Aspects of Green's function methods versus self-consistent field theory

  • Alvin K. Benson
Article

Abstract

The basic methods of solving fully symmetric, nonlinear theories are stated. These are discussed in terms of Green's function methods and self-consistent field theory methods. The equivalence of many-body theory based on Green's functions with quantum field theory, on which the self-consistent field theory is based, is reviewed. A number of similarities, differences, and cautions involved with these methods are determined. In particular, since very often both methods are based upon use of the adiabatic theorem, which is typicallynot applicable to the models under consideration, a deviation in the self-consistent theory is discussed that avoids this problem. A similar idea is used for solution of models with the functional integral method. Ferromagnetic models are used at various places in illustrating some of the ideas. By contrasting these methods further insight may be gained into solving nonlinear, physical theories.

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References

  1. Anderson, P. W. (1961).Physical Review,124, 41.Google Scholar
  2. Baym, G., and Kadanoff, L. P. (1961).Physical Review,124, 287.Google Scholar
  3. Benson, A. K. (1973).Physical Review B,7, 4158.Google Scholar
  4. Benson, A. K., and Hatch, D. M. (1973).Physical Review B,8, 4410.Google Scholar
  5. Benson, A. K. (1975).International Journal of Theoretical Physics,12, 251.Google Scholar
  6. Evenson, W. E., Schrieffer, J. R., and Wang, S. Q. (1970).Journal of Applied Physics,41, 1199.Google Scholar
  7. Hugenholtz, N. M., Parry, W. E., Turner, R. E., ter Haar, D., Rowlinson, J. S., Chester, G. V., and Kubo, R. (1969a).Many-Body Problems. pp. 1–2, 48–51, 210–217. (W. A. Benjamin, New York).Google Scholar
  8. Hugenholtz, N. M., et al. (1969b).Many-Body Problems, pp. 2–9, 200–210. (W. A. Benjamin, New York).Google Scholar
  9. Hugenholtz, N. M., et al. (1969c).Many-Body Problems, pp. 15–18, 48–51. (W. A. Benjamin, New York).Google Scholar
  10. Källén, G. (1968). “Different Approaches to Field Theory,” inFundamental Problems in Elementary Particle Physics, pp. 33–51. (Interscience, New York).Google Scholar
  11. Keiter, H., and Kimball, J. C. (1970).Physical Review Letters,25, 672.Google Scholar
  12. Lange, R. V. (1965).Physical Review Letters,14, 3.Google Scholar
  13. Leplae, L., Sen, R. N., and Umezawa, H. (1967).Nuovo Cimento,49, 1.Google Scholar
  14. Leplae, L., and Umezawa, H. (1969).Journal of Mathematical Physics,10, 2038.Google Scholar
  15. Matsubara, T. (1955).Progress in Theoretical Physics,14, 351.Google Scholar
  16. Mattuck, R. D., and Johansson, B. (1968).Advances in Physics,17, 509.Google Scholar
  17. Mills, R. E. (1970). Private communication (1973) at the University of Louisville.Google Scholar
  18. Noziéres, P. (1968).Interacting Fermi Systems, p. 2. (W. A. Benjamin, New York).Google Scholar
  19. Rajagopal, A. K., Brooks, H., and Ranganathan (1967).Nuovo Cimento Supplement,5, 807.Google Scholar
  20. Stratanovich, R. L. (1958).Soviet Physics-Doklady,2, 416.Google Scholar
  21. Umezawa, H., and Leplae, L. (1964).Nuovo Cimento,33, 379.Google Scholar
  22. Umezawa, H., Leplae, L., and Sen, R. N. (1965).Progress in Theoretical Physics Supplement, 637.Google Scholar
  23. Van Hove, L. (1961). “Ground State Theory of Many-Particle Systems,” inLectures on Field Theory and the Many-Body Problem, pp. 229–240. (Academic Press, New York).Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • Alvin K. Benson
    • 1
  1. 1.Department of PhysicsIndiana University SoutheastNew Albany

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