International Journal of Theoretical Physics
, Volume 15, Issue 7, pp 541556
First online:
Aspects of Green's function methods versus selfconsistent field theory
 Alvin K. BensonAffiliated withDepartment of Physics, Indiana University Southeast
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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.
 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
 197607
 DOI
 10.1007/BF01809507
 Print ISSN
 00207748
 Online ISSN
 15729575
 Publisher
 Kluwer Academic PublishersPlenum Publishers
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 Authors

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

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