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In the framework of quantum electrodynamics (QED) in external potentials, weintroduce a method to compute the time-dependence of the expectation value ofthe current density for time-dependent homogeneous external electric fields. Weapply it to the so-called Sauter pulse. For late times, our results agree withthe asymptotic value due to electron-positron pair production. We correct, andcompare to, a general expression derived by Serber for the linearization in theexternal field. Based on the properties of the current density, we argue thatthe appearance of enhanced quasi-particle densities at intermediate times inslowly varying sub-critical potentials is generic. Also an alternativeapproach, which circumvents these difficulties, is sketched.

The current density in quantum electrodynamics in time-dependent external potentials and the Schwinger effect