Derivative expansion at small mass for the spinor effective action

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 for spinor and scalar theories.