Casimir effect with nonlocal boundary interactions

TL;DR

This paper derives a general formula for the Casimir energy between two parallel mirrors with nonlocal boundary interactions, extending previous models to include nonlocal effects and providing exact solutions for specific cases.

Contribution

It introduces a novel general expression for Casimir energy with nonlocal boundary conditions and verifies its consistency with known limits and specific solutions.

Findings

Derived a general formula for Casimir energy with nonlocal interactions

Validated the formula's limit in the zero-width case

Provided an exact solution for a specific nonlocal kernel case

Abstract

We derive a general expression for the Casimir energy corresponding to two flat parallel mirrors in d+1 dimensions, described by nonlocal interaction potentials. For a real scalar field, the interaction with the mirrors is implemented by a term which is a quadratic form in the field, with a nonlocal kernel. The resulting expression for the energy is a function of the parameters that define the nonlocal kernel. We show that the general expression has the correct limit in the zero width case, and also present the exact solution for a particular case.