An invariant approach to dynamical fuzzy spaces with a three-index variable -- Euclidean models

Details An invariant approach to dynamical fuzzy spaces with a three-index variable -- Euclidean models An invariant approach to dynamical fuzzy spaces with a three-index variable -- Euclidean models

2005-11-15

arxiv.org/abs/hep-th/0511154v2

Physics

High Energy Physics

High Energy Physics - Theory

Typos, 15 pages, 5 eps figures, Latex, Submitted to the Proceedings of the 4th International Symposium "Quantum Theory and Sym

Scientific paper

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.

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