RENORMALIZATION OF THE CHARGED SCALAR FIELD IN CURVED SPACE

The DeWitt-Schwinger proper time point-splitting procedure is applied to a massive complex scalar held with an arbitrary curvature coupling interacting with a classical electromagnetic field in a general curved spacetime. The scalar field current is found to have a linear diverge nce. The presence of the external background gauge field is found to m odify the stress-energy tensor results of Christensen for the neutral scalar held by adding terms of the form (eF)(2) to the logarithmic cou nterterms. These results are shown to be expected from an analysis of the degree of divergence of scalar quantum electrodynamics.