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

The Gel'fand-Yaglom theorem has been used to calculate the one-loop effective action in quantum field theory by means of "partial-wave-cutoff method". This method works well for a wide class background fields and is essentially exact. However, its implementation semi-analytical so far since it involves solving non-linear ordinary differential equation which solutions are general unknown. Within context electrodynamics (QED) $O(2)\times O(3)$ symmetric backgrounds, we present two complementary asymptotic methods that provide approximate analytical this equation. We test these approximations different configurations mass regimes demonstrate can indeed be calculated with good accuracy using expressions. To further probe methods, analyze massless limit obtain divergence structure respect radial suppression parameter field, comparing our findings previously reported results.