ABSTRACT: A method of quantization for non-relativistic physical systems S on a Riemannian manifold M is discussed. To characterize the method, we deduce from geometric considerations abstract postulates consistent with the principles laid down by axiomatic quantum mechanics. We construct a large variety of such quantizations and show that this variety is determined by the topology of M. The problem of finding the “correct” quantum description for a system S on M is discussed. Group actions on M lead, inside the given mathematical framework, to systems of imprimitivity on M.
Physica A: Statistical Mechanics and its Applications.