Photon Propagation in the Casimir Vacuum

TL;DR

This paper establishes a formal analogy between the QED vacuum between parallel plates and finite temperature QED, deriving photon eigenvalues, eigenmodes, and phase velocity in the Casimir vacuum.

Contribution

It introduces a transformation linking the Casimir vacuum to finite temperature QED, enabling the derivation of photon properties in the Casimir setup.

Findings

Eigenvalues and eigenmodes of photon self-energy are obtained independently of approximation.

Two distinct physical eigenvalues and three eigenmodes are identified.

Low energy photon phase velocity in the Casimir vacuum is derived from finite temperature QED results.

Abstract

A transformation that relates the Minkowskian space of the Quantum Electrodynamics (QED) vacuum between parallel conducting plates and the QED vacuum at finite temperature is obtained. From this formal analogy,the eigenvalues and eigenvectors of the photon self-energy for the QED vacuum between parallel conducting plates (Casimir vacuum) are found in an approximation independent form. It leads to two different physical eigenvalues and three eigenmodes. We also apply the transformation to derive the low energy photons phase velocity in the Casimir vacuum from its expression in the QED vacuum at finite temperature.