Regularized Casimir energy for an infinite dielectric cylinder subject to light-velocity conservation

TL;DR

This paper calculates the Casimir energy of an infinite dielectric cylinder with matching light velocity to its surroundings, providing exact and numerical results to understand quantum vacuum effects in such systems.

Contribution

It presents an exact first-order calculation and higher-order numerical analysis of Casimir energy for a dielectric cylinder with light-velocity conservation, avoiding Debye expansions.

Findings

Exact first-order Casimir energy calculation

Numerical results for higher-order corrections

No Debye expansions needed for the analysis

Abstract

The Casimir energy of a dilute dielectric cylinder, with the same light-velocity as in its surrounding medium, is evaluated exactly to first order in $\xi^2$ and numerically to higher orders in $\xi^2$. The first part is carried out using addition formulas for Bessel functions, and no Debye expansions are required.