopole	NOUN
ap-7660	400	6	in	in	ADP
ap-7660	400	7	non	non	ADJ
ap-7660	400	8	-	-	ADJ
ap-7660	400	9	hermitian	hermitian	ADJ
ap-7660	400	10	quantum	quantum	ADJ
ap-7660	400	11	field	field	NOUN
ap-7660	400	12	theory	theory	NOUN
ap-7660	400	13	.	.	PUNCT
ap-7660	401	1	physics	physics	NOUN
ap-7660	401	2	letters	letters	PROPN
ap-7660	401	3	b	b	PROPN
ap-7660	401	4	807:135583	807:135583	NUM
ap-7660	401	5	,	,	PUNCT
ap-7660	401	6	2020	2020	NUM
ap-7660	401	7	.	.	PUNCT
ap-7660	402	1	https://doi.org/10.1016/j.physletb.2020.135583	https://doi.org/10.1016/j.physletb.2020.135583	NOUN
ap-7660	402	2	.	.	PUNCT
ap-7660	403	1	[	[	X
ap-7660	403	2	12	12	NUM
ap-7660	403	3	]	]	PUNCT
ap-7660	403	4	j.	j.	PROPN
ap-7660	403	5	alexandre	alexandre	PROPN
ap-7660	403	6	,	,	PUNCT
ap-7660	403	7	j.	j.	PROPN
ap-7660	403	8	ellis	ellis	PROPN
ap-7660	403	9	,	,	PUNCT
ap-7660	403	10	p.	p.	PROPN
ap-7660	403	11	millington	millington	PROPN
ap-7660	403	12	.	.	PUNCT
ap-7660	404	1	pt	pt	PROPN
ap-7660	404	2	-symmetric	-symmetric	ADJ
ap-7660	404	3	non	non	ADJ
ap-7660	404	4	-	-	ADJ
ap-7660	404	5	hermitian	hermitian	ADJ
ap-7660	404	6	quantum	quantum	ADJ
ap-7660	404	7	field	field	NOUN
ap-7660	404	8	theories	theory	NOUN
ap-7660	404	9	with	with	ADP
ap-7660	404	10	supersymmetry	supersymmetry	NOUN
ap-7660	404	11	.	.	PUNCT
ap-7660	405	1	physical	physical	ADJ
ap-7660	405	2	review	review	PROPN
ap-7660	405	3	d	d	PROPN
ap-7660	405	4	101(8):085015	101(8):085015	PROPN
ap-7660	405	5	,	,	PUNCT
ap-7660	405	6	2020	2020	NUM
ap-7660	405	7	.	.	PUNCT
ap-7660	406	1	https://doi.org/10.1103/physrevd.101.085015	https://doi.org/10.1103/physrevd.101.085015	ADV
ap-7660	406	2	.	.	PUNCT
ap-7660	407	1	[	[	X
ap-7660	407	2	13	13	NUM
ap-7660	407	3	]	]	PUNCT
ap-7660	407	4	m.	m.	NOUN
ap-7660	407	5	n.	n.	PROPN
ap-7660	407	6	chernodub	chernodub	PROPN
ap-7660	407	7	,	,	PUNCT
ap-7660	407	8	a.	a.	NOUN
ap-7660	407	9	cortijo	cortijo	PROPN
ap-7660	407	10	,	,	PUNCT
ap-7660	407	11	m.	m.	NOUN
ap-7660	407	12	ruggieri	ruggieri	PROPN
ap-7660	407	13	.	.	PUNCT
ap-7660	408	1	spontaneous	spontaneous	ADJ
ap-7660	408	2	non	non	ADJ
ap-7660	408	3	-	-	NOUN
ap-7660	408	4	hermiticity	hermiticity	NOUN
ap-7660	408	5	in	in	ADP
ap-7660	408	6	the	the	DET
ap-7660	408	7	nambu	nambu	NOUN
ap-7660	408	8	–	–	PUNCT
ap-7660	408	9	jonalasinio	jonalasinio	NOUN
ap-7660	408	10	model	model	NOUN
ap-7660	408	11	.	.	PUNCT
ap-7660	409	1	physical	physical	ADJ
ap-7660	409	2	review	review	PROPN
ap-7660	409	3	d	d	PROPN
ap-7660	409	4	104(5):056023	104(5):056023	PROPN
ap-7660	409	5	,	,	PUNCT
ap-7660	409	6	2021	2021	NUM
ap-7660	409	7	.	.	PUNCT
ap-7660	410	1	https://doi.org/10.1103/physrevd.104.056023	https://doi.org/10.1103/physrevd.104.056023	X
ap-7660	410	2	.	.	PUNCT
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ap-7660	411	3	]	]	PUNCT
ap-7660	411	4	m.	m.	NOUN
ap-7660	411	5	n.	n.	PROPN
ap-7660	411	6	chernodub	chernodub	PROPN
ap-7660	411	7	,	,	PUNCT
ap-7660	411	8	p.	p.	PROPN
ap-7660	411	9	millington	millington	PROPN
ap-7660	411	10	.	.	PUNCT
ap-7660	412	1	ir	ir	PROPN
ap-7660	412	2	/	/	SYM
ap-7660	412	3	uv	uv	NOUN
