Three Natural Generalizations of Fedosov Quantization
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.
 Publication:

SIGMA
 Pub Date:
 March 2009
 DOI:
 10.3842/SIGMA.2009.036
 arXiv:
 arXiv:0803.4201
 Bibcode:
 2009SIGMA...5..036B
 Keywords:

 deformation quantization;
 Fedosov quantization;
 star product;
 supermanifolds;
 symplectic geometry;
 Mathematics  Quantum Algebra;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Symplectic Geometry;
 53D05;
 53D55;
 58A15;
 58A50;
 58C50;
 58Z05.
 EPrint:
 21 pages, LaTeX. v2,v3,v4,v5: Minor changes, v6: References added, v7,v8: Minor changes, v9: Published version