Quantum electrodynamics near a dispersive and absorbing dielectric

We build up a consistent theory of quantum electrodynamics in the presence of macroscopic polarizable media. We use the Huttner-Barnett model of a dispersive and absorbing dielectric medium and formulate the theory in terms of interacting quantum fields. We integrate out the damped polaritons by using diagrammatic techniques and find an exact expression for the displacement-field (photon) propagator in the presence of a dispersive and absorbing dielectric half-space. This offers a route to traceable perturbative calculations of the same kind as in free-space quantum electrodynamics. As a worked-through example, we consider the interaction of a neutral atom with a dispersive and absorbing dielectric half-space. For that, we use the multipolar coupling D of the atomic dipole moment to the electromagnetic displacement field. We apply this formalism to calculate the one-loop correction to the atomic electron propagator and to find the energy-level shift and changes in the spontaneous decay rates for a neutral atom close to an absorptive dielectric mirror.