Path-integral formulation of real-time quantum field theories at finite temperature

A. Niégawa

doi:10.1103/PhysRevD.40.1199

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Path-integral formulation of real-time quantum field theories at finite temperature

A. Niégawa

Department of Physics, Osaka City University, Sumiyoshi-ku, Osaka 558, Japan

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Phys. Rev. D 40, 1199 – Published 15 August, 1989

DOI: https://doi.org/10.1103/PhysRevD.40.1199

Abstract

A study is made of a path-integral representation of the generating functional for the real-time thermal Green's functions in quantum field theories. The bare thermal propagator is shown to obey the Kubo-Martin-Schwinger condition. It is verified that the statistical factors in thermal propagators with momentum $p$ should be regarded as functions of $| p_{0} |$ rather than of ${(p^{2} + m^{2})}^{\frac{1}{2}}$ . Also rederived is the bare thermal gauge field propagator in a covariant gauge.

References (23)

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R. Mills, Propagators for Many-Particle Systems (Gordon and Breach, New York, 1969)
A. J. Niemi and G. W. Semenoff, Ann. Phys. (N.Y.) 152, 105 (1984) Nucl. Phys. B230, 181 (1984)
H. Matsumoto, Y. Nakano, H. Umezawa, F. Mancini, and M. Marinaro, Prog. Theor. Phys. 70, 599 (1983)
H. Matsumoto, Y. Nakano, and H. Umezawa, J. Math. Phys. 25, 3076 (1984)
N. P. Landsman, Report No. ITFA-85-08 (unpublished)
N. P. Landsman and Ch. G. van Weert, Phys. Rep. 145, 141 (1987)
T. Matsubara, Prog. Theor. Phys. 14, 351 (1955) A. A. Abrikosov, L. P. Gor'kov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Pergamon, Oxford, 1965)
[1,2]
Y. Takahashi and H. Umezawa, Collect. Phenom. 2, 55 (1975)
H. Matsumoto, Fortschr. Phys. 25, 1 (1981) H. Umezawa, H. Matsumoto, and M. Tachiki, Thermo Field Dynamics and Condensed States (North-Holland, Amsterdam, 1982)
G. W. Semenoff and H. Umezawa, Nucl. Phys. B220, 196 (1983)
Y. Fujimoto, H. Matsumoto, H. Umezawa, and I. Ojima, Phys. Rev. D 30, 1400 (1984) ibid.31, 1527(E) (1985)
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R. L. Kobes, G. W. Semenoff, and N. Weiss, Z. Phys. C 29, 371 (1985)
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[3]
[2] ([3,7])
Omitted endnote
Omitted endnote

[c1] J. Schwinger, J. Math. Phys. 2, 407 (1961) L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)] R. A. Craig, J. Math. Phys. 9, 605 (1968) K.-C. Chou, Z.-B. Su, B.-L. Hao, and L. Yu, Phys. Rep. 118, 1 (1985)

[c2] R. Mills, Propagators for Many-Particle Systems (Gordon and Breach, New York, 1969)

[c3] A. J. Niemi and G. W. Semenoff, Ann. Phys. (N.Y.) 152, 105 (1984) Nucl. Phys. B230, 181 (1984)

[c4] H. Matsumoto, Y. Nakano, H. Umezawa, F. Mancini, and M. Marinaro, Prog. Theor. Phys. 70, 599 (1983)

[c5] H. Matsumoto, Y. Nakano, and H. Umezawa, J. Math. Phys. 25, 3076 (1984)

[c6] N. P. Landsman, Report No. ITFA-85-08 (unpublished)

[c7] N. P. Landsman and Ch. G. van Weert, Phys. Rep. 145, 141 (1987)

[c8] T. Matsubara, Prog. Theor. Phys. 14, 351 (1955) A. A. Abrikosov, L. P. Gor'kov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Pergamon, Oxford, 1965)

[c9] [1,2]

[c10] Y. Takahashi and H. Umezawa, Collect. Phenom. 2, 55 (1975)

[c11] H. Matsumoto, Fortschr. Phys. 25, 1 (1981) H. Umezawa, H. Matsumoto, and M. Tachiki, Thermo Field Dynamics and Condensed States (North-Holland, Amsterdam, 1982)

[c12] G. W. Semenoff and H. Umezawa, Nucl. Phys. B220, 196 (1983)

[c13] Y. Fujimoto, H. Matsumoto, H. Umezawa, and I. Ojima, Phys. Rev. D 30, 1400 (1984) ibid.31, 1527(E) (1985)

[c14] H. Matsumoto, Y. Nakano, and H. Umezawa, Phys. Rev. D 28, 1931 (1983) N. P. Landsman, Phys. Lett. B 172, 46 (1986)

[c15] R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957) P. C. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959)

[c16] R. L. Kobes and K. L. Kowalski, Phys. Rev. D 34, 513 (1986)

[c17] R. L. Kobes, G. W. Semenoff, and N. Weiss, Z. Phys. C 29, 371 (1985)

[c18] K. L. Kowalski, Z. Phys. C 36, 665 (1987)

[c19] E. S. Abers and B. W. Lee, Phys. Rep. 9, 1 (1973)

[c20] [3]

[c21] [2] ([3,7])

[c22] Omitted endnote

[c23] Omitted endnote

Physical Review D

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Path-integral formulation of real-time quantum field theories at finite temperature

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References (23)

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