  Based on the equal-time Wigner function for the Klein-Gordon field, we
discuss analytically the mechanism of pair creation in a classical
electromagnetic field including back-reaction. It is shown that the equations
of motion for the Wigner function can be reduced to a variable-frequency
oscillator. The pair-creation rate results then from a calculation analogous to
barrier penetration in nonrelativistic quantum mechanics. The Wigner function
allows one to utilize this treatment for the formulation of an effective
transport theory for the back-reaction problem with a pair-creation source term
including Bose enhancement.
