Electromagnetic Lifshitz formula for small-width mirrors from functional determinants

TL;DR

This paper extends a QFT approach to derive an electromagnetic Lifshitz formula for small-width mirrors, including graphene, using functional determinants and vacuum polarization tensors.

Contribution

It generalizes the Lifshitz formula for electromagnetic fields to small-width mirrors via a QFT framework involving functional determinants.

Findings

Derived a Lifshitz formula for small-width mirrors using QFT methods.

Applied the model to graphene sheets, confirming consistency with previous results.

Provided a unified approach for flat, parallel electromagnetic mirrors of finite width.

Abstract

We extend a recently proposed Quantum Field Theory (QFT) approach to the Lifshitz formula, originally implemented for a real scalar field, to the case of a fluctuating vacuum electromagnetic (EM) field, coupled to two flat, parallel mirrors. The general result is presented in terms of the invariants of the vacuum polarization tensors due to the media on each mirror. We consider mirrors that have small widths, with the zero-width limit as a particular case. We apply the latter to models involving graphene sheets, obtaining results which are consistent with previous ones.