Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD

Abstract We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity...
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Autor*in:	Faria da Veiga, Paulo A. [verfasserIn] O’Carroll, M. Schor, Ricardo

Format:	Artikel
Sprache:	Englisch

Erschienen:	2004

Schlagwörter:	Strong Coupling Coupling Lattice Baryon Spectrum Strong Coupling Lattice

Anmerkung:	© Springer-Verlag Berlin Heidelberg 2004

Übergeordnetes Werk:	Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 245(2004), 2 vom: 23. Jan., Seite 383-405
Übergeordnetes Werk:	volume:245 ; year:2004 ; number:2 ; day:23 ; month:01 ; pages:383-405

Links:	Volltext

DOI / URN:	10.1007/s00220-003-1022-2

Katalog-ID:	OLC2038884099

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520			\|a Abstract We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity which is used to obtain the underlying physical Hilbert space . Then, using a Feynman-Kac formalism, we write the correlation functions for the model as functional integrals over the space of Grassmannian (fermionic) fields for one quark specie and the SU(3) gauge fields. We determine the energy-momentum spectrum associated with gauge invariant local baryon (anti-baryon) fields which are composites of three quark (anti-quark) fields. With the associated correlation functions, we establish a Feynman-Kac formula, and a spectral representation for the Fourier transform of the two-point functions. This representation allows us to show that baryons and anti-baryons arise as tightly bound, bound states of three (anti-)quarks. Labelling the components of the baryon fields by s=3/2,1/2,-1/2,-3/2, we show that the baryon and anti-baryon mass spectrum only depends on \|s\|, and the associated masses are given by Ms= −3lnκ+rs(κ), where rs(κ) is real analytic in κ, for each d=2,3. The mass splitting is M3/2−M1/2=$ 18κ^{6} $, for d=2 and, if any, is at least of ($ κ^{7} $), for d=3. In the subspace o⊂ generated by an odd number of fermions, the baryon and anti-baryon energy-momentum dispersion curves are isolated up to near the baryon-meson threshold −5lnκ (upper gap property), identical and are determined up to ($ κ^{5} $). The symmetries of coordinate reflections, spatial lattice rotations, parity and charge conjugation are established for the correlation functions, and are shown to be implemented on by unitary (anti-unitary, for time reversal) operators.
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allfields	10.1007/s00220-003-1022-2 doi (DE-627)OLC2038884099 (DE-He213)s00220-003-1022-2-p DE-627 ger DE-627 rakwb eng 530 510 VZ Faria da Veiga, Paulo A. verfasserin aut Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity which is used to obtain the underlying physical Hilbert space . Then, using a Feynman-Kac formalism, we write the correlation functions for the model as functional integrals over the space of Grassmannian (fermionic) fields for one quark specie and the SU(3) gauge fields. We determine the energy-momentum spectrum associated with gauge invariant local baryon (anti-baryon) fields which are composites of three quark (anti-quark) fields. With the associated correlation functions, we establish a Feynman-Kac formula, and a spectral representation for the Fourier transform of the two-point functions. This representation allows us to show that baryons and anti-baryons arise as tightly bound, bound states of three (anti-)quarks. Labelling the components of the baryon fields by s=3/2,1/2,-1/2,-3/2, we show that the baryon and anti-baryon mass spectrum only depends on \|s\|, and the associated masses are given by Ms= −3lnκ+rs(κ), where rs(κ) is real analytic in κ, for each d=2,3. The mass splitting is M3/2−M1/2=$ 18κ^{6} $, for d=2 and, if any, is at least of ($ κ^{7} $), for d=3. In the subspace o⊂ generated by an odd number of fermions, the baryon and anti-baryon energy-momentum dispersion curves are isolated up to near the baryon-meson threshold −5lnκ (upper gap property), identical and are determined up to ($ κ^{5} $). The symmetries of coordinate reflections, spatial lattice rotations, parity and charge conjugation are established for the correlation functions, and are shown to be implemented on by unitary (anti-unitary, for time reversal) operators. Strong Coupling Coupling Lattice Baryon Spectrum Strong Coupling Lattice O’Carroll, M. aut Schor, Ricardo aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 245(2004), 2 vom: 23. Jan., Seite 383-405 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:245 year:2004 number:2 day:23 month:01 pages:383-405 https://doi.org/10.1007/s00220-003-1022-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 245 2004 2 23 01 383-405