ap-7660	412	4	mixing	mix	VERB
ap-7660	412	5	from	from	ADP
ap-7660	412	6	local	local	ADJ
ap-7660	412	7	similarity	similarity	NOUN
ap-7660	412	8	maps	map	NOUN
ap-7660	412	9	of	of	ADP
ap-7660	412	10	scalar	scalar	ADJ
ap-7660	412	11	non	non	ADJ
ap-7660	412	12	-	-	ADJ
ap-7660	412	13	hermitian	hermitian	ADJ
ap-7660	412	14	field	field	NOUN
ap-7660	412	15	theories	theory	NOUN
ap-7660	412	16	,	,	PUNCT
ap-7660	412	17	2021	2021	NUM
ap-7660	412	18	.	.	PUNCT
ap-7660	413	1	arxiv:2110.05289	arxiv:2110.05289	VERB
ap-7660	413	2	.	.	PUNCT
ap-7660	414	1	[	[	X
ap-7660	414	2	15	15	NUM
ap-7660	414	3	]	]	X
ap-7660	414	4	a.	a.	NOUN
ap-7660	414	5	fring	fring	NOUN
ap-7660	414	6	.	.	PUNCT
ap-7660	415	1	pt	pt	NOUN
ap-7660	415	2	-symmetric	-symmetric	ADJ
ap-7660	415	3	deformations	deformation	NOUN
ap-7660	415	4	of	of	ADP
ap-7660	415	5	the	the	DET
ap-7660	415	6	korteweg	korteweg	NOUN
ap-7660	415	7	-	-	PUNCT
ap-7660	415	8	de	de	PROPN
ap-7660	415	9	vries	vries	PROPN
ap-7660	415	10	equation	equation	NOUN
ap-7660	415	11	.	.	PUNCT
ap-7660	416	1	journal	journal	PROPN
ap-7660	416	2	of	of	ADP
ap-7660	416	3	physics	physics	PROPN
ap-7660	416	4	a	a	PRON
ap-7660	416	5	:	:	PUNCT
ap-7660	416	6	mathematical	mathematical	ADJ
ap-7660	416	7	and	and	CCONJ
ap-7660	416	8	theoretical	theoretical	ADJ
ap-7660	416	9	40(15):4215–4224	40(15):4215–4224	NOUN
ap-7660	416	10	,	,	PUNCT
ap-7660	416	11	2007	2007	NUM
ap-7660	416	12	.	.	PUNCT
ap-7660	417	1	https://doi.org/10.1088/1751-8113/40/15/012	https://doi.org/10.1088/1751-8113/40/15/012	NOUN
ap-7660	417	2	.	.	PUNCT
ap-7660	418	1	[	[	X
ap-7660	418	2	16	16	NUM
ap-7660	418	3	]	]	X
ap-7660	418	4	f.	f.	PROPN
ap-7660	418	5	g.	g.	PROPN
ap-7660	418	6	scholtz	scholtz	PROPN
ap-7660	418	7	,	,	PUNCT
ap-7660	418	8	h.	h.	PROPN
ap-7660	418	9	b.	b.	PROPN
ap-7660	418	10	geyer	geyer	PROPN
ap-7660	418	11	,	,	PUNCT
ap-7660	418	12	f.	f.	PROPN
ap-7660	418	13	j.	j.	PROPN
ap-7660	418	14	w.	w.	PROPN
ap-7660	418	15	hahne	hahne	PROPN
ap-7660	418	16	.	.	PUNCT
ap-7660	419	1	quasi	quasi	ADJ
ap-7660	419	2	-	-	ADJ
ap-7660	419	3	hermitian	hermitian	ADJ
ap-7660	419	4	operators	operator	NOUN
ap-7660	419	5	in	in	ADP
ap-7660	419	6	quantum	quantum	ADJ
ap-7660	419	7	mechanics	mechanic	NOUN
ap-7660	419	8	and	and	CCONJ
ap-7660	419	9	the	the	DET
ap-7660	419	10	variational	variational	ADJ
ap-7660	419	11	principle	principle	NOUN
ap-7660	419	12	.	.	PUNCT
ap-7660	420	1	annals	annal	NOUN
ap-7660	420	2	of	of	ADP
ap-7660	420	3	physics	physics	NOUN
ap-7660	420	4	213(1):74–101	213(1):74–101	PROPN
ap-7660	420	5	,	,	PUNCT
ap-7660	420	6	1992	1992	NUM
ap-7660	420	7	.	.	PUNCT
ap-7660	421	1	https://doi.org/10.1016/0003-4916(92)90284-s	https://doi.org/10.1016/0003-4916(92)90284-	VERB
ap-7660	421	2	.	.	PUNCT
ap-7660	422	1	[	[	X
ap-7660	422	2	17	17	NUM
ap-7660	422	3	]	]	X
ap-7660	422	4	j.	j.	PROPN
ap-7660	422	5	dieudonné	dieudonné	PROPN
ap-7660	422	6	.	.	PUNCT
ap-7660	423	1	quasi	quasi	ADJ
ap-7660	423	2	-	-	ADJ
ap-7660	423	3	hermitian	hermitian	ADJ
ap-7660	423	4	operators	operator	NOUN
ap-7660	423	5	.	.	PUNCT
