The Derivative Expansion at Small Mass for the Spinor Effective Action

TL;DR

This paper investigates the small mass limit of the one-loop spinor effective action, comparing derivative expansion approximations with exact numerical results for radially symmetric gauge fields in spinor QED.

Contribution

It introduces an extension of the partial-wave-cutoff method to spinor theories and highlights differences in the small mass behavior between spinor and scalar cases.

Findings

Derivative expansion differs from exact results at small mass for spinor theories.

Numerical methods provide precise calculations of the effective action.

Differences between spinor and scalar theories in the small mass limit are significant.

Abstract

We study the small mass limit of the one-loop spinor effective action, comparing the derivative expansion approximation with exact numerical results that are obtained from an extension to spinor theories of the partial-wave-cutoff method. In this approach one can compute numerically the renormalized one-loop effective action, for radially separable gauge field background fields in spinor QED. We highlight an important difference between the small mass limit of the derivative expansion approximation for spinor and scalar theories.