Casimir energy of the massless conformal scalar field on S-2 by the point-splitting method

Abstract

We calculate the Casimir energy of the massless conformal scalar field on the surface (S-2) of a 3 dimensional Riemann sphere by using the point-splitting, mode sum and the ζ-function renormalization methods. We also consider the half space case with both the Dirichlet and the Neumann boundary conditions. This problem is interesting since the Casimir energy could be calculated analytically by various methods, thus allowing us to compare different regularization schemes.