ap-7660	424	1	proceedings	proceeding	NOUN
ap-7660	424	2	of	of	ADP
ap-7660	424	3	the	the	DET
ap-7660	424	4	international	international	ADJ
ap-7660	424	5	symposium	symposium	NOUN
ap-7660	424	6	on	on	ADP
ap-7660	424	7	linear	linear	ADJ
ap-7660	424	8	spaces	space	NOUN
ap-7660	424	9	,	,	PUNCT
ap-7660	424	10	jerusalem	jerusalem	PROPN
ap-7660	424	11	1960	1960	NUM
ap-7660	424	12	,	,	PUNCT
ap-7660	424	13	pergamon	pergamon	NOUN
ap-7660	424	14	,	,	PUNCT
ap-7660	424	15	oxford	oxford	PROPN
ap-7660	424	16	pp	pp	ADV
ap-7660	424	17	.	.	PUNCT
ap-7660	425	1	115–122	115–122	NUM
ap-7660	425	2	,	,	PUNCT
ap-7660	425	3	1961	1961	NUM
ap-7660	425	4	.	.	PUNCT
ap-7660	426	1	206	206	NUM
ap-7660	426	2	https://doi.org/10.1103/physrevd.96.065027	https://doi.org/10.1103/physrevd.96.065027	NOUN
ap-7660	426	3	https://doi.org/10.1103/physrevd.98.045001	https://doi.org/10.1103/physrevd.98.045001	PROPN
ap-7660	426	4	https://doi.org/10.1103/physrevd.99.045006	https://doi.org/10.1103/physrevd.99.045006	NOUN
ap-7660	426	5	https://doi.org/10.1088/1742-6596/1586/1/012001	https://doi.org/10.1088/1742-6596/1586/1/012001	NOUN
ap-7660	426	6	https://doi.org/10.1103/physrevd.101.035008	https://doi.org/10.1103/physrevd.101.035008	NOUN
ap-7660	426	7	https://doi.org/10.1103/physrevd.99.075024	https://doi.org/10.1103/physrevd.99.075024	NOUN
ap-7660	426	8	https://doi.org/10.1103/physrevd.102.125030	https://doi.org/10.1103/physrevd.102.125030	PROPN
ap-7660	426	9	https://doi.org/10.1016/j.nuclphysb.2019.114834	https://doi.org/10.1016/j.nuclphysb.2019.114834	NOUN
ap-7660	426	10	http://arxiv.org/abs/2004.00723	http://arxiv.org/abs/2004.00723	VERB
ap-7660	426	11	https://doi.org/10.1103/physrevd.101.045014	https://doi.org/10.1103/physrevd.101.045014	PROPN
ap-7660	426	12	https://doi.org/10.1016/j.physletb.2020.135583	https://doi.org/10.1016/j.physletb.2020.135583	NOUN
ap-7660	426	13	https://doi.org/10.1103/physrevd.101.085015	https://doi.org/10.1103/physrevd.101.085015	PROPN
ap-7660	426	14	https://doi.org/10.1103/physrevd.104.056023	https://doi.org/10.1103/physrevd.104.056023	PROPN
ap-7660	426	15	http://arxiv.org/abs/2110.05289	http://arxiv.org/abs/2110.05289	ADJ
ap-7660	426	16	https://doi.org/10.1088/1751-8113/40/15/012	https://doi.org/10.1088/1751-8113/40/15/012	NOUN
ap-7660	426	17	https://doi.org/10.1016/0003-4916(92)90284-s	https://doi.org/10.1016/0003-4916(92)90284-s	NOUN
ap-7660	426	18	vol	vol	NOUN
ap-7660	426	19	.	.	PUNCT
ap-7660	427	1	62	62	NUM
ap-7660	427	2	no	no	INTJ
ap-7660	427	3	.	.	PUNCT
ap-7660	428	1	1/2022	1/2022	NUM
ap-7660	428	2	complex	complex	ADJ
ap-7660	428	3	topological	topological	ADJ
ap-7660	428	4	soliton	soliton	NOUN
ap-7660	428	5	with	with	ADP
ap-7660	428	6	real	real	ADJ
ap-7660	428	7	energy	energy	NOUN
ap-7660	428	8	in	in	ADP
ap-7660	428	9	particle	particle	NOUN
ap-7660	428	10	physics	physics	NOUN
ap-7660	428	11	[	[	X
ap-7660	428	12	18	18	NUM
ap-7660	428	13	]	]	PUNCT
ap-7660	428	14	m.	m.	NOUN
ap-7660	428	15	froissart	froissart	NOUN
ap-7660	428	16	.	.	PUNCT
ap-7660	429	1	covariant	covariant	ADJ
ap-7660	429	2	formalism	formalism	NOUN
