Comment on "Casimir energies with finite-width mirrors"

TL;DR

This paper critiques a recent study on Casimir energies for finite-width mirrors, demonstrating that their method is unreliable for certain approximations and providing an alternative approach that aligns with established results.

Contribution

The authors identify a flaw in the previous method and introduce a new calculation technique for Casimir energies in finite-width systems that agrees with known results.

Findings

The previous method is unreliable for piecewise constant profiles.

The new method aligns with perturbation theory and older calculations.

Results differ from the criticized publication.

Abstract

We comment on a recent publication [1] by Fosco, Lombardo and Mazzitelli on Casimir energies for material slabs (`finite width mirrors') and report a discrepancy between results obtained there for a single mirror and some previous calculations. We provide a simple consistency check which proves that the method used in [1] is not reliable when applied to approximations of piecewise constant profile of the mirror. We also present an alternative method for calculation of the Casimir energy in such systems based on our recent work. Our results coincide both with perturbation theory and with some older \cite{Bordag'95} and more recent \cite{Vassilevitch'08} calculations, but differ from those of [1].