On the Algebra of Fluctuation Operators of a Quantum meanfield system

We introduce the notion of a generalized CCR–algebra (GCCR–algebra for short), and we show that certain limit processes in the theory of quantum meanfield systems lead to an algebra of this type, the "algebra of fluctuation operators", in a natural manner. We are able to interpret the generating subset of unitaries as exponentials of fluctuation operators. Moreover we show that the quasifree time evolution on the algebra of fluctuation operators corresponding to a given time evolution of the one–particle system is itself a generalized limit dynamics similar to that one on the intensive observables. The GNS–representation of the algebra corresponding to a product state will give the CCR–algebra of the normal fluctuations of the meanfield system as introduced in [GVV1] and generalized in [GV], [GVV2].