Linear Response, Bethe-Salpeter Equation, and Transport Coefficients

Abstract

The Bethe-Salpeter equation for thermodynamic Green’s functions has been already studied on several occasions, usually with some approximative kernels. In this paper, we wish to point out some general features of this equation and stress its applicability in constructing a linearized kinetic equation with generalized kernel and in calculating the transport coefficients. We shall limit ourselves to a self-bounded infinite system, uniform in space (gas, liquid). To be more definite, we shall consider a normal system of fermions. The central quantity of our interest is the linear response function L(p, k) of the particle number density. This functions describes small deviations from equilibrium when a weak external field is applied to our system. It is well known that the functional derivative of a single-particle Green’s function (linear response) is the same as a nonsymetrized two-particle Green’s function. This justifies the study of the Bethe-Salpeter equation.