Derivative expansion of the electromagnetic Casimir energy for two thin mirrors

TL;DR

This paper extends a derivative expansion method to calculate electromagnetic Casimir energy between two thin, imperfect mirrors, providing a correction to the proximity force approximation for the static Casimir effect.

Contribution

It introduces a derivative expansion approach for electromagnetic Casimir energy with imperfect mirrors described by vacuum polarization tensors, advancing previous work.

Findings

Derived the first correction to the proximity force approximation

Applied the method to static Casimir effect between thin mirrors

Enhanced understanding of electromagnetic Casimir interactions with imperfect surfaces

Abstract

We extend our previous work on a derivative expansion for the Casimir energy, to the case of the electromagnetic field coupled to two thin, imperfect mirrors. The latter are described by means of vacuum polarization tensors localized on the mirrors. We apply the results so obtained to compute the first correction to the proximity force approximation to the static Casimir effect.