Casimir Energy for a Purely Dielectric Cylinder by the Mode Summation Method

TL;DR

This paper calculates the Casimir energy for a dilute dielectric cylinder using mode summation and zeta-function regularization, providing insights into why the energy vanishes.

Contribution

It introduces a transparent mode summation method combined with zeta-function regularization to analyze Casimir energy in dielectric cylinders, clarifying the energy's null result.

Findings

Casimir energy for dilute dielectric cylinder vanishes

Mode summation method effectively applied

Zeta-function regularization clarifies energy calculation

Abstract

We use the mode summation method together with zeta-function regularization to compute the Casimir energy of a dilute dielectric cylinder. The method is very transparent, and sheds light on the reason the resulting energy vanishes.