Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic Shells

TL;DR

This paper provides semiclassical estimates of electromagnetic Casimir energies for spherical and cylindrical shells, closely matching field theory results and highlighting the role of diffraction and fluctuations in these geometries.

Contribution

It introduces semiclassical methods to estimate Casimir energies for spherical and cylindrical shells, emphasizing the role of periodic rays and diffraction effects.

Findings

Semiclassical estimates are within 1% of field theoretical values.

Casimir energy is mainly due to quadratic fluctuations of periodic rays.

Diffraction significantly influences the Casimir energy of cylindrical shells.

Abstract

The leading semiclassical estimates of the electromagnetic Casimir stresses on a spherical and a cylindrical metallic shell are within 1% of the field theoretical values. The electromagnetic Casimir energy for both geometries is given by two decoupled massless scalars that satisfy conformally covariant boundary conditions. Surface contributions vanish for smooth metallic boundaries and the finite electromagnetic Casimir energy in leading semiclassical approximation is due to quadratic fluctuations about periodic rays in the interior of the cavity only. Semiclassically the non-vanishing Casimir energy of a metallic cylindrical shell is almost entirely due to Fresnel diffraction.