Renormalization of the charged scalar field in curved space

TL;DR

This paper applies the DeWitt-Schwinger proper time method to analyze the renormalization of a charged scalar field in curved spacetime, revealing divergence structures and modifications due to electromagnetic interactions.

Contribution

It extends the renormalization analysis of scalar fields in curved space to include electromagnetic interactions and external gauge fields.

Findings

Scalar current exhibits linear divergence.

Electromagnetic background modifies stress-energy tensor counterterms.

Results align with scalar quantum electrodynamics divergence analysis.

Abstract

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