Quantum electrodynamics in the presence of a dielectric

We discuss the formulation of quantized macroscopic electrodynamics interacting with Dirac particles. In particular, we consider the case of a dielectric half-space characterized by a constant, i.e. frequency-independent refractive index n. In contrast to perfectly reflecting boundary conditions, the matching conditions for the field strengths at the surface of the dielectric lead to the appearance of evanescent waves, and their presence modifies the representation of the photon propagator considerably. As an example of a one-loop calculation we determine the self-energy of a free electron on the vacuum side of the boundary. We find that in the limit of perfect reflectivity of the surface the self-energy disagrees with the one that emerges from calculations that assume perfect reflectivity from the outset. We develop calculational techniques for coping with problems that arise specifically due to the imperfect reflection at the surface.