Perturbation theory for a polaron model at finite temperature

A scheme of perturbation theory for the partition function (free energy) of the polaron model is developed. An arbitrary order correction is represented as multiple integral depending parametrically on the temperature. A detailed analysis of the first two perturbation orders is presented. In higher orders a four-point correlation function plays the central role, which is evaluated explicitly. The properties of this correlator are studied in detail. Analogies with the perturbation theory for the S-matrix in quantum field theory are discussed