Nonlinear response of equilibrium strongly coupled Fermi fluids. II. Fourier expansion and partial resummation of expectation values—polarization diagrams

Abstract

This is Paper II of a series of three papers in which a self-consistent propagator resummation of self-energy effects in a strongly coupled Fermi fluid is performed. In the present paper, a generating function for the expectation values of arbitrary one- and two-body operators is introduced and written in the form of a cluster expansion. An explicit expression is written for the magnetization of a strongly coupled Fermi fluid in the presence of a constant and a spatially varying external field, and rules are given for evaluating it in terms of a reaction matrix expansion. A Fourier expansion is performed on a subclass of the diagrams contributing to the grand potential and the magnetization, and a self-consistent resummation of self-energy effects due to both the medium and the external spatially varying field is performed. It is found that traditional perturbation theory techniques for summing self-energy effects cannot be applied to all terms in a reaction matrix expansion. The effect of the external fields on the polarization diagrams is discussed.