Divergencies in the Casimir energy for a medium with realistic ultraviolet behavior

TL;DR

This paper investigates the Casimir energy in a dielectric medium modeled with realistic ultraviolet behavior, finding it contains only one divergence that can be renormalized, unlike in dilute models.

Contribution

It demonstrates that using the Drude model for the medium's ultraviolet behavior reduces divergences in Casimir energy calculations, simplifying renormalization.

Findings

Casimir energy has only a volume divergence in this model.

The divergence can be renormalized with a contact term.

Compared to dilute models, fewer divergences are present.

Abstract

We consider a dielectric medium with an ultraviolet behavior as it follows from the Drude model. Compared with dilute models, this has the advantage that, for large frequencies, two different media behave the same way. As a result one expects the Casimir energy to contain less divergencies than for the dilute media approximation. We show that the Casimir energy of a spherical dielectric ball contains just one divergent term, a volume one, which can be renormalized by introducing a contact term analogous to the volume energy counterterm needed in bag models. PACS: 12.20.Ds, 03.70.+k, 77.22.Ch