Green’s function formulation of the Feynman model of the polaron

Abstract

The Feynman model of the polaron replaces the real polaron problem, in which the convergence of perturbation theory is rather slow, by a model problem in which perturbation theory converges much faster. The present paper demonstrates a relation between the true electronic Green’s functions and the model Green’s functions which enables one to calculate all the properties of the real polaron in terms of the model Green’s functions. This result is essentially similar to the earlier work of Schultz except for a small but significant difference in the handling of the fictitious field of the model. The Green’s function theory is used to calculate a transport equation for the polaron. The lowest-order transport equation is identical to that published earlier by Kadanoff at low temperatures. The derivation indicates, however, that Kadanoff’s equation is wrong at high temperatures.