Pair Production in the Quantum Boltzmann Equation

A source term in the quantum Boltzmann equation, which accounts for the spontaneous creation of $e^{+}{e}^{-}$-pairs in external electric fields, is derived from first principles and evaluated numerically. Careful analysis of time scales reveals that this source term is generally non-Markovian. This implies in particular that there may be temporary violations of the $H$-theorem.