  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.
