HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Supplement (1984) > No.80
| Next Article >

Prog. Theor. Phys. Supplement No.80 (1984) pp. 26-39

[ Full Text PDF : FREE ACCESS (1371K) ]

Methods of Quantum Field Theory in Condensed Matter Physics

— New Perspectives, Extensions and Applications —

Hiroomi Umezawa

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

(Received September 13, 1984)

Abstract:

Throughout the course of its development in the past four decades quantum field theory has gradually acquired a very rich structure (much richer in fact than it was originally intended) and now provides us with an effective method in the analysis of many diverse areas of physics; condensed matter physics, high energy particle physics general relativity and cosmology are among the more notable examples. Since condensed matter physics deals with those phenomena in which a system of quanta exist together with a variety of macroscopic objects at finite temperature, it may be said to manifest the fundamental properties of quantum field theory in its widest sense. Thus condensed matter physics has served as a powerful motivating force throughout the growth and development of quantum field theory. This process was indeed initiated by the celebrated Matsubara formalism of finite temperature Green's function method. This process is by no means complete since recent developments in many areas of physics demand a more sophisticated understanding with regard to the fundamental nature of quantum field theory.
A brief description of this maturing process of quantum field theory in the past, present and prospects for the future will be the main content of this article.


URL : http://ptp.ipap.jp/link?PTPS/80/26/
DOI : 10.1143/PTPS.80.26

[ Full Text PDF : FREE ACCESS (1371K) ] Citation:

References:

