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Prog. Theor. Phys. Vol. 77 No. 1 (1987) pp. 32-52

[ Full Text PDF : FREE ACCESS (910K) ]

Non-Equilibrium Thermo Field Dynamics

Toshihico Arimitsu and Hiroomi Umezawa

Theoretical Physics Institute, Department of Physics, The University of Alberta, Edmonton, Alberta, T6G 2J1

(Received October 25, 1985)

Abstract:

A fundamental framework for the construction of a quantum field theory for open systems, which will be called non-equilibrium thermo field dynamics (NETFD), is built upon two concepts. One is the thermal state in the thermal-Liouville space, by which the quasi-particle superoperator is introduced generally from the thermal state condition. The other is the coarse graining which is realized by projecting out some partial space from the complete thermal-Liouville space, and by which the dissipation is introduced. Most properties of the usual quantum field theory (e.g., the operator formalism, the time-ordered formulation of the Green's functions, the Feynman diagram method in real time, etc.) are preserved in NETFD. The entropy for the nonequilibrium state can be also introduced in NETFD.


URL : http://ptp.ipap.jp/link?PTP/77/32/
DOI : 10.1143/PTP.77.32

[ Full Text PDF : FREE ACCESS (910K) ] Citation:

References:

  1. R. Kbo, Lectures in Theoretical Physics, Vol. I. ed. W. E. Brittin and L. G. Dunham (Interscience Publishers Inc., New York, 1959), p. 120.
  2. S. Nakajima, Prog. Theor. Phys. 20 (1958), 948[PTP].
  3. R. Zwanzig, J. Chem. Phys. 33 (1960), 1338[CrossRef].
  4. F. Shibata, Y. Takahashi and N. hashitsume, J. Stat. Phys. 17 (1977), 171.
  5. S. Chaturvedi and F. Shibata, Z. Phys. B35 (1979), 297.
  6. F. Shibata and T. Arimitsu, J. Phys. Soc. Jpn. 49 (1980), 891[JPSJ].
  7. T. Arimitsu, J. Phys. Soc. Jpn. 51 (1982), 1720[JPSJ]; see also ibid. 379.
  8. J. Schwinger, J. Math. Phys. 2 (1961), 407[CrossRef].
  9. H. Mori, Prog. Theor. Phys. 33 (1965), 423[PTP].
  10. T. Arimitsu and H. Umezawa, Prog. Theor. Phys. 74 (1985), 429[PTP].
  11. L. Leplae, F. Mancini and H. Umezawa, Phys. Rep. 10C (1974), 151.
  12. Y. Takahashi and H. Umezawa, Collect. Phenom. 2 (1975), 55.
  13. H. Matsumoto, Fortschr. Phys. 25 (1977), 1.
  14. I. Ojima, Ann. of Phys. 137 (1981), 1[CrossRef].
  15. H. Umezawa, H. Matsumoto and M. Tachiki, Thermo Field Dynamics and Condensed States (North-Holland, Amsterdam, London, 1982).
  16. H. Umezawa, Prog. Theor. Phys. Suppl. No. 80 (1985), 26[PTP].
  17. H. Matsumoto, Progress in Quantum Field Theory, ed. H. Ezawa and S. Kamefuchi (North-Holland Pub., 1985), to be published.
  18. U. Fano, Rev. Mod. Phys. 29 (1957), 74[APS].
  19. U. Fano, Lectures on the Many-Body Problem, ed. E. R. Caianiello (Academic Press, New York, 1964), p. 217.
  20. J. A. Crawford, Nuovo Cim. 10 (1958), 698.
  21. M. Schmutz, Z. Phys. B30 (1978), 97.
  22. H. Matsumoto, Y. Nakano and H. Umezawa, Phys. Rev. D31 (1985), 429[APS].
  23. Private communications with J. Whitehead. He investigates the case in which the translationally invariance of the thermal state condition is broken.
  24. R. Kubo, J. Phys. Soc. Jpn. 51 (1962), 206[JPSJ].
  25. R. Kubo, J. Math. Phys. 4 (1963), 174[CrossRef].
  26. N. G. van Kampen, Physica 74 (1974), 215[CrossRef]; ibid. 74 (1974), 239[CrossRef].
  27. R. P. Feynman, Phys. Rev. 84 (1951), 108[APS].
  28. R. P. Feynman and F. L. Vernon, Jr., Ann. of Phys. 24 (1963), 118[CrossRef].
  29. L. van Hove, Physica 23 (1957), 441[CrossRef].
  30. R. Kubo, J. Phys. Soc. Jpn. 12 (1957), 570[JPSJ].
  31. P. Martin and J. Schwinger, Phys. Rev. 115 (1959), 1342[APS].
  32. H. Matsumoto, Y. Nakano and H. Umezawa, Phys. Lett. 100A (1984), 125.
  33. T. Arimitsu, Y. Takahashi and F. Shibata, Physica 100A (1980), 507.
  34. T. Arimitsu, Physica 104A (1980), 126.
  35. T. Arimitsu, J. Phys. Soc. Jpn. 51 (1982), 1054[JPSJ].
  36. M. Ban and T. Arimitsu, Physica 129A (1985), 455.
  37. T. Arimitsu and T. Tominaga, J. Phys. Soc. Jpn. 51 (1982), 3102[JPSJ].
  38. T. Tominaga and T. Arimitsu, J. Phys. Soc. Jpn. 53 (1984), 93[JPSJ].
  39. T. Arimitsu and F. Shibata, J. Phys. Soc. Jpn. 51 (1982), 1070[JPSJ].
  40. F. Shibata, T. Arimitsu and Y. Hamano, J. Phys. Soc. Jpn. 51 (1982), 2075[JPSJ].
  41. T. Arimitsu, M. Ban and F. Shibata, Physica 123A (1984), 131.
  42. M. Ban and T. Arimitsu, Physica 129A (1985), 455.
  43. T. Arimitsu and M. Ban, J. Phys. Soc. Jpn. 53 (1984), 74[JPSJ].
  44. T. Arimitsu and M. Ban, J. Phys. Soc. Jpn. 53 (1984), 76[JPSJ].
  45. M. Ban and T. Arimitsu, J. Phys. Soc. Jpn. 53 (1984), 939[JPSJ].
  46. M. Ban and T. Arimitsu, J. Phys. Soc. Jpn. 55 (1986), 1759[JPSJ].
  47. B. Robertson, Phys. Rev. 144 (1966), 151[APS].
  48. K. Kawasaki and J. D. Gunton, Phys. Rev. A8 (1973), 2048[APS].
  49. Y. Takahashi and H. Umezawa, Prog. Theor. Phys. 8 (1952), 493[PTP].
  50. H. Umezawa, Quantum Field Theory (North-Holland, Amsterdam, 1956).
  51. Y. Takahashi and H. Umezawa, Nucl. Phys. 51 (1964), 193[CrossRef].
  52. Y. Takahashi, An Introduction to Field Quantization (Pergamon Press, Oxford, 1969).
  53. T. Arimitsu, J. Pradko and H. Umezawa, Physica 135A (1986), 487.
  54. L. V. Keldysh, Sov. Phys. -JETP 20 (1965), 1018.
  55. R. A. Craig, J. Math. Phys. 9 (1968), 605[CrossRef].
  56. R. Mills, Propagators for Many-Particle Systems (Gordon and Breach Science Publisher, N. Y., 1969).
  57. I. Prigogine, C. George, F. Henin and L. Rosenfeld, Chemica Scripta 4 (1973), 5.
  58. T. Arimitsu, H. Umezawa and M. Guida, (1985) to be submitted.

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