  A quantum kinetic equation has been 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 closed kinetic equation of the non-Markovian type. 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
compare the formula obtained with other approaches and discuss the differences.
