id	sid	tid	token	lemma	pos
ap-1356	1	1	wykresx.eps	wykresx.eps	X
ap-1356	1	2	acta	acta	PROPN
ap-1356	1	3	polytechnica	polytechnica	PROPN
ap-1356	1	4	vol	vol	NOUN
ap-1356	1	5	.	.	PUNCT
ap-1356	2	1	51	51	NUM
ap-1356	2	2	no	no	INTJ
ap-1356	2	3	.	.	PUNCT
ap-1356	3	1	1/2011	1/2011	NUM
ap-1356	4	1	the	the	DET
ap-1356	4	2	velocity	velocity	NOUN
ap-1356	4	3	tensor	tensor	NOUN
ap-1356	4	4	and	and	CCONJ
ap-1356	4	5	the	the	DET
ap-1356	4	6	momentum	momentum	NOUN
ap-1356	4	7	tensor	tensor	NOUN
ap-1356	4	8	t.	t.	PROPN
ap-1356	4	9	lanczewski	lanczewski	PROPN
ap-1356	4	10	abstract	abstract	ADV
ap-1356	4	11	this	this	DET
ap-1356	4	12	paper	paper	NOUN
ap-1356	4	13	introduces	introduce	VERB
ap-1356	4	14	a	a	DET
ap-1356	4	15	new	new	ADJ
ap-1356	4	16	object	object	NOUN
ap-1356	4	17	called	call	VERB
ap-1356	4	18	the	the	DET
ap-1356	4	19	momentum	momentum	NOUN
ap-1356	4	20	tensor	tensor	NOUN
ap-1356	4	21	.	.	PUNCT
ap-1356	5	1	together	together	ADV
ap-1356	5	2	with	with	ADP
ap-1356	5	3	the	the	DET
ap-1356	5	4	velocity	velocity	NOUN
ap-1356	5	5	tensor	tensor	NOUN
ap-1356	5	6	it	it	PRON
ap-1356	5	7	forms	form	VERB
ap-1356	5	8	a	a	DET
ap-1356	5	9	basis	basis	NOUN
ap-1356	5	10	for	for	ADP
ap-1356	5	11	establishing	establish	VERB
ap-1356	5	12	the	the	DET
ap-1356	5	13	tensorial	tensorial	ADJ
ap-1356	5	14	picture	picture	NOUN
ap-1356	5	15	of	of	ADP
ap-1356	5	16	classical	classical	ADJ
ap-1356	5	17	and	and	CCONJ
ap-1356	5	18	relativistic	relativistic	ADJ
ap-1356	5	19	mechanics	mechanic	NOUN
ap-1356	5	20	.	.	PUNCT
ap-1356	6	1	some	some	DET
ap-1356	6	2	properties	property	NOUN
ap-1356	6	3	of	of	ADP
ap-1356	6	4	the	the	DET
ap-1356	6	5	momentum	momentum	NOUN
ap-1356	6	6	tensor	tensor	NOUN
ap-1356	6	7	are	be	AUX
ap-1356	6	8	derived	derive	VERB
ap-1356	6	9	as	as	ADV
ap-1356	6	10	well	well	ADV
ap-1356	6	11	as	as	ADP
ap-1356	6	12	its	its	PRON
ap-1356	6	13	relation	relation	NOUN
ap-1356	6	14	with	with	ADP
ap-1356	6	15	the	the	DET
ap-1356	6	16	velocity	velocity	NOUN
ap-1356	6	17	tensor	tensor	NOUN
ap-1356	6	18	.	.	PUNCT
ap-1356	7	1	for	for	ADP
ap-1356	7	2	the	the	DET
ap-1356	7	3	sake	sake	NOUN
ap-1356	7	4	of	of	ADP
ap-1356	7	5	clarity	clarity	NOUN
ap-1356	7	6	only	only	ADV
ap-1356	7	7	two	two	NUM
ap-1356	7	8	-	-	PUNCT
ap-1356	7	9	dimensional	dimensional	ADJ
ap-1356	7	10	case	case	NOUN
ap-1356	7	11	is	be	AUX
ap-1356	7	12	investigated	investigate	VERB
ap-1356	7	13	.	.	PUNCT
ap-1356	8	1	however	however	ADV
ap-1356	8	2	,	,	PUNCT
ap-1356	8	3	general	general	ADJ
ap-1356	8	4	conclusions	conclusion	NOUN
ap-1356	8	5	are	be	AUX
ap-1356	8	6	also	also	ADV
ap-1356	8	7	valid	valid	ADJ
ap-1356	8	8	for	for	ADP
ap-1356	8	9	higher	high	ADJ
ap-1356	8	10	dimensional	dimensional	ADJ
ap-1356	8	11	spacetimes	spacetime	NOUN
ap-1356	8	12	.	.	PUNCT
ap-1356	9	1	keywords	keyword	NOUN
ap-1356	9	2	:	:	PUNCT
ap-1356	9	3	relativistic	relativistic	ADJ
ap-1356	9	4	classical	classical	ADJ
ap-1356	9	5	mechanics	mechanic	NOUN
ap-1356	9	6	,	,	PUNCT
ap-1356	9	7	velocity	velocity	NOUN
ap-1356	9	8	tensor	tensor	NOUN
ap-1356	9	9	,	,	PUNCT
ap-1356	9	10	momentum	momentum	NOUN
ap-1356	9	11	tensor	tensor	NOUN
ap-1356	9	12	.	.	PUNCT
ap-1356	10	1	1	1	NUM
ap-1356	10	2	introduction	introduction	NOUN
ap-1356	10	3	in	in	ADP
ap-1356	10	4	[	[	X
ap-1356	10	5	1	1	NUM
ap-1356	10	6	]	]	PUNCT
ap-1356	10	7	,	,	PUNCT
ap-1356	10	8	an	an	DET
ap-1356	10	9	object	object	NOUN
ap-1356	10	10	called	call	VERB
ap-1356	10	11	the	the	DET
ap-1356	10	12	velocity	velocity	NOUN
ap-1356	10	13	tensor	tensor	NOUN
ap-1356	10	14	v	v	NOUN
ap-1356	10	15	μ	μ	NOUN
ap-1356	10	16	ν	ν	X
ap-1356	10	17	(	(	PUNCT
ap-1356	10	18	v	v	NOUN
ap-1356	10	19	)	)	PUNCT
ap-1356	10	20	was	be	AUX
ap-1356	10	21	described	describe	VERB
ap-1356	10	22	.	.	PUNCT
ap-1356	11	1	it	it	PRON
ap-1356	11	2	comes	come	VERB
ap-1356	11	3	from	from	ADP
ap-1356	11	4	a	a	DET
ap-1356	11	5	generalization	generalization	NOUN
ap-1356	11	6	of	of	ADP
ap-1356	11	7	the	the	DET
ap-1356	11	8	equation	equation	NOUN
ap-1356	11	9	dx	dx	PROPN
ap-1356	11	10	(	(	PUNCT
ap-1356	11	11	t)−	t)−	PROPN
ap-1356	11	12	v	v	X
ap-1356	11	13	(	(	PUNCT
ap-1356	11	14	t	t	NOUN
ap-1356	11	15	)	)	PUNCT
ap-1356	11	16	dt	dt	NOUN
ap-1356	12	1	=	=	SYM
ap-1356	12	2	0	0	NUM
ap-1356	12	3	(	(	PUNCT
ap-1356	12	4	1	1	NUM
ap-1356	12	5	)	)	PUNCT
ap-1356	12	6	into	into	ADP
ap-1356	12	7	a	a	DET
ap-1356	12	8	generally	generally	ADV
ap-1356	12	9	covariant	covariant	ADJ
ap-1356	12	10	form	form	NOUN
ap-1356	12	11	v	v	ADP
ap-1356	12	12	μ	μ	NOUN
ap-1356	12	13	ν	ν	X
ap-1356	12	14	(	(	PUNCT
ap-1356	12	15	v	v	NOUN
ap-1356	12	16	)	)	PUNCT
ap-1356	12	17	dx	dx	PROPN
ap-1356	12	18	ν	ν	NOUN
ap-1356	12	19	=	=	SYM
ap-1356	12	20	0	0	PROPN
ap-1356	12	21	.	.	PUNCT
ap-1356	13	1	(	(	PUNCT
ap-1356	13	2	2	2	X
ap-1356	13	3	)	)	PUNCT
ap-1356	13	4	the	the	DET
ap-1356	13	5	two	two	NUM
ap-1356	13	6	-	-	PUNCT
ap-1356	13	7	dimensional	dimensional	ADJ
ap-1356	13	8	matrix	matrix	NOUN
ap-1356	13	9	of	of	ADP
ap-1356	13	10	the	the	DET
ap-1356	13	11	classical	classical	ADJ
ap-1356	13	12	velocity	velocity	NOUN
ap-1356	13	13	tensor	tensor	NOUN
ap-1356	13	14	takes	take	VERB
ap-1356	13	15	the	the	DET
ap-1356	13	16	form	form	NOUN
ap-1356	13	17	v	v	ADP
ap-1356	13	18	(	(	PUNCT
ap-1356	13	19	v	v	NOUN
ap-1356	13	20	)	)	PUNCT
ap-1356	13	21	=	=	PUNCT
ap-1356	14	1	v	v	ADP
ap-1356	14	2	01	01	NUM
ap-1356	15	1	(	(	PUNCT
ap-1356	15	2	−v	−v	NOUN
ap-1356	15	3	1	1	NUM
ap-1356	15	4	−v2	−v2	PROPN
ap-1356	15	5	v	v	NOUN
ap-1356	15	6	)	)	PUNCT
ap-1356	15	7	,	,	PUNCT
ap-1356	15	8	(	(	PUNCT
ap-1356	15	9	3	3	X
ap-1356	15	10	)	)	PUNCT
ap-1356	15	11	while	while	SCONJ
ap-1356	15	12	in	in	ADP
ap-1356	15	13	the	the	DET
ap-1356	15	14	relativistic	relativistic	ADJ
ap-1356	15	15	case	case	NOUN
ap-1356	15	16	v	v	ADP
ap-1356	15	17	(	(	PUNCT
ap-1356	15	18	β	β	NOUN
ap-1356	15	19	)	)	PUNCT
ap-1356	15	20	=	=	SYM
ap-1356	15	21	γ2v	γ2v	SYM
ap-1356	15	22	01	01	NUM
ap-1356	16	1	(	(	PUNCT
ap-1356	16	2	−β	−β	NOUN
ap-1356	16	3	1	1	NUM
ap-1356	16	4	−β2	−β2	NOUN
ap-1356	16	5	β	β	X
ap-1356	16	6	)	)	PUNCT
ap-1356	16	7	,	,	PUNCT
ap-1356	16	8	(	(	PUNCT
ap-1356	16	9	4	4	X
ap-1356	16	10	)	)	PUNCT
ap-1356	16	11	where	where	SCONJ
ap-1356	16	12	v	v	NOUN
ap-1356	16	13	01	01	NUM
ap-1356	16	14	is	be	AUX
ap-1356	16	15	some	some	DET
ap-1356	16	16	arbitrary	arbitrary	ADJ
ap-1356	16	17	constant	constant	ADJ
ap-1356	16	18	,	,	PUNCT
ap-1356	16	19	β	β	NOUN
ap-1356	16	20	=	=	SYM
ap-1356	16	21	v	v	PROPN
ap-1356	16	22	/	/	SYM
ap-1356	16	23	c	c	PROPN
ap-1356	16	24	and	and	CCONJ
ap-1356	16	25	γ	γ	X
ap-1356	16	26	=	=	SYM
ap-1356	16	27	(	(	PUNCT
ap-1356	16	28	1−	1−	NUM
ap-1356	16	29	β2	β2	NOUN
ap-1356	16	30	)	)	PUNCT
ap-1356	16	31	−1/2	−1/2	ADJ
ap-1356	16	32	.	.	PUNCT
ap-1356	17	1	as	as	SCONJ
ap-1356	17	2	was	be	AUX
ap-1356	17	3	shown	show	VERB
ap-1356	17	4	in	in	ADP
ap-1356	17	5	[	[	X
ap-1356	17	6	1	1	NUM
ap-1356	17	7	]	]	PUNCT
ap-1356	17	8	,	,	PUNCT
ap-1356	17	9	the	the	DET
ap-1356	17	10	tensorial	tensorial	ADJ
ap-1356	17	11	description	description	NOUN
ap-1356	17	12	has	have	VERB
ap-1356	17	13	an	an	DET
ap-1356	17	14	obvious	obvious	ADJ
ap-1356	17	15	advantage	advantage	NOUN
ap-1356	17	16	over	over	ADP
ap-1356	17	17	a	a	DET
ap-1356	17	18	standard	standard	ADJ
ap-1356	17	19	description	description	NOUN
ap-1356	17	20	since	since	SCONJ
ap-1356	17	21	it	it	PRON
ap-1356	17	22	does	do	AUX
ap-1356	17	23	not	not	PART
ap-1356	17	24	use	use	VERB
ap-1356	17	25	the	the	DET
ap-1356	17	26	notion	notion	NOUN
ap-1356	17	27	of	of	ADP
ap-1356	17	28	the	the	DET
ap-1356	17	29	proper	proper	ADJ
ap-1356	17	30	time	time	NOUN
ap-1356	17	31	τ	τ	PROPN
ap-1356	17	32	=	=	SYM
ap-1356	17	33	t	t	PROPN
ap-1356	17	34	√	√	NOUN
ap-1356	18	1	1−	1−	NUM
ap-1356	19	1	v2	v2	PROPN
ap-1356	19	2	(	(	PUNCT
ap-1356	19	3	t	t	NOUN
ap-1356	19	4	)	)	PUNCT
ap-1356	19	5	c2	c2	PROPN
ap-1356	19	6	(	(	PUNCT
ap-1356	19	7	5	5	NUM
ap-1356	19	8	)	)	PUNCT
ap-1356	19	9	and	and	CCONJ
ap-1356	19	10	therefore	therefore	ADV
ap-1356	19	11	it	it	PRON
ap-1356	19	12	allows	allow	VERB
ap-1356	19	13	a	a	DET
ap-1356	19	14	description	description	NOUN
ap-1356	19	15	of	of	ADP
ap-1356	19	16	non	non	ADJ
ap-1356	19	17	-	-	ADJ
ap-1356	19	18	uniform	uniform	ADJ
ap-1356	19	19	motions	motion	NOUN
ap-1356	19	20	and	and	CCONJ
ap-1356	19	21	systems	system	NOUN
ap-1356	19	22	with	with	ADP
ap-1356	19	23	an	an	DET
ap-1356	19	24	arbitrary	arbitrary	ADJ
ap-1356	19	25	number	number	NOUN
ap-1356	19	26	of	of	ADP
ap-1356	19	27	material	material	NOUN
ap-1356	19	28	points	point	NOUN
ap-1356	19	29	.	.	PUNCT
ap-1356	20	1	it	it	PRON
ap-1356	20	2	also	also	ADV
ap-1356	20	3	provides	provide	VERB
ap-1356	20	4	a	a	DET
ap-1356	20	5	cornerstone	cornerstone	NOUN
ap-1356	20	6	for	for	ADP
ap-1356	20	7	formulating	formulate	VERB
ap-1356	20	8	a	a	DET
ap-1356	20	9	generally	generally	ADV
ap-1356	20	10	covariant	covariant	ADJ
ap-1356	20	11	mechanics	mechanic	NOUN
ap-1356	20	12	.	.	PUNCT
ap-1356	21	1	however	however	ADV
ap-1356	21	2	,	,	PUNCT
ap-1356	21	3	the	the	DET
ap-1356	21	4	velocity	velocity	NOUN
ap-1356	21	5	tensor	tensor	NOUN
ap-1356	21	6	deals	deal	NOUN
ap-1356	21	7	solely	solely	ADV
ap-1356	21	8	with	with	ADP
ap-1356	21	9	kinematical	kinematical	ADJ
ap-1356	21	10	issues	issue	NOUN
ap-1356	21	11	.	.	PUNCT
ap-1356	22	1	to	to	PART
ap-1356	22	2	make	make	VERB
