Renormalized Effective Actions in Radially Symmetric Backgrounds: Exact Calculations Versus Approximation Methods

TL;DR

This paper compares exact numerical calculations of scalar one-loop effective actions in radially symmetric backgrounds with approximation methods, evaluating their accuracy and validity ranges.

Contribution

It introduces an effective combination of the partial wave cutoff method with WKB series for precise evaluation of effective actions in symmetric backgrounds.

Findings

The partial wave cutoff method provides accurate results for scalar effective actions.

WKB series effectively approximates large partial wave contributions.

Approximation methods have specific validity ranges confirmed by comparisons.

Abstract

Our previously-developed calculational method (the partial wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge fields. Our method proves to be particularly effective when it is used in conjunction with a systematic WKB series for the large partial wave contribution to the effective action. By comparing these numerically exact calculations against the predictions based on the large mass expansion and derivative expansion, we discuss the validity ranges of the latter approximation methods.