Functional formulation of microscopic theory of exciton polaritons

Abstract

Exact results obtained from quantum field theory in its functional formulation are used to construct a microscopic theory of exciton polaritons in semiconductors. It is shown that the polariton spectrum is determined by the poles of the two-particle Green's function that describes both the direct Coulomb electron-hole interaction as well as the exchange electron-hole interaction. By means of higher Legendre transformations the Bethe-Salpeter equation for the two-particle Green's function is obtained from Schwinger's equations. The polariton spectrum and the permittivity tensor are determined from the solution of the Bethe-Salpeter equation. The nontrivial normalization condition obtained in the paper for the wave functions of the polaritons has made it possible for the first time to connect their energy and momentum to the Minkowski tensor for the energy and momentum densities of the electromagnetic field in a dispersive medium.