The Free Stochastic Limit of Interacting Quantum Fields

Abstract

The problem of obtaining the quantum stochastic limit for a system interacting with a reservoir is investigated when both are considered as quantum fields. The pre-limit fields are as encountered in standard quantum field theory and in particular we do not resort to the simplifying responseless interaction for the reservoir field. In the separation of time scales between the unperturbed (slow) and interaction (fast) dynamics we find a new quantum stochastic noise emerging which describes multi-particle scatterings and has extended free statistics. We give explicit diagrammatic rules to compute the 2n-point correlators of the noise.