A perturbation solution to generalized linear Boltzmann equation

A perturbation method to solve the generalized linear Boltzmann equation is presented for the calculation of dynamic conductivity of a normal metal at low temperatures. The method is applied to the ordinary Boltzmann equation. The following three cases are considered: i) when only electron-impurity interactions are dominant, ii) when the metal may be considered as pure plasma, and iii) when both of the interactions are present. The expressions for conductivity are presented in the binary collision approximation. The connected diagram expansion method is extended for the direct calculation of the conductivity. Finally the method is extended for the calculation of conductivity by the correlation function formula.