Ward-Takahashi Identities and Mass Spectra in (2+1) Dimensional <EM>SU</EM>(2) Four-fermi Model

SHEN Kun; QIU Zhong-Ping

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1993, Vol. 17> Issue(1) : 17-27

Ward-Takahashi Identities and Mass Spectra in (2+1) Dimensional SU(2) Four-fermi Model

SHEN Kun ^, ,
QIU Zhong-Ping

Institute of Particle Physics,Hua-Zhong Normal University,Wuhan 430070

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Abstract：
Ward-Takahashi identities with composite fields are utilized to inverstigate (2+1) dimensional model with SU(2) four-fermion couplings.When SU(2) chiral symmetry is both explicitly and dynamically broken,fermion mass is dynamically generated and mass spectra of the bound states are obtained The properties of vector and axial-vector currents are discussed.It turns out that the bound state π_α acquires a mass and the axial-vector current is partially conserved,and the Goldberger-Treimab relation is approximately valid in the case of small fermion current masses.

References

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W. Weisc, Progress in Pnrticle and Nuclear Physics, Vol. 20 P. 113, Edited by A. Faessler, Pergaman Press(1989);E. V. Shuryak, Phys. Rtp., 115(1984), 151.[2]E. Witten, Nucl. Phys, B223(1983), 422, 435.O. Kaymakcalan and J. Schecbter, Phys. Rev., D31(1985), 1109:[3]D. Ebert and M. K. Volkov, Z. Pays., C16(1983), 205; D. Ebert and H. Reinhardt, Nucl.Phys B271(1986). 188.[4]沈坤、裘忠平，高能物理与核物理，16(1992),29,[5]G. Parisi, Nucl, Plzys, BI00(1975), 3G8;K. Shizuya, Phys. Rev., D21(1980), 2.127;B. Rosenstein, B. J. Warr and S. H. Park, Phys. Rev. Lctt., 62(1989), 1433.[6]B.Rosenstein, B.J.Warr ,md S.H.Park,Phys.Lca.,B219(1989),469;B.Rosensteinand B.J.Warn,Phys.Lett.B218(19fi9),465;G.Gat,A.Kovner, B.Rosensteinand B.J.Warn, Phys. Lett., B240(1990), 158.[7]D. J. Gross and A. Neveu, Phys Rev., D10(,1974), 3235.[8]M. K. Volkov, Ann. of Phys., 157(1984), 782.[9]M. L. Goldberger and S. B. Treiman, Phys. Rev., 110(1957), 1178.[10]Y. Nambu and G. Jona-Lasinio, Phys, Rev., 122(1961), 345; 124(1961), 246.[11]S, Adler and R. Dashen, Current Algelzras, Benjamin, New York (1968).

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SHEN Kun and QIU Zhong-Ping. Ward-Takahashi Identities and Mass Spectra in (2+1) Dimensional SU(2) Four-fermi Model[J]. Chinese Physics C, 1993, 17(1): 17-27.

SHEN Kun and QIU Zhong-Ping. Ward-Takahashi Identities and Mass Spectra in (2+1) Dimensional SU(2) Four-fermi Model[J]. Chinese Physics C, 1993, 17(1): 17-27. shu

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Ward-Takahashi Identities and Mass Spectra in (2+1) Dimensional SU(2) Four-fermi Model

SHEN Kun ^,
QIU Zhong-Ping

Corresponding author: SHEN Kun,

Institute of Particle Physics,Hua-Zhong Normal University,Wuhan 430070

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1993-01-05

Abstract: Ward-Takahashi identities with composite fields are utilized to inverstigate (2+1) dimensional model with SU(2) four-fermion couplings.When SU(2) chiral symmetry is both explicitly and dynamically broken,fermion mass is dynamically generated and mass spectra of the bound states are obtained The properties of vector and axial-vector currents are discussed.It turns out that the bound state π_α acquires a mass and the axial-vector current is partially conserved,and the Goldberger-Treimab relation is approximately valid in the case of small fermion current masses.