Complete zeta-function approach to the electromagnetic Casimir effect for spheres and circles

TL;DR

This paper introduces a zeta function regularization method for calculating the electromagnetic Casimir energy in spherical and circular geometries, providing new results such as the Casimir energy for a circular wire.

Contribution

It develops a complete zeta-function approach for electromagnetic Casimir effects in spheres and circles, including novel calculations for circular wires.

Findings

Zeta-regularized Casimir energy for a circular wire is obtained.

Properties of Bessel and related zeta functions are analyzed.

The method unambiguously applies zeta function regularization from the start.

Abstract

A technique for evaluating the electromagnetic Casimir energy in situations involving spherical or circular boundaries is presented. Zeta function regularization is unambiguously used from the start and the properties of Bessel and related zeta functions are central. Nontrivial results concerning these functions are given. While part of their application agrees with previous knowledge, new results like the zeta-regularized electromagnetic Casimir energy for a circular wire are included.