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

January 26, 2015

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. For sub-critical
peak field strengths, or results agree very well with the general expression
derived by Serber for the linearization in the external field. In particular,
the expectation value of the current density at intermediate times can be much
greater than at asymptotic times. We comment on consequences of these findings
for recent proposals to test the Schwinger effect with high intensity lasers
using processes at intermediate times.

Keywords:

locally covariant quantum field theory, external potentials