Casimir energy and dilute dielectric ball

TL;DR

This paper develops a new divergence-free method to calculate the Casimir energy of a dilute dielectric ball, demonstrating the equivalence with dipole-dipole interactions and reviewing various approaches.

Contribution

It introduces a novel divergence-free approach for calculating Casimir energy of dilute dielectric spheres, linking it to dipole interactions and reviewing existing methods.

Findings

Derived a divergence-free formula for Casimir energy of a dilute dielectric ball.

Established the equivalence between Casimir energy and dipole-dipole interaction in dilute dielectrics.

Reviewed different methods for calculating Casimir energy in dielectric spheres.

Abstract

General formalism of quantum field theory and addition theorem for Bessel functions are applied to derive formula for Casimir-Polder energy of interaction between a polarizable particle and a dilute dielectric ball. The equivalence of dipole-dipole interaction and Casimir energy for dilute homogeneous dielectrics is shown. A novel method is used to derive Casimir energy of a dilute dielectric ball without divergences in calculations. Physically realistic model of a dilute ball is discussed. Different approaches to the calculation of Casimir energy of a dielectric ball are reviewed.