1998/02/16 by Olga Kravchenko, Kravchenko, Olga
Mathematics · Physics and Astronomy · #32G08 #58F06 #58H15 #81S10 #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.DG #math.QA #msc:32G08 #msc:58F06 #msc:58H15 #msc:81S10
paper · pdf · doi:10.48550/arxiv.math/9802070
35 pages, uses pb-diagram,lamsarrow,pb-lams
arxiv created 1998/02/16 · openalex publication_date 1998/02/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A symplectic fibration is a fibre bundle in the symplectic category. We find the relation between deformation quantization of the base and the fibre, and the total space. We use the weak coupling form of Guillemin, Lerman, Sternberg and find the characteristic class of deformation of symplectic fibration. We also prove that the classical moment map could be quantized if there exists an equivariant connection. Along the way we touch upon the general question of quantization with values in a bundle of algebras. We consider Fedosov's construction of deformation quantization in general. In the Appendix we show how to calculate step by step the Fedosov connection, flat sections of the Weyl algebra bundle corresponding to functions and their star-product.