Interpretation and resolution of pinch singularities in non-equilibrium quantum field theory

Abstract

Ill-defined pinch singularities arising in a perturbative expansion in out of equilibrium quantum field theory have a natural analogue to standard scattering theory. We explicitly demonstrate that the occurrence of such terms is directly related to Fermi's golden rule known from elementary scattering theory and is thus of no mystery. We further argue that within the process of thermalization of a plasma one has to resum such contributions to all orders as the process itself is of non-perturbative nature. In this way the resummed propagators obtain a finite width. Within the Markov approximation of kinetic theory the actual phase space distribution at a given time of the evolution enters explicitly.