ap-1356	22	3	the	the	DET
ap-1356	22	4	tensor	tensor	NOUN
ap-1356	22	5	description	description	NOUN
ap-1356	22	6	complete	complete	ADJ
ap-1356	22	7	we	we	PRON
ap-1356	22	8	need	need	VERB
ap-1356	22	9	to	to	PART
ap-1356	22	10	introduce	introduce	VERB
ap-1356	22	11	another	another	DET
ap-1356	22	12	tensorial	tensorial	ADJ
ap-1356	22	13	object	object	NOUN
ap-1356	22	14	called	call	VERB
ap-1356	22	15	the	the	DET
ap-1356	22	16	momentum	momentum	NOUN
ap-1356	22	17	tensor	tensor	NOUN
ap-1356	22	18	πμ	πμ	NOUN
ap-1356	22	19	ν	ν	X
ap-1356	22	20	(	(	PUNCT
ap-1356	22	21	v	v	NOUN
ap-1356	22	22	)	)	PUNCT
ap-1356	22	23	.	.	PUNCT
ap-1356	23	1	by	by	ADP
ap-1356	23	2	means	mean	NOUN
ap-1356	23	3	of	of	ADP
ap-1356	23	4	this	this	DET
ap-1356	23	5	tensor	tensor	NOUN
ap-1356	23	6	it	it	PRON
ap-1356	23	7	is	be	AUX
ap-1356	23	8	possible	possible	ADJ
ap-1356	23	9	to	to	PART
ap-1356	23	10	solve	solve	VERB
ap-1356	23	11	dynamical	dynamical	ADJ
ap-1356	23	12	problems	problem	NOUN
ap-1356	23	13	.	.	PUNCT
ap-1356	24	1	2	2	NUM
ap-1356	24	2	definition	definition	NOUN
ap-1356	24	3	of	of	ADP
ap-1356	24	4	the	the	DET
ap-1356	24	5	momentum	momentum	NOUN
ap-1356	24	6	tensor	tensor	NOUN
ap-1356	24	7	in	in	ADP
ap-1356	24	8	classical	classical	ADJ
ap-1356	24	9	and	and	CCONJ
ap-1356	24	10	relativistic	relativistic	ADJ
ap-1356	24	11	mechanics	mechanic	NOUN
ap-1356	24	12	the	the	DET
ap-1356	24	13	following	follow	VERB
ap-1356	24	14	formula	formula	NOUN
ap-1356	24	15	holds	hold	VERB
ap-1356	24	16	true	true	ADJ
ap-1356	24	17	[	[	X
ap-1356	24	18	2	2	NUM
ap-1356	24	19	]	]	PUNCT
ap-1356	24	20	:	:	PUNCT
ap-1356	24	21	dp(x	dp(x	PROPN
ap-1356	24	22	,	,	PUNCT
ap-1356	24	23	t	t	PROPN
ap-1356	24	24	)	)	PUNCT
ap-1356	24	25	dt	dt	NOUN
ap-1356	25	1	=	=	SYM
ap-1356	25	2	f	f	PROPN
ap-1356	25	3	(	(	PUNCT
ap-1356	25	4	x	x	PROPN
ap-1356	25	5	,	,	PUNCT
ap-1356	25	6	t	t	PROPN
ap-1356	25	7	)	)	PUNCT
ap-1356	25	8	.	.	PUNCT
ap-1356	26	1	(	(	PUNCT
ap-1356	26	2	6	6	X
ap-1356	26	3	)	)	PUNCT
ap-1356	26	4	the	the	DET
ap-1356	26	5	tensorial	tensorial	ADJ
ap-1356	26	6	equivalent	equivalent	NOUN
ap-1356	26	7	of	of	ADP
ap-1356	26	8	eq	eq	PROPN
ap-1356	26	9	.	.	PUNCT
ap-1356	27	1	(	(	PUNCT
ap-1356	27	2	6	6	NUM
ap-1356	27	3	)	)	PUNCT
ap-1356	27	4	is	be	AUX
ap-1356	27	5	presumed	presume	VERB
ap-1356	27	6	to	to	PART
ap-1356	27	7	be	be	AUX
ap-1356	27	8	∂μπ	∂μπ	PROPN
ap-1356	27	9	μ	μ	NOUN
ap-1356	27	10	ν	ν	NOUN
ap-1356	27	11	(	(	PUNCT
ap-1356	27	12	x	x	NOUN
ap-1356	27	13	,	,	PUNCT
ap-1356	27	14	t	t	PROPN
ap-1356	27	15	)	)	PUNCT
ap-1356	27	16	=	=	SYM
ap-1356	27	17	φν(x	φν(x	PROPN
ap-1356	27	18	,	,	PUNCT
ap-1356	27	19	t	t	PROPN
ap-1356	27	20	)	)	PUNCT
ap-1356	27	21	,	,	PUNCT
ap-1356	27	22	(	(	PUNCT
ap-1356	27	23	7	7	X
ap-1356	27	24	)	)	PUNCT
ap-1356	27	25	where	where	SCONJ
ap-1356	27	26	πμ	πμ	ADP
ap-1356	27	27	ν	ν	X
ap-1356	27	28	(	(	PUNCT
ap-1356	27	29	x	x	X
ap-1356	27	30	,	,	PUNCT
ap-1356	27	31	t	t	PROPN
ap-1356	27	32	)	)	PUNCT
ap-1356	27	33	is	be	AUX
ap-1356	27	34	the	the	DET
ap-1356	27	35	momentum	momentum	NOUN
ap-1356	27	36	tensor	tensor	NOUN
ap-1356	27	37	and	and	CCONJ
ap-1356	27	38	φν(x	φν(x	ADP
ap-1356	27	39	,	,	PUNCT
ap-1356	27	40	t	t	PROPN
ap-1356	27	41	)	)	PUNCT
ap-1356	27	42	is	be	AUX
ap-1356	27	43	an	an	DET
ap-1356	27	44	influence	influence	NOUN
ap-1356	27	45	of	of	ADP
ap-1356	27	46	the	the	DET
ap-1356	27	47	exterior	exterior	NOUN
ap-1356	27	48	on	on	ADP
ap-1356	27	49	a	a	DET
ap-1356	27	50	body	body	NOUN
ap-1356	27	51	.	.	PUNCT
ap-1356	28	1	it	it	PRON
ap-1356	28	2	should	should	AUX
ap-1356	28	3	be	be	AUX
ap-1356	28	4	stressed	stress	VERB
ap-1356	28	5	here	here	ADV
ap-1356	28	6	that	that	SCONJ
ap-1356	28	7	we	we	PRON
ap-1356	28	8	do	do	AUX
ap-1356	28	9	not	not	PART
ap-1356	28	10	assume	assume	VERB
ap-1356	28	11	a	a	DET
ap-1356	28	12	priori	priori	ADJ
ap-1356	28	13	the	the	DET
ap-1356	28	14	relationship	relationship	NOUN
ap-1356	28	15	between	between	ADP
ap-1356	28	16	f	f	PROPN
ap-1356	28	17	(	(	PUNCT
ap-1356	28	18	x	x	PROPN
ap-1356	28	19	,	,	PUNCT
ap-1356	28	20	t	t	PROPN
ap-1356	28	21	)	)	PUNCT
ap-1356	28	22	and	and	CCONJ
ap-1356	28	23	φν(x	φν(x	NUM
ap-1356	28	24	,	,	PUNCT
ap-1356	28	25	t	t	PROPN
ap-1356	28	26	)	)	PUNCT
ap-1356	28	27	.	.	PUNCT
ap-1356	29	1	the	the	DET
ap-1356	29	2	choice	choice	NOUN
ap-1356	29	3	of	of	ADP
ap-1356	29	4	the	the	DET
ap-1356	29	5	form	form	NOUN
ap-1356	29	6	of	of	ADP
ap-1356	29	7	the	the	DET
ap-1356	29	8	mixed	mixed	ADJ
ap-1356	29	9	tensor	tensor	NOUN
ap-1356	29	10	πμ	πμ	NOUN
ap-1356	29	11	ν	ν	NOUN
ap-1356	29	12	(	(	PUNCT
ap-1356	29	13	x	x	X
ap-1356	29	14	,	,	PUNCT
ap-1356	29	15	t	t	PROPN
ap-1356	29	16	)	)	PUNCT
ap-1356	29	17	comes	come	VERB
ap-1356	29	18	from	from	ADP
ap-1356	29	19	the	the	DET
ap-1356	29	20	assumption	assumption	NOUN
ap-1356	29	21	that	that	SCONJ
ap-1356	29	22	the	the	DET
ap-1356	29	23	momentum	momentum	NOUN
ap-1356	29	24	tensor	tensor	NOUN
ap-1356	29	25	should	should	AUX
ap-1356	29	26	be	be	AUX
ap-1356	29	27	some	some	DET
ap-1356	29	28	function	function	NOUN
ap-1356	29	29	of	of	ADP
ap-1356	29	30	the	the	DET
ap-1356	29	31	velocity	velocity	NOUN
ap-1356	29	32	tensor	tensor	NOUN
ap-1356	29	33	.	.	PUNCT
ap-1356	30	1	since	since	SCONJ
ap-1356	30	2	the	the	DET
ap-1356	30	3	velocity	velocity	NOUN
ap-1356	30	4	tensor	tensor	NOUN
ap-1356	30	5	is	be	AUX
ap-1356	30	6	a	a	DET
ap-1356	30	7	function	function	NOUN
ap-1356	30	8	of	of	ADP
ap-1356	30	9	a	a	DET
ap-1356	30	10	classical	classical	ADJ
ap-1356	30	11	velocity	velocity	NOUN
ap-1356	30	12	v	v	NOUN
ap-1356	30	13	,	,	PUNCT
ap-1356	30	14	the	the	DET
ap-1356	30	15	momentum	momentum	NOUN
ap-1356	30	16	tensor	tensor	NOUN
ap-1356	30	17	is	be	AUX
ap-1356	30	18	πμ	πμ	ADP
ap-1356	30	19	ν	ν	X
ap-1356	30	20	(	(	PUNCT
ap-1356	30	21	x	x	X
ap-1356	30	22	,	,	PUNCT
ap-1356	30	23	t	t	PROPN
ap-1356	30	24	)	)	PUNCT
ap-1356	30	25	:	:	PUNCT
ap-1356	31	1	=	=	PUNCT
ap-1356	31	2	πμ	πμ	ADP
ap-1356	31	3	ν	ν	X
ap-1356	31	4	(	(	PUNCT
ap-1356	31	5	v	v	NOUN
ap-1356	31	6	)	)	PUNCT
ap-1356	31	7	.	.	PUNCT
ap-1356	32	1	42	42	NUM
ap-1356	32	2	acta	acta	PROPN
ap-1356	32	3	polytechnica	polytechnica	PROPN
ap-1356	32	4	vol	vol	NOUN
ap-1356	32	5	.	.	PUNCT
ap-1356	33	1	51	51	NUM
ap-1356	33	2	no	no	NOUN
ap-1356	33	3	.	.	PUNCT
ap-1356	34	1	1/2011	1/2011	NUM
ap-1356	34	2	3	3	NUM
ap-1356	34	3	general	general	ADJ
ap-1356	34	4	construction	construction	NOUN
ap-1356	34	5	of	of	ADP
ap-1356	34	6	the	the	DET
ap-1356	34	7	momentum	momentum	NOUN
ap-1356	34	8	tensor	tensor	NOUN
ap-1356	34	9	in	in	ADP
ap-1356	34	10	general	general	ADJ
ap-1356	34	11	,	,	PUNCT
ap-1356	34	12	the	the	DET
ap-1356	34	13	momentum	momentum	NOUN
ap-1356	34	14	tensor	tensor	NOUN
ap-1356	34	15	πμ	πμ	VERB
ap-1356	34	16	ν	ν	X
ap-1356	34	17	(	(	PUNCT
ap-1356	34	18	v	v	NOUN
ap-1356	34	19	)	)	PUNCT
ap-1356	34	20	is	be	AUX
ap-1356	34	21	represented	represent	VERB
ap-1356	34	22	by	by	ADP
ap-1356	34	23	a	a	DET
ap-1356	34	24	square	square	ADJ
ap-1356	34	25	matrix	matrix	NOUN
ap-1356	34	26	π(v	π(v	NOUN
ap-1356	34	27	)	)	PUNCT
ap-1356	35	1	=	=	SYM
ap-1356	35	2	⎛⎜⎜⎜⎜⎜⎝	⎛⎜⎜⎜⎜⎜⎝	NUM
ap-1356	35	3	π00(v	π00(v	NOUN
ap-1356	35	4	)	)	PUNCT
ap-1356	36	1	π	π	NOUN
ap-1356	36	2	0	0	NUM
ap-1356	36	3	1(v	1(v	NUM
ap-1356	36	4	)	)	PUNCT
ap-1356	36	5	·	·	PUNCT
ap-1356	36	6	·	·	PUNCT
ap-1356	36	7	·	·	PUNCT
ap-1356	36	8	π0n(v	π0n(v	PROPN
ap-1356	36	9	)	)	PUNCT
ap-1356	36	10	π10(v	π10(v	PRON
ap-1356	36	11	)	)	PUNCT
ap-1356	37	1	π	π	NOUN
ap-1356	37	2	1	1	NUM
ap-1356	37	3	1(v	1(v	NUM
ap-1356	37	4	)	)	PUNCT
ap-1356	37	5	·	·	PUNCT
ap-1356	37	6	·	·	PUNCT
ap-1356	37	7	·	·	PUNCT
ap-1356	37	8	π1n(v	π1n(v	X
ap-1356	37	9	)	)	PUNCT
ap-1356	37	10	...	...	PUNCT
ap-1356	37	11	...	...	PUNCT
ap-1356	37	12	.	.	PUNCT
ap-1356	37	13	.	.	PUNCT
ap-1356	37	14	.	.	PUNCT
ap-1356	38	1	...	...	PUNCT
ap-1356	39	1	πn	πn	INTJ
ap-1356	39	2	0	0	NUM
ap-1356	39	3	(	(	PUNCT
ap-1356	39	4	v	v	NOUN
ap-1356	39	5	)	)	PUNCT
ap-1356	39	6	π	π	PROPN
ap-1356	39	7	n	n	ADP
ap-1356	39	8	1	1	NUM
ap-1356	39	9	(	(	PUNCT
ap-1356	39	10	v	v	NOUN
ap-1356	39	11	)	)	PUNCT
ap-1356	39	12	·	·	PUNCT
ap-1356	39	13	·	·	PUNCT
ap-1356	39	14	·	·	PUNCT
ap-1356	39	15	πn	πn	X
ap-1356	39	16	n(v	n(v	PROPN
ap-1356	39	17	)	)	PUNCT
ap-1356	39	18	⎞⎟⎟⎟⎟⎟⎠	⎞⎟⎟⎟⎟⎟⎠	NOUN
ap-1356	39	19	,	,	PUNCT
ap-1356	39	20	where	where	SCONJ
ap-1356	39	21	the	the	DET
ap-1356	39	22	elements	element	NOUN
ap-1356	39	23	πμ	πμ	VERB
ap-1356	39	24	ν	ν	NOUN
ap-1356	39	25	(	(	PUNCT
ap-1356	39	26	v	v	NOUN
ap-1356	39	27	)	)	PUNCT
ap-1356	39	28	are	be	AUX
ap-1356	39	29	some	some	DET
ap-1356	39	30	functions	function	NOUN
ap-1356	39	31	of	of	ADP
ap-1356	39	32	velocity	velocity	NOUN
ap-1356	39	33	v	v	ADP
ap-1356	39	34	variable	variable	NOUN
ap-1356	39	35	with	with	ADP
ap-1356	39	36	time	time	NOUN
ap-1356	39	37	.	.	PUNCT
ap-1356	40	1	in	in	ADP
ap-1356	40	2	order	order	NOUN
ap-1356	40	3	to	to	PART
ap-1356	40	4	determine	determine	VERB
ap-1356	40	5	them	they	PRON
ap-1356	40	6	,	,	PUNCT
ap-1356	40	7	we	we	PRON
ap-1356	40	8	make	make	VERB
ap-1356	40	9	use	use	NOUN
ap-1356	40	10	of	of	ADP
ap-1356	40	11	the	the	DET
ap-1356	40	12	transformation	transformation	NOUN
ap-1356	40	13	relation	relation	NOUN
ap-1356	40	14	for	for	ADP
ap-1356	40	15	a	a	DET
ap-1356	40	16	mixed	mixed	ADJ
ap-1356	40	17	tensor	tensor	NOUN
ap-1356	40	18	.	.	PUNCT
