Casimir force between planes as a boundary finite size effect

TL;DR

This paper derives a universal expression for the Casimir energy in boundary quantum field theories, highlighting its dependence on boundary conditions and demonstrating its application to scalar fields with Robin boundary conditions.

Contribution

It introduces a general formula for Casimir energy in planar geometries that accounts for boundary conditions through reflection amplitudes, applicable to various models.

Findings

Universal Casimir energy expression derived

Application to free scalar field with Robin boundary condition

Reproduction of known results in the literature

Abstract

The ground state energy of a boundary quantum field theory is derived in planar geometry in D+1 dimensional spacetime. It provides a universal expression for the Casimir energy which exhibits its dependence on the boundary conditions via the reflection amplitudes of the low energy particle excitations. We demonstrate the easy and straightforward applicability of the general expression by analyzing the free scalar field with Robin boundary condition and by rederiving the most important results available in the literature for this geometry.