On the calculation of the Casimir forces

TL;DR

This paper reviews methods for calculating Casimir forces, emphasizing vacuum fluctuation suppression by boundaries, and discusses divergences in curved geometries with specific examples.

Contribution

It provides a unified approach to compute Casimir forces via vacuum fluctuations and addresses divergence issues in curved geometries with a new perspective.

Findings

Finite universal force in planar geometries

Divergences in curved geometries attributed to boundary self-energy

Support for divergence explanation through wedge-arc geometry analysis

Abstract

Casimir forces are a manifestation of the change in the zero-point energy of the vacuum caused by the insertion of boundaries. We show how the Casimir force can be computed by consideration of the vacuum fluctuations that are suppressed by the boundaries, and rederive the scalar Casimir effects for a series of geometries. For the planar case a finite universal force is automatically found. For curved geometries formally divergent expressions are encountered which we argue are largely due to the divergent self-energy of the boundary contributing to the force. This idea is supported by computing the effect for a fixed perimeter wedge-arc geometry in two dimensions.