On the QED Effective Action in Time Dependent Electric Backgrounds

TL;DR

This paper develops a resolvent technique to compute the QED effective action in time-dependent electric fields, revealing both real and imaginary parts linked to pair production, and derives a general semiclassical expression akin to Schwinger's classic result.

Contribution

It introduces a novel application of the resolvent technique to time-dependent electric backgrounds, connecting magnetic and electric cases via dispersion relations and providing a general semiclassical formula.

Findings

Derived a general semiclassical expression for time-dependent electric fields.

Connected magnetic and electric effective actions through dispersion relations.

Revealed the nonperturbative nature of pair production in electric backgrounds.

Abstract

We apply the resolvent technique to the computation of the QED effective action in time dependent electric field backgrounds. The effective action has both real and imaginary parts, and the imaginary part is related to the pair production probability in such a background. The resolvent technique has been applied previously to spatially inhomogeneous magnetic backgrounds, for which the effective action is real. We explain how dispersion relations connect these two cases, the magnetic case which is essentially perturbative in nature, and the electric case where the imaginary part is nonperturbative. Finally, we use a uniform semiclassical approximation to find an expression for very general time dependence for the background field. This expression is remarkably similar in form to Schwinger's classic result for the constant electric background.