Communications in Mathematical Physics

, Volume 197, Issue 1, pp 167–197

Fedosov *-Products and Quantum Momentum Maps

DOI: 10.1007/s002200050446

Cite this article as:
Xu, P. Comm Math Phys (1998) 197: 167. doi:10.1007/s002200050446


The purpose of this paper is to study various aspects of star products on a symplectic manifold related to the Fedosov method. By introducing the notion of “quantum exponential maps” we give a characterization of Fedosov connections. As an application, 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, we find that every *-product is equivalent to a Vey *-product, a classical result of Lichnerowicz. Quantization of a hamiltonian G-space, and in particular, quantum momentum maps are studied. Lagrangian submanifolds are also studied under a deformation quantization.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • P. Xu
    • 1
  1. 1.Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.¶E-mail: ping@math.psu.eduUS

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