The differential geometry of Fedosov's quantization

Details The differential geometry of Fedosov's quantization The differential geometry of Fedosov's quantization

1993-11-17

arxiv.org/abs/hep-th/9311094v2

Physics

High Energy Physics

High Energy Physics - Theory

20 pages

Scientific paper

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.

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