Quantum stochastic linearization of multi-Linear interactions

The weak coupling limit for a quantum system, with discrete spectrum, in interaction with a quantum field reservoir is considered. Depending on the nature of the reservoir (i.e. bosonic or fermionic) and the degree of nonlinearity of the interaction, we discover that either a bosonization or fermionization of the collective multi-linear reservoir operators emerges. The stochastic evolution is determined after the weak coupling limit and is shown to be unitary: also we show that our calculations for the system-only dynamics coincide with those previously postulated by physicists.