Nonstandard formulation of perturbation theory for Green's function

Eleftherios N. Economou

M. N. Aliev

D. I. Kadyrov

Vyacheslav I. Yukalov

The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the Correlated Iteration Theory, which has been developed by the author. This approach differs from all other known variants of perturbation theory for Green's functions by the combination of two factors: the systematic formulation of an algorithm for obtaining subsequent approximations and the consistent consideration of interparticle correlations at each step of the procedure.

J. Manjavidze

The paper contains the real-time perturbation theory for description of a statistical system with the nonuniform temperature distribution. the formalism based on the Wigner-functions approach. The perturbation theory is formulated in terms of the local-temperature Green functions.