Casimir Energy for a Dielectric Cylinder

TL;DR

This paper calculates the Casimir energy for a dielectric-diamagnetic cylinder with differing internal and external light speeds, revealing conditions under which the energy is finite and self-stress vanishes.

Contribution

It provides a detailed calculation of Casimir energy for a dielectric cylinder with differing internal and external properties, including divergence handling and self-stress analysis.

Findings

Casimir energy calculation for dielectric cylinders with speed of light mismatch

Self-stress vanishes to second order in permittivity deviation

Results consistent with van der Waals force calculations

Abstract

In this paper we calculate the Casimir energy for a dielectric-diamagnetic cylinder with the speed of light differing on the inside and outside. Although the result is in general divergent, special cases are meaningful. The well-known results for a uniform speed of light are reproduced. The self-stress on a purely dielectric cylinder is shown to vanish through second order in the deviation of the permittivity from its vacuum value, in agreement with the result calculated from the sum of van der Waals forces.These results are unambiguously separated from divergent terms.