Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 036, 21 pages      arXiv:0803.4201      https://doi.org/10.3842/SIGMA.2009.036
Contribution to the Special Issue on Deformation Quantization

Three Natural Generalizations of Fedosov Quantization

Klaus Bering
Institute for Theoretical Physics & Astrophysics, Masaryk University, Kotlárská 2, CZ-611 37 Brno, Czech Republic

Received May 19, 2008, in final form February 14, 2009; Published online March 25, 2009

Abstract
Fedosov's simple geometrical construction for deformation quantization of symplectic manifolds is generalized in three ways without introducing new variables: (1) The base manifold is allowed to be a supermanifold. (2) The star product does not have to be of Weyl/symmetric or Wick/normal type. (3) The initial geometric structures are allowed to depend on Planck's constant.

Key words: deformation quantization; Fedosov quantization; star product; supermanifolds; symplectic geometry.

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