Casimir Energies for Spherically Symmetric Cavities

TL;DR

This paper provides a comprehensive analytical and numerical framework for calculating Casimir energies in spherically symmetric cavities across various fields, boundary conditions, and dimensions, using Barnes zeta functions.

Contribution

It introduces a general method for computing Casimir energies in arbitrary dimensions for different fields and boundary conditions, with explicit analytical formulas and precise numerical evaluation.

Findings

Derived closed-form expressions using Barnes zeta functions.

Achieved highly accurate numerical results for various configurations.

Unified treatment of scalar, spinor, and electromagnetic fields.

Abstract

A general calculation of Casimir energies --in an arbitrary number of dimensions-- for massless quantized fields in spherically symmetric cavities is carried out. All the most common situations, including scalar and spinor fields, the electromagnetic field, and various boundary conditions are treated with care. The final results are given as analytical (closed) expressions in terms of Barnes zeta functions. A direct, straightforward numerical evaluation of the formulas is then performed, which yields highly accurate numbers of, in principle, arbitrarily good precision.