Worldline Numerics for Energy-Momentum Tensors in Casimir Geometries

TL;DR

This paper introduces a worldline Monte Carlo method for calculating energy-momentum tensors in Casimir geometries, enabling efficient numerical analysis of quantum field effects with potential for broad geometric applications.

Contribution

It develops a novel worldline formalism for composite operators like the energy-momentum tensor in Casimir setups, validated through benchmark cases.

Findings

Validated the numerical method against analytical solutions for simple geometries

Demonstrated the method's applicability to complex Casimir configurations

Analyzed statistical and systematic errors in the Monte Carlo approach

Abstract

We develop the worldline formalism for computations of composite operators such as the fluctuation induced energy-momentum tensor. As an example, we use a fluctuating real scalar field subject to Dirichlet boundary conditions. The resulting worldline representation can be evaluated by worldline Monte-Carlo methods in continuous spacetime. We benchmark this worldline numerical algorithm with the aid of analytically accessible single-plate and parallel-plate Casimir configurations, providing a detailed analysis of statistical and systematic errors. The method generalizes straightforwardly to arbitrary Casimir geometries and general background potentials.