Electrical conductivity of interacting fermions .1. General formulation

Electrical conductivity sigma(omega,T) of a lattice electron system due only to mutual Coulomb interaction is studied on the basis of the Fermi liquid theory, omega and T being the external frequency and the temperature, respectively. Based on the Kubo formula to respect the consistency between the selfenergy and the vertex corrections, a formulation of sigma(omega, T) is given in terms of memory function which is extended to the matrix form. In this formulation, it is explicitly demonstrated that. in the absence of Umklapp processes, T-2-term in the resistivity vanishes as it should in spite of the fact that the total current is not conserved.