Casimir energy calculations within the formalism of the noncompact lattice QED

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.