Abstract
Some of the most intriguing and important phenomena in modern many-body physics are explainable in terms of self-consistent quantum mechanical field theory. This is the powerful theory developed by Umezawa and co-workers and modified by Benson and Hatch in applications to ferromagnetism. It is usually lengthy and involved mathematically. Thus, it is very helpful and meaningful to see its overall step-by-step progress in simple, diagrammatic flow starting from basic principles, with a ferromagnetic model as an example. As one immediately notes, there are two paths leading to very powerful physical conclusions and implications, and something most interesting is that each path implies the other. Many useful examples of applications of these methods are noted and some future possible applications are cited.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. K. Benson,Int. J. Theoret. Phys., to be published; H. Umezawa,Acta Phys. Hung. 19, 9 (1965).
J. von Neumann,Math. Ann. 104, 570 (1931).
D. M. Hatch, private communication, Brigham Young Univ. (1972).
A. K. Benson,Phys. Rev. B 7, 4158 (1973); A. K. Benson and D. M. Hatch,Phys. Rev. B 8, 4410 (1973).
A. K. Benson,Int. J. Theoret. Phys., to be published.
G. Jona-Lasinio and Y. Nambu,Phys. Rev. 122, 345 (1961).
H. Umezawa,Nuovo Cimento 40A, 450 (1965).
H. Matsumoto, N. J. Papastamatiou, and H. Umezawa,Nucl. Phys. B97, 61 (1975); H. Matsumoto, H. Umezawa, G. Vitiello, and J. K. Wyly,Phys. Rev. D 9, 2806 (1974); H. Umezawa, Self-Consistent Quantum Field Theory and Symmetry Breaking, inRenormalization and Invariance in Quantum Field Theory (Plenum Publishing Co., New York, 1973).
H. P. Dürr, Goldstone Theorem and Possible Applications, inFundamental Problems in Elementary Particle Physics (Interscience, New York, 1968); K. L. Nagy, T. Nagy, and G. Pósik,Acta Phys. Hung. 19, 91 (1965); K. Nakagawa,Nuovo Cimento 50A, 37 (1967).
G. S. Guralnik,Phys. Rev. 136, 1404 (1964).
H. C. Ohanian,Phys. Rev. 184, 1305 (1969).
H. C. Tze and Z. F. Ezawa,Phys. Lett. 55B, 63 (1975).
H. Matsumoto, N. J. Papastamatiou, and H. Umezawa,Nucl. Phys. B97, 90 (1975).
B. Johansson and R. D. Mattuck,Adv. Phys. 17, 509 (1968).
G. Emch,J. Math. Phys. 8, 13 (1967).
A. K. Benson,Int. J. Theoret. Phys., to be published.
M. S. Green, Critical Phenomena, inMany-Body Problems and Other Selected Topics in Theoretical Physics (Gordon and Breach, New York, 1968); R. A. Ferrell, Field Theory of Phase Transitions, inContemporary Physics I (International Atomic Energy Agency, Vienna, 1969); R. Brout,Phase Transitions (Benjamin, New York, 1965).
A. Coniglio and M. Marinaro,Nuovo Cimento 48B, 262 (1967).
A. DeLuca, L. M. Ricciardi, and H. Umezawa,Physica 40, 61 (1968).
L. Leplae and H. Umezawa,Nuovo Cimento 44, 410 (1966).
L. Leplae and H. Umezawa,J. Math. Phys. 10, 2038 (1969); L. Leplae, H. Umezawa, and F. Mancini,Phys. Reports 10C (1974).
L. Leplae, F. Mancini, and H. Umezawa,Nuovo Cimento Lett. 3, 153 (1970);Nuovo Cimento 10B, 267 (1972);Nuovo Cimento 9B, 233 (1972);Nuovo Cimento Lett. 9, 711 (1974); L. Leplae, V. Srinivasan, and H. Umezawa,Phys. Lett. 45A, 177 (1973).
Y. Takahashi and H. Umezawa,Collective Phenomena,2, 55 (1975).
L. Leplae, R. N. Sen, and H. Umezawa,Nuovo Cimento 49, 1 (1967).
D. M. Hatch, private communication, Brigham Young Univ. (1972); K. Hepp,Helv. Phys. Acta 45, 237 (1972).
D. M. Hatch,Int. J. Quant. Chem. 9, 649 (1975).
I. Stuart, Y. Takahashi, and H. Umezawa, Preprint, Univ. of Alberta (1975).
P. C. Martin, Solid-State Problems, inContemporary Physics I (International Atomic Energy Agency, Vienna, 1969).
A. K. Benson and D. M. Hatch,Phys. Rev. B 8, 4410 (1973).
A. K. Benson,Phys. Rev. B 7, 4158 (1973).
A. K. Benson and D. M. Hatch,Int. J. Theoret. Phys. 12, 321 (1975).
R. V. Lange,Phys. Rev. Lett. 14, 3 (1965).
A. K. Benson and D. M. Hatch,Phys. Rev. B 8, 4410 (1973).
M. N. Shah, H. Umezawa, and G. Vitiello,Phys. Rev. B 10, 4724 (1974).
A. K. Benson,Phys. Rev. B 7, 4158 (1973).
A. K. Benson and D. M. Hatch,Phys. Rev. B 8, 4410 (1973).
H. Wagner,Z. Phys. 195, 273 (1966).
A. K. Benson,Int. J. Theoret. Phys., to be published.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Benson, A.K. Diagrammatic review and implications of the self-consistent field theory method. Found Phys 7, 723–733 (1977). https://doi.org/10.1007/BF00708591
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00708591