Two-dimensional electron system in electromagnetic radiation field

We consider a two-dimensional electron gas in the presence of a monochromatic linear polarized electromagnetic field, within the Floquet formalism. The Floquet states have a simple relation with the energy eigenstates in the absence of the field. Therefore the single-particle and the two-particle Green functions of the many-body system with Coulomb interactions, in the radiation field, can be formally calculated by the standard diagrammatic techniques, as for the conservative system. We derive the elementary excitations of quasi-particle type, the plasma dispersion relation, and the ground state quasi-energy, and we relate them to the corresponding results for the conservative system.