Natural star products on symplectic manifolds and quantum moment maps

Details Natural star products on symplectic manifolds and quantum moment maps Natural star products on symplectic manifolds and quantum moment maps

2003-04-30

arxiv.org/abs/math/0304498v2

Mathematics

Symplectic Geometry

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Scientific paper

10.1023/B:MATH.0000017717.51035.

We define a natural class of star products: those which are given by a series of bidifferential operators which at order $k$ in the deformation parameter have at most $k$ derivatives in each argument. We show that any such star product on a symplectic manifold defines a unique symplectic connection. We parametrise such star products, study their invariance and give necessary and sufficient conditions for them to yield a quantum moment map. We show that Kravchenko's sufficient condition for a moment map for a Fedosov star product is also necessary.

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