Geometrical origin of the *-product in the Fedosov formalism
arXiv:hep-th/0405157 · doi:10.1016/j.geomphys.2004.12.010
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.
arXiv commentLaTeX, 39 pages
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- Remarks on generalized Fedosov algebras
- Local differential calculus over Fedosov algebra
- Deformation Quantization: From Quantum Mechanics to Quantum Field Theory