Signature for chiral-symmetry breaking at high temperatures

Lay-Nam Chang; Ngee-Pong Chang; Kuang-Chao Chou

doi:10.1103/PhysRevD.43.596

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Signature for chiral-symmetry breaking at high temperatures

Lay-Nam Chang

Ngee-Pong Chang

Kuang-Chao Chou

Physics Department, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

Department of Physics, The City College of The City University of New York, New York, New York 10031

Institute of Theoretical Physics, Academia Sinica, Beijing, China

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Phys. Rev. D 43, 596 – Published 15 January, 1991

DOI: https://doi.org/10.1103/PhysRevD.43.596

Abstract

In this paper we study the temperature dependence of chiral-symmetry breaking. Our real-time calculation shows that the thermal fermion propagator has a Lorentz-invariant massive particle pole even as ${〈 vac | \bar{ψ} ψ | vac 〉}_{β}$ vanishes for $T > Λ_{c} e^{\frac{2}{3}}$ . The traditional signature of chiral-symmetry breaking is found only after transforming the Dirac field to the new chiral basis at high temperatures.

References (9)

Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961) ibid.124, 246 (1961)
M. Cini and B. Touschek, Nuovo Cimento 7, 422 (1958) L. L. Foldy and S. A. Wouthuysen, Phys. Rev. 78, 29 (1950)
L. N. Chang, N. P. Chang, and K. C. Chou, in Third Asia-Pacific Physics Conference, proceedings, Hong Kong, 1988, edited by Y. W. Chan, A. F. Leung, C. N. Yang, and K. Young (World Scientific, Singapore, 1988)
Zhou Guang-zhao (K. C. Chou), Su Zhao-bin, Hao Bai-lin, and Yu Lu, Phys. Rep. 118, 1 (1985) H. Umezawa, H. Matsumoto, and M. Tachiki, Thermofield Dynamics and Condensed States (North-Holland, Amsterdam, 1982) R. L. Kobes, G. W. Semenoff, and N. Weiss, Z. Phys. C 29, 371 (1985) A. Niemi and G. W. Semenoff, Nucl. Phys. B230, 181 (1984) Ann. Phys. (N.Y.) 152, 105 (1984)
L. N. Chang and N. P. Chang, Phys. Rev. Lett. 54, 2407 (1985) Phys. Rev. D 29, 312 (1984) N. P. Chang and D. X. Li, ibid. 30, 790 (1984)
H. A. Weldon, Phys. Rev. D 26, 2789 (1982)
J. F. Donoghue and B. R. Holstein, Phys. Rev. D 28, 340 (1983) ibid.29, 3004(E) (1984) J. F. Donoghue, B. R. Holstein, and R. W. Robinett, Ann. Phys. (N.Y.) 164, 233 (1985) R. Pisarski, Nucl. Phys. A498, 423C (1989) G. Barton, Ann. Phys. (N.Y.) 200, 271 (1990)
[9]
A. Ukawa, in Lattice '89, proceedings of the International Symposium, Capri, Italy, 1989, edited by R. Petronzio [Nucl. Phys. B (Proc. Suppl.) (in press)]

[c1] Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961) ibid.124, 246 (1961)

[c2] M. Cini and B. Touschek, Nuovo Cimento 7, 422 (1958) L. L. Foldy and S. A. Wouthuysen, Phys. Rev. 78, 29 (1950)

[c3] L. N. Chang, N. P. Chang, and K. C. Chou, in Third Asia-Pacific Physics Conference, proceedings, Hong Kong, 1988, edited by Y. W. Chan, A. F. Leung, C. N. Yang, and K. Young (World Scientific, Singapore, 1988)

[c4] Zhou Guang-zhao (K. C. Chou), Su Zhao-bin, Hao Bai-lin, and Yu Lu, Phys. Rep. 118, 1 (1985) H. Umezawa, H. Matsumoto, and M. Tachiki, Thermofield Dynamics and Condensed States (North-Holland, Amsterdam, 1982) R. L. Kobes, G. W. Semenoff, and N. Weiss, Z. Phys. C 29, 371 (1985) A. Niemi and G. W. Semenoff, Nucl. Phys. B230, 181 (1984) Ann. Phys. (N.Y.) 152, 105 (1984)

[c5] L. N. Chang and N. P. Chang, Phys. Rev. Lett. 54, 2407 (1985) Phys. Rev. D 29, 312 (1984) N. P. Chang and D. X. Li, ibid. 30, 790 (1984)

[c6] H. A. Weldon, Phys. Rev. D 26, 2789 (1982)

[c7] J. F. Donoghue and B. R. Holstein, Phys. Rev. D 28, 340 (1983) ibid.29, 3004(E) (1984) J. F. Donoghue, B. R. Holstein, and R. W. Robinett, Ann. Phys. (N.Y.) 164, 233 (1985) R. Pisarski, Nucl. Phys. A498, 423C (1989) G. Barton, Ann. Phys. (N.Y.) 200, 271 (1990)

[c8] [9]

[c9] A. Ukawa, in Lattice '89, proceedings of the International Symposium, Capri, Italy, 1989, edited by R. Petronzio [Nucl. Phys. B (Proc. Suppl.) (in press)]

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Signature for chiral-symmetry breaking at high temperatures

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