Scalar Casimir Energies for Separable Coordinate Systems: Application to Semi-transparent Planes in an Annulus

TL;DR

This paper derives a simplified formula for scalar Casimir energies in separable coordinates and applies it to semi-transparent planes in an annular region, providing analytical and numerical insights.

Contribution

It introduces a general expression for two-body scalar Casimir energy in separable coordinate systems and demonstrates its application to a specific annular geometry.

Findings

Derived a simplified expression for Casimir energy in separable coordinates

Applied the method to semi-transparent planes in an annular region

Provided analytical and numerical results for the specific configuration

Abstract

We derive a simplified general expression for the two-body scalar Casimir energy in generalized separable coordinate systems. We apply this technique to the case of radial semi-transparent planes in the annular region between two concentric Dirichlet cylinders. This situation is explored both analytically and numerically.