Fedosov *-products and quantum momentum maps

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Abstract

The purpose of this paper is to study various aspects of star products on a symplectic manifold related to the Fedosov method. By introducing the notion of "quantum exponential maps" we give a characterization of Fedosov connections. As an application, a geometric realization is obtained for the equivalence between an arbitrary *-product and a Fedosov one. Every Fedosov *-product is shown to be a Vey *-product. Consequently, we find that every *-product is equivalent to a Vey *-product, a classical result of Lichnerowicz. Quantization of a hamiltonian G-space, and in particular, quantum momentum maps are studied. Lagrangian submanifolds are also studied under a deformation quantization.

Original languageEnglish (US)
Pages (from-to)167-197
Number of pages31
JournalCommunications In Mathematical Physics
Volume197
Issue number1
DOIs
StatePublished - Jan 1 1998

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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