Stochastic interpretation of Kadanoff-Baym equations

Abstract

We show that the nonperturbative transport equations, the so called `Kadanoff-Baym equations', within the non-equilibrium real time Green's function description can be be understood as the ensemble average over stochastic equations of Langevin type. For this we couple a free scalar boson quantum field to an environmental heat bath with some given temperature T. The inherent presence of noise and dissipation related by the fluctuation-dissipation theorem guarantees that the modes or particles become thermally populated on average in the long-time limit. This interpretation leads to a more intuitive physical picture of the process of thermalization and of the interpretation of the Kadanoff-Baym equations. One also immediately understands that the emerging wave equations for long wavelength modes with momenta much smaller than temperature behave nearly as classical fields. We also demonstrate how the problem of so called pinch singularities is resolved by a clear physical necessity of damping within the one-particle propagator. The occurrence of such ill-defined terms arising solely in a strictly perturbative expansion in out of equilibrium quantum field theory has a natural interpretation in analogy to Fermi's golden rule.