Diffractive Effects and General Boundary Conditions in Casimir Energy

TL;DR

This paper extends a formalism for calculating Casimir energy to general boundary conditions, enabling analysis of diffractive effects and boundary influences in complex geometries.

Contribution

The authors generalize an existing boundary field theory approach to arbitrary boundary conditions, broadening its applicability to diverse physical setups.

Findings

Formalism successfully applied to various boundary conditions.

Results agree with known cases like Dirichlet and Neumann.

Method effectively captures diffractive effects in Casimir energy.

Abstract

The effect of edges and apertures on the Casimir energy of an arrangement of plates and boundaries can be calculated in terms of an effective nonlocal lower-dimensional field theory that lives on the boundary. This formalism has been developed in a number of previous papers and applied to specific examples with Dirichlet boundary conditions. Here we generalize the formalism to arbitrary boundary conditions. As a specific example, the geometry of a flat plate and a half-plate placed parallel to it is considered for a number of different boundary conditions and the area-dependent and edge dependent contributions to the Casimir energy are evaluated. While our results agree with known results for those special cases (such as the Dirichlet and Neumann limits) for which other methods of calculation have been used, our formalism is suitable for general boundary conditions, especially for the diffractive effects.