Perturbation theory in statistical mechanics

D. J. Thouless

C. De Dominicis

Sergei Vladimirovich Tyablikov

Francisco Marcelo Fernández

We discuss the application of perturbation theory to statistical mechanics both in the operator form of Schwinger and in the scalar form as a sum over states. We briefly consider and compare the use of variational parameters in both approaches. By means of a simple model we show that Schwinger perturbation theory might fail when the eigenfunctions satisfy Dirichlet boundary conditions. On the other hand, the sum over states gives accurate results.

Luigi E. Picasso, L. Bracci, Emilio d’Emilio

Alexander Stewart

A version of quantum and statistical mechanics, including perturbation theory, is described in which explicit electromagnetic gauge arbitrariness is maintained at every stage. Any gauge may be used for a calculation provided that the wave equation operator is gauge invariant.