Connes' tangent groupoid and strict quantization
Abstract
We address one of the open problems in quantization theory recently listed by Rieffel. By developing in detail Connes' tangent groupoid principle and using previous work by Landsman, we show how to construct a strict flabby quantization, which is moreover an asymptotic morphism and satisfies the reality and traciality constraints, on any oriented Riemannian manifold. That construction generalizes the standard Moyal rule. The paper can be considered as an introduction to quantization theory from Connes' point of view.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 1999
 DOI:
 10.1016/S03930440(98)00028X
 arXiv:
 arXiv:math/9802102
 Bibcode:
 1999JGP....32...79C
 Keywords:

 Mathematics  Differential Geometry;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Quantum Algebra;
 Quantum Physics;
 81S10 (Primary);
 58H05;
 58H15;
 58B30 (Secondary)
 EPrint:
 LaTeX file, 22 pages (elsart.cls required). Minor changes. Final version to appear in J. Geom. and Phys