The Fuzzy S^4 by Quantum Deformation
High Energy Physics - Theory
2010-04-05 v1
Abstract
The fuzzy algebra of S^4 is discussed by quantum deformation. To this end we embed the classical S^4 in the Kaehler coset space SO(5)/U(2). The harmonic functions of S^4 are constructed in terms of the complex coordinates of SO(5)/U(2). Being endowed with the symplectic structure they can be deformed by the Fedosov formalism. We show that they generate the fuzzy algebra \hat A_\infty (S^4) under the * product defined therein, by using the Darboux coordinate system. The fuzzy spheres of higher even dimensions can be discussed similarly. We give basic arguments for the generalization as well.
Keywords
Cite
@article{arxiv.hep-th/0212214,
title = {The Fuzzy S^4 by Quantum Deformation},
author = {S. Aoyama and T. Masuda},
journal= {arXiv preprint arXiv:hep-th/0212214},
year = {2010}
}
Comments
20 pages, LaTex, no figure