Casimir energy calculations within the formalism of the noncompact lattice QED

TL;DR

This paper introduces a Monte-Carlo lattice QED method to compute Casimir energies, effectively handling complex boundary conditions relevant for thin film interactions while maintaining gauge invariance.

Contribution

It presents a novel lattice QED approach for Casimir energy calculations that accommodates oblique boundary conditions via a gauge-invariant Chern-Simons boundary term.

Findings

Validated the method with standard parallel plane Casimir setup

Successfully incorporated oblique boundary conditions

Demonstrated gauge invariance in the lattice formulation

Abstract

A new method based on the Monte-Carlo calculation on the lattice is proposed to study the Casimir effect in the noncompact lattice QED. 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.