Covariant Weyl quantization, symbolic calculus, and the product formula
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.
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