  A quantum kinetic equation is derived for the description of pair production
in a time-dependent homogeneous electric field $E(t)$. As a source term, the
Schwinger mechanism for particle creation is incorporated. Possible particle
production due to collisions and collisional damping are neglected. The main
result is a kinetic equation of non-Markovian character. In the low density
approximation, the source term is reduced to the leading part of the well known
Schwinger formula for the probability of pair creation. We discuss the momentum
and time dependence of the derived source term and compare with other
approaches.
