Time evolution automorphisms in generalized mean-field theories

A general class of time evolutions τQ of infinite quantum systems is rigorously defined. It generalizes thermodynamic limits of polynomial mean-field evolution of quantum spin lattices, the simplest case of which is the strong coupling version of the quasi spin B.C.S.-model of superconductivity. A distinguished feature of the considered type of time evolution is the τQ-non-invariance of the usually considered C*-algebra A of quasilocal observables of the infinite system. A larger C*-algebra C containing A as a subalgebra is introduced in such a way that τQ has a natural extension to a one-parameter group of *-automorphisms of C. Algebra C contains a commutative subalgebra of classical observables (consisting of the intensive observables of the large quantal system determined by a Lie group G action σ(G) is an element of *-aut A) denoted by N which is τQ invariant and the restriction of τQ to N reproduces the classical Hamiltonian flow φQ corresponding to the chosen classical Hamiltonian function Q on the classical phase space of the intensive observables. The evolution τQ is determined uniquely by the classical Hamiltonian function Q as well as by the action σ(G). The continuity properties of τQ are considered and reviewed. (author). 13 refs