Quantum Field Theoretic Treatment of the Casimir Effect. Quantization Procedure and Perturbation Theory in Covariant Gauge

摘要

A nontrivial quantum field theoretical treatment of the Casimir effect demands the quantization of spinor electrodynamics with boundary conditions in a covariant gauge. The boundary conditions are realized by two superconducting infinitely thin parallel plates. As 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 of the advantages of the procedure is the derivation of a closed expression for this modified photon propagator which allows the explicit calculation of loop diagrams. Up to the order e exp 2 we determine the radiative corrections for vacuum energy expressions. A formal expression for the Casimir force up to the order in e exp 2 which will be discussed in a following paper is obtained. (Atomindex citation 15:039518)