  We study the behavior of exciton polaritons in an optical microcavity with an
embedded semiconductor quantum well. We use two-component exciton-photon
approach formulated in terms of path integral formalism. In order to describe
spatial distributions of the exciton and photon condensate densities, the two
coupled equations of the Gross-Pitaevskii type are derived. For a homogeneous
system, we find the noncondensate photon and exciton spectra, calculate the
coefficients of transformation from the exciton-photon basis to the lower-upper
polariton basis, and obtain the exciton and photon occupation numbers of the
lower and upper polariton branches for nonzero temperatures. For an
inhomogeneous system, the set of coupled equations of the Bogoliubov-de-Gennes
type is derived. The equations govern the spectra and spatial distributions of
noncondensate photons and excitons.
