Heat kernel Coefficients and Divergencies of the Casimir Energy for the Dispersive Sphere

TL;DR

This paper calculates heat kernel coefficients for a dispersive sphere and discusses the resulting divergences in Casimir energy, highlighting challenges in interpreting the ground-state energy due to ultraviolet infinities.

Contribution

It provides the first calculation of heat kernel coefficients for a dispersive dielectric sphere with high-frequency permittivity behavior.

Findings

Divergences in vacuum energy are identified for dispersive spheres.

Ultraviolet divergences affect the interpretation of Casimir energies.

Pressure can become infinite in models with fixed atom number.

Abstract

The first heat kernel coefficients are calculated for a dispersive ball whose permittivity at high frequency differs from unity by inverse powers of the frequency. The corresponding divergent part of the vacuum energy of the electromagnetic field is given and ultraviolet divergencies are seen to be present. Also in a model where the number of atoms is fixed the pressure exhibits infinities. As a consequence, the ground-state energy for a dispersive dielectric ball cannot be interpreted easily.