Fedosov ∗-products and quantum momentum maps
نویسنده
چکیده
The purpose of the 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 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 G-space, and in particular, quantum momentum maps are studied. Lagrangian submanifolds are also studied under a deformation quantization.
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