, Volume 197, Issue 1, pp 167-197

Fedosov *-Products and Quantum Momentum Maps

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Abstract:

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.

Received: 8 July 1997 / Accepted: 4 March 1998