  We prescribe a formulation of the particle production with real-time
Stochastic Quantization. To construct the retarded and the time-ordered
propagators we decompose the stochastic variables into positive- and
negative-energy parts. In this way we demonstrate how to derive a standard
formula for the Schwinger mechanism under time-dependent electric fields. We
discuss a mapping to the Schwinger-Keldysh formalism and a relation to the
classical statistical simulation.
