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Nonequilibrium thermofield dynamics and the nonequilibrium statistical operator method

I. Basic relations

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Literature Cited

  1. N. N. Bogolyubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, 3rd ed., Wiley, New York (1980).

    Google Scholar 

  2. C. Itzykson and J.-B. Zuber, Quantum Field Theory, McGraw-Hill, New York (1980).

    Google Scholar 

  3. A. A. Slavnov and L. D. Faddeev, Gauge Fields, Introduction to Quantum Theory (Frontiers in Physics, Vol. 50), Reading, Mass. (1980).

  4. P. Ramon, Field Theory. A Modern Introductory Course [Russian translation], Mir, Moscow (1984).

    Google Scholar 

  5. G. V. Efimov, Problems of the Quantum Theory of Nonlocal Interactions [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  6. V. N. Popov, Functional Integrals in Quantum Field Theory and Statistical Physics [in Russian], Atomizdat, Moscow (1976).

    Google Scholar 

  7. R. Rajaraman, Solitons and Instantons, North-Holland, Amsterdam (1984).

    Google Scholar 

  8. Ta-Pei Cheng and Ling-Fong Li, Gauge Theory of Elementary Particle Physics, Clarendon Press, Oxford (1984).

    Google Scholar 

  9. N. N. Bogolyubov, “Problems of a dynamical theory in statistical physics,” in: Studies in Statistical Mechanics, Vol. 1 (eds. J. de Boer and G. E. Uhlenbeck), North-Holland, Amsterdam (1962).

    Google Scholar 

  10. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics, Plenum, New York (1974).

    Google Scholar 

  11. A. I. Akhiezer and S. V. Peletminskii, Methods of Statistical Mechanics [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  12. Statistical Physics and Quantum Field Theory [Russian collection], (ed. N. N. Bogolyubov), Nauka, Moscow (1973).

    Google Scholar 

  13. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics Wiley-Interscience, New York (1975).

    Google Scholar 

  14. D. N. Zubarev, “Modern methods of the statistical theory of nonequilibrium processes,” in: Reviews of Science and Technology. Modern Problems of Mathematics, Vol. 15 [in Russian], VINITI, Moscow (1980), pp. 131–226.

    Google Scholar 

  15. D. N. Zubarev and Yu. A. Tserkovnikov, “The method of two-time finite-temperature Green's functions in equilibrium and nonequilibrium statistical mechanics” Tr. Mosk. Inst. Akad. Nauk SSSR,175, 134 (1986).

    Google Scholar 

  16. G. Röpke, Nonequilibrium Statistical Mechanics [Russian translation], Mir, Moscow (1990).

    Google Scholar 

  17. N. N. Bogolyubov and S. V. Tyablikov, Dokl. Akad. Nauk SSSR,126, 53 (1959).

    Google Scholar 

  18. D. N. Zubarev, Usp. Fiz. Nauk,71, 71 (1960).

    Google Scholar 

  19. V. L. Bonch-Bruevich and S. V. Tyablikov, The Green Function Method in Statistical Mechanics North-Holland, Amsterdam (1962).

    Google Scholar 

  20. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, Englewood Cliffs (1963).

  21. S. V. Tyablikov, Methods of Quantum Theory of Magnetism, Plenum Press, New York (1967).

    Google Scholar 

  22. K. G. Wilson and J. Kogut, “The renormalization group and the ε expansion,” Phys. Rep. Phys. Lett. C,12, No. 2, 75 (1974).

    Google Scholar 

  23. Quantum Field Theory and the Physics of Phase Transitions. New Results in Fundamental Physics [Russian translations], Mir, Moscow (1975).

