Stochastic interpretation of Kadanoff-Baym equations and their relation toLangevin processes

We study stochastic aspects inherent to the (non-)equilibrium real time Gre en's function description (or "closed time path Green's function"-CTPGF) of transport equations, the so-called "Kadanoff-Baym equations." We couple a free scalar boson quantum field to an environmental heat bath with some giv en temperature T. It will be shown hr detail that the emerging transport eq uations have to be understood as the ensemble average over stochastic equat ions of Langevin type. This corresponds to the equivalence of the influence functional approach by Feynman and Vernon and the CTP technique. The forme r, however, gives a more intuitive physical picture. In particular the phys ical role of (quantum) noise and the connection oi its correlation kernel t o the Kadanoff-Baym equations will be discussed in depth. The inherent pres ence of noise and dissipation related by the fluctuation-dissipation theore m guarantees that the modes or particles become thermally populated on aver age in the long-time limit. For long wavelength modes with momenta \k\ much less than T the emerging wave equations behave nearly as classical fields. On the other hand, a kinetic transport description can be obtained in the semi-classical particle regime. Including fluctuations, its form resembles that of a phenomenological Boltzmann-Langevin description. However, we will point out some severe discrepancies in comparison to the Boltzmann Langevi n scheme. As a Further byproduct we also note how the occurrence of so call ed pinch singularities is circumvented by a clear physical necessity of dam ping within the one-particle propagator. (C) 1998 Academic Press.