ap-1356	41	1	passing	pass	VERB
ap-1356	41	2	from	from	ADP
ap-1356	41	3	an	an	DET
ap-1356	41	4	inertial	inertial	ADJ
ap-1356	41	5	reference	reference	NOUN
ap-1356	41	6	frame	frame	NOUN
ap-1356	41	7	s	s	AUX
ap-1356	41	8	to	to	ADP
ap-1356	41	9	an	an	DET
ap-1356	41	10	inertial	inertial	ADJ
ap-1356	41	11	system	system	NOUN
ap-1356	41	12	s′	s′	PUNCT
ap-1356	41	13	that	that	PRON
ap-1356	41	14	moves	move	VERB
ap-1356	41	15	with	with	ADP
ap-1356	41	16	velocity	velocity	NOUN
ap-1356	41	17	u	u	NOUN
ap-1356	41	18	relative	relative	ADJ
ap-1356	41	19	to	to	ADP
ap-1356	41	20	s	s	PRON
ap-1356	41	21	,	,	PUNCT
ap-1356	41	22	the	the	DET
ap-1356	41	23	momentum	momentum	NOUN
ap-1356	41	24	tensor	tensor	NOUN
ap-1356	41	25	πμ	πμ	VERB
ap-1356	41	26	ν	ν	X
ap-1356	41	27	(	(	PUNCT
ap-1356	41	28	v	v	NOUN
ap-1356	41	29	)	)	PUNCT
ap-1356	41	30	transforms	transform	VERB
ap-1356	41	31	in	in	ADP
ap-1356	41	32	accordance	accordance	NOUN
ap-1356	41	33	with	with	ADP
ap-1356	41	34	the	the	DET
ap-1356	41	35	following	follow	VERB
ap-1356	41	36	formula	formula	NOUN
ap-1356	41	37	πμ	πμ	VERB
ap-1356	41	38	ν	ν	NOUN
ap-1356	41	39	(	(	PUNCT
ap-1356	41	40	v)→	v)→	ADJ
ap-1356	41	41	π	π	NOUN
ap-1356	41	42	μ′	μ′	PRON
ap-1356	41	43	ν′	ν′	NOUN
ap-1356	41	44	(	(	PUNCT
ap-1356	41	45	v′	v′	NUM
ap-1356	41	46	)	)	PUNCT
ap-1356	42	1	=	=	SYM
ap-1356	42	2	lμ′	lμ′	PROPN
ap-1356	42	3	μ	μ	PROPN
ap-1356	42	4	(	(	PUNCT
ap-1356	42	5	u)π	u)π	NOUN
ap-1356	42	6	μ	μ	NOUN
ap-1356	42	7	ν	ν	NOUN
ap-1356	42	8	(	(	PUNCT
ap-1356	42	9	v)l	v)l	PUNCT
ap-1356	42	10	ν	ν	X
ap-1356	42	11	ν′(u	ν′(u	PROPN
ap-1356	42	12	)	)	PUNCT
ap-1356	42	13	,	,	PUNCT
ap-1356	42	14	(	(	PUNCT
ap-1356	42	15	8)	8)	NUM
ap-1356	42	16	or	or	CCONJ
ap-1356	42	17	in	in	ADP
ap-1356	42	18	matrix	matrix	NOUN
ap-1356	42	19	notation	notation	NOUN
ap-1356	42	20	π(v)→	π(v)→	NOUN
ap-1356	42	21	π	π	NOUN
ap-1356	42	22	′(v′	′(v′	NOUN
ap-1356	42	23	)	)	PUNCT
ap-1356	42	24	=	=	SYM
ap-1356	42	25	l(u)π(v)l(−u	l(u)π(v)l(−u	NOUN
ap-1356	42	26	)	)	PUNCT
ap-1356	42	27	.	.	PUNCT
ap-1356	43	1	(	(	PUNCT
ap-1356	43	2	9	9	X
ap-1356	43	3	)	)	PUNCT
ap-1356	43	4	assuming	assume	VERB
ap-1356	43	5	that	that	SCONJ
ap-1356	43	6	π(v	π(v	NOUN
ap-1356	43	7	)	)	PUNCT
ap-1356	43	8	is	be	AUX
ap-1356	43	9	form	form	NOUN
ap-1356	43	10	-	-	PUNCT
ap-1356	43	11	invariant	invariant	ADJ
ap-1356	43	12	,	,	PUNCT
ap-1356	43	13	i.e.	i.e.	X
ap-1356	43	14	π	π	NOUN
ap-1356	43	15	′(v′	′(v′	NOUN
ap-1356	43	16	)	)	PUNCT
ap-1356	44	1	=	=	NOUN
ap-1356	44	2	π(v′	π(v′	PROPN
ap-1356	44	3	)	)	PUNCT
ap-1356	44	4	,	,	PUNCT
ap-1356	44	5	we	we	PRON
ap-1356	44	6	arrive	arrive	VERB
ap-1356	44	7	at	at	ADP
ap-1356	44	8	a	a	DET
ap-1356	44	9	functional	functional	ADJ
ap-1356	44	10	equation	equation	NOUN
ap-1356	44	11	for	for	ADP
ap-1356	44	12	π(v	π(v	NOUN
ap-1356	44	13	)	)	PUNCT
ap-1356	44	14	in	in	ADP
ap-1356	44	15	the	the	DET
ap-1356	44	16	form	form	NOUN
ap-1356	44	17	π(v′	π(v′	NOUN
ap-1356	44	18	)	)	PUNCT
ap-1356	44	19	=	=	SYM
ap-1356	44	20	l(u)π(v)l(−u	l(u)π(v)l(−u	NOUN
ap-1356	44	21	)	)	PUNCT
ap-1356	44	22	,	,	PUNCT
ap-1356	44	23	(	(	PUNCT
ap-1356	44	24	10	10	NUM
ap-1356	44	25	)	)	PUNCT
ap-1356	44	26	where	where	SCONJ
ap-1356	44	27	v′	v′	NOUN
ap-1356	44	28	is	be	AUX
ap-1356	44	29	the	the	DET
ap-1356	44	30	velocity	velocity	NOUN
ap-1356	44	31	of	of	ADP
ap-1356	44	32	a	a	DET
ap-1356	44	33	material	material	NOUN
ap-1356	44	34	point	point	NOUN
ap-1356	44	35	in	in	ADP
ap-1356	44	36	the	the	DET
ap-1356	44	37	system	system	NOUN
ap-1356	44	38	s′	s′	VERB
ap-1356	44	39	and	and	CCONJ
ap-1356	44	40	v	v	NOUN
ap-1356	44	41	is	be	AUX
ap-1356	44	42	its	its	PRON
ap-1356	44	43	velocity	velocity	NOUN
ap-1356	44	44	in	in	ADP
ap-1356	44	45	s.	s.	PROPN
ap-1356	44	46	it	it	PRON
ap-1356	44	47	is	be	AUX
ap-1356	44	48	easy	easy	ADJ
ap-1356	44	49	to	to	PART
ap-1356	44	50	prove	prove	VERB
ap-1356	44	51	[	[	X
ap-1356	44	52	1	1	X
ap-1356	44	53	]	]	PUNCT
ap-1356	44	54	that	that	SCONJ
ap-1356	44	55	after	after	ADP
ap-1356	44	56	some	some	DET
ap-1356	44	57	simple	simple	ADJ
ap-1356	44	58	substitutions	substitution	NOUN
ap-1356	44	59	and	and	CCONJ
ap-1356	44	60	rearrangements	rearrangement	NOUN
ap-1356	44	61	in	in	ADP
ap-1356	44	62	eq	eq	ADP
ap-1356	44	63	.	.	PUNCT
ap-1356	45	1	(	(	PUNCT
ap-1356	45	2	10	10	NUM
ap-1356	45	3	)	)	PUNCT
ap-1356	45	4	we	we	PRON
ap-1356	45	5	get	get	VERB
ap-1356	45	6	the	the	DET
ap-1356	45	7	solution	solution	NOUN
ap-1356	45	8	π(v	π(v	NOUN
ap-1356	45	9	)	)	PUNCT
ap-1356	46	1	=	=	SYM
ap-1356	46	2	l(−v)π(0)l(v	l(−v)π(0)l(v	PROPN
ap-1356	46	3	)	)	PUNCT
ap-1356	46	4	,	,	PUNCT
ap-1356	46	5	(	(	PUNCT
ap-1356	46	6	11	11	NUM
ap-1356	46	7	)	)	PUNCT
ap-1356	46	8	where	where	SCONJ
ap-1356	46	9	π(0	π(0	NOUN
ap-1356	46	10	)	)	PUNCT
ap-1356	46	11	is	be	AUX
ap-1356	46	12	an	an	DET
ap-1356	46	13	arbitrary	arbitrary	ADJ
ap-1356	46	14	square	square	ADJ
ap-1356	46	15	matrix	matrix	NOUN
ap-1356	46	16	formed	form	VERB
ap-1356	46	17	by	by	ADP
ap-1356	46	18	constant	constant	ADJ
ap-1356	46	19	elements	element	NOUN
ap-1356	46	20	.	.	PUNCT
ap-1356	47	1	4	4	NUM
ap-1356	47	2	two	two	NUM
ap-1356	47	3	-	-	PUNCT
ap-1356	47	4	dimensional	dimensional	ADJ
ap-1356	47	5	momentum	momentum	NOUN
ap-1356	47	6	tensor	tensor	NOUN
ap-1356	47	7	4.1	4.1	NUM
ap-1356	47	8	non	non	ADJ
ap-1356	47	9	-	-	ADJ
ap-1356	47	10	relativistic	relativistic	ADJ
ap-1356	47	11	case	case	NOUN
ap-1356	47	12	in	in	ADP
ap-1356	47	13	this	this	DET
ap-1356	47	14	case	case	NOUN
ap-1356	47	15	we	we	PRON
ap-1356	47	16	substitute	substitute	VERB
ap-1356	47	17	in	in	ADP
ap-1356	47	18	eq	eq	ADP
ap-1356	47	19	.	.	PUNCT
ap-1356	48	1	(	(	PUNCT
ap-1356	48	2	11	11	NUM
ap-1356	48	3	)	)	PUNCT
ap-1356	48	4	the	the	DET
ap-1356	48	5	galilean	galilean	PROPN
ap-1356	48	6	transformation	transformation	NOUN
ap-1356	48	7	in	in	ADP
ap-1356	48	8	the	the	DET
ap-1356	48	9	form	form	NOUN
ap-1356	48	10	g(v	g(v	X
ap-1356	48	11	)	)	PUNCT
ap-1356	48	12	=	=	PUNCT
ap-1356	49	1	(	(	PUNCT
ap-1356	49	2	1	1	NUM
ap-1356	49	3	0	0	NUM
ap-1356	49	4	−v	−v	NOUN
ap-1356	49	5	1	1	NUM
ap-1356	49	6	)	)	PUNCT
ap-1356	49	7	and	and	CCONJ
ap-1356	49	8	hence	hence	ADV
ap-1356	49	9	we	we	PRON
ap-1356	49	10	get	get	VERB
ap-1356	49	11	π(v	π(v	NOUN
ap-1356	49	12	)	)	PUNCT
ap-1356	49	13	=	=	PUNCT
ap-1356	49	14	(	(	PUNCT
ap-1356	49	15	1	1	NUM
ap-1356	49	16	0	0	NUM
ap-1356	49	17	v	v	NOUN
ap-1356	49	18	1	1	NUM
ap-1356	49	19	)	)	PUNCT
ap-1356	49	20	(	(	PUNCT
ap-1356	49	21	π00	π00	NOUN
ap-1356	49	22	π01	π01	NOUN
ap-1356	49	23	π10	π10	X
ap-1356	49	24	π11	π11	NOUN
ap-1356	49	25	)	)	PUNCT
ap-1356	49	26	(	(	PUNCT
ap-1356	49	27	1	1	NUM
ap-1356	49	28	0	0	NUM
ap-1356	49	29	−v	−v	NOUN
ap-1356	49	30	1	1	NUM
ap-1356	49	31	)	)	PUNCT
ap-1356	49	32	=	=	SYM
ap-1356	49	33	(	(	PUNCT
ap-1356	49	34	π00	π00	NOUN
ap-1356	49	35	−	−	PROPN
ap-1356	49	36	vπ01	vπ01	PROPN
ap-1356	49	37	π01	π01	NOUN
ap-1356	49	38	π10	π10	VERB
ap-1356	49	39	+	+	CCONJ
ap-1356	49	40	v	v	NOUN
ap-1356	49	41	(	(	PUNCT
ap-1356	49	42	π00	π00	NOUN
ap-1356	49	43	−π11	−π11	NUM
ap-1356	49	44	)	)	PUNCT
ap-1356	49	45	−	−	PROPN
ap-1356	50	1	v2π01	v2π01	NOUN
ap-1356	50	2	π11	π11	NOUN
ap-1356	50	3	+	+	CCONJ
ap-1356	50	4	vπ01	vπ01	PROPN
ap-1356	50	5	)	)	PUNCT
ap-1356	50	6	,	,	PUNCT
ap-1356	50	7	(	(	PUNCT
ap-1356	50	8	12	12	NUM
ap-1356	50	9	)	)	PUNCT
ap-1356	50	10	where	where	SCONJ
ap-1356	50	11	all	all	DET
ap-1356	50	12	elements	element	NOUN
ap-1356	50	13	πμ	πμ	VERB
ap-1356	50	14	ν	ν	NOUN
ap-1356	50	15	in	in	ADP
ap-1356	50	16	eq	eq	ADP
ap-1356	50	17	.	.	PUNCT
ap-1356	51	1	(	(	PUNCT
ap-1356	51	2	12	12	NUM
ap-1356	51	3	)	)	PUNCT
ap-1356	51	4	are	be	AUX
ap-1356	51	5	constant	constant	ADJ
ap-1356	51	6	.	.	PUNCT
ap-1356	52	1	since	since	SCONJ
ap-1356	52	2	the	the	DET
ap-1356	52	3	above	above	ADJ
ap-1356	52	4	equation	equation	NOUN
ap-1356	52	5	is	be	AUX
ap-1356	52	6	only	only	ADV
ap-1356	52	7	time	time	NOUN
ap-1356	52	8	-	-	PUNCT
ap-1356	52	9	dependent	dependent	ADJ
ap-1356	52	10	,	,	PUNCT
ap-1356	52	11	eq	eq	NOUN
ap-1356	52	12	.	.	PUNCT
ap-1356	53	1	(	(	PUNCT
ap-1356	53	2	7	7	X
ap-1356	53	3	)	)	PUNCT
ap-1356	53	4	leads	lead	VERB
ap-1356	53	5	to	to	ADP
ap-1356	53	6	the	the	DET
ap-1356	53	7	expression	expression	NOUN
ap-1356	53	8	∂0π0ν(v	∂0π0ν(v	NOUN
ap-1356	53	9	)	)	PUNCT
ap-1356	54	1	=	=	SYM
ap-1356	54	2	φν	φν	PROPN
ap-1356	54	3	,	,	PUNCT
ap-1356	54	4	(	(	PUNCT
ap-1356	54	5	13	13	NUM
ap-1356	54	6	)	)	PUNCT
ap-1356	54	7	where	where	SCONJ
ap-1356	54	8	∂0	∂0	NOUN
ap-1356	55	1	=	=	NOUN
ap-1356	56	1	d	d	X
ap-1356	56	2	/	/	SYM
ap-1356	56	3	dt	dt	PROPN
ap-1356	56	4	,	,	PUNCT
ap-1356	56	5	and	and	CCONJ
ap-1356	56	6	therefore	therefore	ADV
ap-1356	56	7	we	we	PRON
ap-1356	56	8	get	get	VERB
ap-1356	56	9	φ0	φ0	PROPN
ap-1356	56	10	=	=	SYM
ap-1356	56	11	∂0π00(v	∂0π00(v	PROPN
ap-1356	56	12	)	)	PUNCT
ap-1356	57	1	=	=	SYM
ap-1356	57	2	∂0	∂0	NOUN
ap-1356	57	3	(	(	PUNCT
ap-1356	57	4	π00	π00	NOUN
ap-1356	57	5	−	−	PROPN
ap-1356	57	6	vπ01	vπ01	PROPN
ap-1356	57	7	)	)	PUNCT
ap-1356	58	1	=	=	PUNCT
ap-1356	58	2	−v̇π01	−v̇π01	NOUN
ap-1356	58	3	(	(	PUNCT
ap-1356	58	4	14	14	NUM
ap-1356	58	5	)	)	PUNCT
ap-1356	58	6	and	and	CCONJ
ap-1356	58	7	φ1	φ1	NOUN
ap-1356	58	8	=	=	PUNCT
ap-1356	58	9	∂0π	∂0π	NOUN
ap-1356	58	10	0	0	NUM
ap-1356	58	11	1(v	1(v	NUM
ap-1356	58	12	)	)	PUNCT
ap-1356	58	13	=	=	VERB
ap-1356	58	14	∂0π	∂0π	NOUN
ap-1356	58	15	0	0	NUM
