Green's Dyadic Approach of the Self-Stress on a Dielectric-Diamagnetic Cylinder with Non-Uniform Speed of Light

TL;DR

This paper develops a Green's dyadic method to compute the Casimir energy and self-stress on a dielectric-diamagnetic cylinder with varying speed of light, revealing divergence issues and special case results.

Contribution

It introduces a novel Green's dyadic formulation for Casimir energy in cylindrical geometries with non-uniform light speed, connecting to van der Waals force calculations.

Findings

Self-stress vanishes to second order in permittivity deviation for purely dielectric cylinders.

General Casimir energy calculations are divergent, but special cases yield meaningful results.

The approach links Casimir effects with van der Waals forces in dielectric materials.

Abstract

We present a Green's dyadic formulation to 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. It is pointed out how the self-stress on a purely dielectric cylinder vanishes 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.