Applicability of the Wigner functional approach to evolution of quantum   fields
  Evolution of highly excited quantum field is considered in the framework of Keldysh formalism . It is demonstrated that leading order (LO) term of semiclassical approximation appears as well-known Classical Statistical Approximation (CSA). In simple case of spatially homogeneous scalar field analytical expressions for leading and next-to-leading (NLO) order are presented. It is shown that the range of applicability of CSA strongly depends on the properties of the initial state of the system 
Andrey Leonidov, Anna Radovskaya
hep-ph nucl-th