ap-7660	429	3	of	of	ADP
ap-7660	429	4	a	a	DET
ap-7660	429	5	field	field	NOUN
ap-7660	429	6	with	with	ADP
ap-7660	429	7	indefinite	indefinite	ADJ
ap-7660	429	8	metric	metric	ADJ
ap-7660	429	9	.	.	PUNCT
ap-7660	430	1	il	il	PROPN
ap-7660	430	2	nuovo	nuovo	PROPN
ap-7660	430	3	cimento	cimento	PROPN
ap-7660	430	4	14:197–204	14:197–204	NUM
ap-7660	430	5	,	,	PUNCT
ap-7660	430	6	1959	1959	NUM
ap-7660	430	7	.	.	PUNCT
ap-7660	431	1	https://doi.org/10.1007/bf02724848	https://doi.org/10.1007/bf02724848	X
ap-7660	431	2	.	.	PUNCT
ap-7660	432	1	[	[	X
ap-7660	432	2	19	19	NUM
ap-7660	432	3	]	]	X
ap-7660	432	4	f.	f.	PROPN
ap-7660	432	5	j.	j.	PROPN
ap-7660	432	6	dyson	dyson	PROPN
ap-7660	432	7	.	.	PUNCT
ap-7660	433	1	thermodynamic	thermodynamic	ADJ
ap-7660	433	2	behavior	behavior	NOUN
ap-7660	433	3	of	of	ADP
ap-7660	433	4	an	an	DET
ap-7660	433	5	ideal	ideal	ADJ
ap-7660	433	6	ferromagnet	ferromagnet	NOUN
ap-7660	433	7	.	.	PUNCT
ap-7660	434	1	physical	physical	ADJ
ap-7660	434	2	review	review	NOUN
ap-7660	434	3	102(5):1230–1244	102(5):1230–1244	PROPN
ap-7660	434	4	,	,	PUNCT
ap-7660	434	5	1956	1956	NUM
ap-7660	434	6	.	.	PUNCT
ap-7660	435	1	https://doi.org/10.1103/physrev.102.1230	https://doi.org/10.1103/physrev.102.1230	X
ap-7660	435	2	.	.	PUNCT
ap-7660	436	1	[	[	X
ap-7660	436	2	20	20	NUM
ap-7660	436	3	]	]	PUNCT
ap-7660	436	4	t.	t.	PROPN
ap-7660	436	5	marumori	marumori	PROPN
ap-7660	436	6	,	,	PUNCT
ap-7660	436	7	m.	m.	NOUN
ap-7660	436	8	yamamura	yamamura	PROPN
ap-7660	436	9	,	,	PUNCT
ap-7660	436	10	a.	a.	NOUN
ap-7660	436	11	tokunaga	tokunaga	NOUN
ap-7660	436	12	.	.	PUNCT
ap-7660	437	1	on	on	ADP
ap-7660	437	2	the	the	DET
ap-7660	437	3	“	"	PUNCT
ap-7660	437	4	anharmonic	anharmonic	ADJ
ap-7660	437	5	effects	effect	NOUN
ap-7660	437	6	”	"	PUNCT
ap-7660	437	7	on	on	ADP
ap-7660	437	8	the	the	DET
ap-7660	437	9	collective	collective	ADJ
ap-7660	437	10	oscillations	oscillation	NOUN
ap-7660	437	11	in	in	ADP
ap-7660	437	12	spherical	spherical	ADJ
ap-7660	437	13	even	even	ADV
ap-7660	437	14	nuclei	nucleus	NOUN
ap-7660	437	15	.	.	PUNCT
ap-7660	438	1	i.	i.	PROPN
ap-7660	438	2	progress	progress	NOUN
ap-7660	438	3	of	of	ADP
ap-7660	438	4	theoretical	theoretical	ADJ
ap-7660	438	5	physics	physics	NOUN
ap-7660	438	6	31(6):1009–1025	31(6):1009–1025	NUM
ap-7660	438	7	,	,	PUNCT
ap-7660	438	8	1964	1964	NUM
ap-7660	438	9	.	.	PUNCT
ap-7660	439	1	https://doi.org/10.1143/ptp.31.1009	https://doi.org/10.1143/ptp.31.1009	X
ap-7660	439	2	.	.	PUNCT
ap-7660	440	1	[	[	X
ap-7660	440	2	21	21	NUM
ap-7660	440	3	]	]	PUNCT
ap-7660	440	4	s.	s.	PROPN
ap-7660	440	5	t.	t.	PROPN
ap-7660	440	6	beliaev	beliaev	PROPN
ap-7660	440	7	,	,	PUNCT
ap-7660	440	8	v.	v.	ADP
ap-7660	440	9	g.	g.	PROPN
ap-7660	440	10	zelevinsky	zelevinsky	PROPN
ap-7660	440	11	.	.	PUNCT
ap-7660	441	1	anharmonic	anharmonic	ADJ
ap-7660	441	2	effects	effect	NOUN
ap-7660	441	3	of	of	ADP
ap-7660	441	4	quadrupole	quadrupole	NOUN
ap-7660	441	5	oscillations	oscillation	NOUN
ap-7660	441	6	of	of	ADP
ap-7660	441	7	spherical	spherical	ADJ
ap-7660	441	8	nuclei	nucleus	NOUN
