Retarded Casimir interaction in the asymptotic domain of an electron and a dielectric wall.

Abstract

A number of different approaches have been used to determine the interactions between a variety of pairs of polarizable systems asymptotically far apart; these are examples of retardation or Casimir interactions. The pairs include two dielectric walls, and an atom and a dielectric wall, but not an electron and a dielectric wall. (The asymptotic value of the interaction between an electron and an ideal conducting wall has been evaluated.) We here apply a method not previously used in the evaluation of retardation potentials, quantized Fresnel modes, to determine the interaction in the asymptotic domain of a polarizable system and a dielectric wall. We thereby reproduce the known result for an atom and a dielectric wall and obtain a previously unobtained result, that for an electron and a dielectric wall. The result simplifies greatly for an ideal metallic wall and for a wall made from a material such as liquid helium for which the dielectric constant is very close to unity. We also discuss the question of a connection between the electron--dielectric-wall interaction and Lifshitz's force per unit area between two dielectric walls. The determination of the amplitudes of the Fresnel modes, by quantization, is the only nonclassical element in the calculation.