Semiclassical Electromagnetic Casimir Self-Energies

TL;DR

This paper uses semiclassical methods to analyze electromagnetic Casimir energies of spherical and cylindrical cavities, finding good agreement with known results for spheres and revealing boundary-dependent effects for cylinders.

Contribution

It demonstrates the semiclassical calculation of Casimir energies for cavities, clarifies boundary condition effects, and discusses extensions to realistic systems.

Findings

Spherical cavity Casimir energy matches field theory within 1%.

Cylindrical cavity energy vanishes with real reflection coefficients.

Boundary nature critically affects cylindrical Casimir energy calculations.

Abstract

The electromagnetic Casimir energies of a spherical and a cylindrical cavity are analyzed semiclassically. The field theoretical self-stress of a spherical cavity with ideal metallic boundary conditions is reproduced to better than 1%. The subtractions in this case are unambiguous and the good agreement is interpreted as evidence that finite contributions from the exterior of the cavity are small. The semiclassical electromagnetic Casimir energy of a cylindrical cavity on the other hand vanishes to any order in the real reflection coefficients. The Casimir energy of a cylindrical cavity with a perfect metallic and infinitesimally thin boundary on the other hand is finite and negative [17]. Contrary to the spherical case and in agreement with Barton's perturbative analysis [31], the subtractions in the spectral density for the cylinder are not universal when only the interior modes of are taken into account [43]. The Casimir energy of a cylindrical cavity therefore depends sensitively on the physical nature of the boundary in the ultraviolet whereas the Casimir energy of a spherical one does not. The extension of the semiclassical approach to more realistic systems is sketched.