The Casimir Effect in Spheroidal Geometries

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.

24 pages, 3 figures. To appear in Phys. Rev. D

References in corpus (6)

• Scattering Theory Approach to Electrodynamic Casimir Forces
• Zeta Functions and the Casimir Energy
• Measurement of the Casimir force between a gold sphere and silicon surface with nanoscale trench arrays
• Casimir interaction of dielectric gratings
• Recent Developments in the Casimir Effect
• Perturbative zero-point energy for a cylinder of elliptical section

Cited by in corpus (3)

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• Vacuum Polarization and Casimir Energy of a Dirac Field Induced by a Scalar Potential in One Spatial Dimension