Covariant operator formalism of gauge theories and its extension to finite temperature

  • Izumi Ojima
Gauge Theories III
Part of the Lecture Notes in Physics book series (LNP, volume 176)


On the basis of “thermo field dynamics” allowing the application of the Feynman diagram method to real-time Green's functions at T≠0°K, a field-theoretical formulation of finite-temperature gauge theory is presented. It is an extension of the covariant operator formalism of gauge theory based upon the BRS invariance: The subsidiary condition specifying physical states, the notion of observables, and the structure of the physical subspace at finite temperatures are clarified together with the key formula characterizing the temperature-dependent “vacuum”.


Gauge Theory Finite Temperature Negative Norm Bogoliubov Transformation Physical Subspace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Y. Takahashi and H. Umezawa, Collective Phenom. 2, 55 (1975); H. Umezawa, H. Matsumoto and M. Tachiki, “Thermo Field Dynamics and Condensed States,” NorthHolland, Amsterdam/New York/Oxford, 1982.Google Scholar
  2. 2.
    I. Ojima, Ann. Phys. 137, 1 (1981).Google Scholar
  3. 3.
    T. Kugo and I. Ojima, Suppl. Prog. Theor. Phys. No.66 (1979).Google Scholar
  4. 4.
    R. Kubo, J. Phys. Soc. Japan 12, 570 (1957); P. C. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959).Google Scholar
  5. 5.
    O. Bratteli and D. W. Robinson, “Operator Algebras and Quantum Statistical Mechanics”, Springer, Berlin/Heidelberg/New York, 1979.Google Scholar
  6. 6.
    R. Haag, N. M. Hugenholtz and M. Winnink, Comm. Math. Phys. 5, 215 (1967).Google Scholar
  7. 7.
    I. Ojima, Nucl. Phys. B143, 340 (1978); Z. Phys. C5, 227 (1980).Google Scholar
  8. 8.
    H. Hata and T. Kugo, Phys. Rev. D21, 3333 (1980).Google Scholar
  9. 9.
    C. Bernard, Phys. Rev. D9, 3312 (1974).Google Scholar
  10. 10.
    H. Matsumoto, I. Ojima and H. Umezawa, in preparation.Google Scholar
  11. 11.
    I. Ojima, unpablished.Google Scholar
  12. 12.
    W. Israel, Phys. Lett. 57A, 107 (1976).Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Izumi Ojima
    • 1
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

Personalised recommendations