$O(\alpha)$ Radiative Correction to the Casimir Energy for Penetrable Mirrors

TL;DR

This paper calculates the leading radiative correction to the Casimir energy for penetrable mirrors within QED, showing it is of order alpha and remains subleading compared to ideal mirror corrections.

Contribution

It provides the first explicit calculation of the O(alpha) radiative correction for penetrable mirrors in the Casimir effect.

Findings

Correction is of order alpha, similar to ideal mirrors.

Correction differs by a monotonic, powerlike function of transparency frequency.

O(alpha^2) correction remains subleading for penetrable mirrors.

Abstract

The leading radiative correction to the Casimir energy for two parallel penetrable mirrors is calculated within QED perturbation theory. It is found to be of the order $\alpha$ like the known radiative correction for ideally reflecting mirrors from which it differs only by a monotonic, powerlike function of the frequency at which the mirrors become transparent. This shows that the $O(\alpha^2)$ radiative correction calculated recently by Kong and Ravndal for ideally reflecting mirrors on the basis of effective field theory methods remains subleading even for the physical case of penetrable mirrors.