Ferminoic Casimir effect between spheres

TL;DR

This paper derives the Casimir interaction energy between two spheres for massless Dirac fields with MIT-bag boundary conditions, providing explicit formulas and analyzing behavior at large and small separations.

Contribution

It introduces a new operator approach to derive the TGTG-formula for fermionic Casimir interactions between spheres, including explicit translation matrices.

Findings

Casimir energy scales as L^{-5} at large separation

Leading order matches proximity force approximation

Next-to-leading order compared to scalar and electromagnetic cases

Abstract

We consider the Casimir interaction between two spheres corresponding to massless Dirac fields with MIT-bag boundary conditions. Using operator approach, we derive the TGTG-formula for the Casimir interaction energy between the two spheres. A byproduct is the explicit formula for the translation matrix that relates the fermionic spherical waves in different coordinate systems. In the large separation limit, it is found that the order of the Casimir interaction energy is $L^{-5}$, where $L$ is the separation between the centers of the spheres. This order is intermediate between that of two Dirichlet spheres (of order $L^{-3}$) and two Neumann spheres (of order $L^{-7}$). In the small separation limit, we derive analytically the asymptotic expansion of the Casimir interaction energy up to the next-to-leading order term. The leading term agrees with the proximity force approximation. The result for the next-to-leading order term is compared to the corresponding results for scalar fields and electromagnetic fields.