S-matrix interpretation of finite-temperature real-time field theories

The aim of the article is to construct the S-matrix interpretation of the perturbation theory for the Wigner functions generating functional at a finite temperature. The temperature is introduced in the theory by the way typical for the microcanonical description. The perturbation theory contains the two-temperature Green functions. The two possible boundary conditions are considered. One of them is usual in a field theory vacuum boundary condition. The corresponding generating functional can be used in the particle physics. Another type of the boundary condition assumes that the system under consideration is in environment of the free particles background field. This leads to the theory with Kubo-Martin-Schwinger boundary conditions ones at the one-temperature limit.