Bilinear electromagnetic response of an electron gas in many-body perturbation theory

Abstract

The bilinear response of an interacting electron gas to an external electromagnetic field is investigated by many-body perturbation theory. The Coulomb interaction and the interaction of the electrons with the external field are treated as perturbations on the motion of the free electrons. The analysis is based on the pair approximation introduced by Gell-Mann and Brueckner to treat the Coulomb interaction up to all orders. In the perturbation expansion, terms up to the second order in the external field are retained in order to calculate expectation values of the current and charge densities in the perturbed state. By interpreting the results obtained for the linear and bilinear current densities in terms of the induced field set up in the high-density electron gas, these are shown to be equivalent to the results which may be derived by using a self-consistent-field approach.