Connes' Tangent Groupoid and Strict Quantization
Carinena, José F. ; Clemente-Gallardo, Jesús ; Follana, Eduardo ; Gracia-Bondía, José M. ; Rivero, Alejandro ; Varilly, Joseph C.
arXiv, 9802102 / Harvested from arXiv
Text on arXiv
We address one of the open problems in quantization theory recently listed by Rieffel. By developping 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.
Publié le : 1998-02-20
Classification:  Mathematics - Differential Geometry,  High Energy Physics - Theory,  Mathematical Physics,  Mathematics - Quantum Algebra,  Quantum Physics,  81S10 (Primary), 58H05, 58H15, 58B30 (Secondary) 
@article{9802102,
     author = {Carinena, Jos\'e F. and Clemente-Gallardo, Jes\'us and Follana, Eduardo and Gracia-Bond\'\i a, Jos\'e M. and Rivero, Alejandro and Varilly, Joseph C.},
     title = {Connes' Tangent Groupoid and Strict Quantization},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9802102}
}

Carinena, José F.; Clemente-Gallardo, Jesús; Follana, Eduardo; Gracia-Bondía, José M.; Rivero, Alejandro; Varilly, Joseph C. Connes' Tangent Groupoid and Strict Quantization. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9802102/