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