Fermionic van der Waals and Casimir-Polder interactions

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.