Casimir energy for a spherical boundary within the surface impedance approach: Obtaining negative values

TL;DR

This paper calculates the Casimir energy for a spherical boundary using a surface impedance approach with plasma model, revealing conditions under which the energy can be negative, and discusses the model's applicability.

Contribution

It introduces an analytical method to compute Casimir energy with surface impedance, showing negative values are achievable within certain parameters.

Findings

Negative Casimir energy possible for specific parameters

Explicit divergences computed using zeta function regularization

Limits of the model's applicability discussed

Abstract

We compute the Casimir Energy of a spherical region using a Surface Impedance approach. We characterize the Surface Impedance of the boundary using plasma model. Exact analytical formulae are obtained by means of the zeta function regularization method and all the divergencies are explicitly computed. We find that it is possible to have negative Casimir energy for some range of values of the relevant parameter. Limits of applicability of the model are discussed.