Connes' Tangent Groupoid and Strict Quantization
Differential Geometry
2016-08-15 v3 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Algebra
Quantum Physics
Abstract
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.
Cite
@article{arxiv.math/9802102,
title = {Connes' Tangent Groupoid and Strict Quantization},
author = {José F. Carinena and Jesús Clemente-Gallardo and Eduardo Follana and José M. Gracia-Bondía and Alejandro Rivero and Joseph C. Varilly},
journal= {arXiv preprint arXiv:math/9802102},
year = {2016}
}
Comments
LaTeX file, 22 pages (elsart.cls required). Minor changes. Final version to appear in J. Geom. and Phys