Geometrical origin of the *-product in the Fedosov formalism

Details Geometrical origin of the *-product in the Fedosov formalism Geometrical origin of the *-product in the Fedosov formalism

2004-05-18

arxiv.org/abs/hep-th/0405157v1

J.Geom.Phys.55:316-352,2005

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 39 pages

Scientific paper

10.1016/j.geomphys.2004.12.010

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.

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