Casimir forces from a loop integral formulation

TL;DR

This paper introduces a loop integral formulation for calculating Casimir forces in complex backgrounds, utilizing path-ordered exponentials and a pseudo-action approach to simplify the computation.

Contribution

It presents a novel loop integral framework for Casimir force calculations, extending traditional methods to non-trivial backgrounds with a path-ordered exponential approach.

Findings

Provides a new mathematical formulation for Casimir forces.

Enables computation of forces in complex scattering environments.

Introduces the pseudo-action concept for operator-valued evaluations.

Abstract

We reformulate the Casimir force in the presence of a non-trivial background. The force may be written in terms of loop variables, the loop being a curve around the scattering sites. A natural path ordering of exponentials take place when a particular representation of the scattering centres is given. The basic object to be evaluated is a reduced (or abbreviated) classical pseudo-action that can be operator valued.