Quantum Hall Effect on the Hyperbolic Plane
dg-ga
2008-11-26 v1 funct-an
高能物理 - 理论
微分几何
泛函分析
摘要
In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables. We define a twisted analogue of the Kasparov map, which enables us to use the pairing between -theory and cyclic cohomology theory, to identify this geometric invariant with a topological index, thereby proving the integrality of the Hall conductivity in this case.
引用
@article{arxiv.dg-ga/9704006,
title = {Quantum Hall Effect on the Hyperbolic Plane},
author = {A. Carey and K. Hannabus and V. Mathai and P. McCann},
journal= {arXiv preprint arXiv:dg-ga/9704006},
year = {2008}
}
备注
AMS-LaTeX, 28 pages