QED effective action for an O(2)xO(3) symmetric field in the full mass range

TL;DR

This paper numerically analyzes the QED effective action for O(2)xO(3) symmetric fields across all mass ranges, confirming asymptotic behaviors and the finiteness of the massless limit after anomaly removal.

Contribution

It applies the partial-wave-cutoff method to compute the effective action in full mass range, including massless limit, for the first time with detailed numerical validation.

Findings

Matching asymptotic behavior at large mass

Finite effective action in the massless limit after anomaly removal

Numerical results consistent with theoretical predictions

Abstract

An interesting class of background field configurations in QED are the O(2)xO(3) symmetric fields. Those backgrounds have some instanton-like properties and yield a one-loop effective action that is highly nontrivial but amenable to numerical calculation, for both scalar and spinor QED. Here we use the recently developed "partial-wave-cutoff method" for a numerical analysis of both effective actions in the full mass range. In particular, at large mass we are able to match the asymptotic behavior of the physically renormalized effective action against the leading two mass levels of the inverse mass (or heat kernel) expansion. At small mass we obtain good numerical results even in the massless case for the appropriately (unphysically) renormalized effective action after the removal of the chiral anomaly term through a small radial cutoff factor. In particular, we show that the effective action after this removal remains finite in the massless limit, which also provides indirect support for M. Fry's hypothesis that the QED effective action in this limit is dominated by the chiral anomaly term.