Complete positivity and subdynamics in quantum field theory

The relevance that the property of complete positivity has had in the determination of quantum structures is briefly reviewed, together with recent applications to neutron optics and quantum Brownian motion. A possible useful application and generalization of this property to the description of macroscopic systems in quantum mechanics is discussed on the basis of recent work on the derivation of subdynamics in the Heisenberg picture of slowly varying degrees of freedom inside nonrelativistic quantum field theory.