The Casimir Effect in Spheroidal Geometries

TL;DR

This paper investigates the Casimir effect in spheroidal geometries, demonstrating that zero-point energy remains constant under small boundary deformations for scalar fields and exploring implications for the stability of the MIT bag model.

Contribution

It provides analytical and approximate methods to evaluate zero-point energy in spheroidal geometries and tests the boundary deformation conjecture for scalar and vector fields.

Findings

Zero-point energy for scalar fields remains constant under small boundary deformations.

Zonal approximation for vector fields disagrees with the boundary deformation conjecture.

Results suggest the MIT bag model's zero-point energy stabilizes against shape deformations.

Abstract

We study the zero point energy of massless scalar and vector fields subject to spheroidal boundary conditions. For massless scalar fields and small ellipticity the zero-point energy can be found using both zeta function and Green's function methods. The result agrees with the conjecture that the zero point energy for a boundary remains constant under small deformations of the boundary that preserve volume (the boundary deformation conjecture), formulated in the case of an elliptic-cylindrical boundary. In the case of massless vector fields, an exact solution is not possible. We show that a zonal approximation disagrees with the result of the boundary deformation conjecture. Applying our results to the MIT bag model, we find that the zero point energy of the bag should stabilize the bag against deformations from a spherical shape.