Abstract
We investigate, in the context of the effective potential, the temperature dependent imaginary terms which appear in the finite temperature perturbation based on Thermo Field Dynamics. It is shown that the imaginary terms cancell with each other and thus the effective potential is real.
Similar content being viewed by others
References
Y. Takahashi, H. Umezawa: Collective Phenomena2, 55 (1975); L. Leplae, F. Mancini, H. Umezawa: Phys. Rep.10C, 151 (1974); H. Matsumoto: Fortschr. Phys.25, 1 (1977); H. Umezawa, H. Matsumoto, M. Tachiki: Thermo field dynamics and condenced states. Amsterdam: North Holland 1982; I. Ojima: Ann. Phys.137, 1 (1981)
J. Schwinger: J. Math. Phys.2, 407 (1961); L.V. Keldysh: Sov. Phys. JETP20, 1018 (1965); R. Craig: J. Math. Phys.10, 605 (1968); M. Schmutz: Z. Phys. B — Condensed Matter39, 97
T. Matsubara: Prog. Theor. Phys.14, 351 (1955); A. Kirzhnits, A.D. Linde: Phys. Lett.B43, 471 (1972); C. Bernard: Phys. Rev.D9 3312 (1974); L. Dolan, R. Jackiw: Phys. Rev.D9, 3320 (1974); S. Weinberg: Phys. Rev.D9, 3357 (1974)
H. Matsumoto, I. Ojima, H. Umezawa: Ann. Phys.152, 348 (1984); A. Niemi, G. Semenoff: Nucl. Phys.B230, 181 (1984)
Y. Fujimoto R. Grigjanis, R. Kobes: Prog. Theor. Phys.73, 434 (1985); Y. Fujimoto, R. Grigjanis: Z. Phys. C — Particles and Fieds28, 395 (1985); Y. Fujimoto, R. Grigjanis: RIFP-582 (to be published in Prog. Theor. Phys.); Y. Fujimoto, H. Nishino: RIFP-589. (Phys. Rev. D. in press)
Y. Fujimoto, R. Grigjanis, H. Nishino: Phys. Lett.B141, 83 (1984)
Y. Fujimoto, R. Grigjanis: in [5]——
I.E. Dzyaloshinski: Sov. Phys. JETP15, 778 (1962); H.A. Weldon: Phys. Rev.D28, 2007 (1983). This work contains a physical interpretation of the imaginary part; A. Hosoya, M. Sakagami: Phys. Rev.D29, 2228 (1984); A. Hosoya, M. Sakagami, M. Takao: Ann. Phys.154, 229 (1984)
R. Kobes, G.W. Semenoff: Univ. of Washington preprint 1985; Y. Fujimoto, M. Morikawa, M. Sasaki: Kyoto University preprint 1985. (to be published in Phys. Rev. D)
H. Matsumoto, Y. Nakano, H. Umezawa: Phys. Rev.D31 1495 (1985); I. Ojima: (unpublished)
R. Fukuda: Prog. Theor. Phys.56, 258 (1976); Y. Fujimoto, G. Paravicini, L. O'Raifeartaigh: Nucl. Phys.B212, 268 (1983) and references therein
The proof presented hereafter is also known to I. Ojima (RIMP, Kyoto University)
H. Matsumoto, Y. Nakano, H. Umezawa: J. Math. Phys.25, 3076 (1984); H. Matsumoto: Thermo field dynamics and its development to appear in: Progress in quantum field theory. H. Ezawa, S. Kamefuchi (eds.) Amsterdam: North Holland phys. Rev.D32, 2167 (1985)
G. Semenoff, H. Umezawa: Nucl. Phys.B220, 196 (1983)
Y. Fujimoto, S. Midorikawa (unpublished); Y. Fujimoto, K. Shigemoto: J. Phys. A18, 3259 (1985)
Y. Fujimoto, R. Grigjanis, R. Kobes: in [5]—— Y. Fujimoto, H. Matsumoto, I. Ojima, H. Umezawa: Phys. Rev.D30, 1400 (1984)
Y. Fujimoto, R. Grigjanis: RIFP-582 in [5]——
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fujimoto, Y. A comment on the perturbation in thermo field dynamics. Z. Phys. C - Particles and Fields 30, 99–102 (1986). https://doi.org/10.1007/BF01560682
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01560682