Mass zeros in the one-loop effective actions of QED in 1+1 and 3+1 dimensions

TL;DR

This paper investigates the behavior of the one-loop effective actions in QED in 1+1 and 3+1 dimensions, revealing conditions under which the actions vanish or simplify depending on the fermion mass and external field flux.

Contribution

It demonstrates that the quadratic nature of the effective action in massless QED persists for certain nonzero masses and flux conditions, extending understanding of mass effects in quantum field theory.

Findings

Effective action in QED2 remains quadratic for specific nonzero masses and fluxes.

In QED4, the effective action vanishes at certain fermion masses for particular gauge fields.

The results suggest a connection between massless limits and effective action behavior in different dimensions.

Abstract

It is known that the one-loop effective action of ${QED}_2$ is a quadratic in the field strength when the fermion mass is zero: all potential higher order contributions beyond second order vanish. For nonzero fermion mass it is shown that this behavior persists for a general class of fields for at least one value of the fermion mass when the external field's flux $\Phi$ satisfies $0<|e\Phi|<2\pi$. For ${QED}_4$ the mass-shell renormalized one-loop effective action vanishes for at least one value of the fermion mass for a class of smooth, square integrable background gauge fields provided a plausible zero-mass limit exists.