Casimir energy in noncompact lattice electrodynamics

We propose a new lattice method for calculating the Casimir energy for a $U(1)$ gauge theory. Using this method, we analyze the standard problem of the Casimir interaction of two planar parallel plates with the boundary conditions induced by an additional Chern–Simons action localized on these boundary surfaces. From the physical standpoint, this boundary value problem models the interaction of two thin metal plates. The proposed method can be generalized to the case of more complicated surface shapes.