ap-7660	441	9	.	.	PUNCT
ap-7660	442	1	nuclear	nuclear	ADJ
ap-7660	442	2	physics	physics	NOUN
ap-7660	442	3	39:582–604	39:582–604	PROPN
ap-7660	442	4	,	,	PUNCT
ap-7660	442	5	1962	1962	NUM
ap-7660	442	6	.	.	PUNCT
ap-7660	443	1	https://doi.org/10.1016/0029-5582(62)90416-9	https://doi.org/10.1016/0029-5582(62)90416-9	NOUN
ap-7660	443	2	.	.	PUNCT
ap-7660	444	1	[	[	X
ap-7660	444	2	22	22	NUM
ap-7660	444	3	]	]	X
ap-7660	444	4	d.	d.	PROPN
ap-7660	444	5	janssen	janssen	PROPN
ap-7660	444	6	,	,	PUNCT
ap-7660	444	7	f.	f.	PROPN
ap-7660	444	8	dönau	dönau	PROPN
ap-7660	444	9	,	,	PUNCT
ap-7660	444	10	s.	s.	PROPN
ap-7660	444	11	frauendorf	frauendorf	PROPN
ap-7660	444	12	,	,	PUNCT
ap-7660	444	13	r.	r.	PROPN
ap-7660	444	14	jolos	jolos	PROPN
ap-7660	444	15	.	.	PUNCT
ap-7660	445	1	boson	boson	NOUN
ap-7660	445	2	description	description	NOUN
ap-7660	445	3	of	of	ADP
ap-7660	445	4	collective	collective	ADJ
ap-7660	445	5	states	state	NOUN
ap-7660	445	6	.	.	PUNCT
ap-7660	446	1	nuclear	nuclear	ADJ
ap-7660	446	2	physics	physics	PROPN
ap-7660	446	3	a	a	DET
ap-7660	446	4	172(1):145–165	172(1):145–165	NUM
ap-7660	446	5	,	,	PUNCT
ap-7660	446	6	1971	1971	NUM
ap-7660	446	7	.	.	PUNCT
ap-7660	447	1	https://doi.org/10.1016/0375-9474(71)90122-9	https://doi.org/10.1016/0375-9474(71)90122-9	NOUN
ap-7660	447	2	.	.	PUNCT
ap-7660	448	1	[	[	X
ap-7660	448	2	23	23	NUM
ap-7660	448	3	]	]	PUNCT
ap-7660	448	4	a.	a.	NOUN
ap-7660	448	5	fring	fring	NOUN
ap-7660	448	6	,	,	PUNCT
ap-7660	448	7	t.	t.	PROPN
ap-7660	448	8	taira	taira	PROPN
ap-7660	448	9	.	.	PUNCT
ap-7660	449	1	non	non	ADJ
ap-7660	449	2	-	-	ADJ
ap-7660	449	3	hermitian	hermitian	ADJ
ap-7660	449	4	gauge	gauge	NOUN
ap-7660	449	5	field	field	NOUN
ap-7660	449	6	theories	theory	NOUN
ap-7660	449	7	and	and	CCONJ
ap-7660	449	8	bps	bps	NOUN
ap-7660	449	9	limits	limit	NOUN
ap-7660	449	10	.	.	PUNCT
ap-7660	450	1	journal	journal	NOUN
ap-7660	450	2	of	of	ADP
ap-7660	450	3	physics	physics	PROPN
ap-7660	450	4	:	:	PUNCT
ap-7660	450	5	conference	conference	NOUN
ap-7660	450	6	series	series	NOUN
ap-7660	450	7	2038(1):012010	2038(1):012010	NOUN
ap-7660	450	8	,	,	PUNCT
ap-7660	450	9	2021	2021	NUM
ap-7660	450	10	.	.	PUNCT
ap-7660	451	1	https://doi.org/10.1088/1742-6596/2038/1/012010	https://doi.org/10.1088/1742-6596/2038/1/012010	PROPN
ap-7660	451	2	.	.	PUNCT
ap-7660	452	1	[	[	X
ap-7660	452	2	24	24	NUM
ap-7660	452	3	]	]	PUNCT
ap-7660	452	4	d.	d.	PROPN
ap-7660	452	5	p.	p.	PROPN
ap-7660	452	6	musumbu	musumbu	PROPN
ap-7660	452	7	,	,	PUNCT
ap-7660	452	8	h.	h.	PROPN
ap-7660	452	9	b.	b.	PROPN
ap-7660	452	10	geyer	geyer	PROPN
ap-7660	452	11	,	,	PUNCT
ap-7660	452	12	w.	w.	PROPN
ap-7660	452	13	d.	d.	PROPN
ap-7660	452	14	heiss	heiss	PROPN
ap-7660	452	15	.	.	PUNCT
ap-7660	453	1	choice	choice	NOUN
ap-7660	453	2	of	of	ADP
ap-7660	453	3	a	a	DET
ap-7660	453	4	metric	metric	NOUN
ap-7660	453	5	for	for	ADP
ap-7660	453	6	the	the	DET
ap-7660	453	7	non	non	ADJ
ap-7660	453	8	-	-	ADJ
ap-7660	453	9	hermitian	hermitian	ADJ
ap-7660	453	10	oscillator	oscillator	NOUN
ap-7660	453	11	.	.	PUNCT
