Connes' Tangent Groupoid and Strict Quantization
微分几何
2016-08-15 v3 高能物理 - 理论
数学物理
math.MP
量子代数
量子物理
摘要
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.
引用
@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}
}
备注
LaTeX file, 22 pages (elsart.cls required). Minor changes. Final version to appear in J. Geom. and Phys