Kinetic Equations from the Two – Particle – Irreducible 1 / N – Expansion

We present kinetic equations that describe the evolution of O(N)–symmetric real scalar quantum fields out of thermal equilibrium in a systematic nonperturbative approximation scheme. This description starts from the 1/N –expansion of the 2PI effective action to next–to–leading order, which includes scattering and memory effects. From this starting point one is lead to evolution equations for the propagator, which are nonlocal in time. Numerical solutions showed that the propagator depends only very slightly on the center coordinates already after moderate times, and that correlations between earlier and later times are suppressed exponentially, which causes an effective memory loss. Exploiting these two observations, we combine a first order gradient expansion with a Wigner transformation to derive our kinetic equations, which are local in time, from the nonlocal evolution equations. In contrast to standard descriptions based on loop expansions, our kinetic equations remain valid even for nonperturba-tively large fluctuations. Additionally, employing a quasi–particle approximation, we eventually arrive at a generalized Boltzmann equation.