ap-7660	454	1	journal	journal	PROPN
ap-7660	454	2	of	of	ADP
ap-7660	454	3	physics	physics	PROPN
ap-7660	454	4	a	a	PRON
ap-7660	454	5	:	:	PUNCT
ap-7660	454	6	mathematical	mathematical	ADJ
ap-7660	454	7	and	and	CCONJ
ap-7660	454	8	theoretical	theoretical	ADJ
ap-7660	454	9	40(2):f75	40(2):f75	PROPN
ap-7660	454	10	–	–	PUNCT
ap-7660	454	11	f80	f80	NOUN
ap-7660	454	12	,	,	PUNCT
ap-7660	454	13	2007	2007	NUM
ap-7660	454	14	.	.	PUNCT
ap-7660	455	1	https://doi.org/10.1088/1751-8113/40/2/f03	https://doi.org/10.1088/1751-8113/40/2/f03	PROPN
ap-7660	455	2	.	.	PUNCT
ap-7660	456	1	[	[	X
ap-7660	456	2	25	25	NUM
ap-7660	456	3	]	]	X
ap-7660	456	4	g.	g.	PROPN
ap-7660	456	5	h.	h.	PROPN
ap-7660	456	6	derrick	derrick	PROPN
ap-7660	456	7	.	.	PUNCT
ap-7660	457	1	comments	comment	NOUN
ap-7660	457	2	on	on	ADP
ap-7660	457	3	nonlinear	nonlinear	ADJ
ap-7660	457	4	wave	wave	NOUN
ap-7660	457	5	equations	equation	NOUN
ap-7660	457	6	as	as	ADP
ap-7660	457	7	models	model	NOUN
ap-7660	457	8	for	for	ADP
ap-7660	457	9	elementary	elementary	ADJ
ap-7660	457	10	particles	particle	NOUN
ap-7660	457	11	.	.	PUNCT
ap-7660	458	1	journal	journal	NOUN
ap-7660	458	2	of	of	ADP
ap-7660	458	3	mathematical	mathematical	ADJ
ap-7660	458	4	physics	physics	PROPN
ap-7660	458	5	5(9):1252–1254	5(9):1252–1254	PROPN
ap-7660	458	6	,	,	PUNCT
ap-7660	458	7	1964	1964	NUM
ap-7660	458	8	.	.	PUNCT
ap-7660	459	1	https://doi.org/10.1063/1.1704233	https://doi.org/10.1063/1.1704233	X
ap-7660	459	2	.	.	PUNCT
ap-7660	460	1	[	[	X
ap-7660	460	2	26	26	NUM
ap-7660	460	3	]	]	PUNCT
ap-7660	460	4	m.	m.	NOUN
ap-7660	460	5	k.	k.	PROPN
ap-7660	460	6	prasad	prasad	PROPN
ap-7660	460	7	,	,	PUNCT
ap-7660	460	8	c.	c.	PROPN
ap-7660	460	9	m.	m.	PROPN
ap-7660	460	10	sommerfield	sommerfield	PROPN
ap-7660	460	11	.	.	PUNCT
ap-7660	461	1	exact	exact	ADJ
ap-7660	461	2	classical	classical	ADJ
ap-7660	461	3	solution	solution	NOUN
ap-7660	461	4	for	for	ADP
ap-7660	461	5	the’t	the’t	NUM
ap-7660	461	6	hooft	hooft	PROPN
ap-7660	461	7	monopole	monopole	NOUN
ap-7660	461	8	and	and	CCONJ
ap-7660	461	9	the	the	DET
ap-7660	461	10	julia	julia	PROPN
ap-7660	461	11	-	-	PUNCT
ap-7660	461	12	zee	zee	PROPN
ap-7660	461	13	dyon	dyon	NOUN
ap-7660	461	14	.	.	PUNCT
ap-7660	462	1	physical	physical	ADJ
ap-7660	462	2	review	review	NOUN
ap-7660	462	3	letters	letter	NOUN
ap-7660	462	4	35(12):760–762	35(12):760–762	NUM
ap-7660	462	5	,	,	PUNCT
ap-7660	462	6	1975	1975	NUM
ap-7660	462	7	.	.	PUNCT
ap-7660	463	1	https://doi.org/10.1103/physrevlett.35.760	https://doi.org/10.1103/physrevlett.35.760	PROPN
ap-7660	463	2	.	.	PUNCT
ap-7660	464	1	[	[	X
ap-7660	464	2	27	27	NUM
ap-7660	464	3	]	]	X
ap-7660	464	4	e.	e.	PROPN
ap-7660	464	5	b.	b.	PROPN
ap-7660	464	6	bogomolny	bogomolny	PROPN
ap-7660	464	7	.	.	PUNCT
ap-7660	465	1	the	the	DET
ap-7660	465	2	stability	stability	NOUN
ap-7660	465	3	of	of	ADP
ap-7660	465	4	classical	classical	ADJ
ap-7660	465	5	solutions	solution	NOUN
ap-7660	465	6	.	.	PUNCT
ap-7660	466	1	soviet	soviet	ADJ
ap-7660	466	2	journal	journal	PROPN
ap-7660	466	3	of	of	ADP
ap-7660	466	4	nuclear	nuclear	ADJ
