  We apply the formalism of Chiral Perturbation Theory out of thermal
equilibrium to describe explosive production of pions via the parametric
resonance mechanism. To lowest order the lagrangian is that of the Nonlinear
Sigma Model where the pion decay constant becomes a time-dependent function.
This model alows for a consistent nonequilibrium formulation within the
framework of the closed time path method, where one-loop effects can be
systematically accounted for and renormalized. We work in the narrow resonance
regime where there is only one resonant band. The present approach is limited
to remain below the back-reaction time, although it accounts for nearly all the
pion production during the typical plasma lifetime. The space and time
components of the pion decay constant are also analyzed.
