Casimir energy and realistic model of dilute dielectric ball

TL;DR

This paper derives an analytical expression for the Casimir energy of a dilute dielectric ball considering realistic frequency dispersion, introducing a physical cutoff to avoid divergences present in previous models.

Contribution

It provides the first analytical derivation of Casimir energy for a dielectric ball with arbitrary dispersion, incorporating a microscopic model and a physical cutoff to eliminate divergences.

Findings

Analytical Casimir energy expression for dielectric ball

Introduction of a physical cutoff based on interatomic distance

Resolution of divergence issues in macroscopic approaches

Abstract

The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically for the first time for an arbitrary physically possible frequency dispersion of dielectric permittivity $\epsilon(i\omega)$. A microscopic model of dielectrics is considered, divergences are absent in calculations because an average interatomic distance $\lambda$ is a {\it physical} cut-off in the theory. This fact has been overlooked before, which led to divergences in various macroscopic approaches to the Casimir energy of connected dielectrics.