Casimir's energy of a conducting sphere and of a dilute dielectric ball

TL;DR

This paper derives exact integral formulas for calculating the Casimir energy of a conducting sphere and a dielectric ball, enabling precise computations without regularization, and critically examines the mode summation technique.

Contribution

It introduces a novel mode summation approach with contour integrals for Casimir energy calculations, avoiding regularization procedures.

Findings

Derived closed-form integral expressions for Casimir energies.

Provided a critical analysis of the mode summation technique.

Enabled calculations to all orders without regularization.

Abstract

In this paper we sum over the spherical modes appearing in the expression for the Casimir energy of a conducting sphere and of a dielectric ball (assuming the same speed of light inside and outside), before doing the frequency integration. We derive closed integral expressions that allow the calculations to be done to all orders, without the use of regularization procedures. The technique of mode summation using a contour integral is critically examined.