Matrix algebras converge to the sphere for quantum Gromov--Hausdorff distance
Operator Algebras
2007-05-23 v2 High Energy Physics - Theory
Metric Geometry
Representation Theory
Quantum Physics
Abstract
On looking at the literature associated with string theory one finds statements that a sequence of matrix algebras converges to the 2-sphere (or to other spaces). There is often careful bookkeeping with lengths, which suggests that one is dealing with ``quantum metric spaces''. We show how to make these ideas precise by means of Berezin quantization using coherent states. We work in the general setting of integral coadjoint orbits for compact Lie groups.
Keywords
Cite
@article{arxiv.math/0108005,
title = {Matrix algebras converge to the sphere for quantum Gromov--Hausdorff distance},
author = {Marc A. Rieffel},
journal= {arXiv preprint arXiv:math/0108005},
year = {2007}
}
Comments
28 pages. various minor improvements.To appear Memoirs Amer. Math. Soc