Deformation Quantization of Symplectic Fibrations
Abstract
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 starproduct.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 1998
 DOI:
 10.48550/arXiv.math/9802070
 arXiv:
 arXiv:math/9802070
 Bibcode:
 1998math......2070K
 Keywords:

 Quantum Algebra;
 Differential Geometry;
 58F06;
 81S10;
 58H15;
 32G08
 EPrint:
 35 pages, uses pbdiagram,lamsarrow,pblams