Casimir Effect on the Worldline

TL;DR

This paper introduces a novel numerical method based on worldline quantum field theory to accurately compute Casimir forces for complex geometries, including sphere-plate configurations, revealing significant curvature effects.

Contribution

It develops a flexible, Monte Carlo-based worldline approach for Casimir calculations applicable to arbitrary shapes, improving upon traditional approximation methods.

Findings

Curvature effects are significant for certain geometries.

The method accurately reproduces known configurations like parallel plates.

Efficient algorithms for Gaussian loop generation are introduced.

Abstract

We develop a method to compute the Casimir effect for arbitrary geometries. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Concentrating on Casimir forces between rigid bodies induced by a fluctuating scalar field, we test our method with the parallel-plate configuration. For the experimentally relevant sphere-plate configuration, we study curvature effects quantitatively and perform a comparison with the ``proximity force approximation'', which is the standard approximation technique. Sizable curvature effects are found for a distance-to-curvature-radius ratio of a/R >~ 0.02. Our method is embedded in renormalizable quantum field theory with a controlled treatment of the UV divergencies. As a technical by-product, we develop various efficient algorithms for generating closed-loop ensembles with Gaussian distribution.