Covariant Weyl quantization, symbolic calculus, and the product formula

by Gunturk, Kamil Serkan

Abstract (Summary)
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.
Bibliographical Information:

Advisor:Fulling, Stephen A.; Battle, Guy; Pope, Christopher; Sezgin, Ergin; White, James T.

School:Texas A&M University

School Location:USA - Texas

Source Type:Master's Thesis

Keywords:weyl quantization calculus symbolic pseudo differential operators geometry point seperation method wigner function world semi classical physics faa di bruno formula


Date of Publication:05/01/2003

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