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1	Covariant Weyl quantization, symbolic calculus, and the product formula Gunturk, Kamil Serkan 16 August 2006 (has links) A covariant Wigner-Weyl quantization formalism on the manifold that uses pseudo-differential operators is proposed. The asymptotic product formula that leads to the symbol calculus in the presence of gauge and gravitational fields is presented. The new definition is used to get covariant differential operators from momentum polynomial symbols. A covariant Wigner function is defined and shown to give gauge-invariant results for the Landau problem. An example of the covariant Wigner function on the 2-sphere is also included. Weyl quantization Weyl calculus symbolic calculus pseudo-differential operators differential geometry point seperation method Wigner function world function semi-classical physics Faa di Bruno formula