  24. H. Umezawa, H. Matsumoto, and M. Tachiki, Thermo Field Dynamics, and Condensed States, Amsterdam (1982).

  25. L. Leplae, U. Umezawa, and F. Mancini, Phys. Rep. C,10, 151 (1974).

    Google Scholar 

  26. Y. Takahashi and H. Umezawa, Collective Phenomena,2, 55 (1975).

    Google Scholar 

  27. T. Arimitsu and H. Umezawa, Prog. Theor. Phys., Prog. Lett.,75, 429 (1985).

    Google Scholar 

  28. T. Arimitsu and H. Umezawa, Prog. Theor. Phys.,77, 32 (1987).

    Google Scholar 

  29. T. Arimitsu and H. Umezawa, Prog. Theor. Phys.,77, 53 (1987).

    Google Scholar 

  30. V. Fano, Rev. Mod. Phys.,29, 74 (1957).

    Google Scholar 

  31. M. Schmutz, Z. Phys. B,30, 97 (1978).

    Google Scholar 

  32. K. Blum, Density Matrix Theory and Its Applications, Plenum Press, New York (1981).

    Google Scholar 

  33. H. Gabriel, Phys. Rev.,181, 506 (1969).

    Google Scholar 

  34. S. Nakajima, Prog. Theor. Phys.,20, 848 (1958).

    Google Scholar 

  35. R. Zwanzig, J. Chem. Phys.,33, 1338 (1960); Physica (Utrecht),30, 1109 (1964).

    Google Scholar 

  36. H. Umezawa and Y. Yamanaka, Advan. Phys.,37, 531 (1988).

    Google Scholar 

  37. T. Arimitsu, J. Pradko, and H. Umezawa, Physica (Utrecht) A,135, 487 (1986).

    Google Scholar 

  38. K. Nakamura, Y. Yamanaka, and H. Umezawa, Physica (Utrecht) A,152, 29 (1988).

    Google Scholar 

  39. T. Arimitsu, M. Guida, and H. Umezawa, Physica (Utrecht) A,148, 1 (1988).

    Google Scholar 

  40. T. Arimitsu, H. Umezawa, Y. Yamanaka, and N. Papastamation Physica (Utrecht) A,148, 27 (1988).

    Google Scholar 

  41. T. Arimitsu, Physica (Utrecht) A,148, 427 (1988).

    Google Scholar 

  42. T. Arimitsu, Physica (Utrecht) A,158, 371 (1989).

    Google Scholar 

  43. H. Matsumoto, Prog. Theor. Phys.,79, 373 (1988).

    Google Scholar 

  44. H. Matsumoto, Prog. Theor. Phys.,79, 627 (1988).

    Google Scholar 

  45. H. Matsumoto, Physica (Utrecht) A,158, 291 (1989).

    Google Scholar 

  46. I. Shirai, M. Jimbo, and T. Kon, J. Phys. Soc. Jpn., No. 7, 2597 (1989).

    Google Scholar 

  47. J. Hardman, H. Umezawa, and Y. Yamanaka, Physica (Utrecht) A,158, 326 (1989).

    Google Scholar 

  48. K. Kawasaki and J. D. Gunton, Phys. Rev. A,8, 2048 (1973).

    Google Scholar 

  49. R. Jackiw, Physica (Utrecht) A,158, 269 (1989).

    Google Scholar 

  50. T. M. Bibilashvili and I. V. Paziashvili, “Real-time finite-temperature Green functions for nonuniform nonstationary media,” Preprint HE-3, Tbilisi (1990).

  51. A. J. Niemi and G. W. Semenoff, Ann. Phys. (N.Y.)152, 105 (1984).

    Google Scholar 

  52. D. N. Zubarev and M. V. Tokarchuk, “Nonequilibrium thermofield dynamics and the nonequilibrium statistical operator method,” Preprint 89-68R [in Russian], Institute of Theoretical Physics, Ukrainian SSR Academy of Sciences, Kiev (1989).

    Google Scholar 

  53. V. P. Kalashnikov, Teor. Mat. Fiz.,34, 412 (1978).

    Google Scholar 

  54. V. G. Morozov, Teor. Mat. Fiz.,47, 407 (1981).

    Google Scholar 

  55. T. Arimitsu, H. Umezawa, and Y. Yamanaka, J. Math. Phys.,28, 2741 (1987).

    Google Scholar 

  56. H. Matsumoto, H. Umezawa, and J. P. Whitehed, Prog. Theor. Phys.,76, 260 (1986).

    Google Scholar 

  57. A. Hosoja, M. Sakadami, and M. Takao, Ann., Phys. (N.Y.)154, 229 (1984).

    Google Scholar 

  58. I. E. Dzyaloshinskii, Zh. Eksp. Teor. Fiz.,15, 778 (1962).

    Google Scholar 

  59. D. N. Zubarev, A. V. Prozorkevich, and S. A. Smolyanskii, Teor. Mat. Fiz.,40, 394 (1979).

    Google Scholar 

  60. A. V. Prozorkevich, V. A. Samorodov and S. A. Smolyanskii, Teor. Mat. Fiz.,52, 463 (1982).

    Google Scholar 

  61. S. A. Smolyanskii, Teor. Mat. Fiz.,52, 292 (1982).

    Google Scholar 

  62. G. Röpke and H. Schutz, Nucl. Phys.,477, 472 (1988).

    Google Scholar 

  63. T. Tominaga, T. Arimitsu, J. Pradko, and H. Umezawa, Physica (Utrecht) A,150, 97 (1988).

    Google Scholar 

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Additional information

V. A. Steklov Mathematics Institute, USSR Academy of Sciences; Institute of the Physics of Condensed Systems, Ukrainian SSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 88, No. 2, pp. 286–310, August, 1991.

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Zubarev, D.N., Tokarchuk, M.V. Nonequilibrium thermofield dynamics and the nonequilibrium statistical operator method. Theor Math Phys 88, 876–893 (1991). https://doi.org/10.1007/BF01019114

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