Casimir energy in the compact QED on the lattice

TL;DR

This paper introduces a Monte-Carlo lattice method to study the Casimir effect in compact U(1) gauge theory, enabling analysis of boundary conditions relevant to material films and gauge invariance.

Contribution

A novel lattice Monte-Carlo approach for calculating Casimir energies with flexible boundary conditions in gauge theories.

Findings

Validated method with parallel plane surfaces

Applicable to oblique boundary conditions

Potential for complex geometries and other gauge groups

Abstract

A new method based on the Monte-Carlo calculation on the lattice is proposed to study the Casimir effect in the compact lattice U(1) theory with Wilson action. We have studied the standard Casimir problem with two parallel plane surfaces (mirrors) and oblique boundary conditions on those as a test of our method. Physically, this boundary conditions may appear in the problem of modelling of the thin material films interaction and are generated by additional Chern-Simons boundary term. This approach for the boundary condition generation is very suitable for the lattice formulation of the Casimir problem due to gauge invariance. This method can be simply generalized on the case of more complicated geometries and other gauge groups.