The symmetric tensor Lichnerowicz algebra and a novel associative Fourier-Jacobi algebra.
Contact Quantization: Quantum Mechanics = Parallel transport
Quantization together with quantum dynamics can be simultaneously formulated as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Contact geometry treats time, generalized positions and momenta as points on an underlying phase-spacetime and reduces classical mechanics to contact topology. Contact quantization describes quantum dynamics in terms of parallel transport for a flat connection; the ultimate goal being to also handle quantum systems in terms...
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