Attractive and Repulsive Casimir Vacuum Energy with General Boundary Conditions

TL;DR

This paper investigates how general boundary conditions affect the Casimir vacuum energy between plates, revealing conditions for attractive, repulsive, or null forces, with potential physical implementations using metamaterials.

Contribution

It introduces a comprehensive method to determine the nature of Casimir forces under general boundary conditions, extending beyond traditional cases.

Findings

Periodic boundary conditions produce the strongest attractive force.

Anti-periodic boundary conditions yield the strongest repulsive force.

A family of boundary conditions results in no Casimir force.

Abstract

The infrared behavior of quantum field theories confined in bounded domains is strongly dependent on the shape and structure of space boundaries. The most significant physical effect arises in the behaviour of the vacuum energy. The Casimir energy can be attractive or repulsive depending on the nature of the boundary. We calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary conditions depending on four parameters. The analysis provides a powerful method to identify which boundary conditions generate attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We also show that the attractive regime holds far beyond identical boundary conditions for the two plates required by the Kenneth-Klich theorem and that the strongest attractive Casimir force appears for periodic boundary conditions whereas the strongest repulsive Casimir force corresponds to anti-periodic boundary conditions. Most of the analysed boundary conditions are new and some of them can be physically implemented with metamaterials.