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Tilde substitution law in thermo field dynamics: Thermal state conditions
Phys. Rev. D 31, 429 – Published 15 January, 1985
DOI: https://doi.org/10.1103/PhysRevD.31.429
Abstract
The tilde substitution law (which will be called in this paper the thermal state condition) plays an important role in determining the temperature-dependent ground state in thermo field dynamics (a real-time operator formalism of quantum field theory at finite temperature). Rules which define the phase conventions for the tilde substitution for any arbitrary Heisenberg operator are derived. These rules also lead to a clear correspondence between the perturbation series obtained in thermo field dynamics and the path-ordered formalism of the statistical average.
References (14)
- L. Leplae, H. Umezawa and F. Mancini, Phys. Rep. 10C, 151 (1974); Y. Takahashi and H. Umezawa, Collect. Phenom. 2, 55 (1975); H. Matsumoto, Fortschr. Phys. 25, 1 (1977).
- H. Umezawa, H. Matsumoto, and M. Tachiki, Thermo Field Dynamics and Condensed States (North-Holland, Amsterdam, 1982).
- I. Ojima, Ann. Phys. (N.Y.) 137, 1 (1981).
- 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).
- A. J. Niemi and G. W. Semenoff, Ann. Phys. (N.Y.) 152, 105 (1984).
- H. Matsumoto, I. Ojima and H. Umezawa, Ann. Phys. (N.Y.) 152, 348 (1984).
- H. Matsumoto, Y. Nakano and H. Umezawa, Phys. Rev. D 29, 1116 (1984).
- J. Whitehead, H. Matsumoto and H. Umezawa, Phys. Rev. B 29, 423 (1984).
- H. Matsumoto, M. Nakahara, Y. Nakano and H. Umezawa, Phys. Lett. 140B, 53 (1984); Phys. Rev. D 29, 2838 (1984).
- R. Kubo, J. Phys. Soc. Jpn. 12, 507 (1957); P. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959).
- H. Matsumoto and H. Umezawa, Phys. Lett. 103A, 405 (1984); J. P. Whitehead, H. Matsumoto and H. Umezawa, ibid. 103A, 408 (1984).
- H. Matsumoto and H. Umezawa, Universtiy of Alberta report, 1984 (unpublished).
- H. Matsumoto, Y. Nakano and H. Umezawa, Phys. Lett. 100A, 125 (1984).
- J. Schwinger, J. Math. Phys. 2, 407 (1961); L. V. Keldysh, Zh. Eskp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]; R. A. Craig, Ann. Phys. (N.Y.) 40, 416 (1966).