New asymptotic techniques for the partial-wave-cutoff method for calculating the QED one-loop effective action

Abstract

The Gel’fand–Yaglom theorem has been used to calculate the one-loop effective action in quantum field theory (QFT) by means of the “partial-wave-cutoff method.” This method works well for a class of radially symmetric background fields, allowing the inclusion of an arbitrary profile function in the background and does not require approximations. However, its implementation has been semi-analytical so far since it involves solving a nonlinear ordinary differential equation (ODE) for which solutions are in general only available in numerical form. Within the context of quantum electrodynamics (QED) and [Formula: see text] symmetric backgrounds, we present two complementary asymptotic methods that provide approximate analytical solutions to this equation. We test these approximations for different background field configurations and mass regimes, and demonstrate that the effective action can indeed be calculated using these asymptotic expressions. To further probe one of these methods, we analyze the massless limit of the effective action and obtain its divergence structure with respect to the radial suppression parameter of the background field, comparing our findings with previously reported results.