  1. T. Matsubara, Prog. Theor. Phys. 14 (1955), 351[PTP].
  2. P. Debye, Ann. de Phys. 39 (1912), 789.
  3. F. Bloch, Z. Phys. 61 (1930), 206.
    J. C. Slater, Phys. Rev. 35 (1930), 509[APS].
  4. V. Fock, Z. Phys. 75 (1932), 622.
  5. H. Lehmann, K. Symanzik and W. Zimmermann, Nuovo Cim. 6 (1957), 319.
  6. H. Umezawa, Nuovo Cim. 40 (1965), 450.
    L. Leplae, R. N. Sen and H. Umezawa, Prog. Theor. Phys. Suppl. Extra Number (1965), 637[PTP].
    L. Leplae and H. Umezawa, Nuovo Cim. 44 (1966), 410.
  7. H. Umezawa, H. Matsumoto and M. Tachiki, Thermo Field Dynamics and Condensed States (North-Holland Publishing Company, 1982).
  8. K. O. Friedrichs, Mathematical Aspects of the Quantum Theory of Fields (Interscience, New York, 1953).
  9. A. S. Wightman and S. S. Schweber, Phys. Rev. 98 (1955), 812[APS].
    L. Gärding and A. S. Wightman, Proc. Natl. Acad. Sci. USA 40 (1954), 617; ibid. 40 (1954), 622.
  10. J. Bardeen, L. Cooper and J. Schrieffer, Phys. Rev. 108 (1957), 1175[APS].
  11. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961), 345[APS]; ibid. 124 (1961), 246[APS].
  12. J. Goldstone, A. Salam and S. Weinberg, Phys. Rev. 127 (1962), 965[APS].
  13. J. P. Whitehead, Aspects of Magnetism and Superconductivity, PhD-thesis, The University of Alberta (1984). See also Ref. 7).
  14. J. C. Ward, Phys. Rev. 78 (1950), 182[APS].
    Y. Takahashi, Nuovo Cim. 6 (1957), 370.
  15. T. Moriya and A. Kawabata, J. Phys. Soc. Jpn. 34 (1973), 639[JPSJ].
    T. Moriya, J. Magn. Magn. Mater 14 (1979), 1[CrossRef].
  16. J. P. Whitehead, H. Matsumoto and H. Umezawa, Phys. Rev. B 25 (1982), 4737[APS].
  17. J. P. Whitehead, H. Matsumoto and H. Umezawa, Phys. Rev. B 29 (1984), 423[APS].
  18. H. Matsumoto, H. Umezawa and N. J. Papastamatiou, Phys. Rev. D 28 (1983), 1434[APS].
  19. J. L. Gervais and B. Sakita, Phys. Rev. D 11 (1975), 2943[APS].
    J. L. Gervais, A. Jevicki and B. Sakita, Phys. Rev. D 12 (1975), 1038[APS].
    C. G. Callan, Jr. and D. J. Gross, Nucl. Phys. B 93 (1975), 29[CrossRef].
    H. Matsumoto, G. Oberlechner, M. Umezawa and H. Umezawa, J. Math. Phys. 20 (1979), 2088[CrossRef].
  20. C. N. Yang and D. Feldman, Phys. Rev. 79 (1950), 972[APS].
  21. H. Matsumoto, P. Sodano and H. Umezawa, Phys. Rev. D 19 (1979), 511[APS].
  22. L. Leplae, H. Umezawa and F. Manicini, Phys. Rep. 10 (1974), 151[CrossRef].
  23. H. Matsumoto, G. Semenoff, M. Tachiki and H. Umezawa, Fortschr. Phys. 28 (1980), 67.
    M. Fusco-Girard, F. Manicini and M. Marinaro, Fortschr. Phys. 28 (1980), 355.
  24. H. Fröhlich, Phys. Lett. A 26 (1968), 402; ibid. 39 (1972), 153; ibid. 51 (1975), 21.
  25. L. Mercaldo, I. Rabuffo and G. Vitiello, Nucl. Phys. B 188 (1981), 193.
    J. A. Tuszynski, R. Paul. R. Chatterjee and S. R. Sreenivasan, Preprint (1984).
  26. H. Ezawa, Y. Tomozawa and H. Umezawa, Nuovo Cim. 5 (1957), 810.
  27. A. A. Abrikosov, L. P. Gor'kov and I. E. Dzyaloshinski, J. Exptl. Theoret. Phys. (U. S. S. R.) 36 (March, 1959), 900.
  28. J. Schwinger, J. Math. Phys. 2 (1961), 407[CrossRef].
    L. V. Keldysh, Sov. Phys. -JETP 20 (1965), 1018.
    R. A. Craig, J. Math. Phys. 9 (1968), 605[CrossRef].
    R. Mills, Propagators for Many-Particle Systems (Gordon and Breach Science Publisher, N. Y., 1969).
  29. H. Araki and E. J. Woods, J. Math. Phys. 4 (1963), 637[CrossRef].
    H. Araki and W. Wyss, Helv. Phys. Acta 37 (1964), 136.
    R. Haag, N. W. Hugenholtz and M. Winnihk, Commun. Math. Phys. 5 (1967), 215[CrossRef].
  30. Y. Takahashi and H. Umezawa, Collective Phenomena 2 (1975), 55.
  31. H. Matsumoto, Fortschr. Phys. 25 (1977), 1.
  32. I. Ojima, Ann. of Phys. 137 (1981), 1[CrossRef].
  33. H. Matsumoto, Y. Nakano, H. Umezawa, F. Mancini and M. Marinaro, Prog. Theor. Phys. 70 (1983), 599[PTP].
    An argument in M. Schmutz, Z. Phys. B 30 (1978), 97, is also useful in understanding a feature of this subject.
  34. A. J. Niemi and G. W. Semenoff, Ann. of Phys. 152 (1984), 105[CrossRef].
  35. H. Matsumoto, M. Nakahara, Y. Nakano and H. Umezawa, Phys. Rev. D 29 (1984), 2838[APS].
    H. Aoyama and D. Boyanovsky, Preprint (1984).
  36. H. Matsumoto, Y. Nakano and H. Umezawa, Phys. Rev. D 29 (1984), 1116[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 74 No. 5 (1985) pp. 1168-1172 :
    Inhomogeneous Particle Distributions in Non-Equilibrium Thermofield Dynamics
    J. P. Whitehead
  2. Progress of Theoretical Physics Vol. 76 No. 1 (1986) pp. 260-282 :
    Vacuum Diagrams in Perturbative Thermo Field Dynamics
    H. Matsumoto, H. Umezawa and J. P. Whitehead
  3. Progress of Theoretical Physics Vol. 77 No. 1 (1987) pp. 32-52 :
    Non-Equilibrium Thermo Field Dynamics
    Toshihico Arimitsu and Hiroomi Umezawa
  4. Progress of Theoretical Physics Vol. 77 No. 1 (1987) pp. 53-67 :
    General Structure of Non-Equilibrium Thermo Field Dynamics
    Toshihico Arimitsu and Hiroomi Umezawa
  5. Progress of Theoretical Physics Vol. 114 No. 5 (2005) pp. 907-927 :
    A Quantum Field Theoretical Approach to the TCLE Method
    Mizuhiko Saeki
  6. Progress of Theoretical Physics Vol. 124 No. 1 (2010) pp. 95-123 :
    Non-Equilibrium Thermo-Field Dynamics for a Fourth-Order Hamiltonian
    Mizuhiko Saeki

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.