The covariant electromagnetic Casimir effect for real conducting spherical shells

TL;DR

This paper calculates the electromagnetic Casimir force on a real conducting spherical shell using a covariant approach, considering realistic material properties and avoiding mode decomposition, providing more accurate force estimations.

Contribution

It extends the covariant electromagnetic Casimir effect framework to spherical geometries with real conductors, incorporating plasma frequency renormalization without mode decomposition.

Findings

Casimir force for gold and silver spheres computed

Covariant approach simplifies boundary condition handling

Results applicable to realistic conducting materials

Abstract

Using the covariant electromagnetic Casimir effect (previously introduced for real conducting cylindrical shells [1]), the Casimir force experienced by a spherical shell, under Dirichlet boundary condition, is calculated. The renormalization procedure is based on the plasma cut-off frequency for real conductors. The real case of a gold (silver) sphere is considered and the corresponding electromagnetic Casimir force is computed. In the covariant approach, there isn't any decomposition of fields to TE and TM modes; thus, we do not need to consider the Neumann boundary condition in parallel to the Dirichlet problem and then add their corresponding results.