Aspects of Green's function methods versus selfconsistent field theory
 Alvin K. Benson
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The basic methods of solving fully symmetric, nonlinear theories are stated. These are discussed in terms of Green's function methods and selfconsistent field theory methods. The equivalence of manybody theory based on Green's functions with quantum field theory, on which the selfconsistent 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 selfconsistent 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.
 Anderson, P. W. (1961) Physical Review 124: pp. 4141
 Baym, G., Kadanoff, L. P. (1961) Physical Review 124: pp. 287287
 Benson, A. K. (1973) Physical Review B 7: pp. 41584158
 Benson, A. K., Hatch, D. M. (1973) Physical Review B 8: pp. 44104410
 Benson, A. K. (1975) International Journal of Theoretical Physics 12: pp. 251251
 Evenson, W. E., Schrieffer, J. R., Wang, S. Q. (1970) Journal of Applied Physics 41: pp. 11991199
 Hugenholtz, N. M., Parry, W. E., Turner, R. E., Haar, D., Rowlinson, J. S., Chester, G. V., Kubo, R. (1969) ManyBody Problems. W. A. Benjamin, New York, pp. 12
 Hugenholtz, N. M. (1969) ManyBody Problems. W. A. Benjamin, New York
 Hugenholtz, N. M. (1969) ManyBody Problems. W. A. Benjamin, New York
 Källén, G. (1968) Different Approaches to Field Theory. Fundamental Problems in Elementary Particle Physics. Interscience, New York, pp. 3351
 Keiter, H., Kimball, J. C. (1970) Physical Review Letters 25: pp. 672672
 Lange, R. V. (1965) Physical Review Letters 14: pp. 33
 Leplae, L., Sen, R. N., Umezawa, H. (1967) Nuovo Cimento 49: pp. 11
 Leplae, L., Umezawa, H. (1969) Journal of Mathematical Physics 10: pp. 20382038
 Matsubara, T. (1955) Progress in Theoretical Physics 14: pp. 351351
 Mattuck, R. D., Johansson, B. (1968) Advances in Physics 17: pp. 509509
 Mills, R. E. (1970). Private communication (1973) at the University of Louisville.
 Noziéres, P. (1968) Interacting Fermi Systems. W. A. Benjamin, New York
 Rajagopal, A. K., Brooks, H., Ranganathan, (1967) Nuovo Cimento Supplement 5: pp. 807807
 Stratanovich, R. L. (1958) Soviet PhysicsDoklady 2: pp. 416416
 Umezawa, H., Leplae, L. (1964) Nuovo Cimento 33: pp. 379379
 Umezawa, H., Leplae, L., and Sen, R. N. (1965).Progress in Theoretical Physics Supplement, 637.
 Hove, L. (1961) Ground State Theory of ManyParticle Systems. Lectures on Field Theory and the ManyBody Problem. Academic Press, New York, pp. 229240
 Title
 Aspects of Green's function methods versus selfconsistent field theory
 Journal

International Journal of Theoretical Physics
Volume 15, Issue 7 , pp 541556
 Cover Date
 19760701
 DOI
 10.1007/BF01809507
 Print ISSN
 00207748
 Online ISSN
 15729575
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
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 Authors

 Alvin K. Benson ^{(1)}
 Author Affiliations

 1. Department of Physics, Indiana University Southeast, 47150, New Albany, Indiana