ap-1356	58	16	1	1	NUM
ap-1356	58	17	=	=	SYM
ap-1356	58	18	0	0	NUM
ap-1356	58	19	.	.	PUNCT
ap-1356	58	20	(	(	PUNCT
ap-1356	58	21	15	15	NUM
ap-1356	58	22	)	)	PUNCT
ap-1356	58	23	hence	hence	ADV
ap-1356	58	24	,	,	PUNCT
ap-1356	58	25	in	in	ADP
ap-1356	58	26	order	order	NOUN
ap-1356	58	27	to	to	PART
ap-1356	58	28	reconstruct	reconstruct	VERB
ap-1356	58	29	the	the	DET
ap-1356	58	30	classical	classical	ADJ
ap-1356	58	31	newtonian	newtonian	ADJ
ap-1356	58	32	equation	equation	NOUN
ap-1356	58	33	of	of	ADP
ap-1356	58	34	motion	motion	NOUN
ap-1356	58	35	we	we	PRON
ap-1356	58	36	have	have	VERB
ap-1356	58	37	to	to	PART
ap-1356	58	38	assume	assume	VERB
ap-1356	58	39	that	that	SCONJ
ap-1356	58	40	π01	π01	NOUN
ap-1356	58	41	=	=	SYM
ap-1356	58	42	m	m	NOUN
ap-1356	58	43	and	and	CCONJ
ap-1356	58	44	φ0	φ0	PROPN
ap-1356	58	45	=	=	SYM
ap-1356	58	46	−f	−f	PROPN
ap-1356	58	47	,	,	PUNCT
ap-1356	58	48	(	(	PUNCT
ap-1356	58	49	16	16	NUM
ap-1356	58	50	)	)	PUNCT
ap-1356	58	51	43	43	NUM
ap-1356	58	52	acta	acta	PROPN
ap-1356	58	53	polytechnica	polytechnica	PROPN
ap-1356	58	54	vol	vol	NOUN
ap-1356	58	55	.	.	PUNCT
ap-1356	59	1	51	51	NUM
ap-1356	60	1	no	no	NOUN
ap-1356	60	2	.	.	PUNCT
ap-1356	61	1	1/2011	1/2011	NUM
ap-1356	61	2	where	where	SCONJ
ap-1356	61	3	m	m	NOUN
ap-1356	61	4	is	be	AUX
ap-1356	61	5	mass	mass	ADJ
ap-1356	61	6	of	of	ADP
ap-1356	61	7	a	a	DET
ap-1356	61	8	material	material	NOUN
ap-1356	61	9	point	point	NOUN
ap-1356	61	10	and	and	CCONJ
ap-1356	61	11	f	f	PROPN
ap-1356	61	12	is	be	AUX
ap-1356	61	13	a	a	DET
ap-1356	61	14	classical	classical	ADJ
ap-1356	61	15	newtonian	newtonian	ADJ
ap-1356	61	16	force	force	NOUN
ap-1356	61	17	in	in	ADP
ap-1356	61	18	a	a	DET
ap-1356	61	19	two	two	NUM
ap-1356	61	20	-	-	PUNCT
ap-1356	61	21	dimensional	dimensional	ADJ
ap-1356	61	22	spacetime	spacetime	NOUN
ap-1356	61	23	.	.	PUNCT
ap-1356	62	1	the	the	DET
ap-1356	62	2	choice	choice	NOUN
ap-1356	62	3	of	of	ADP
ap-1356	62	4	the	the	DET
ap-1356	62	5	sign	sign	NOUN
ap-1356	62	6	in	in	ADP
ap-1356	62	7	eq	eq	PROPN
ap-1356	62	8	.	.	PUNCT
ap-1356	63	1	(	(	PUNCT
ap-1356	63	2	16	16	NUM
ap-1356	63	3	)	)	PUNCT
ap-1356	63	4	results	result	NOUN
ap-1356	63	5	from	from	ADP
ap-1356	63	6	considerations	consideration	NOUN
ap-1356	63	7	in	in	ADP
ap-1356	63	8	higher	high	ADJ
ap-1356	63	9	dimensional	dimensional	ADJ
ap-1356	63	10	spacetimes	spacetime	NOUN
ap-1356	63	11	.	.	PUNCT
ap-1356	64	1	it	it	PRON
ap-1356	64	2	results	result	VERB
ap-1356	64	3	from	from	ADP
ap-1356	64	4	eqs	eqs	PROPN
ap-1356	64	5	.	.	PUNCT
ap-1356	65	1	(	(	PUNCT
ap-1356	65	2	12	12	NUM
ap-1356	65	3	)	)	PUNCT
ap-1356	65	4	,	,	PUNCT
ap-1356	65	5	(	(	PUNCT
ap-1356	65	6	14	14	NUM
ap-1356	65	7	)	)	PUNCT
ap-1356	65	8	and	and	CCONJ
ap-1356	65	9	(	(	PUNCT
ap-1356	65	10	15	15	NUM
ap-1356	65	11	)	)	PUNCT
ap-1356	65	12	that	that	SCONJ
ap-1356	65	13	only	only	ADV
ap-1356	65	14	the	the	DET
ap-1356	65	15	element	element	NOUN
ap-1356	65	16	π01	π01	NOUN
ap-1356	65	17	takes	take	VERB
ap-1356	65	18	part	part	NOUN
ap-1356	65	19	in	in	ADP
ap-1356	65	20	dynamical	dynamical	ADJ
ap-1356	65	21	processes	process	NOUN
ap-1356	65	22	since	since	SCONJ
ap-1356	65	23	no	no	DET
ap-1356	65	24	other	other	ADJ
ap-1356	65	25	coefficient	coefficient	NOUN
ap-1356	65	26	appears	appear	VERB
ap-1356	65	27	in	in	ADP
ap-1356	65	28	eq	eq	ADP
ap-1356	65	29	.	.	PUNCT
ap-1356	66	1	(	(	PUNCT
ap-1356	66	2	14	14	NUM
ap-1356	66	3	)	)	PUNCT
ap-1356	66	4	.	.	PUNCT
ap-1356	67	1	therefore	therefore	ADV
ap-1356	67	2	,	,	PUNCT
ap-1356	67	3	the	the	DET
ap-1356	67	4	other	other	ADJ
ap-1356	67	5	elements	element	NOUN
ap-1356	67	6	may	may	AUX
ap-1356	67	7	take	take	VERB
ap-1356	67	8	arbitrary	arbitrary	ADJ
ap-1356	67	9	values	value	NOUN
ap-1356	67	10	and	and	CCONJ
ap-1356	67	11	each	each	DET
ap-1356	67	12	specific	specific	ADJ
ap-1356	67	13	choice	choice	NOUN
ap-1356	67	14	among	among	ADP
ap-1356	67	15	them	they	PRON
ap-1356	67	16	will	will	AUX
ap-1356	67	17	lead	lead	VERB
ap-1356	67	18	to	to	ADP
ap-1356	67	19	the	the	DET
ap-1356	67	20	same	same	ADJ
ap-1356	67	21	dynamics	dynamic	NOUN
ap-1356	67	22	.	.	PUNCT
ap-1356	68	1	in	in	ADP
ap-1356	68	2	particular	particular	ADJ
ap-1356	68	3	,	,	PUNCT
ap-1356	68	4	we	we	PRON
ap-1356	68	5	may	may	AUX
ap-1356	68	6	choose	choose	VERB
ap-1356	68	7	them	they	PRON
ap-1356	68	8	in	in	ADP
ap-1356	68	9	such	such	ADJ
ap-1356	68	10	way	way	NOUN
ap-1356	68	11	that	that	SCONJ
ap-1356	68	12	the	the	DET
ap-1356	68	13	relation	relation	NOUN
ap-1356	68	14	π(v	π(v	NOUN
ap-1356	68	15	)	)	PUNCT
ap-1356	68	16	=	=	SYM
ap-1356	68	17	mv	mv	X
ap-1356	68	18	(	(	PUNCT
ap-1356	68	19	v	v	NOUN
ap-1356	68	20	)	)	PUNCT
ap-1356	68	21	(	(	PUNCT
ap-1356	68	22	17	17	NUM
ap-1356	68	23	)	)	PUNCT
ap-1356	68	24	is	be	AUX
ap-1356	68	25	satisfied	satisfied	ADJ
ap-1356	68	26	.	.	PUNCT
ap-1356	69	1	keeping	keep	VERB
ap-1356	69	2	in	in	ADP
ap-1356	69	3	mind	mind	NOUN
ap-1356	69	4	that	that	SCONJ
ap-1356	69	5	v	v	X
ap-1356	69	6	(	(	PUNCT
ap-1356	69	7	v	v	NOUN
ap-1356	69	8	)	)	PUNCT
ap-1356	69	9	is	be	AUX
ap-1356	69	10	given	give	VERB
ap-1356	69	11	by	by	ADP
ap-1356	69	12	eq	eq	PROPN
ap-1356	69	13	.	.	PUNCT
ap-1356	70	1	(	(	PUNCT
ap-1356	70	2	3	3	NUM
ap-1356	70	3	)	)	PUNCT
ap-1356	70	4	,	,	PUNCT
ap-1356	70	5	we	we	PRON
ap-1356	70	6	get	get	VERB
ap-1356	70	7	that	that	DET
ap-1356	70	8	π(v	π(v	NOUN
ap-1356	70	9	)	)	PUNCT
ap-1356	70	10	=	=	SYM
ap-1356	70	11	π01	π01	NOUN
ap-1356	70	12	(	(	PUNCT
ap-1356	70	13	−v	−v	NOUN
ap-1356	70	14	1	1	NUM
ap-1356	70	15	−v2	−v2	PROPN
ap-1356	70	16	v	v	NOUN
ap-1356	70	17	)	)	PUNCT
ap-1356	70	18	.	.	PUNCT
ap-1356	71	1	(	(	PUNCT
ap-1356	71	2	18	18	NUM
ap-1356	71	3	)	)	PUNCT
ap-1356	71	4	the	the	DET
ap-1356	71	5	fact	fact	NOUN
ap-1356	71	6	that	that	SCONJ
ap-1356	71	7	in	in	ADP
ap-1356	71	8	the	the	DET
ap-1356	71	9	considered	considered	ADJ
ap-1356	71	10	case	case	NOUN
ap-1356	71	11	φ1	φ1	NOUN
ap-1356	71	12	=	=	SYM
ap-1356	71	13	0	0	NUM
ap-1356	71	14	leads	lead	VERB
ap-1356	71	15	to	to	ADP
ap-1356	71	16	the	the	DET
ap-1356	71	17	general	general	ADJ
ap-1356	71	18	assumption	assumption	NOUN
ap-1356	71	19	that	that	SCONJ
ap-1356	71	20	the	the	DET
ap-1356	71	21	component	component	NOUN
ap-1356	71	22	φ0	φ0	PROPN
ap-1356	71	23	plays	play	VERB
ap-1356	71	24	a	a	DET
ap-1356	71	25	key	key	ADJ
ap-1356	71	26	role	role	NOUN
ap-1356	71	27	in	in	ADP
ap-1356	71	28	the	the	DET
ap-1356	71	29	dynamics	dynamic	NOUN
ap-1356	71	30	,	,	PUNCT
ap-1356	71	31	and	and	CCONJ
ap-1356	71	32	the	the	DET
ap-1356	71	33	components	component	NOUN
ap-1356	71	34	φk	φk	AUX
ap-1356	71	35	are	be	AUX
ap-1356	71	36	auxiliary	auxiliary	ADJ
ap-1356	71	37	quantities	quantity	NOUN
ap-1356	71	38	that	that	PRON
ap-1356	71	39	provide	provide	VERB
ap-1356	71	40	the	the	DET
ap-1356	71	41	formalism	formalism	NOUN
ap-1356	71	42	covariance	covariance	NOUN
ap-1356	71	43	.	.	PUNCT
ap-1356	72	1	4.2	4.2	NUM
ap-1356	72	2	relativistic	relativistic	ADJ
ap-1356	72	3	case	case	NOUN
ap-1356	72	4	in	in	ADP
ap-1356	72	5	the	the	DET
ap-1356	72	6	case	case	NOUN
ap-1356	72	7	of	of	ADP
ap-1356	72	8	substituting	substitute	VERB
ap-1356	72	9	into	into	ADP
ap-1356	72	10	eq	eq	NOUN
ap-1356	72	11	.	.	PUNCT
ap-1356	73	1	(	(	PUNCT
ap-1356	73	2	11	11	NUM
ap-1356	73	3	)	)	PUNCT
ap-1356	73	4	the	the	DET
ap-1356	73	5	lorentz	lorentz	PROPN
ap-1356	73	6	transformation	transformation	NOUN
ap-1356	73	7	given	give	VERB
ap-1356	73	8	by	by	ADP
ap-1356	73	9	l(β	l(β	PROPN
ap-1356	73	10	)	)	PUNCT
ap-1356	74	1	=	=	SYM
ap-1356	74	2	γ	γ	X
ap-1356	74	3	(	(	PUNCT
ap-1356	74	4	1	1	NUM
ap-1356	74	5	−β	−β	NOUN
ap-1356	74	6	−β	−β	NOUN
ap-1356	74	7	1	1	NUM
ap-1356	74	8	)	)	PUNCT
ap-1356	74	9	we	we	PRON
ap-1356	74	10	get	get	VERB
ap-1356	74	11	that	that	DET
ap-1356	74	12	π(β	π(β	NOUN
ap-1356	74	13	)	)	PUNCT
ap-1356	75	1	=	=	SYM
ap-1356	75	2	γ2	γ2	NOUN
ap-1356	75	3	(	(	PUNCT
ap-1356	75	4	π00	π00	NOUN
ap-1356	75	5	+	+	CCONJ
ap-1356	75	6	β(π10	β(π10	X
ap-1356	76	1	−π01)−	−π01)−	PROPN
ap-1356	76	2	β2π11	β2π11	NOUN
ap-1356	76	3	π01	π01	NOUN
ap-1356	76	4	+	+	CCONJ
ap-1356	76	5	β(π11	β(π11	NOUN
ap-1356	76	6	−π00)−	−π00)−	NUM
ap-1356	76	7	β2π10	β2π10	PUNCT
ap-1356	76	8	π10	π10	VERB
ap-1356	76	9	+	+	CCONJ
ap-1356	76	10	β(π00	β(π00	NUM
ap-1356	76	11	−π11)−	−π11)−	NOUN
ap-1356	76	12	β2π01	β2π01	NOUN
ap-1356	76	13	π11	π11	NOUN
ap-1356	76	14	+	+	CCONJ
ap-1356	76	15	β(π01	β(π01	ADV
ap-1356	76	16	−π10)−	−π10)−	NOUN
ap-1356	76	17	β2π00	β2π00	PUNCT
ap-1356	76	18	)	)	PUNCT
ap-1356	76	19	.	.	PUNCT
ap-1356	77	1	(	(	PUNCT
ap-1356	77	2	19	19	NUM
ap-1356	77	3	)	)	PUNCT
ap-1356	77	4	according	accord	VERB
ap-1356	77	5	to	to	ADP
ap-1356	77	6	eq	eq	PROPN
ap-1356	77	7	.	.	PUNCT
ap-1356	78	1	(	(	PUNCT
ap-1356	78	2	13	13	NUM
ap-1356	78	3	)	)	PUNCT
ap-1356	78	4	we	we	PRON
ap-1356	78	5	obtain	obtain	VERB
ap-1356	78	6	that	that	DET
ap-1356	78	7	φ0	φ0	PROPN
ap-1356	78	8	=	=	SYM
ap-1356	78	9	∂0π00(β	∂0π00(β	PROPN
ap-1356	78	10	)	)	PUNCT
ap-1356	78	11	=	=	SYM
ap-1356	78	12	∂0γ	∂0γ	NOUN
ap-1356	78	13	2	2	NUM
ap-1356	78	14	[	[	PUNCT
ap-1356	78	15	π00	π00	NOUN
ap-1356	78	16	+	+	CCONJ
ap-1356	78	17	β(π10	β(π10	NOUN
ap-1356	78	18	−	−	X
ap-1356	78	19	π01)−	π01)−	X
ap-1356	78	20	β2π11	β2π11	PUNCT
ap-1356	78	21	]	]	PUNCT
ap-1356	79	1	=	=	PUNCT
ap-1356	79	2	γ4β̇	γ4β̇	ADP
ap-1356	79	3	[	[	X
ap-1356	79	4	(	(	PUNCT
