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

Abstract

We consider a dielectric medium with an ultraviolet behaviour as follows from the Drude model. Compared with dilute models, this has the advantage that, for large frequencies, two different media behave in the same way. As a result one expects the Casimir energy to contain fewer 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.