Simple method for calculating the Casimir energy for sphere

Abstract

A simple method for calculating the Casimir energy for a sphere is developed which is based on a direct mode summation and counter integration in a complex plane of eigenfrequencies. The method uses only classical equations determining the eigenfrequencies of the quantum field under consideration. Efficiency of this approach is demonstrated by calculation of the Casimir energy for a perfectly conducting spherical shell and for a massless scalar field obeying the Dirichlet and Neumann boundary conditions on sphere. The possibility of rationalizing the removal of divergences in this problem as a renormalization of both the energy and the radius of the sphere is discussed.