ap-1356	79	5	1	1	NUM
ap-1356	79	6	+	+	CCONJ
ap-1356	79	7	β2	β2	NOUN
ap-1356	79	8	)	)	PUNCT
ap-1356	79	9	(	(	PUNCT
ap-1356	79	10	π10	π10	X
ap-1356	79	11	−π01	−π01	SYM
ap-1356	79	12	)	)	PUNCT
ap-1356	80	1	+	+	CCONJ
ap-1356	80	2	2β	2β	NOUN
ap-1356	80	3	(	(	PUNCT
ap-1356	80	4	π00	π00	NOUN
ap-1356	80	5	−π11	−π11	NUM
ap-1356	80	6	)	)	PUNCT
ap-1356	80	7	]	]	PUNCT
ap-1356	80	8	,	,	PUNCT
ap-1356	80	9	(	(	PUNCT
ap-1356	80	10	20	20	X
ap-1356	80	11	)	)	PUNCT
ap-1356	80	12	φ1	φ1	NOUN
ap-1356	80	13	=	=	SYM
ap-1356	80	14	∂0π01(β	∂0π01(β	PROPN
ap-1356	80	15	)	)	PUNCT
ap-1356	80	16	=	=	SYM
ap-1356	80	17	∂0γ	∂0γ	NOUN
ap-1356	80	18	2	2	NUM
ap-1356	80	19	[	[	PUNCT
ap-1356	80	20	π01	π01	NOUN
ap-1356	80	21	+	+	CCONJ
ap-1356	80	22	β(π11	β(π11	NOUN
ap-1356	80	23	−	−	NOUN
ap-1356	80	24	π00)−	π00)−	PROPN
ap-1356	80	25	β2π10	β2π10	X
ap-1356	80	26	]	]	PUNCT
ap-1356	80	27	=	=	PUNCT
ap-1356	80	28	γ4β̇	γ4β̇	ADP
ap-1356	80	29	[	[	X
ap-1356	80	30	(	(	PUNCT
ap-1356	80	31	1	1	NUM
ap-1356	80	32	+	+	CCONJ
ap-1356	80	33	β2	β2	NOUN
ap-1356	80	34	)	)	PUNCT
ap-1356	80	35	(	(	PUNCT
ap-1356	80	36	π11	π11	NOUN
ap-1356	80	37	−π00	−π00	NOUN
ap-1356	80	38	)	)	PUNCT
ap-1356	81	1	+	+	CCONJ
ap-1356	81	2	2β	2β	NOUN
ap-1356	81	3	(	(	PUNCT
ap-1356	81	4	π01	π01	NOUN
ap-1356	81	5	−π10	−π10	NUM
ap-1356	81	6	)	)	PUNCT
ap-1356	81	7	]	]	PUNCT
ap-1356	81	8	.	.	PUNCT
ap-1356	82	1	(	(	PUNCT
ap-1356	82	2	21	21	NUM
ap-1356	82	3	)	)	PUNCT
ap-1356	82	4	as	as	SCONJ
ap-1356	82	5	we	we	PRON
ap-1356	82	6	can	can	AUX
ap-1356	82	7	observe	observe	VERB
ap-1356	82	8	,	,	PUNCT
ap-1356	82	9	generally	generally	ADV
ap-1356	82	10	all	all	DET
ap-1356	82	11	coefficients	coefficient	NOUN
ap-1356	82	12	πμ	πμ	VERB
ap-1356	82	13	ν	ν	NOUN
ap-1356	82	14	take	take	VERB
ap-1356	82	15	part	part	NOUN
ap-1356	82	16	in	in	ADP
ap-1356	82	17	the	the	DET
ap-1356	82	18	dynamics	dynamic	NOUN
ap-1356	82	19	in	in	ADP
ap-1356	82	20	this	this	DET
ap-1356	82	21	case	case	NOUN
ap-1356	82	22	since	since	SCONJ
ap-1356	82	23	all	all	PRON
ap-1356	82	24	of	of	ADP
ap-1356	82	25	them	they	PRON
ap-1356	82	26	are	be	AUX
ap-1356	82	27	present	present	ADJ
ap-1356	82	28	in	in	ADP
ap-1356	82	29	eq	eq	ADP
ap-1356	82	30	.	.	PUNCT
ap-1356	83	1	(	(	PUNCT
ap-1356	83	2	20	20	NUM
ap-1356	83	3	)	)	PUNCT
ap-1356	83	4	.	.	PUNCT
ap-1356	84	1	in	in	ADP
ap-1356	84	2	order	order	NOUN
ap-1356	84	3	to	to	PART
ap-1356	84	4	illustrate	illustrate	VERB
ap-1356	84	5	the	the	DET
ap-1356	84	6	role	role	NOUN
ap-1356	84	7	of	of	ADP
ap-1356	84	8	parameters	parameter	NOUN
ap-1356	84	9	πμ	πμ	AUX
ap-1356	84	10	ν	ν	NOUN
ap-1356	84	11	let	let	VERB
ap-1356	84	12	us	we	PRON
ap-1356	84	13	consider	consider	VERB
ap-1356	84	14	a	a	DET
ap-1356	84	15	general	general	ADJ
ap-1356	84	16	case	case	NOUN
ap-1356	84	17	of	of	ADP
ap-1356	84	18	dynamics	dynamic	NOUN
ap-1356	84	19	where	where	SCONJ
ap-1356	84	20	φ0	φ0	PROPN
ap-1356	84	21	=	=	PUNCT
ap-1356	84	22	const	const	PROPN
ap-1356	84	23	.	.	PUNCT
ap-1356	85	1	after	after	ADP
ap-1356	85	2	the	the	DET
ap-1356	85	3	integration	integration	NOUN
ap-1356	85	4	of	of	ADP
ap-1356	85	5	eq	eq	PROPN
ap-1356	85	6	.	.	PUNCT
ap-1356	86	1	(	(	PUNCT
ap-1356	86	2	20	20	NUM
ap-1356	86	3	)	)	PUNCT
ap-1356	86	4	we	we	PRON
ap-1356	86	5	find	find	VERB
ap-1356	86	6	that	that	SCONJ
ap-1356	86	7	γ2	γ2	NOUN
ap-1356	86	8	[	[	PUNCT
ap-1356	86	9	π00	π00	NOUN
ap-1356	86	10	+	+	CCONJ
ap-1356	86	11	β(π10	β(π10	X
ap-1356	87	1	−π01)−	−π01)−	PROPN
ap-1356	87	2	β2π11	β2π11	PUNCT
ap-1356	87	3	]	]	PUNCT
ap-1356	88	1	=	=	PUNCT
ap-1356	88	2	φ0t+	φ0t+	ADJ
ap-1356	88	3	c	c	X
ap-1356	88	4	,	,	PUNCT
ap-1356	88	5	(	(	PUNCT
ap-1356	88	6	22	22	NUM
ap-1356	88	7	)	)	PUNCT
ap-1356	88	8	where	where	SCONJ
ap-1356	88	9	c	c	NOUN
ap-1356	88	10	is	be	AUX
ap-1356	88	11	an	an	DET
ap-1356	88	12	integration	integration	NOUN
ap-1356	88	13	constant	constant	ADJ
ap-1356	88	14	.	.	PUNCT
ap-1356	89	1	taking	take	VERB
ap-1356	89	2	into	into	ADP
ap-1356	89	3	consideration	consideration	NOUN
ap-1356	89	4	the	the	DET
ap-1356	89	5	initial	initial	ADJ
ap-1356	89	6	condition	condition	NOUN
ap-1356	89	7	for	for	ADP
ap-1356	89	8	t	t	NOUN
ap-1356	89	9	=	=	SYM
ap-1356	89	10	0	0	NUM
ap-1356	89	11	we	we	PRON
ap-1356	89	12	obtain	obtain	VERB
ap-1356	89	13	that	that	DET
ap-1356	89	14	c	c	NOUN
ap-1356	89	15	=	=	SYM
ap-1356	89	16	γ20	γ20	PROPN
ap-1356	89	17	[	[	PUNCT
ap-1356	89	18	π00	π00	NOUN
ap-1356	89	19	+	+	CCONJ
ap-1356	89	20	β0(π10	β0(π10	NOUN
ap-1356	89	21	−π01)−	−π01)−	PROPN
ap-1356	89	22	β20π	β20π	PROPN
ap-1356	89	23	1	1	NUM
ap-1356	89	24	1	1	NUM
ap-1356	89	25	]	]	PUNCT
ap-1356	89	26	,	,	PUNCT
ap-1356	89	27	where	where	SCONJ
ap-1356	89	28	β0	β0	NOUN
ap-1356	89	29	and	and	CCONJ
ap-1356	89	30	γ0	γ0	NOUN
ap-1356	89	31	are	be	AUX
ap-1356	89	32	the	the	DET
ap-1356	89	33	values	value	NOUN
ap-1356	89	34	for	for	ADP
ap-1356	89	35	t	t	NOUN
ap-1356	89	36	=	=	SYM
ap-1356	89	37	0	0	PROPN
ap-1356	89	38	.	.	PUNCT
ap-1356	90	1	if	if	SCONJ
ap-1356	90	2	we	we	PRON
ap-1356	90	3	additionally	additionally	ADV
ap-1356	90	4	assume	assume	VERB
ap-1356	90	5	that	that	SCONJ
ap-1356	90	6	β0	β0	NOUN
ap-1356	90	7	=	=	SYM
ap-1356	90	8	0	0	NUM
ap-1356	90	9	(	(	PUNCT
ap-1356	90	10	i.e.	i.e.	X
ap-1356	90	11	γ0	γ0	X
ap-1356	90	12	=	=	SYM
ap-1356	90	13	1	1	NUM
ap-1356	90	14	)	)	PUNCT
ap-1356	90	15	then	then	ADV
ap-1356	90	16	c	c	NOUN
ap-1356	90	17	=	=	SYM
ap-1356	90	18	π00	π00	NOUN
ap-1356	90	19	.	.	PUNCT
ap-1356	91	1	substituting	substitute	VERB
ap-1356	91	2	this	this	PRON
ap-1356	91	3	into	into	ADP
ap-1356	91	4	eq	eq	NOUN
ap-1356	91	5	.	.	PUNCT
ap-1356	92	1	(	(	PUNCT
ap-1356	92	2	22	22	NUM
ap-1356	92	3	)	)	PUNCT
ap-1356	92	4	and	and	CCONJ
ap-1356	92	5	making	make	VERB
ap-1356	92	6	simple	simple	ADJ
ap-1356	92	7	rearrangements	rearrangement	NOUN
ap-1356	92	8	we	we	PRON
ap-1356	92	9	arrive	arrive	VERB
ap-1356	92	10	at	at	ADP
ap-1356	92	11	the	the	DET
ap-1356	92	12	following	following	NOUN
ap-1356	92	13	:	:	PUNCT
ap-1356	93	1	β2	β2	NOUN
ap-1356	93	2	(	(	PUNCT
ap-1356	93	3	φ0t+π	φ0t+π	NOUN
ap-1356	93	4	0	0	NUM
ap-1356	93	5	0	0	NUM
ap-1356	93	6	−π11	−π11	NUM
ap-1356	93	7	)	)	PUNCT
ap-1356	94	1	+	+	CCONJ
ap-1356	94	2	β	β	X
ap-1356	94	3	(	(	PUNCT
ap-1356	94	4	π10	π10	X
ap-1356	94	5	−π01	−π01	PRON
ap-1356	94	6	)	)	PUNCT
ap-1356	94	7	−	−	PROPN
ap-1356	95	1	φ0	φ0	ADJ
ap-1356	95	2	t	t	NOUN
ap-1356	95	3	=	=	SYM
ap-1356	95	4	0	0	PROPN
ap-1356	95	5	.	.	PUNCT
ap-1356	96	1	(	(	PUNCT
ap-1356	96	2	23	23	NUM
ap-1356	96	3	)	)	PUNCT
ap-1356	96	4	the	the	DET
ap-1356	96	5	solutions	solution	NOUN
ap-1356	96	6	of	of	ADP
ap-1356	96	7	the	the	DET
ap-1356	96	8	above	above	ADJ
ap-1356	96	9	equation	equation	NOUN
ap-1356	96	10	are	be	AUX
ap-1356	96	11	of	of	ADP
ap-1356	96	12	the	the	DET
ap-1356	96	13	form	form	NOUN
ap-1356	96	14	β±	β±	NOUN
ap-1356	96	15	=	=	PRON
ap-1356	96	16	(	(	PUNCT
ap-1356	96	17	π01	π01	PROPN
ap-1356	96	18	−π10	−π10	SYM
ap-1356	96	19	)	)	PUNCT
ap-1356	96	20	±	±	NUM
ap-1356	96	21	√	√	PROPN
ap-1356	96	22	(	(	PUNCT
ap-1356	96	23	π01	π01	PROPN
ap-1356	96	24	−π10	−π10	NOUN
ap-1356	96	25	)	)	PUNCT
ap-1356	96	26	2	2	NUM
ap-1356	97	1	+	+	NUM
ap-1356	97	2	4φ0	4φ0	NUM
ap-1356	97	3	t	t	NOUN
ap-1356	97	4	(	(	PUNCT
ap-1356	97	5	φ0t+π00	φ0t+π00	PROPN
ap-1356	97	6	−π11	−π11	ADJ
ap-1356	97	7	)	)	PUNCT
ap-1356	97	8	2	2	NUM
ap-1356	97	9	(	(	PUNCT
ap-1356	97	10	φ0t+π00	φ0t+π00	PROPN
ap-1356	97	11	−π11	−π11	NUM
ap-1356	97	12	)	)	PUNCT
ap-1356	97	13	.	.	PUNCT
ap-1356	98	1	(	(	PUNCT
ap-1356	98	2	24	24	NUM
ap-1356	98	3	)	)	PUNCT
ap-1356	98	4	in	in	ADP
ap-1356	98	5	the	the	DET
ap-1356	98	6	standard	standard	ADJ
ap-1356	98	7	formalism	formalism	NOUN
ap-1356	98	8	of	of	ADP
ap-1356	98	9	the	the	DET
ap-1356	98	10	special	special	ADJ
ap-1356	98	11	theory	theory	NOUN
ap-1356	98	12	of	of	ADP
ap-1356	98	13	relativity	relativity	NOUN
ap-1356	98	14	[	[	X
ap-1356	98	15	3	3	NUM
ap-1356	98	16	]	]	PUNCT
ap-1356	98	17	,	,	PUNCT
ap-1356	98	18	when	when	SCONJ
ap-1356	98	19	a	a	DET
ap-1356	98	20	constant	constant	ADJ
ap-1356	98	21	force	force	NOUN
ap-1356	98	22	f	f	PROPN
ap-1356	98	23	is	be	AUX
ap-1356	98	24	applied	apply	VERB
ap-1356	98	25	to	to	ADP
ap-1356	98	26	a	a	DET
ap-1356	98	27	body	body	NOUN
ap-1356	98	28	one	one	NOUN
ap-1356	98	29	gets	get	VERB
ap-1356	98	30	the	the	DET
ap-1356	98	31	following	follow	VERB
ap-1356	98	32	solutions	solution	NOUN
ap-1356	98	33	of	of	ADP
ap-1356	98	34	the	the	DET
ap-1356	98	35	equations	equation	NOUN
ap-1356	98	36	of	of	ADP
ap-1356	98	37	motion	motion	NOUN
ap-1356	98	38	for	for	ADP
ap-1356	98	39	a	a	DET
ap-1356	98	40	velocity	velocity	NOUN
ap-1356	98	41	:	:	PUNCT
ap-1356	98	42	βstr	βstr	NOUN
ap-1356	98	43	±	±	PROPN
ap-1356	98	44	=	=	SYM
ap-1356	98	45	±	±	PROPN
ap-1356	99	1	√	√	PROPN
ap-1356	99	2	f	f	PROPN
ap-1356	100	1	2t2	2t2	NUM
ap-1356	100	2	m2c2	m2c2	NOUN
ap-1356	101	1	+	+	NUM
ap-1356	101	2	f	f	PROPN
ap-1356	101	3	2t2	2t2	NUM
ap-1356	101	4	.	.	PUNCT
ap-1356	102	1	(	(	PUNCT
ap-1356	102	2	25	25	NUM
ap-1356	102	3	)	)	PUNCT
ap-1356	102	4	44	44	NUM
ap-1356	102	5	acta	acta	PROPN
ap-1356	102	6	polytechnica	polytechnica	PROPN
ap-1356	102	7	vol	vol	NOUN
ap-1356	102	8	.	.	PUNCT
ap-1356	103	1	51	51	NUM
ap-1356	103	2	no	no	INTJ
ap-1356	103	3	.	.	PUNCT
ap-1356	104	1	1/2011	1/2011	NUM
ap-1356	104	2	if	if	SCONJ
ap-1356	104	3	we	we	PRON
ap-1356	104	4	expect	expect	VERB
