Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions

TL;DR

This paper introduces a numerical lattice gauge theory method to compute the Casimir effect, demonstrating its effectiveness by accurately reproducing known theoretical results for parallel wires in 2D U(1) gauge theory.

Contribution

The paper presents a novel numerical approach for studying the Casimir effect in lattice gauge theories, addressing lattice-specific challenges and validating results against established theory.

Findings

Successful calculation of Casimir energy density around finite permittivity wires

Extrapolation to ideal conductor limit matches theoretical predictions

Method applicable to various lattice gauge theory configurations

Abstract

We propose a general numerical method to study the Casimir effect in lattice gauge theories. We illustrate the method by calculating the energy density of zero-point fluctuations around two parallel wires of finite static permittivity in Abelian gauge theory in two spatial dimensions. We discuss various subtle issues related to the lattice formulation of the problem and show how they can successfully be resolved. Finally, we calculate the Casimir potential between the wires of a fixed permittivity, extrapolate our results to the limit of ideally conducting wires and demonstrate excellent agreement with a known theoretical result.