Fedosov *products and quantum momentum maps
Abstract
We study various aspects of Fedosov starproducts on symplectic manifolds. By introducing the notion of "quantum exponential maps", we give a criterion characterizing Fedosov connections. As a consequence, a geometric realization is obtained for the equivalence between an arbitrary *product and a Fedosov one. Every Fedosov *product is shown to be a Vey *product. Consequently, one obtains that every *product is equivalent to a Vey * product, a classical result of Lichnerowicz. Quantization of a hamiltonian Gspace, and in particular, quantum momentum maps are studied. Lagrangian submanifolds are also studied under a deformation quantization.
 Publication:

eprint arXiv:qalg/9608006
 Pub Date:
 August 1996
 DOI:
 10.48550/arXiv.qalg/9608006
 arXiv:
 arXiv:qalg/9608006
 Bibcode:
 1996q.alg.....8006X
 Keywords:

 Mathematics  Quantum Algebra;
 58F05
 EPrint:
 LaTeX 2e, 34 pages