  Exact analytical solutions are presented for the time evolution of the
density of pairs produced in the QED vacuum by a time-independent, uniform
electric field. The mathematical tool used here to describe the pair production
is the Dirac-Heisenberg-Wigner function introduced before [Phys. Rev. D 44,
1825 (1991)]. The initial value problem for this function is solved by
decomposing the solution into a product of spinors. The equations for spinors
are much simpler and are solved analytically. These calculations are
nonperturbative since pair production is due to quantum-mechanical tunneling
and the explicit solutions clearly exhibit their nonanalytic behavior.
