Fuzzy Sphere and Hyperbolic Space from Deformation Quantization
High Energy Physics - Theory
2010-02-03 v3
Abstract
We explicitly construct noncommutative * products on circularly symmetric two dimensional space by using the technique of Fedosov's deformation quantization. Especially, on constant curvature spaces i.e., S^2 and H^2, we get su(2) and su(1,1) algebra respectively. These are candidates of * products applicable to noncommutative field theories or noncommutative gauge theories on spaces with nontrivial symplectic structure.
Cite
@article{arxiv.hep-th/0103018,
title = {Fuzzy Sphere and Hyperbolic Space from Deformation Quantization},
author = {Isao Kishimoto},
journal= {arXiv preprint arXiv:hep-th/0103018},
year = {2010}
}
Comments
10pages, references added, typos corrected