spelling	10.1007/s00220-003-1022-2 doi (DE-627)OLC2038884099 (DE-He213)s00220-003-1022-2-p DE-627 ger DE-627 rakwb eng 530 510 VZ Faria da Veiga, Paulo A. verfasserin aut Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity which is used to obtain the underlying physical Hilbert space . Then, using a Feynman-Kac formalism, we write the correlation functions for the model as functional integrals over the space of Grassmannian (fermionic) fields for one quark specie and the SU(3) gauge fields. We determine the energy-momentum spectrum associated with gauge invariant local baryon (anti-baryon) fields which are composites of three quark (anti-quark) fields. With the associated correlation functions, we establish a Feynman-Kac formula, and a spectral representation for the Fourier transform of the two-point functions. This representation allows us to show that baryons and anti-baryons arise as tightly bound, bound states of three (anti-)quarks. Labelling the components of the baryon fields by s=3/2,1/2,-1/2,-3/2, we show that the baryon and anti-baryon mass spectrum only depends on \|s\|, and the associated masses are given by Ms= −3lnκ+rs(κ), where rs(κ) is real analytic in κ, for each d=2,3. The mass splitting is M3/2−M1/2=$ 18κ^{6} $, for d=2 and, if any, is at least of ($ κ^{7} $), for d=3. In the subspace o⊂ generated by an odd number of fermions, the baryon and anti-baryon energy-momentum dispersion curves are isolated up to near the baryon-meson threshold −5lnκ (upper gap property), identical and are determined up to ($ κ^{5} $). The symmetries of coordinate reflections, spatial lattice rotations, parity and charge conjugation are established for the correlation functions, and are shown to be implemented on by unitary (anti-unitary, for time reversal) operators. Strong Coupling Coupling Lattice Baryon Spectrum Strong Coupling Lattice O’Carroll, M. aut Schor, Ricardo aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 245(2004), 2 vom: 23. Jan., Seite 383-405 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:245 year:2004 number:2 day:23 month:01 pages:383-405 https://doi.org/10.1007/s00220-003-1022-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 245 2004 2 23 01 383-405
allfields_unstemmed	10.1007/s00220-003-1022-2 doi (DE-627)OLC2038884099 (DE-He213)s00220-003-1022-2-p DE-627 ger DE-627 rakwb eng 530 510 VZ Faria da Veiga, Paulo A. verfasserin aut Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity which is used to obtain the underlying physical Hilbert space . Then, using a Feynman-Kac formalism, we write the correlation functions for the model as functional integrals over the space of Grassmannian (fermionic) fields for one quark specie and the SU(3) gauge fields. We determine the energy-momentum spectrum associated with gauge invariant local baryon (anti-baryon) fields which are composites of three quark (anti-quark) fields. With the associated correlation functions, we establish a Feynman-Kac formula, and a spectral representation for the Fourier transform of the two-point functions. This representation allows us to show that baryons and anti-baryons arise as tightly bound, bound states of three (anti-)quarks. Labelling the components of the baryon fields by s=3/2,1/2,-1/2,-3/2, we show that the baryon and anti-baryon mass spectrum only depends on \|s\|, and the associated masses are given by Ms= −3lnκ+rs(κ), where rs(κ) is real analytic in κ, for each d=2,3. The mass splitting is M3/2−M1/2=$ 18κ^{6} $, for d=2 and, if any, is at least of ($ κ^{7} $), for d=3. In the subspace o⊂ generated by an odd number of fermions, the baryon and anti-baryon energy-momentum dispersion curves are isolated up to near the baryon-meson threshold −5lnκ (upper gap property), identical and are determined up to ($ κ^{5} $). The symmetries of coordinate reflections, spatial lattice rotations, parity and charge conjugation are established for the correlation functions, and are shown to be implemented on by unitary (anti-unitary, for time reversal) operators. Strong Coupling Coupling Lattice Baryon Spectrum Strong Coupling Lattice O’Carroll, M. aut Schor, Ricardo aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 245(2004), 2 vom: 23. Jan., Seite 383-405 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:245 year:2004 number:2 day:23 month:01 pages:383-405 https://doi.org/10.1007/s00220-003-1022-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 245 2004 2 23 01 383-405
allfieldsGer	10.1007/s00220-003-1022-2 doi (DE-627)OLC2038884099 (DE-He213)s00220-003-1022-2-p DE-627 ger DE-627 rakwb eng 530 510 VZ Faria da Veiga, Paulo A. verfasserin aut Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity which is used to obtain the underlying physical Hilbert space . Then, using a Feynman-Kac formalism, we write the correlation functions for the model as functional integrals over the space of Grassmannian (fermionic) fields for one quark specie and the SU(3) gauge fields. We determine the energy-momentum spectrum associated with gauge invariant local baryon (anti-baryon) fields which are composites of three quark (anti-quark) fields. With the associated correlation functions, we establish a Feynman-Kac formula, and a spectral representation for the Fourier transform of the two-point functions. This representation allows us to show that baryons and anti-baryons arise as tightly bound, bound states of three (anti-)quarks. Labelling the components of the baryon fields by s=3/2,1/2,-1/2,-3/2, we show that the baryon