Electrical Conductivity of Interacting Fermions. I. General Formulation

Electrical conductivity σ(ω, T ) of a lattice electron system due only to mutual Coulomb interaction is studied on the basis of the Fermi liquid theory, ω 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 σ(ω, 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.