Casimir interaction and gauge invariance in finite width mirrors

TL;DR

This paper analyzes the Casimir interaction between finite-width mirrors using vacuum polarization tensors, ensuring gauge invariance and deriving the energy by reducing the problem to one-dimensional systems.

Contribution

It provides a general framework for calculating Casimir forces between finite-width mirrors with gauge invariance constraints, extending previous models.

Findings

Derived solutions to Ward identities for vacuum polarization tensors.

Reduced the Casimir energy calculation to a set of one-dimensional problems.

Established a general approach applicable to various mirror properties.

Abstract

We study the general form of the Casimir interaction between two flat finite-width, parallel, infinite mirrors, described by their respective vacuum polarization tensors, under the assumption of translation invariance along the directions parallel to the planes of the mirrors. Their properties along the normal coordinates are left, on the other hand, rather arbitrary, but constrained by the Ward identity for the vacuum polarization tensors. We construct solutions to those identities, evaluating the corresponding Casimir energy of the system by reducing the problem to a collection of one-dimensional systems.