On the Sign of the Casimir Force Between Two Bodies Coupled to a Dirac field

TL;DR

This paper derives a theorem indicating that the Casimir force between two objects coupled to a Dirac field can be repulsive if their geometric configuration is symmetric under a specific reflection operation, extending previous results.

Contribution

It introduces a new theorem linking geometric symmetry to the sign of the Casimir force for objects coupled to a Dirac field, expanding theoretical understanding.

Findings

Repulsive Casimir force occurs under certain symmetric configurations.

Theorem applies to objects with specific reflection symmetry.

Extends previous work by Kenneth and Klich on Casimir interactions.

Abstract

We apply the result of Kenneth and I. Klich, Phys. Rev. Lett.97, 160401 (2006) to derive a theorem for two objects coupled to a Dirac field. We demonstrate that a sufficient condition for the Casimir interaction to be repulsive, is for their geometric configuration to be odd under the same reflection operation considered in that work.