Casimir energies with finite-width mirrors

TL;DR

This paper develops a functional approach to compute the Casimir energy for a scalar field interacting with finite-width mirrors, generalizing the traditional boundary condition limit and providing explicit results for specific configurations.

Contribution

It introduces a method to evaluate Casimir energies with finite-width, frequency-dependent mirrors, extending beyond idealized boundary conditions.

Findings

Exact vacuum energy expressions for finite-width mirrors

Explicit Casimir energy results for specific mirror configurations

Generalization of boundary condition limits to realistic mirror models

Abstract

We use a functional approach to the Casimir effect in order to evaluate the exact vacuum energy for a real scalar field in $d+1$ dimensions, in the presence of backgrounds that, in a particular limit, impose Dirichlet boundary conditions on one or two parallel surfaces. Outside of that limit, the background may be thought of as describing finite-width mirrors with frequency-dependent transmission and reflection coefficients. We provide new explicit results for the Casimir energy in some particular backgrounds