The heat kernel expansion for the electromagnetic field in a cavity

TL;DR

This paper derives the first six heat kernel coefficients for the electromagnetic field in a cavity, linking them to Laplace operator expansions, and confirms the finiteness of the electromagnetic Casimir energy.

Contribution

It provides explicit heat kernel coefficients for the electromagnetic field in a cavity, enhancing understanding of quantum field effects in confined geometries.

Findings

First six heat kernel coefficients derived

Electromagnetic Casimir energy shown to be finite

Method relates electromagnetic field to Laplace operator on forms

Abstract

We derive the first six coefficients of the heat kernel expansion for the electromagnetic field in a cavity by relating it to the expansion for the Laplace operator acting on forms. As an application we verify that the electromagnetic Casimir energy is finite.