We propose a projector-based renormalization framework to study exciton-polariton Bose-Einstein condensation in a microcavity matter-light system. Treating Coulomb interaction and electron-hole/photon coupling effects on an equal footing we analyze t
he ground-state properties of the exciton polariton model according to the detuning and the excitation density. We demonstrate that the condensate by its nature shows a crossover from an excitonic insulator (of Bose-Einstein respectively BCS type) to a polariton and finally photonic condensed state as the excitation density increases at large detuning. If the detuning is weak polariton or photonic phases dominate. While in both cases a notable renormalization of the quasiparticle band structure occurs that strongly affects the coherent part of the excitonic luminescence, the incoherent wavevector-resolved luminescence spectrum develops a flat bottom only for small detuning.
