QUANTUM STOCHASTIC FEYNMAN-RULES AND EXTENDED WIGNER STATISTICS

We introduce a Feynman diagram calculus for quantum stochastic fields and show that from the weak coupling limit of a Bose quantum field res ervoir in a Gaussian state one obtains a quantum stochastic field proc ess which has extended Wigner statistics. That is, we calculate explic itly the moments using the diagram rules and show that only moments co rresponding to non-crossing diagrams are non-trivial. We further give the physical mechanism underlying this fact; namely the combination of momentum conservation (arising from the correct treatment of the full responsive interaction) and the mass-shell energy conservation for th e virtual (stochastic) reservoir quanta. In our analysis we introduce a volume cut-off initially for the system particle to discretize its e nergy spectrum and then take the weak coupling limit. The individual n oise fields associated with energy state transitions were Gaussian how ever, when the volume cut-off is then removed and we recover the noise correlations. Thus for this problem the removal of the cut-off and th e weak coupling limit are in fact interchangeable.