ap-7660	466	5	physics	physics	NOUN
ap-7660	466	6	(	(	PUNCT
ap-7660	466	7	english	english	PROPN
ap-7660	466	8	translation	translation	NOUN
ap-7660	466	9	,	,	PUNCT
ap-7660	466	10	united	united	PROPN
ap-7660	466	11	states	states	PROPN
ap-7660	466	12	)	)	PUNCT
ap-7660	466	13	24(4	24(4	NUM
ap-7660	466	14	)	)	PUNCT
ap-7660	466	15	,	,	PUNCT
ap-7660	466	16	1976	1976	NUM
ap-7660	466	17	.	.	PUNCT
ap-7660	467	1	[	[	X
ap-7660	467	2	28	28	NUM
ap-7660	467	3	]	]	X
ap-7660	467	4	j.	j.	PROPN
ap-7660	467	5	arafune	arafune	PROPN
ap-7660	467	6	,	,	PUNCT
ap-7660	467	7	p.	p.	PROPN
ap-7660	467	8	g.	g.	PROPN
ap-7660	467	9	o.	o.	PROPN
ap-7660	467	10	freund	freund	PROPN
ap-7660	467	11	,	,	PUNCT
ap-7660	467	12	c.	c.	PROPN
ap-7660	467	13	j.	j.	PROPN
ap-7660	467	14	goebel	goebel	PROPN
ap-7660	467	15	.	.	PUNCT
ap-7660	468	1	topology	topology	NOUN
ap-7660	468	2	of	of	ADP
ap-7660	468	3	higgs	higgs	PROPN
ap-7660	468	4	fields	fields	PROPN
ap-7660	468	5	.	.	PUNCT
ap-7660	469	1	journal	journal	PROPN
ap-7660	469	2	of	of	ADP
ap-7660	469	3	mathematical	mathematical	ADJ
ap-7660	469	4	physics	physics	NOUN
ap-7660	469	5	16(2):433	16(2):433	PROPN
ap-7660	469	6	–	–	PUNCT
ap-7660	469	7	437	437	NUM
ap-7660	469	8	,	,	PUNCT
ap-7660	469	9	1975	1975	NUM
ap-7660	469	10	.	.	PUNCT
ap-7660	470	1	https://doi.org/10.1063/1.522518	https://doi.org/10.1063/1.522518	PROPN
ap-7660	470	2	.	.	PUNCT
ap-7660	471	1	[	[	X
ap-7660	471	2	29	29	NUM
ap-7660	471	3	]	]	PUNCT
ap-7660	471	4	t.	t.	PROPN
ap-7660	471	5	w.	w.	PROPN
ap-7660	471	6	kirkman	kirkman	PROPN
ap-7660	471	7	,	,	PUNCT
ap-7660	471	8	c.	c.	PROPN
ap-7660	471	9	k.	k.	PROPN
ap-7660	471	10	zachos	zachos	PROPN
ap-7660	471	11	.	.	PUNCT
ap-7660	472	1	asymptotic	asymptotic	ADJ
ap-7660	472	2	analysis	analysis	NOUN
ap-7660	472	3	of	of	ADP
ap-7660	472	4	the	the	DET
ap-7660	472	5	monopole	monopole	ADJ
ap-7660	472	6	structure	structure	NOUN
ap-7660	472	7	.	.	PUNCT
ap-7660	473	1	physical	physical	ADJ
ap-7660	473	2	review	review	PROPN
ap-7660	473	3	d	d	PROPN
ap-7660	473	4	24(4):999–1004	24(4):999–1004	NUM
ap-7660	473	5	,	,	PUNCT
ap-7660	473	6	1981	1981	NUM
ap-7660	473	7	.	.	PUNCT
ap-7660	474	1	https://doi.org/10.1103/physrevd.24.999	https://doi.org/10.1103/physrevd.24.999	PROPN
ap-7660	474	2	.	.	PUNCT
ap-7660	475	1	[	[	X
ap-7660	475	2	30	30	NUM
ap-7660	475	3	]	]	X
ap-7660	475	4	f.	f.	PROPN
ap-7660	475	5	correa	correa	PROPN
ap-7660	475	6	,	,	PUNCT
ap-7660	475	7	a.	a.	NOUN
ap-7660	475	8	fring	fring	PROPN
ap-7660	475	9	,	,	PUNCT
ap-7660	475	10	t.	t.	PROPN
ap-7660	475	11	taira	taira	PROPN
ap-7660	475	12	.	.	PUNCT
ap-7660	476	1	complex	complex	ADJ
ap-7660	476	2	bps	bps	NOUN
ap-7660	476	3	skyrmions	skyrmion	NOUN
ap-7660	476	4	with	with	ADP
ap-7660	476	5	real	real	ADJ
ap-7660	476	6	energy	energy	NOUN
ap-7660	476	7	.	.	PUNCT
ap-7660	477	1	nuclear	nuclear	ADJ
ap-7660	477	2	physics	physics	PROPN
ap-7660	477	3	b	b	PROPN
ap-7660	477	4	971(2):115516	971(2):115516	NUM
ap-7660	477	5	,	,	PUNCT
ap-7660	477	6	2021	2021	NUM
ap-7660	477	7	.	.	PUNCT
