Quantum Electromagnetic Zero-Point Energy of a Conducting Spherical Shell

Abstract

The quantum zero‐point energy of a conducting spherical shell was first calculated by Boyer [Phys. Rev. 174, 1764 (1968)]. Because of the importance of this calculation and also of Boyer's uncertainty about the analytical dependence of the energy on the cutoff function, we have checked the calculation independently. We determine an analytic continuation of the energy function using the Mellin transform, and thereby show how an exact value of the self‐energy can be obtained from the divergent series. We also compute an approximate value of the self‐energy by extrapolating a direct numerical evaluation of the cutoff integrals. These calculations confirm Bover's result.