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

Abstract

It is known that the one-loop effective action of ${\mathrm{QED}}_{2}$ is a quadratic in the field strength when the fermion mass is zero: all potential higher order contributions beyond second order vanish. For a 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 $\ensuremath{\Phi}$ satisfies $0l|e\ensuremath{\Phi}|l2\ensuremath{\pi}.$ For ${\mathrm{QED}}_{4}$ with (anti-)self-dual fields the mass-shell renormalized one-loop effective action vanishes for at least one value of the fermion mass provided a plausible zero-mass limit exists.