ap-1356	104	5	that	that	PRON
ap-1356	104	6	eq	eq	ADP
ap-1356	104	7	.	.	PUNCT
ap-1356	105	1	(	(	PUNCT
ap-1356	105	2	23	23	NUM
ap-1356	105	3	)	)	PUNCT
ap-1356	105	4	also	also	ADV
ap-1356	105	5	has	have	VERB
ap-1356	105	6	two	two	NUM
ap-1356	105	7	symmetric	symmetric	ADJ
ap-1356	105	8	solutions	solution	NOUN
ap-1356	105	9	,	,	PUNCT
ap-1356	105	10	we	we	PRON
ap-1356	105	11	have	have	VERB
ap-1356	105	12	to	to	PART
ap-1356	105	13	assume	assume	VERB
ap-1356	105	14	that	that	SCONJ
ap-1356	105	15	π01	π01	NOUN
ap-1356	105	16	=	=	SYM
ap-1356	105	17	π	π	PROPN
ap-1356	105	18	1	1	NUM
ap-1356	105	19	0	0	NUM
ap-1356	105	20	.	.	PUNCT
ap-1356	106	1	hence	hence	ADV
ap-1356	106	2	in	in	ADP
ap-1356	106	3	this	this	DET
ap-1356	106	4	case	case	NOUN
ap-1356	106	5	we	we	PRON
ap-1356	106	6	find	find	VERB
ap-1356	106	7	that	that	SCONJ
ap-1356	106	8	β±	β±	PRON
ap-1356	106	9	=	=	SYM
ap-1356	106	10	±	±	PROPN
ap-1356	106	11	√	√	PROPN
ap-1356	106	12	φ0	φ0	PROPN
ap-1356	106	13	t	t	PROPN
ap-1356	106	14	φ0t+	φ0t+	PROPN
ap-1356	106	15	π00	π00	NOUN
ap-1356	106	16	−π11	−π11	X
ap-1356	106	17	.	.	PUNCT
ap-1356	107	1	(	(	PUNCT
ap-1356	107	2	26	26	NUM
ap-1356	107	3	)	)	PUNCT
ap-1356	107	4	0	0	NUM
ap-1356	108	1	0.1	0.1	NUM
ap-1356	108	2	0.2	0.2	NUM
ap-1356	108	3	0.3	0.3	NUM
ap-1356	108	4	0.4	0.4	NUM
ap-1356	108	5	0.5	0.5	NUM
ap-1356	108	6	0.6	0.6	NUM
ap-1356	108	7	0.7	0.7	NUM
ap-1356	108	8	0.8	0.8	NUM
ap-1356	108	9	0.9	0.9	NUM
ap-1356	108	10	1	1	NUM
ap-1356	108	11	0	0	NUM
ap-1356	108	12	1	1	NUM
ap-1356	108	13	2	2	NUM
ap-1356	108	14	3	3	NUM
ap-1356	108	15	4	4	NUM
ap-1356	108	16	5	5	NUM
ap-1356	108	17	6	6	NUM
ap-1356	108	18	7	7	NUM
ap-1356	108	19	v/	v/	NOUN
ap-1356	108	20	c	c	PROPN
ap-1356	108	21	t	t	NOUN
ap-1356	108	22	fig	fig	NOUN
ap-1356	108	23	.	.	PUNCT
ap-1356	109	1	1	1	NUM
ap-1356	109	2	:	:	PUNCT
ap-1356	109	3	comparison	comparison	NOUN
ap-1356	109	4	of	of	ADP
ap-1356	109	5	β(t	β(t	PROPN
ap-1356	109	6	)	)	PUNCT
ap-1356	109	7	(	(	PUNCT
ap-1356	109	8	green	green	PROPN
ap-1356	109	9	dashed	dash	VERB
ap-1356	109	10	)	)	PUNCT
ap-1356	109	11	and	and	CCONJ
ap-1356	109	12	βstr(t	βstr(t	NUM
ap-1356	109	13	)	)	PUNCT
ap-1356	109	14	(	(	PUNCT
ap-1356	109	15	red	red	NOUN
ap-1356	109	16	)	)	PUNCT
ap-1356	109	17	.	.	PUNCT
ap-1356	110	1	f	f	X
ap-1356	111	1	=	=	NOUN
ap-1356	111	2	φ0	φ0	PROPN
ap-1356	111	3	=	=	SYM
ap-1356	111	4	1	1	NUM
ap-1356	111	5	,	,	PUNCT
ap-1356	111	6	m	m	VERB
ap-1356	111	7	2c2	2c2	NUM
ap-1356	111	8	=	=	SYM
ap-1356	111	9	π00	π00	NOUN
ap-1356	111	10	−π11	−π11	ADJ
ap-1356	111	11	=	=	SYM
ap-1356	111	12	1	1	NUM
ap-1356	111	13	are	be	AUX
ap-1356	111	14	assumed	assume	VERB
ap-1356	111	15	here	here	ADV
ap-1356	111	16	it	it	PRON
ap-1356	111	17	should	should	AUX
ap-1356	111	18	be	be	AUX
ap-1356	111	19	stressed	stress	VERB
ap-1356	111	20	here	here	ADV
ap-1356	111	21	that	that	SCONJ
ap-1356	111	22	the	the	DET
ap-1356	111	23	asymptotes	asymptote	NOUN
ap-1356	111	24	of	of	ADP
ap-1356	111	25	eqs	eqs	PROPN
ap-1356	111	26	.	.	PUNCT
ap-1356	112	1	(	(	PUNCT
ap-1356	112	2	25	25	NUM
ap-1356	112	3	)	)	PUNCT
ap-1356	112	4	and	and	CCONJ
ap-1356	112	5	(	(	PUNCT
ap-1356	112	6	26	26	NUM
ap-1356	112	7	)	)	PUNCT
ap-1356	112	8	are	be	AUX
ap-1356	112	9	identical	identical	ADJ
ap-1356	112	10	,	,	PUNCT
ap-1356	112	11	i.e.	i.e.	X
ap-1356	112	12	:	:	PUNCT
ap-1356	112	13	lim	lim	PROPN
ap-1356	112	14	t→∞	t→∞	NUM
ap-1356	112	15	βstr	βstr	NOUN
ap-1356	112	16	±	±	PROPN
ap-1356	113	1	=	=	PROPN
ap-1356	113	2	lim	lim	PROPN
ap-1356	113	3	t→∞	t→∞	X
ap-1356	113	4	β±	β±	PROPN
ap-1356	113	5	=	=	SYM
ap-1356	113	6	±1	±1	PROPN
ap-1356	113	7	and	and	CCONJ
ap-1356	113	8	lim	lim	PROPN
ap-1356	113	9	t→0	t→0	PROPN
ap-1356	113	10	βstr	βstr	PROPN
ap-1356	113	11	±	±	PROPN
ap-1356	114	1	=	=	SYM
ap-1356	114	2	lim	lim	PROPN
ap-1356	114	3	t→0	t→0	PUNCT
ap-1356	114	4	β±	β±	PUNCT
ap-1356	115	1	=	=	SYM
ap-1356	115	2	0	0	X
ap-1356	115	3	.	.	PUNCT
ap-1356	116	1	as	as	SCONJ
ap-1356	116	2	we	we	PRON
ap-1356	116	3	can	can	AUX
ap-1356	116	4	see	see	VERB
ap-1356	116	5	from	from	ADP
ap-1356	116	6	eq	eq	NOUN
ap-1356	116	7	.	.	PUNCT
ap-1356	117	1	(	(	PUNCT
ap-1356	117	2	26	26	NUM
ap-1356	117	3	)	)	PUNCT
ap-1356	117	4	,	,	PUNCT
ap-1356	117	5	the	the	DET
ap-1356	117	6	constant	constant	ADJ
ap-1356	117	7	π11	π11	NOUN
ap-1356	117	8	plays	play	VERB
ap-1356	117	9	the	the	DET
ap-1356	117	10	role	role	NOUN
ap-1356	117	11	of	of	ADP
ap-1356	117	12	a	a	DET
ap-1356	117	13	“	"	PUNCT
ap-1356	117	14	renormalization	renormalization	NOUN
ap-1356	117	15	”	"	PUNCT
ap-1356	117	16	constant	constant	ADJ
ap-1356	117	17	for	for	ADP
ap-1356	117	18	π	π	PROPN
ap-1356	117	19	0	0	NUM
ap-1356	117	20	0	0	NUM
ap-1356	117	21	,	,	PUNCT
ap-1356	117	22	hence	hence	ADV
ap-1356	117	23	it	it	PRON
ap-1356	117	24	can	can	AUX
ap-1356	117	25	be	be	AUX
ap-1356	117	26	discarded	discard	VERB
ap-1356	117	27	without	without	ADP
ap-1356	117	28	losing	lose	VERB
ap-1356	117	29	the	the	DET
ap-1356	117	30	generality	generality	NOUN
ap-1356	117	31	of	of	ADP
ap-1356	117	32	considerations	consideration	NOUN
ap-1356	117	33	.	.	PUNCT
ap-1356	118	1	then	then	ADV
ap-1356	118	2	matrix	matrix	NOUN
ap-1356	118	3	(	(	PUNCT
ap-1356	118	4	19	19	NUM
ap-1356	118	5	)	)	PUNCT
ap-1356	118	6	takes	take	VERB
ap-1356	118	7	the	the	DET
ap-1356	118	8	form	form	NOUN
ap-1356	118	9	π(β	π(β	NOUN
ap-1356	118	10	)	)	PUNCT
ap-1356	119	1	=	=	SYM
ap-1356	119	2	γ2	γ2	NOUN
ap-1356	119	3	(	(	PUNCT
ap-1356	119	4	π00	π00	NOUN
ap-1356	119	5	π01	π01	NOUN
ap-1356	119	6	−	−	PROPN
ap-1356	119	7	βπ00	βπ00	PROPN
ap-1356	119	8	−	−	PROPN
ap-1356	119	9	β2π01	β2π01	NOUN
ap-1356	119	10	π01	π01	NOUN
ap-1356	119	11	+	+	CCONJ
ap-1356	119	12	βπ00	βπ00	PROPN
ap-1356	119	13	−	−	PROPN
ap-1356	119	14	β2π01	β2π01	PUNCT
ap-1356	119	15	−β2π00	−β2π00	PROPN
ap-1356	119	16	)	)	PUNCT
ap-1356	119	17	.	.	PUNCT
ap-1356	120	1	(	(	PUNCT
ap-1356	120	2	27	27	NUM
ap-1356	120	3	)	)	PUNCT
ap-1356	120	4	matrix	matrix	NOUN
ap-1356	120	5	(	(	PUNCT
ap-1356	120	6	27	27	NUM
ap-1356	120	7	)	)	PUNCT
ap-1356	120	8	can	can	AUX
ap-1356	120	9	also	also	ADV
ap-1356	120	10	be	be	AUX
ap-1356	120	11	rewritten	rewrite	VERB
ap-1356	120	12	as	as	ADP
ap-1356	120	13	π(β	π(β	NOUN
ap-1356	120	14	)	)	PUNCT
ap-1356	121	1	=	=	SYM
ap-1356	121	2	γ2π00	γ2π00	NOUN
ap-1356	121	3	(	(	PUNCT
ap-1356	121	4	1	1	NUM
ap-1356	121	5	−β	−β	PROPN
ap-1356	121	6	β	β	X
ap-1356	121	7	−β2	−β2	PROPN
ap-1356	121	8	)	)	PUNCT
ap-1356	122	1	+	+	PUNCT
ap-1356	122	2	π01	π01	NOUN
ap-1356	122	3	(	(	PUNCT
ap-1356	122	4	0	0	NUM
ap-1356	122	5	1	1	NUM
ap-1356	122	6	1	1	NUM
ap-1356	122	7	0	0	NUM
ap-1356	122	8	)	)	PUNCT
ap-1356	122	9	,	,	PUNCT
ap-1356	122	10	(	(	PUNCT
ap-1356	122	11	28	28	NUM
ap-1356	122	12	)	)	PUNCT
ap-1356	122	13	where	where	SCONJ
ap-1356	122	14	the	the	DET
ap-1356	122	15	second	second	ADJ
ap-1356	122	16	matrix	matrix	NOUN
ap-1356	122	17	on	on	ADP
ap-1356	122	18	the	the	DET
ap-1356	122	19	right	right	ADJ
ap-1356	122	20	hand	hand	NOUN
ap-1356	122	21	side	side	NOUN
ap-1356	122	22	of	of	ADP
ap-1356	122	23	eq	eq	PROPN
ap-1356	122	24	.	.	PUNCT
ap-1356	123	1	(	(	PUNCT
ap-1356	123	2	28	28	NUM
ap-1356	123	3	)	)	PUNCT
ap-1356	123	4	is	be	AUX
ap-1356	123	5	constant	constant	ADJ
ap-1356	123	6	in	in	ADP
ap-1356	123	7	time	time	NOUN
ap-1356	123	8	.	.	PUNCT
ap-1356	124	1	assuming	assume	VERB
ap-1356	124	2	that	that	SCONJ
ap-1356	124	3	π01	π01	NOUN
ap-1356	124	4	=	=	SYM
ap-1356	124	5	π	π	PROPN
ap-1356	124	6	1	1	NUM
ap-1356	124	7	0	0	NUM
ap-1356	124	8	and	and	CCONJ
ap-1356	124	9	π	π	PROPN
ap-1356	124	10	1	1	NUM
ap-1356	124	11	1	1	NUM
ap-1356	124	12	=	=	SYM
ap-1356	124	13	0	0	NUM
ap-1356	124	14	,	,	PUNCT
ap-1356	124	15	eqs	eqs	X
ap-1356	124	16	.	.	PUNCT
ap-1356	125	1	(	(	PUNCT
ap-1356	125	2	20	20	NUM
ap-1356	125	3	)	)	PUNCT
ap-1356	125	4	and	and	CCONJ
ap-1356	125	5	(	(	PUNCT
ap-1356	125	6	21	21	NUM
ap-1356	125	7	)	)	PUNCT
ap-1356	125	8	turn	turn	VERB
ap-1356	125	9	into	into	ADP
ap-1356	125	10	φ0	φ0	PROPN
ap-1356	125	11	=	=	PUNCT
ap-1356	125	12	∂0π00(β	∂0π00(β	PROPN
ap-1356	125	13	)	)	PUNCT
ap-1356	125	14	=	=	SYM
ap-1356	125	15	∂0γ	∂0γ	NOUN
ap-1356	125	16	2π00	2π00	NOUN
ap-1356	125	17	=	=	SYM
ap-1356	125	18	2γ	2γ	NUM
ap-1356	125	19	4β̇βπ00	4β̇βπ00	NUM
ap-1356	125	20	,	,	PUNCT
ap-1356	125	21	(	(	PUNCT
ap-1356	125	22	29	29	NUM
ap-1356	125	23	)	)	PUNCT
ap-1356	125	24	φ1	φ1	NOUN
ap-1356	125	25	=	=	SYM
ap-1356	125	26	∂0π01(β	∂0π01(β	PROPN
ap-1356	125	27	)	)	PUNCT
ap-1356	126	1	=	=	SYM
ap-1356	126	2	∂0γ	∂0γ	NOUN
ap-1356	126	3	2	2	NUM
ap-1356	126	4	(	(	PUNCT
ap-1356	126	5	−βπ00	−βπ00	NOUN
ap-1356	126	6	)	)	PUNCT
ap-1356	127	1	=	=	SYM
ap-1356	127	2	−γ4β̇	−γ4β̇	PROPN
ap-1356	127	3	(	(	PUNCT
ap-1356	127	4	1	1	NUM
ap-1356	127	5	+	+	CCONJ
ap-1356	127	6	β2	β2	NOUN
ap-1356	127	7	)	)	PUNCT
ap-1356	127	8	π00	π00	NOUN
ap-1356	127	9	.	.	PUNCT
ap-1356	128	1	in	in	ADP
ap-1356	128	2	order	order	NOUN
ap-1356	128	3	to	to	PART
ap-1356	128	4	compare	compare	VERB
ap-1356	128	5	it	it	PRON
ap-1356	128	6	with	with	ADP
ap-1356	128	7	the	the	DET
ap-1356	128	8	standard	standard	ADJ
ap-1356	128	9	formalism	formalism	NOUN
ap-1356	128	10	of	of	ADP
ap-1356	128	11	the	the	DET
ap-1356	128	12	special	special	ADJ
ap-1356	128	13	theory	theory	NOUN
ap-1356	128	14	of	of	ADP
ap-1356	128	15	relativity	relativity	NOUN
ap-1356	128	16	,	,	PUNCT
ap-1356	128	17	let	let	VERB
ap-1356	128	18	us	we	PRON
