On the Stochastic Limit of Quantum Field Theory

The weak coupling limit for a quantum system, with discrete energy spectrum, coupled to a Bose reservoir with the most general linear interaction is considered: under this limit we have a quantum noise processes substituting for the field. We obtain a limiting evolution unitary on the system and noise space which, when reduced to the system’s degrees of freedom, provide the master and Langevin equations that are postulated on heuristic grounds by physicists. In addition we give a concrete application of our results by deriving the evolution of an atomic system interacting with the electrodynamic field without recourse to either rotating wave or dipole approximations.