A simple out-of-equilibrium field theory formalism ?

In this paper, we determine a condition of applicability of a very simple formalism for the calculation of a fast process taking place in a non-equilibrium medium, in which the particle distribution functions are frozen in time. Indeed, a well known obstacle for the use of such a naive formalism is the appearance of the so-called ``pinch singularities''. We argue that these potentially dangerous terms can be regularized, and that they are negligible if the characteristic time-scale of the process under study is small compared to the relaxation time of the system.