1993/11/17 by C. Emmrich, Claudio Emmrich, A. J. Weinstein +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #hep-th #math.DG #math.QA
paper · pdf · doi:10.48550/arxiv.hep-th/9311094
20 pages
arxiv created 1993/11/19 · arxiv updated 2009/11/30
B. Fedosov has given a simple and very natural construction of a deformation quantization for any symplectic manifold, using a flat connection on the bundle of formal Weyl algebras associated to the tangent bundle of a symplectic manifold. The connection is obtained by affinizing, nonlinearizing, and iteratively flattening a given torsion free symplectic connection. In this paper, a classical analog of Fedosov's operations on connections is analyzed and shown to produce the usual exponential mapping of a linear connection on an ordinary manifold. A symplectic version is also analyzed. Finally, some remarks are made on the implications for deformation quantization of Fedosov's index theorem on general symplectic manifolds.