Functional formulation of microscopic theory of exciton polaritons

A microscopic approach to the description of exciton – polariton in semiconductors is presented which is based on exact results obtained by means of functional methods of field theory. It is shown that the polariton energies are given by the positions of poles of the two-particle Green function for particle-hole scattering due to the Coulomb interaction and the electron-hole exchange. By using the Legendre transformations, an equation of the Bethe–Salpeter type for the two-particle Green function is derived from the Schwinger equations. The polariton energies and the dielectric constant are obtained by means of solving the Bethe–Salpeter equation. A nontrivial normalization condition enables one to relate the polariton energy and momentum with the Minkowski energy-momentum tensor of the electromagnetic field in dispersive medium.