Covariant Weyl quantization, symbolic calculus, and the product formula

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Title: Covariant Weyl quantization, symbolic calculus, and the product formula
Author: Gunturk, Kamil Serkan, 1974-
Abstract: 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.
Publisher: Texas A&M University
Subject: 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
URI: http://handle.tamu.edu/1969.1/3963
Date: 2003-05

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