  The Hartree-Fock-Popov theory of interacting Bose particles is developed, for
modeling exciton-polaritons in semiconductor microcavities undergoing
Bose-Einstein condensation. A self-consistent treatment of the linear
exciton-photon coupling and of the exciton non-linearity provides a thermal
equilibrium description of the collective excitation spectrum, of the polariton
energy shifts and of the phase diagram. Quantitative predictions support recent
experimental findings.
