The Casimir Energy for a Hyperboloid Facing a Plate in the Optical Approximation

TL;DR

This paper calculates the Casimir energy for a scalar field near a hyperboloid facing a plate using an optical approximation, revealing significant differences from traditional methods and considering finite size effects.

Contribution

It introduces an optical approximation method including multiple reflections for Casimir energy calculation in complex geometries, comparing it with existing approaches.

Findings

Optical approximation yields sizable differences from proximity force approximation.

Finite size effects significantly influence the Casimir energy.

The method captures qualitative differences in energy predictions.

Abstract

We study the Casimir energy of a massless scalar field that obeys Dirichlet boundary conditions on a hyperboloid facing a plate. We use the optical approximation including the first six reflections and compare the results with the predictions of the proximity force approximation and the semi-classical method. We also consider finite size effects by contrasting the infinite with a finite plate. We find sizable and qualitative differences between the new optical method and the more traditional approaches.