  The spectrum of an exactly solvable non-relativistic system of a charged
particle interacting with a quantized electromagnetic mode is studied with
various polarizations. Quasiparticle dispersion relations can be derived from
the diagonalized Hamiltonian which, in the case of a linearly polarized field,
indicates a bulk plasmon excitation, whereas in the elliptically and circularly
polarized cases the dispersions exhibit a global minimum and show a singular
behavior as the wavenumber tends to zero. These new type of dispersion
relations lead to modified plasma frequencies and reflectivities, as well as to
negative group velocities. It is shown that the zero-point energy of the system
implies a repulsive force between two parallel plates, which vanishes when the
charge is set to zero.
