2003/04/30 by Simone Gutt, John Rawnsley · 35 citations
Mathematics · Physics and Astronomy · #Class (philosophy) #Geometric and Algebraic Topology #Geometry and complex manifolds #Manifold (fluid mechanics) #Moment (physics) #Moment map #Product (mathematics) #Quantum chaos and dynamical systems #Star (game theory) #Star product #Symplectic geometry #math.QA #math.SG #msc:53D55
paper · pdf · doi:10.1023/b:math.0000017717.51035.f1
published in Letters in Mathematical Physics 66(1-2), 123-139 (Springer Science+Business Media) · Expanded bibliography
arxiv created 2003/07/17 · openalex publication_date 2003/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.