An invariant approach to dynamical fuzzy spaces with a three-index variable -- Euclidean models
Abstract
A dynamical fuzzy space might be described in terms of a dynamical three-index variable C_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c of the functions f_a on a fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on f_a. The solutions to the invariant equations of motion of C_{ab}^c can be generally constructed from the invariant tensors of Lie groups. Euclidean models the actions of which are bounded from below are introduced. Lie group symmetric solutions to a class of Euclidean model are obtained. The analysis of the fluctuations around the SO(3) symmetric solution shows that the solution can be regarded as a fuzzy S^2/Z_2.
Keywords
Cite
@article{arxiv.hep-th/0511154,
title = {An invariant approach to dynamical fuzzy spaces with a three-index variable -- Euclidean models},
author = {Naoki Sasakura},
journal= {arXiv preprint arXiv:hep-th/0511154},
year = {2007}
}
Comments
Typos, 15 pages, 5 eps figures, Latex, Submitted to the Proceedings of the 4th International Symposium "Quantum Theory and Symmetries" (QTS-4), 15-21 August 2005, Varna, Bulgaria