QUANTUM ANYON-LIKE SYSTEMS WITH TOPOLOGICAL CHARGES ON U(1) BUNDLES

We investigate some classes of locally Hamiltonian systems. To formula te a global Hamiltonian formalism a nontrivial principal U(1) bundle o ver a multi-particle dynamical space is constructed. Lift of dynamics to the total space is considered for the models. Absence of a transpos ition operator lifting to the bundle space forces us to review a stati stics theme from a new standpoint. A topological invariant to characte rize system properties is generalized by using geometrical methods and the anyon analogy.