Worldline Approach To The Casimir Effect

TL;DR

This paper introduces a novel worldline Monte Carlo method to compute quantum energies and Casimir forces, effectively capturing curvature effects beyond traditional approximations.

Contribution

The paper develops a new worldline approach combined with Monte Carlo techniques for calculating Casimir energies, including curvature effects, which improves upon existing approximation methods.

Findings

The method accurately reproduces the parallel-plate Casimir force.

Curvature effects become significant for a/R > 0.02.

Numerical results compare favorably with the proximity force approximation.

Abstract

We present a new method to compute quantum energies in presence of a background field. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Our procedure is applied to the study of the Casimir force between rigid bodies induced by a fluctuating real scalar field. We test our method with the classic parallel-plate configuration and study curvature effects quantitatively for the sphere-plate configuration. The numerical estimates are compared with the ``proximity force approximation''. Sizable curvature effects are found for a distance-to-curvature-radius ratio of a/R>0.02.