Ward-Takahashi identities at finite temperature and phase structure in (2 + 1)-dimensional chiral Gross-Neveu model

Kun Shen; Zhongping Qiu

doi:10.1103/PhysRevD.48.1801

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Ward-Takahashi identities at finite temperature and phase structure in (2 + 1)-dimensional chiral Gross-Neveu model

Kun Shen

Zhongping Qiu

CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, China; Institute of Particle Physics, Hua-Zhong Normal University, Wuhan 430070, China; and Institute of Modern Physics, Tsinghua University, Beijing 100084, China

CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, China and Institute of Particle Physics, Hua-Zhong Normal University, Wuhan 430070, China

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Phys. Rev. D 48, 1801 – Published 15 August, 1993

DOI: https://doi.org/10.1103/PhysRevD.48.1801

Abstract

Chiral Ward-Takahashi identities with composite fields are generalized to finite temperature and applied to investigate the chiral phase transition and phase structure in the (2 + 1)-dimensional chiral Gross-Neveu model. In terms of these identities, the mass spectra of fermions and bound states and the Goldberger-Treiman relation at finite temperature are obtained. The vertex correction between the fermion and bound states $σ$ is evaluated beyond the leading order in the $\frac{1}{N}$ expansion at zero and finite temperatures. With the aid of the gap equation derived from Ward-Takahashi identities, the phase structure is discussed at zero and finite temperatures. It turns out that (i) at zero temperature, the vertex correction is very small and its influence on the phase structure can be neglected and (ii) at nonzero temperature, the infrared divergence in the vertex correction will make the results of the chiral phase transition obtained at the leading order invalid in next to the leading order and the phase structure is in agreement with Coleman's theorem.

References (17)

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[c1] E. V. Shuryak, Phys. Rep. 115, 151 (1984)

[c2] Shen Kun and Qiu Zhongping, Phys. Rev. D 45, 3877 (1992)

[c3] G. Parisi, Nucl. Phys. B100, 368 (1975) D. J. Gross, in Methods in Field Theory, Proceedings of the Les Houches Summer School, Les Houches, France, 1975, edited by R. Balian and J. Zinn-Justin, Les Houches Summer School Proceedings Vol. XXVIII (North-Holland, Amsterdam, 1976)

[c4] K. Shizuya, Phys. Rev. D 21, 2327 (1980) B. Rosenstein, B. J. Warr, and S. H. Park, Phys. Rev. Lett. 62, 1433 (1989)

[c5] G. W. Semenoff, P. Sodano, and Y. S. Wu, Phys. Rev. Lett. 62, 715 (1989) J. B. Kogut, E. Dagotto, and A. Kocic, ibid. 62, 1001 (1989) M. Burgess and D. J. Toms, ibid. 64, 1639 (1990) T. Appelquist, M. J. Bowick, E. Cohler, and L. C. R. Wijewardhana, Phys. Rev. D 33, 3704 (1986) ibid.33, 3774 (1986)

[c6] G. W. Semenoff and L. C. R. Wijewardhana, Phys. Rev. Lett. 63, 2633 (1989) A. L. Fetter, C. B. Hanna, and R. B. Laughlin, Phys. Rev. B 39, 9679 (1989)

[c7] Shen Kun and Qiu Zhongping, J. Phys. G 18, 745 (1992)

[c8] D. J. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974)

[c9] C. W. Bernard, Phys. Rev. D 9, 3212 (1974) L. Dolan and R. Jackiw, ibid. 9, 3320 (1974)

[c10] B. Rosenstein, B. J. Warr, and S. H. Park, Phys. Lett. B 219, 469 (1989) B. Rosenstein and B. J. Warr, ibid. 218, 465 (1989) G. Gat, A. Kovner, B. Rosenstein, and B. J. Warr, ibid. 240, 158 (1990)

[c11] J. Goldstone, Nuovo Cimento 19, 154 (1961) J. Goldstone, A. Salam, and S. Weinberg, Phys. Rev. 127, 965 (1962)

[c12] M. L. Goldberger and S. B. Treiman, Phys. Rev. 110, 1178 (1958)

[c13] B. Rosenstein, B. J. Warr, and S. H. Park, Phys. Rep. 205, 59 (1991)

[c14] B. Rosenstein, B. J. Warr, and S. H. Park, Phys. Rev. D 39, 3088 (1989)

[c15] T. Hatsuda and T. Kunihiro, Phys. Lett. B 188, 304 (1987) V. Bernard, Ulf-G. Meissner, and I. Zahed, Phys. Rev. D 39, 819 (1989)

[c16] S. Coleman, Commun. Math. Phys. 31, 259 (1973)

[c17] M. Carena, T. E. Clark, and C. E. M. Wagner, Nucl. Phys. B356, 117 (1991)

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Ward-Takahashi identities at finite temperature and phase structure in (2 + 1)-dimensional chiral Gross-Neveu model

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