Geometrical origin of the ∗product in the Fedosov formalism
Abstract
The construction of the ∗product proposed by Fedosov is implemented in terms of the theory of fibre bundles. The geometrical origin of the Weyl algebra and the Weyl bundle is shown. Several properties of the product in the Weyl algebra are proved. Symplectic and abelian connections in the Weyl algebra bundle are introduced. Relations between them and the symplectic connection on a phase space M are established. Elements of differential symplectic geometry are included. Examples of the Fedosov formalism in quantum mechanics are given.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 November 2005
 DOI:
 10.1016/j.geomphys.2004.12.010
 arXiv:
 arXiv:hepth/0405157
 Bibcode:
 2005JGP....55..316G
 Keywords:

 02.40.Hw;
 03.65.Ca;
 Classical differential geometry;
 Formalism;
 High Energy Physics  Theory
 EPrint:
 LaTeX, 39 pages