and anti-baryon mass spectrum only depends on \|s\|, and the associated masses are given by Ms= −3lnκ+rs(κ), where rs(κ) is real analytic in κ, for each d=2,3. The mass splitting is M3/2−M1/2=$ 18κ^{6} $, for d=2 and, if any, is at least of ($ κ^{7} $), for d=3. In the subspace o⊂ generated by an odd number of fermions, the baryon and anti-baryon energy-momentum dispersion curves are isolated up to near the baryon-meson threshold −5lnκ (upper gap property), identical and are determined up to ($ κ^{5} $). The symmetries of coordinate reflections, spatial lattice rotations, parity and charge conjugation are established for the correlation functions, and are shown to be implemented on by unitary (anti-unitary, for time reversal) operators. Strong Coupling Coupling Lattice Baryon Spectrum Strong Coupling Lattice O’Carroll, M. aut Schor, Ricardo aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 245(2004), 2 vom: 23. Jan., Seite 383-405 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:245 year:2004 number:2 day:23 month:01 pages:383-405 https://doi.org/10.1007/s00220-003-1022-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 245 2004 2 23 01 383-405
allfieldsSound	10.1007/s00220-003-1022-2 doi (DE-627)OLC2038884099 (DE-He213)s00220-003-1022-2-p DE-627 ger DE-627 rakwb eng 530 510 VZ Faria da Veiga, Paulo A. verfasserin aut Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity which is used to obtain the underlying physical Hilbert space . Then, using a Feynman-Kac formalism, we write the correlation functions for the model as functional integrals over the space of Grassmannian (fermionic) fields for one quark specie and the SU(3) gauge fields. We determine the energy-momentum spectrum associated with gauge invariant local baryon (anti-baryon) fields which are composites of three quark (anti-quark) fields. With the associated correlation functions, we establish a Feynman-Kac formula, and a spectral representation for the Fourier transform of the two-point functions. This representation allows us to show that baryons and anti-baryons arise as tightly bound, bound states of three (anti-)quarks. Labelling the components of the baryon fields by s=3/2,1/2,-1/2,-3/2, we show that the baryon and anti-baryon mass spectrum only depends on \|s\|, and the associated masses are given by Ms= −3lnκ+rs(κ), where rs(κ) is real analytic in κ, for each d=2,3. The mass splitting is M3/2−M1/2=$ 18κ^{6} $, for d=2 and, if any, is at least of ($ κ^{7} $), for d=3. In the subspace o⊂ generated by an odd number of fermions, the baryon and anti-baryon energy-momentum dispersion curves are isolated up to near the baryon-meson threshold −5lnκ (upper gap property), identical and are determined up to ($ κ^{5} $). The symmetries of coordinate reflections, spatial lattice rotations, parity and charge conjugation are established for the correlation functions, and are shown to be implemented on by unitary (anti-unitary, for time reversal) operators. Strong Coupling Coupling Lattice Baryon Spectrum Strong Coupling Lattice O’Carroll, M. aut Schor, Ricardo aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 245(2004), 2 vom: 23. Jan., Seite 383-405 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:245 year:2004 number:2 day:23 month:01 pages:383-405 https://doi.org/10.1007/s00220-003-1022-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 245 2004 2 23 01 383-405
language	English
source	Enthalten in Communications in mathematical physics 245(2004), 2 vom: 23. Jan., Seite 383-405 volume:245 year:2004 number:2 day:23 month:01 pages:383-405
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topic_facet	Strong Coupling Coupling Lattice Baryon Spectrum Strong Coupling Lattice
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author	Faria da Veiga, Paulo A.
spellingShingle	Faria da Veiga, Paulo A. ddc 530 misc Strong Coupling misc Coupling Lattice misc Baryon Spectrum misc Strong Coupling Lattice Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD
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topic_title	530 510 VZ Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD Strong Coupling Coupling Lattice Baryon Spectrum Strong Coupling Lattice
topic	ddc 530 misc Strong Coupling misc Coupling Lattice misc Baryon Spectrum misc Strong Coupling Lattice
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title	Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD
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title_full	Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD
author_sort	Faria da Veiga, Paulo A.
journal	Communications in mathematical physics
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author_browse	Faria da Veiga, Paulo A. O’Carroll, M. Schor, Ricardo
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title_sort	existence of baryons, baryon spectrum and mass splitting in strong coupling lattice qcd
title_auth	Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD
