On the vacuum energy of a spherical plasma shell

TL;DR

This paper calculates the vacuum energy of electromagnetic fields interacting with a spherical plasma shell, including renormalization, and connects it to classical models and known ideal conductor results.

Contribution

It provides a detailed calculation of the vacuum energy for a spherical plasma shell, including heat kernel coefficients and renormalization, extending previous ideal conductor results.

Findings

Renormalized vacuum energy matches Boyer's 1968 results in the ideal conductor limit.

Calculated heat kernel coefficients for TM modes.

Established a consistent classical and quantum model for plasma shells.

Abstract

We consider the vacuum energy of the electromagnetic field interacting with a spherical plasma shell together with a model for the classical motion of the shell. We calculate the heat kernel coefficients, especially that for the TM mode, and carry out the renormalization by redefining the parameters of the classical model. It turns out that this is possible and results in a model, which in the limit of the plasma shell becoming an ideal conductor reproduces the vacuum energy found by Boyer in 1968.