English

The differential geometry of Fedosov's quantization

High Energy Physics - Theory 2009-09-25 v2 Differential Geometry Quantum Algebra

Abstract

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.

Keywords

Cite

@article{arxiv.hep-th/9311094,
  title  = {The differential geometry of Fedosov's quantization},
  author = {Claudio Emmrich and Alan Weinstein},
  journal= {arXiv preprint arXiv:hep-th/9311094},
  year   = {2009}
}

Comments

20 pages

R2 v1 2026-07-22T15:48:01.876Z