abstract	Abstract We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity which is used to obtain the underlying physical Hilbert space . Then, using a Feynman-Kac formalism, we write the correlation functions for the model as functional integrals over the space of Grassmannian (fermionic) fields for one quark specie and the SU(3) gauge fields. We determine the energy-momentum spectrum associated with gauge invariant local baryon (anti-baryon) fields which are composites of three quark (anti-quark) fields. With the associated correlation functions, we establish a Feynman-Kac formula, and a spectral representation for the Fourier transform of the two-point functions. This representation allows us to show that baryons and anti-baryons arise as tightly bound, bound states of three (anti-)quarks. Labelling the components of the baryon fields by s=3/2,1/2,-1/2,-3/2, we show that the baryon and anti-baryon mass spectrum only depends on \|s\|, and the associated masses are given by Ms= −3lnκ+rs(κ), where rs(κ) is real analytic in κ, for each d=2,3. The mass splitting is M3/2−M1/2=$ 18κ^{6} $, for d=2 and, if any, is at least of ($ κ^{7} $), for d=3. In the subspace o⊂ generated by an odd number of fermions, the baryon and anti-baryon energy-momentum dispersion curves are isolated up to near the baryon-meson threshold −5lnκ (upper gap property), identical and are determined up to ($ κ^{5} $). The symmetries of coordinate reflections, spatial lattice rotations, parity and charge conjugation are established for the correlation functions, and are shown to be implemented on by unitary (anti-unitary, for time reversal) operators. © Springer-Verlag Berlin Heidelberg 2004
abstractGer	Abstract We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity which is used to obtain the underlying physical Hilbert space . Then, using a Feynman-Kac formalism, we write the correlation functions for the model as functional integrals over the space of Grassmannian (fermionic) fields for one quark specie and the SU(3) gauge fields. We determine the energy-momentum spectrum associated with gauge invariant local baryon (anti-baryon) fields which are composites of three quark (anti-quark) fields. With the associated correlation functions, we establish a Feynman-Kac formula, and a spectral representation for the Fourier transform of the two-point functions. This representation allows us to show that baryons and anti-baryons arise as tightly bound, bound states of three (anti-)quarks. Labelling the components of the baryon fields by s=3/2,1/2,-1/2,-3/2, we show that the baryon and anti-baryon mass spectrum only depends on \|s\|, and the associated masses are given by Ms= −3lnκ+rs(κ), where rs(κ) is real analytic in κ, for each d=2,3. The mass splitting is M3/2−M1/2=$ 18κ^{6} $, for d=2 and, if any, is at least of ($ κ^{7} $), for d=3. In the subspace o⊂ generated by an odd number of fermions, the baryon and anti-baryon energy-momentum dispersion curves are isolated up to near the baryon-meson threshold −5lnκ (upper gap property), identical and are determined up to ($ κ^{5} $). The symmetries of coordinate reflections, spatial lattice rotations, parity and charge conjugation are established for the correlation functions, and are shown to be implemented on by unitary (anti-unitary, for time reversal) operators. © Springer-Verlag Berlin Heidelberg 2004
abstract_unstemmed	Abstract We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity which is used to obtain the underlying physical Hilbert space . Then, using a Feynman-Kac formalism, we write the correlation functions for the model as functional integrals over the space of Grassmannian (fermionic) fields for one quark specie and the SU(3) gauge fields. We determine the energy-momentum spectrum associated with gauge invariant local baryon (anti-baryon) fields which are composites of three quark (anti-quark) fields. With the associated correlation functions, we establish a Feynman-Kac formula, and a spectral representation for the Fourier transform of the two-point functions. This representation allows us to show that baryons and anti-baryons arise as tightly bound, bound states of three (anti-)quarks. Labelling the components of the baryon fields by s=3/2,1/2,-1/2,-3/2, we show that the baryon and anti-baryon mass spectrum only depends on \|s\|, and the associated masses are given by Ms= −3lnκ+rs(κ), where rs(κ) is real analytic in κ, for each d=2,3. The mass splitting is M3/2−M1/2=$ 18κ^{6} $, for d=2 and, if any, is at least of ($ κ^{7} $), for d=3. In the subspace o⊂ generated by an odd number of fermions, the baryon and anti-baryon energy-momentum dispersion curves are isolated up to near the baryon-meson threshold −5lnκ (upper gap property), identical and are determined up to ($ κ^{5} $). The symmetries of coordinate reflections, spatial lattice rotations, parity and charge conjugation are established for the correlation functions, and are shown to be implemented on by unitary (anti-unitary, for time reversal) operators. © Springer-Verlag Berlin Heidelberg 2004
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title_short	Existence of Baryons, Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD
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