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.
- E-Print:
- 21 pages, LaTeX. v2,v3,v4,v5: Minor changes, v6: References added, v7,v8: Minor changes, v9: Published version