ap-7660	478	1	https://doi.org/10.1016/j.nuclphysb.2021.115516	https://doi.org/10.1016/j.nuclphysb.2021.115516	NOUN
ap-7660	478	2	.	.	PUNCT
ap-7660	479	1	207	207	NUM
ap-7660	480	1	https://doi.org/10.1007/bf02724848	https://doi.org/10.1007/bf02724848	NUM
ap-7660	480	2	https://doi.org/10.1103/physrev.102.1230	https://doi.org/10.1103/physrev.102.1230	PROPN
ap-7660	480	3	https://doi.org/10.1143/ptp.31.1009	https://doi.org/10.1143/ptp.31.1009	X
ap-7660	480	4	https://doi.org/10.1016/0029-5582(62)90416-9	https://doi.org/10.1016/0029-5582(62)90416-9	NOUN
ap-7660	480	5	https://doi.org/10.1016/0375-9474(71)90122-9	https://doi.org/10.1016/0375-9474(71)90122-9	NOUN
ap-7660	480	6	https://doi.org/10.1088/1742-6596/2038/1/012010	https://doi.org/10.1088/1742-6596/2038/1/012010	NOUN
ap-7660	480	7	https://doi.org/10.1088/1751-8113/40/2/f03	https://doi.org/10.1088/1751-8113/40/2/f03	PROPN
ap-7660	480	8	https://doi.org/10.1063/1.1704233	https://doi.org/10.1063/1.1704233	PROPN
ap-7660	480	9	https://doi.org/10.1103/physrevlett.35.760	https://doi.org/10.1103/physrevlett.35.760	PROPN
ap-7660	481	1	https://doi.org/10.1063/1.522518	https://doi.org/10.1063/1.522518	PROPN
ap-7660	481	2	https://doi.org/10.1103/physrevd.24.999	https://doi.org/10.1103/physrevd.24.999	PROPN
ap-7660	481	3	https://doi.org/10.1016/j.nuclphysb.2021.115516	https://doi.org/10.1016/j.nuclphysb.2021.115516	PROPN
ap-7660	481	4	acta	acta	PROPN
ap-7660	481	5	polytechnica	polytechnica	PROPN
ap-7660	481	6	62(1):197–207	62(1):197–207	NOUN
ap-7660	481	7	,	,	PUNCT
ap-7660	481	8	2022	2022	NUM
ap-7660	481	9	1	1	NUM
ap-7660	481	10	introduction	introduction	NOUN
ap-7660	481	11	2	2	NUM
ap-7660	481	12	methods	method	NOUN
ap-7660	481	13	2.1	2.1	NUM
ap-7660	481	14	higgs	higg	NOUN
ap-7660	481	15	and	and	CCONJ
ap-7660	481	16	gauge	gauge	ADJ
ap-7660	481	17	masses	masse	NOUN
ap-7660	481	18	2.2	2.2	NUM
ap-7660	481	19	t'hooft	t'hooft	PROPN
ap-7660	481	20	-	-	PUNCT
ap-7660	481	21	polyakov	polyakov	NOUN
ap-7660	481	22	monopole	monopole	NOUN
ap-7660	481	23	2.3	2.3	NUM
ap-7660	481	24	the	the	DET
ap-7660	481	25	energy	energy	NOUN
ap-7660	481	26	bound	bind	VERB
ap-7660	481	27	2.4	2.4	NUM
ap-7660	481	28	the	the	DET
ap-7660	481	29	fourfold	fourfold	ADJ
ap-7660	481	30	bps	bps	NOUN
ap-7660	481	31	scaling	scaling	NOUN
ap-7660	481	32	limit	limit	VERB
ap-7660	481	33	3	3	NUM
ap-7660	481	34	results	result	NOUN
ap-7660	481	35	and	and	CCONJ
ap-7660	481	36	discussion	discussion	NOUN
ap-7660	481	37	3.1	3.1	NUM
ap-7660	481	38	higgs	higgs	NOUN
ap-7660	481	39	mass	mass	PROPN
ap-7660	481	40	and	and	CCONJ
ap-7660	481	41	exceptional	exceptional	ADJ
ap-7660	481	42	points	point	NOUN
ap-7660	481	43	3.2	3.2	NUM
ap-7660	481	44	change	change	NOUN
ap-7660	481	45	in	in	ADP
ap-7660	481	46	cpt	cpt	PROPN
ap-7660	481	47	symmetry	symmetry	NOUN
ap-7660	481	48	and	and	CCONJ
ap-7660	481	49	complex	complex	ADJ
ap-7660	481	50	monopole	monopole	ADJ
ap-7660	481	51	solution	solution	NOUN
ap-7660	481	52	4	4	NUM
ap-7660	481	53	conclusions	conclusion	NOUN
ap-7660	481	54	acknowledgements	acknowledgement	NOUN
ap-7660	481	55	references	reference	NOUN