Geometrical origin of the *-product in the Fedosov formalism

[摘要] 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. (c) 2005 Elsevier B.V. All rights reserved.

[发布日期] 2005-11-01

[关键词] Weyl bundle;connection in a vector bundle;deformation quantization;Fedosov formalism