Scalar Casimir effect between Dirichlet spheres or a plate and a sphere

TL;DR

This paper introduces a straightforward method for calculating the scalar Casimir energy between spheres and a plane, applicable at any separation, and compares exact results with approximation schemes.

Contribution

The authors develop a versatile formalism for scalar Casimir energy calculations that can be extended to multiple objects, boundary conditions, and higher dimensions.

Findings

Exact results are provided for sphere-sphere and sphere-plane configurations.

Approximation schemes are evaluated for their accuracy at different separations.

The formalism is adaptable to various boundary conditions and non-ideal reflectors.

Abstract

We present a simple formalism for the evaluation of the Casimir energy for two spheres and a sphere and a plane, in case of a scalar fluctuating field, valid at any separations. We compare the exact results with various approximation schemes and establish when such schemes become useful. The formalism can be easily extended to any number of spheres and/or planes in three or arbitrary dimensions, with a variety of boundary conditions or non-overlapping potentials/non-ideal reflectors.