Quantization and the tangent groupoid
数学物理
2007-05-23 v2 math.MP
算子代数
摘要
This is a survey of the relationship between C*-algebraic deformation quantization and the tangent groupoid in noncommutative geometry, emphasizing the role of index theory. We first explain how C*-algebraic versions of deformation quantization are related to the bivariant E-theory of Connes and Higson. With this background, we review how Weyl--Moyal quantization may be described using the tangent groupoid. Subsequently, we explain how the Baum--Connes analytic assembly map in E-theory may be seen as an equivariant version of Weyl--Moyal quantization. Finally, we expose Connes's tangent groupoid proof of the Atiyah--Singer index theorem
引用
@article{arxiv.math-ph/0208004,
title = {Quantization and the tangent groupoid},
author = {N. P. Landsman},
journal= {arXiv preprint arXiv:math-ph/0208004},
year = {2007}
}
备注
16 pages, Proc. Constanta 2001