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

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