On the QED Effective Action in Time Dependent Electric Backgrounds

Details On the QED Effective Action in Time Dependent Electric Backgrounds On the QED Effective Action in Time Dependent Electric Backgrounds

1998-07-03

arxiv.org/abs/hep-th/9807031v2

Phys.Rev. D58 (1998) 105022

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, no figures; reference added

Scientific paper

10.1103/PhysRevD.58.105022

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.

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