  Intersubband polaritons are light-matter excitations originating from the
strong coupling between an intersubband quantum well electronic transition and
a microcavity photon mode. In this paper we study how the Coulomb
electron-electron interaction and the Pauli saturation of the electronic
transitions affect the physics of intersubband polaritons. We develop a
microscopic many-body theory for the physics of such composite bosonic
excitations in a microcavity-embedded two-dimensional electron gas. As a first
application, we calculate the modification of the depolarization shifts and the
efficiency of intersubband polariton-polariton scattering processes.
