A formal Fedosov-type quantization of the standard contact seven-sphere converges, at Planck constants hbar=1/m, to finite-dimensional unitary representations of U(2,H) and yields quantum dynamical systems on subbundles.
Contact Geometry and Quantum Mechanics
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We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics.
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Seven Sphere Quantization
A formal Fedosov-type quantization of the standard contact seven-sphere converges, at Planck constants hbar=1/m, to finite-dimensional unitary representations of U(2,H) and yields quantum dynamical systems on subbundles.