Fluctuating Surface Currents: A New Algorithm for Efficient Prediction of Casimir Interactions among Arbitrary Materials in Arbitrary Geometries. I. Theory

TL;DR

This paper introduces a novel, efficient numerical method for calculating Casimir interactions in complex geometries and materials by modeling surface currents, unifying stress-tensor and path-integral approaches.

Contribution

The paper develops a new algorithm that models Casimir effects via surface currents, unifying two major theoretical frameworks for the first time.

Findings

Enables efficient computation of Casimir forces in arbitrary geometries.

Provides a unified framework combining stress-tensor and path-integral methods.

Applicable to materials with arbitrary frequency-dependent properties.

Abstract

This paper presents a new method for the efficient numerical computation of Casimir interactions between objects of arbitrary geometries, composed of materials with arbitrary frequency-dependent electrical properties. Our method formulates the Casimir effect as an interaction between effective electric and magnetic current distributions on the surfaces of material bodies, and obtains Casimir energies, forces, and torques from the spectral properties of a matrix that quantifies the interactions of these surface currents. The method can be formulated and understood in two distinct ways: \textbf{(1)} as a consequence of the familiar \textit{stress-tensor} approach to Casimir physics, or, alternatively, \textbf{(2)} as a particular case of the \textit{path-integral} approach to Casimir physics, and we present both formulations in full detail. In addition to providing an algorithm for computing Casimir interactions in geometries that could not be efficiently handled by any other method, the framework proposed here thus achieves an explicit unification of two seemingly disparate approaches to computational Casimir physics.