Quantum field theoretic treatment of the casimir effect

Abstract

A nontrivial quantum field theoretical treatment of the Casimir effect demands the quantization of spinor electrodynamics with boundary conditions. The boundary conditions are realized by two super conducting infinitely thin parallel plates. As a technical tool we use the path integral method. It is shown that in perturbation theoretical calculations the standard Feynman rules remain valid up to a modification of the photon propagator. One advantage of our procedure is the derivation of a closed expression for this modified photon propagator in a covariant gauge which allows the explicit calculation of loop diagrams. Up to the order e2 we determine the radiative correction for vacuum energy density expression and the Casimir force. It turns out that the distance dependent part of the energy density and thereby the Casimir force is ultraviolet finite. An explicit value is obtained in the limit of large distances (in comparison with the Compton wave length).