Calculation of polaron conductivity by functional integration

A new approach to the calculation of polaron electrical conductivity by functional integration is proposed. By means of Kubo's formula the polaron conductivity is expressed in terms of the two-time commutator Green's function, which can be obtained by analytic continuation of a temperature-dependent Green's function of current-current type. This last is expressed exactly in terms of an integral over the electron paths. The calculation of this integral in the framework of the variational principle for the polaron free energy leads in the zeroth order to the results of Feynman, Hellwarth, Iddings, and Platzman. Expressions are obtained for the effective mass and the polaron lifetime at low temperatures; a comparison with the results of other studies is made. The origin of the incorrect low-temperature dependence in the expression for the drift mobility is discussed.