ap-1356	128	19	recall	recall	VERB
ap-1356	128	20	that	that	SCONJ
ap-1356	128	21	in	in	ADP
ap-1356	128	22	the	the	DET
ap-1356	128	23	standard	standard	ADJ
ap-1356	128	24	description	description	NOUN
ap-1356	128	25	the	the	DET
ap-1356	128	26	equation	equation	NOUN
ap-1356	128	27	of	of	ADP
ap-1356	128	28	motion	motion	NOUN
ap-1356	128	29	is	be	AUX
ap-1356	128	30	given	give	VERB
ap-1356	128	31	by	by	ADP
ap-1356	128	32	[	[	X
ap-1356	128	33	3	3	NUM
ap-1356	128	34	]	]	X
ap-1356	128	35	f	f	NOUN
ap-1356	128	36	=	=	PUNCT
ap-1356	128	37	dp	dp	NOUN
ap-1356	128	38	dt	dt	NOUN
ap-1356	128	39	=	=	SYM
ap-1356	128	40	mcβ̇	mcβ̇	ADJ
ap-1356	128	41	(	(	PUNCT
ap-1356	128	42	1−	1−	NUM
ap-1356	128	43	β2)3/2	β2)3/2	NOUN
ap-1356	128	44	=	=	PUNCT
ap-1356	128	45	γ3mcβ̇	γ3mcβ̇	NOUN
ap-1356	128	46	,	,	PUNCT
ap-1356	128	47	and	and	CCONJ
ap-1356	128	48	therefore	therefore	ADV
ap-1356	128	49	β̇	β̇	PROPN
ap-1356	129	1	=	=	SYM
ap-1356	129	2	γ−3	γ−3	PROPN
ap-1356	129	3	f	f	PROPN
ap-1356	129	4	mc	mc	PROPN
ap-1356	129	5	.	.	PUNCT
ap-1356	130	1	substituting	substitute	VERB
ap-1356	130	2	this	this	DET
ap-1356	130	3	expression	expression	NOUN
ap-1356	130	4	into	into	ADP
ap-1356	130	5	eq	eq	NOUN
ap-1356	130	6	.	.	PUNCT
ap-1356	131	1	(	(	PUNCT
ap-1356	131	2	29	29	NUM
ap-1356	131	3	)	)	PUNCT
ap-1356	131	4	we	we	PRON
ap-1356	131	5	get	get	VERB
ap-1356	131	6	φ0	φ0	ADJ
ap-1356	131	7	=	=	NOUN
ap-1356	131	8	2γ	2γ	NOUN
ap-1356	131	9	f	f	X
ap-1356	131	10	mc	mc	PROPN
ap-1356	131	11	β̇βπ00	β̇βπ00	PROPN
ap-1356	131	12	,	,	PUNCT
ap-1356	131	13	(	(	PUNCT
ap-1356	131	14	30	30	X
ap-1356	131	15	)	)	PUNCT
ap-1356	131	16	φ1	φ1	NOUN
ap-1356	131	17	=	=	SYM
ap-1356	132	1	−γ	−γ	NOUN
ap-1356	132	2	f	f	PROPN
ap-1356	132	3	mc	mc	PROPN
ap-1356	132	4	β̇	β̇	PROPN
ap-1356	132	5	(	(	PUNCT
ap-1356	132	6	1	1	NUM
ap-1356	132	7	+	+	CCONJ
ap-1356	132	8	β2	β2	NOUN
ap-1356	132	9	)	)	PUNCT
ap-1356	132	10	π00	π00	NOUN
ap-1356	132	11	.	.	PUNCT
ap-1356	133	1	45	45	NUM
ap-1356	133	2	acta	acta	PROPN
ap-1356	133	3	polytechnica	polytechnica	PROPN
ap-1356	133	4	vol	vol	NOUN
ap-1356	133	5	.	.	PUNCT
ap-1356	134	1	51	51	NUM
ap-1356	134	2	no	no	INTJ
ap-1356	134	3	.	.	PUNCT
ap-1356	135	1	1/2011	1/2011	NUM
ap-1356	135	2	this	this	PRON
ap-1356	135	3	indicates	indicate	VERB
ap-1356	135	4	that	that	SCONJ
ap-1356	135	5	the	the	DET
ap-1356	135	6	assumption	assumption	NOUN
ap-1356	135	7	that	that	SCONJ
ap-1356	135	8	β̇	β̇	PRON
ap-1356	135	9	in	in	ADP
ap-1356	135	10	this	this	DET
ap-1356	135	11	formalism	formalism	NOUN
ap-1356	135	12	and	and	CCONJ
ap-1356	135	13	the	the	DET
ap-1356	135	14	standard	standard	ADJ
ap-1356	135	15	description	description	NOUN
ap-1356	135	16	is	be	AUX
ap-1356	135	17	the	the	DET
ap-1356	135	18	same	same	ADJ
ap-1356	135	19	leads	lead	NOUN
ap-1356	135	20	to	to	ADP
ap-1356	135	21	the	the	DET
ap-1356	135	22	conclusion	conclusion	NOUN
ap-1356	135	23	that	that	SCONJ
ap-1356	135	24	for	for	ADP
ap-1356	135	25	a	a	DET
ap-1356	135	26	force	force	NOUN
ap-1356	135	27	f	f	PROPN
ap-1356	135	28	constant	constant	ADJ
ap-1356	135	29	in	in	ADP
ap-1356	135	30	time	time	NOUN
ap-1356	135	31	the	the	DET
ap-1356	135	32	component	component	NOUN
ap-1356	135	33	φ0	φ0	PROPN
ap-1356	135	34	is	be	AUX
ap-1356	135	35	not	not	PART
ap-1356	135	36	constant	constant	ADJ
ap-1356	135	37	in	in	ADP
ap-1356	135	38	time	time	NOUN
ap-1356	135	39	,	,	PUNCT
ap-1356	135	40	and	and	CCONJ
ap-1356	135	41	vice	vice	ADV
ap-1356	135	42	versa	versa	ADV
ap-1356	135	43	.	.	PUNCT
ap-1356	136	1	however	however	ADV
ap-1356	136	2	,	,	PUNCT
ap-1356	136	3	the	the	DET
ap-1356	136	4	uniform	uniform	ADJ
ap-1356	136	5	motion	motion	NOUN
ap-1356	136	6	(	(	PUNCT
ap-1356	136	7	β̇	β̇	NOUN
ap-1356	136	8	=	=	SYM
ap-1356	136	9	0	0	NUM
ap-1356	136	10	)	)	PUNCT
ap-1356	136	11	in	in	ADP
ap-1356	136	12	both	both	DET
ap-1356	136	13	formalisms	formalism	NOUN
ap-1356	136	14	occurs	occur	VERB
ap-1356	136	15	simultaneously	simultaneously	ADV
ap-1356	136	16	.	.	PUNCT
ap-1356	137	1	the	the	DET
ap-1356	137	2	non	non	ADJ
ap-1356	137	3	-	-	ADJ
ap-1356	137	4	trivial	trivial	ADJ
ap-1356	137	5	part	part	NOUN
ap-1356	137	6	of	of	ADP
ap-1356	137	7	the	the	DET
ap-1356	137	8	matrix	matrix	NOUN
ap-1356	137	9	(	(	PUNCT
ap-1356	137	10	28	28	NUM
ap-1356	137	11	)	)	PUNCT
ap-1356	137	12	can	can	AUX
ap-1356	137	13	also	also	ADV
ap-1356	137	14	be	be	AUX
ap-1356	137	15	expressed	express	VERB
ap-1356	137	16	by	by	ADP
ap-1356	137	17	means	mean	NOUN
ap-1356	137	18	of	of	ADP
ap-1356	137	19	well	well	ADV
ap-1356	137	20	-	-	PUNCT
ap-1356	137	21	known	know	VERB
ap-1356	137	22	relativistic	relativistic	ADJ
ap-1356	137	23	quantities	quantity	NOUN
ap-1356	137	24	such	such	ADJ
ap-1356	137	25	as	as	ADP
ap-1356	137	26	energy	energy	NOUN
ap-1356	137	27	and	and	CCONJ
ap-1356	137	28	momentum	momentum	NOUN
ap-1356	137	29	:	:	PUNCT
ap-1356	138	1	e	e	X
ap-1356	138	2	=	=	PUNCT
ap-1356	138	3	γmc2	γmc2	PROPN
ap-1356	138	4	,	,	PUNCT
ap-1356	138	5	p	p	NOUN
ap-1356	138	6	=	=	PUNCT
ap-1356	138	7	γmcβ	γmcβ	ADJ
ap-1356	138	8	.	.	PUNCT
ap-1356	139	1	therefore	therefore	ADV
ap-1356	139	2	we	we	PRON
ap-1356	139	3	get	get	VERB
ap-1356	139	4	π(β	π(β	NOUN
ap-1356	139	5	)	)	PUNCT
ap-1356	140	1	=	=	SYM
ap-1356	140	2	π00	π00	NOUN
ap-1356	140	3	m2c4	m2c4	PROPN
ap-1356	140	4	(	(	PUNCT
ap-1356	140	5	e2	e2	PROPN
ap-1356	140	6	−epc	−epc	PROPN
ap-1356	140	7	epc	epc	PROPN
ap-1356	140	8	−p2c2	−p2c2	PROPN
ap-1356	140	9	)	)	PUNCT
ap-1356	141	1	+	+	NOUN
ap-1356	141	2	π01	π01	NOUN
ap-1356	141	3	(	(	PUNCT
ap-1356	141	4	0	0	NUM
ap-1356	141	5	1	1	NUM
ap-1356	141	6	1	1	NUM
ap-1356	141	7	0	0	NUM
ap-1356	141	8	)	)	PUNCT
ap-1356	141	9	.	.	PUNCT
ap-1356	142	1	(	(	PUNCT
ap-1356	142	2	31	31	NUM
ap-1356	142	3	)	)	PUNCT
ap-1356	142	4	it	it	PRON
ap-1356	142	5	should	should	AUX
ap-1356	142	6	be	be	AUX
ap-1356	142	7	highlighted	highlight	VERB
ap-1356	142	8	here	here	ADV
ap-1356	142	9	that	that	PRON
ap-1356	142	10	—	—	PUNCT
ap-1356	142	11	as	as	SCONJ
ap-1356	142	12	was	be	AUX
ap-1356	142	13	mentioned	mention	VERB
ap-1356	142	14	before	before	ADV
ap-1356	142	15	—	—	PUNCT
ap-1356	142	16	it	it	PRON
ap-1356	142	17	is	be	AUX
ap-1356	142	18	possible	possible	ADJ
ap-1356	142	19	to	to	PART
ap-1356	142	20	choose	choose	VERB
ap-1356	142	21	a	a	DET
ap-1356	142	22	different	different	ADJ
ap-1356	142	23	special	special	ADJ
ap-1356	142	24	form	form	NOUN
ap-1356	142	25	of	of	ADP
ap-1356	142	26	the	the	DET
ap-1356	142	27	relativistic	relativistic	ADJ
ap-1356	142	28	velocity	velocity	NOUN
ap-1356	142	29	tensor	tensor	NOUN
ap-1356	142	30	matrix	matrix	NOUN
ap-1356	142	31	and	and	CCONJ
ap-1356	142	32	—	—	PUNCT
ap-1356	142	33	consequently	consequently	ADV
ap-1356	142	34	—	—	PUNCT
ap-1356	142	35	a	a	DET
ap-1356	142	36	different	different	ADJ
ap-1356	142	37	description	description	NOUN
ap-1356	142	38	of	of	ADP
ap-1356	142	39	dynamics	dynamic	NOUN
ap-1356	142	40	.	.	PUNCT
ap-1356	143	1	for	for	ADP
ap-1356	143	2	instance	instance	NOUN
ap-1356	143	3	,	,	PUNCT
ap-1356	143	4	by	by	ADP
ap-1356	143	5	analogy	analogy	NOUN
ap-1356	143	6	with	with	ADP
ap-1356	143	7	the	the	DET
ap-1356	143	8	non	non	ADJ
ap-1356	143	9	-	-	ADJ
ap-1356	143	10	relativistic	relativistic	ADJ
ap-1356	143	11	solution	solution	NOUN
ap-1356	143	12	,	,	PUNCT
ap-1356	143	13	we	we	PRON
ap-1356	143	14	can	can	AUX
ap-1356	143	15	assume	assume	VERB
ap-1356	143	16	that	that	SCONJ
ap-1356	143	17	the	the	DET
ap-1356	143	18	relation	relation	NOUN
ap-1356	143	19	between	between	ADP
ap-1356	143	20	the	the	DET
ap-1356	143	21	velocity	velocity	NOUN
ap-1356	143	22	tensor	tensor	NOUN
ap-1356	143	23	described	describe	VERB
ap-1356	143	24	by	by	ADP
ap-1356	143	25	eq	eq	PROPN
ap-1356	143	26	.	.	PUNCT
ap-1356	144	1	(	(	PUNCT
ap-1356	144	2	4	4	NUM
ap-1356	144	3	)	)	PUNCT
ap-1356	144	4	and	and	CCONJ
ap-1356	144	5	the	the	DET
ap-1356	144	6	momentum	momentum	NOUN
ap-1356	144	7	tensor	tensor	NOUN
ap-1356	144	8	is	be	AUX
ap-1356	144	9	given	give	VERB
ap-1356	144	10	by	by	ADP
ap-1356	144	11	eq	eq	PROPN
ap-1356	144	12	.	.	PUNCT
ap-1356	145	1	(	(	PUNCT
ap-1356	145	2	17	17	NUM
ap-1356	145	3	)	)	PUNCT
ap-1356	145	4	.	.	PUNCT
ap-1356	146	1	hence	hence	ADV
ap-1356	146	2	in	in	ADP
ap-1356	146	3	order	order	NOUN
ap-1356	146	4	to	to	PART
ap-1356	146	5	reproduce	reproduce	VERB
ap-1356	146	6	eq	eq	ADP
ap-1356	146	7	.	.	PUNCT
ap-1356	146	8	(	(	PUNCT
ap-1356	146	9	17	17	NUM
ap-1356	146	10	)	)	PUNCT
ap-1356	146	11	the	the	DET
ap-1356	146	12	general	general	ADJ
ap-1356	146	13	form	form	NOUN
ap-1356	146	14	of	of	ADP
ap-1356	146	15	the	the	DET
ap-1356	146	16	momentum	momentum	NOUN
ap-1356	146	17	tensor	tensor	NOUN
ap-1356	146	18	matrix	matrix	NOUN
ap-1356	146	19	(	(	PUNCT
ap-1356	146	20	19	19	NUM
ap-1356	146	21	)	)	PUNCT
ap-1356	146	22	has	have	VERB
ap-1356	146	23	to	to	PART
ap-1356	146	24	be	be	AUX
ap-1356	146	25	reduced	reduce	VERB
ap-1356	146	26	to	to	ADP
ap-1356	146	27	the	the	DET
ap-1356	146	28	matrix	matrix	NOUN
ap-1356	146	29	π(β	π(β	NOUN
ap-1356	146	30	)	)	PUNCT
ap-1356	147	1	=	=	SYM
ap-1356	147	2	γ2π01	γ2π01	ADP
ap-1356	147	3	(	(	PUNCT
ap-1356	147	4	−β	−β	PROPN
ap-1356	147	5	1	1	NUM
ap-1356	147	6	−β2	−β2	NOUN
ap-1356	147	7	β	β	X
ap-1356	147	8	)	)	PUNCT
ap-1356	147	9	,	,	PUNCT
ap-1356	147	10	(	(	PUNCT
ap-1356	147	11	32	32	NUM
ap-1356	147	12	)	)	PUNCT
