Applicability of the Wigner functional approach to evolution of quantum fields

TL;DR

This paper explores the use of the Wigner functional approach within the Keldysh formalism to analyze the evolution of highly excited quantum fields, highlighting the conditions under which classical statistical approximation is valid.

Contribution

It demonstrates that the leading order of the semiclassical approximation aligns with the classical statistical approximation and provides analytical expressions for homogeneous scalar fields.

Findings

Leading order matches classical statistical approximation

Applicability of CSA depends on initial state properties

Analytical expressions derived for scalar fields

Abstract

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