On the fermionic van der Waals and Casimir-Polder interactions

TL;DR

This paper develops fermionic analogs of van der Waals and Casimir-Polder interactions across multiple dimensions, revealing that certain configurations produce repulsive forces, expanding understanding of quantum field interactions with localized systems.

Contribution

It introduces fermionic versions of van der Waals and Casimir-Polder interactions for any number of dimensions, with novel properties such as repulsion under specific boundary conditions.

Findings

Fermionic interactions are formulated in multiple dimensions.

Bag-model boundary conditions lead to repulsive Casimir-Polder forces.

The interactions involve two-level systems coupled to a Dirac vacuum field.

Abstract

We formulate fermionic versions, for any number of spatial dimensions, of the van der Waals and Casimir-Polder interactions, and study their properties. In both cases, the systems we introduce contain localized `atoms': two-level systems, coupled to a vacuum Dirac field. This Dirac field plays here a role akin to the electromagnetic field in the van der Waals case. In this context, bag-model conditions for the Dirac field serve as the analog of the 'mirror' in the Casimir-Polder effect. We found that, in this case, the resulting interaction is repulsive.