ap-1356	147	13	where	where	SCONJ
ap-1356	147	14	—	—	PUNCT
ap-1356	147	15	as	as	SCONJ
ap-1356	147	16	we	we	PRON
ap-1356	147	17	have	have	AUX
ap-1356	147	18	shown	show	VERB
ap-1356	147	19	for	for	ADP
ap-1356	147	20	the	the	DET
ap-1356	147	21	non	non	ADJ
ap-1356	147	22	-	-	ADJ
ap-1356	147	23	relativistic	relativistic	ADJ
ap-1356	147	24	case	case	NOUN
ap-1356	147	25	—	—	PUNCT
ap-1356	147	26	the	the	DET
ap-1356	147	27	constant	constant	ADJ
ap-1356	147	28	π01	π01	NOUN
ap-1356	147	29	can	can	AUX
ap-1356	147	30	be	be	AUX
ap-1356	147	31	identified	identify	VERB
ap-1356	147	32	with	with	ADP
ap-1356	147	33	mass	mass	NOUN
ap-1356	147	34	m	m	PROPN
ap-1356	147	35	of	of	ADP
ap-1356	147	36	a	a	DET
ap-1356	147	37	material	material	NOUN
ap-1356	147	38	point	point	NOUN
ap-1356	147	39	.	.	PUNCT
ap-1356	148	1	it	it	PRON
ap-1356	148	2	is	be	AUX
ap-1356	148	3	easy	easy	ADJ
ap-1356	148	4	to	to	PART
ap-1356	148	5	observe	observe	VERB
ap-1356	148	6	that	that	DET
ap-1356	148	7	form	form	NOUN
ap-1356	148	8	(	(	PUNCT
ap-1356	148	9	32	32	NUM
ap-1356	148	10	)	)	PUNCT
ap-1356	148	11	is	be	AUX
ap-1356	148	12	obtained	obtain	VERB
ap-1356	148	13	from	from	ADP
ap-1356	148	14	eq	eq	PROPN
ap-1356	148	15	.	.	PUNCT
ap-1356	149	1	(	(	PUNCT
ap-1356	149	2	19	19	NUM
ap-1356	149	3	)	)	PUNCT
ap-1356	149	4	,	,	PUNCT
ap-1356	149	5	where	where	SCONJ
ap-1356	149	6	all	all	DET
ap-1356	149	7	coefficients	coefficient	NOUN
ap-1356	149	8	with	with	ADP
ap-1356	149	9	the	the	DET
ap-1356	149	10	exception	exception	NOUN
ap-1356	149	11	of	of	ADP
ap-1356	149	12	π01	π01	NOUN
ap-1356	149	13	vanish	vanish	VERB
ap-1356	149	14	.	.	PUNCT
ap-1356	150	1	therefore	therefore	ADV
ap-1356	150	2	,	,	PUNCT
ap-1356	150	3	eqs	eqs	PROPN
ap-1356	150	4	.	.	PUNCT
ap-1356	150	5	(	(	PUNCT
ap-1356	150	6	20	20	NUM
ap-1356	150	7	)	)	PUNCT
ap-1356	150	8	and	and	CCONJ
ap-1356	150	9	(	(	PUNCT
ap-1356	150	10	21	21	NUM
ap-1356	150	11	)	)	PUNCT
ap-1356	150	12	can	can	AUX
ap-1356	150	13	be	be	AUX
ap-1356	150	14	written	write	VERB
ap-1356	150	15	down	down	ADP
ap-1356	150	16	as	as	ADP
ap-1356	150	17	:	:	PUNCT
ap-1356	150	18	φ0	φ0	PROPN
ap-1356	150	19	=	=	PROPN
ap-1356	150	20	−γ4	−γ4	PROPN
ap-1356	150	21	(	(	PUNCT
ap-1356	150	22	1	1	NUM
ap-1356	150	23	+	+	CCONJ
ap-1356	150	24	β2	β2	NOUN
ap-1356	150	25	)	)	PUNCT
ap-1356	150	26	β̇π01	β̇π01	NOUN
ap-1356	150	27	,	,	PUNCT
ap-1356	150	28	φ1	φ1	PROPN
ap-1356	150	29	=	=	SYM
ap-1356	150	30	2γ4ββ̇π01	2γ4ββ̇π01	NUM
ap-1356	150	31	.	.	NOUN
ap-1356	150	32	5	5	NUM
ap-1356	150	33	conclusions	conclusion	NOUN
ap-1356	150	34	the	the	DET
ap-1356	150	35	aim	aim	NOUN
ap-1356	150	36	of	of	ADP
ap-1356	150	37	this	this	DET
ap-1356	150	38	paper	paper	NOUN
ap-1356	150	39	was	be	AUX
ap-1356	150	40	to	to	PART
ap-1356	150	41	introduce	introduce	VERB
ap-1356	150	42	a	a	DET
ap-1356	150	43	new	new	ADJ
ap-1356	150	44	dynamical	dynamical	ADJ
ap-1356	150	45	object	object	NOUN
ap-1356	150	46	called	call	VERB
ap-1356	150	47	the	the	DET
ap-1356	150	48	momentum	momentum	NOUN
ap-1356	150	49	tensor	tensor	NOUN
ap-1356	150	50	as	as	ADP
ap-1356	150	51	an	an	DET
ap-1356	150	52	analogue	analogue	NOUN
ap-1356	150	53	to	to	ADP
ap-1356	150	54	the	the	DET
ap-1356	150	55	kinematical	kinematical	ADJ
ap-1356	150	56	velocity	velocity	NOUN
ap-1356	150	57	tensor	tensor	NOUN
ap-1356	150	58	,	,	PUNCT
ap-1356	150	59	and	and	CCONJ
ap-1356	150	60	therefore	therefore	ADV
ap-1356	150	61	to	to	PART
ap-1356	150	62	complete	complete	VERB
ap-1356	150	63	the	the	DET
ap-1356	150	64	tensorial	tensorial	ADJ
ap-1356	150	65	description	description	NOUN
ap-1356	150	66	of	of	ADP
ap-1356	150	67	classical	classical	ADJ
ap-1356	150	68	and	and	CCONJ
ap-1356	150	69	relativistic	relativistic	ADJ
ap-1356	150	70	mechanics	mechanic	NOUN
ap-1356	150	71	.	.	PUNCT
ap-1356	151	1	calculations	calculation	NOUN
ap-1356	151	2	show	show	VERB
ap-1356	151	3	that	that	SCONJ
ap-1356	151	4	the	the	DET
ap-1356	151	5	choice	choice	NOUN
ap-1356	151	6	of	of	ADP
ap-1356	151	7	constants	constant	NOUN
ap-1356	151	8	in	in	ADP
ap-1356	151	9	the	the	DET
ap-1356	151	10	momentum	momentum	NOUN
ap-1356	151	11	tensor	tensor	NOUN
ap-1356	151	12	matrix	matrix	NOUN
ap-1356	151	13	results	result	NOUN
ap-1356	151	14	in	in	ADP
ap-1356	151	15	different	different	ADJ
ap-1356	151	16	models	model	NOUN
ap-1356	151	17	of	of	ADP
ap-1356	151	18	dynamics	dynamic	NOUN
ap-1356	151	19	in	in	ADP
ap-1356	151	20	the	the	DET
ap-1356	151	21	relativistic	relativistic	ADJ
ap-1356	151	22	case	case	NOUN
ap-1356	151	23	.	.	PUNCT
ap-1356	152	1	another	another	DET
ap-1356	152	2	important	important	ADJ
ap-1356	152	3	fact	fact	NOUN
ap-1356	152	4	is	be	AUX
ap-1356	152	5	that	that	SCONJ
ap-1356	152	6	the	the	DET
ap-1356	152	7	naturally	naturally	ADV
ap-1356	152	8	assumed	assume	VERB
ap-1356	152	9	relation	relation	NOUN
ap-1356	152	10	between	between	ADP
ap-1356	152	11	the	the	DET
ap-1356	152	12	tensors	tensor	NOUN
ap-1356	152	13	:	:	PUNCT
ap-1356	152	14	π(v	π(v	NOUN
ap-1356	152	15	)	)	PUNCT
ap-1356	152	16	=	=	SYM
ap-1356	152	17	mv	mv	PROPN
ap-1356	152	18	(	(	PUNCT
ap-1356	152	19	v	v	NOUN
ap-1356	152	20	)	)	PUNCT
ap-1356	152	21	is	be	AUX
ap-1356	152	22	just	just	ADV
ap-1356	152	23	one	one	NUM
ap-1356	152	24	among	among	ADP
ap-1356	152	25	many	many	ADJ
ap-1356	152	26	.	.	PUNCT
ap-1356	153	1	further	further	ADJ
ap-1356	153	2	investigations	investigation	NOUN
ap-1356	153	3	will	will	AUX
ap-1356	153	4	focus	focus	VERB
ap-1356	153	5	on	on	ADP
ap-1356	153	6	verifying	verify	VERB
ap-1356	153	7	the	the	DET
ap-1356	153	8	other	other	ADJ
ap-1356	153	9	models	model	NOUN
ap-1356	153	10	.	.	PUNCT
ap-1356	154	1	acknowledgement	acknowledgement	NOUN
ap-1356	154	2	i	i	PRON
ap-1356	154	3	would	would	AUX
ap-1356	154	4	like	like	VERB
ap-1356	154	5	to	to	PART
ap-1356	154	6	thank	thank	VERB
ap-1356	154	7	prof	prof	PROPN
ap-1356	154	8	.	.	PUNCT
ap-1356	155	1	edward	edward	PROPN
ap-1356	155	2	kapuścik	kapuścik	PROPN
ap-1356	155	3	for	for	ADP
ap-1356	155	4	his	his	PRON
ap-1356	155	5	scientific	scientific	ADJ
ap-1356	155	6	advice	advice	NOUN
ap-1356	155	7	,	,	PUNCT
ap-1356	155	8	and	and	CCONJ
ap-1356	155	9	also	also	ADV
ap-1356	155	10	for	for	ADP
ap-1356	155	11	useful	useful	ADJ
ap-1356	155	12	comments	comment	NOUN
ap-1356	155	13	and	and	CCONJ
ap-1356	155	14	ideas	idea	NOUN
ap-1356	155	15	on	on	ADP
ap-1356	155	16	this	this	DET
ap-1356	155	17	subject	subject	NOUN
ap-1356	155	18	.	.	PUNCT
ap-1356	156	1	references	reference	NOUN
ap-1356	156	2	[	[	X
ap-1356	156	3	1	1	X
ap-1356	156	4	]	]	X
ap-1356	156	5	kapuścik	kapuścik	PROPN
ap-1356	156	6	,	,	PUNCT
ap-1356	156	7	e.	e.	PROPN
ap-1356	156	8	,	,	PUNCT
ap-1356	156	9	lanczewski	lanczewski	NOUN
ap-1356	156	10	,	,	PUNCT
ap-1356	156	11	t.	t.	PROPN
ap-1356	156	12	:	:	PUNCT
ap-1356	156	13	on	on	ADP
ap-1356	156	14	the	the	DET
ap-1356	156	15	velocity	velocity	NOUN
ap-1356	156	16	tensors	tensor	NOUN
ap-1356	156	17	,	,	PUNCT
ap-1356	156	18	physics	physics	NOUN
ap-1356	156	19	of	of	ADP
ap-1356	156	20	atomic	atomic	ADJ
ap-1356	156	21	nuclei	nucleus	NOUN
ap-1356	156	22	,	,	PUNCT
ap-1356	156	23	72	72	NUM
ap-1356	156	24	(	(	PUNCT
ap-1356	156	25	2009	2009	NUM
ap-1356	156	26	)	)	PUNCT
ap-1356	156	27	809	809	NUM
ap-1356	156	28	.	.	PUNCT
ap-1356	157	1	[	[	X
ap-1356	157	2	2	2	NUM
ap-1356	157	3	]	]	X
ap-1356	157	4	goldstein	goldstein	PROPN
ap-1356	157	5	,	,	PUNCT
ap-1356	157	6	h.	h.	PROPN
ap-1356	157	7	:	:	PUNCT
ap-1356	157	8	classical	classical	ADJ
ap-1356	157	9	mechanics	mechanic	NOUN
ap-1356	157	10	,	,	PUNCT
ap-1356	157	11	addison	addison	PROPN
ap-1356	157	12	-	-	PUNCT
ap-1356	157	13	wesley	wesley	PROPN
ap-1356	157	14	,	,	PUNCT
ap-1356	157	15	reading	reading	NOUN
ap-1356	157	16	,	,	PUNCT
ap-1356	157	17	1980	1980	NUM
ap-1356	157	18	.	.	PUNCT
ap-1356	158	1	[	[	X
ap-1356	158	2	3	3	NUM
ap-1356	158	3	]	]	PUNCT
ap-1356	158	4	landau	landau	NOUN
ap-1356	158	5	,	,	PUNCT
ap-1356	158	6	l.	l.	PROPN
ap-1356	158	7	d.	d.	PROPN
ap-1356	158	8	,	,	PUNCT
ap-1356	158	9	lifshitz	lifshitz	PROPN
ap-1356	158	10	,	,	PUNCT
ap-1356	158	11	e.	e.	PROPN
ap-1356	158	12	m.	m.	PROPN
ap-1356	158	13	:	:	PUNCT
ap-1356	158	14	classical	classical	ADJ
ap-1356	158	15	theory	theory	NOUN
ap-1356	158	16	of	of	ADP
ap-1356	158	17	fields	field	NOUN
ap-1356	158	18	,	,	PUNCT
ap-1356	158	19	pwn	pwn	PROPN
ap-1356	158	20	warsaw	warsaw	PROPN
ap-1356	158	21	,	,	PUNCT
ap-1356	158	22	1980	1980	NUM
ap-1356	158	23	.	.	PUNCT
ap-1356	159	1	tomasz	tomasz	PROPN
ap-1356	159	2	lanczewski	lanczewski	PROPN
ap-1356	159	3	e	e	NOUN
ap-1356	160	1	-	-	NOUN
ap-1356	160	2	mail	mail	NOUN
ap-1356	160	3	:	:	PUNCT
ap-1356	160	4	tomasz.lanczewski@ifj.edu.pl	tomasz.lanczewski@ifj.edu.pl	PROPN
ap-1356	160	5	h.	h.	PROPN
ap-1356	160	6	niewodniczański	niewodniczański	PROPN
ap-1356	160	7	institute	institute	PROPN
ap-1356	160	8	of	of	ADP
ap-1356	160	9	nuclear	nuclear	ADJ
ap-1356	160	10	physics	physics	PROPN
ap-1356	160	11	polish	polish	PROPN
ap-1356	160	12	academy	academy	PROPN
ap-1356	160	13	of	of	ADP
ap-1356	160	14	sciences	sciences	PROPN
ap-1356	160	15	radzikowskiego	radzikowskiego	PROPN
ap-1356	160	16	152	152	NUM
ap-1356	160	17	,	,	PUNCT
ap-1356	160	18	pl	pl	PROPN
ap-1356	160	19	31342	31342	NUM
ap-1356	160	20	kraków	kraków	PROPN
ap-1356	160	21	,	,	PUNCT
ap-1356	160	22	poland	poland	PROPN
ap-1356	160	23	46	46	NUM