Covariant Weyl quantization, symbolic calculus, and the product formula
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.
Subject
Weyl quantizationWeyl calculus
symbolic calculus
pseudo-differential operators
differential geometry
point seperation method
Wigner function
world function
semi-classical physics
Faa di Bruno formula
Citation
Gunturk, Kamil Serkan (2003). Covariant Weyl quantization, symbolic calculus, and the product formula. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /3963.