Abstract
Starting from the axioms of quantum mechanics as formalized by the systems of imprimitivity for homogeneous Riemannian manifolds, the classical theory is derived as a consequence, complete with its phase space realized as the space of pure classical states, a generalized version of the Wigner–Moyal correspondence rule, the Jordan and Lie algebra structures of functions on the cotangent bundle, given by point-wise multiplication and Poisson bracket, and the momentum map. A comparison is also given of the quantum and classical dynamics and equilibrium statistical mechanics of free particles on compact manifolds of constant negative curvature.
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