The Casimir interaction of a massive vector field between concentric spherical bodies

TL;DR

This paper calculates the Casimir interaction energy for a massive vector field between concentric spherical bodies, revealing that the force is always attractive and generalizes known massless cases with complex TM mode contributions.

Contribution

It provides a detailed computation of the Casimir energy for a massive vector field in spherical geometry, extending previous massless analyses with new TM mode insights.

Findings

Casimir force is always attractive between the spheres.

TE mode contribution generalizes the massless case.

TM modes are more complex, involving longitudinal and transverse components.

Abstract

The Casimir interaction energy due to the vacuum fluctuations of a massive vector field between two perfectly conducting concentric spherical bodies is computed. The TE contribution to the Casimir interaction energy is a direct generalization of the massless case but the TM contribution is much more complicated. Each TM mode is a linear combination of a transverse mode which is the generalization of a TM mode in the massless case and a longitudinal mode that does not appear in the massless case. In contrast to the case of two parallel perfectly conducting plates, the are no TM discrete modes that vanish identically in the perfectly conducting spherical bodies. Numerical simulations show that the Casimir interaction force between the two bodies is always attractive.