The Weyl bundle as a differentiable manifold
Copyright policy )The Weyl bundle as a differentiable manifold
Construction of an infinite dimensional differentiable manifold ${\mathbb R}^{\infty}$ not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra and a Weyl algebra bundle are presented. Continuity of the $\circ$-product in the Tichonov topology is proved. Construction of the $*$-product of the Fedosov type in terms of theory of connection in a fibre bundle is explained.
31 pages; revised version - some typoes have been eliminated, notation has been simplified
- Polish Academy of Sciences Poland
- Institute of Physics Poland
- Lodz University of Technology Poland
Deformation quantization, star products, Applications of variational problems in infinite-dimensional spaces to the sciences, FOS: Physical sciences, Mathematical Physics (math-ph), 53D55, Tichonov topology, 53C07, 53C07;53D55, Geometry and quantization, symplectic methods, Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory, Homotopy and topological questions for infinite-dimensional manifolds, infinite dimensional differentiable manifold, Weyl bundle, Mathematical Physics
Deformation quantization, star products, Applications of variational problems in infinite-dimensional spaces to the sciences, FOS: Physical sciences, Mathematical Physics (math-ph), 53D55, Tichonov topology, 53C07, 53C07;53D55, Geometry and quantization, symplectic methods, Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory, Homotopy and topological questions for infinite-dimensional manifolds, infinite dimensional differentiable manifold, Weyl bundle, Mathematical Physics
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