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

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

2005-06-23

arxiv.org/abs/hep-th/0506192v2

Mod.Phys.Lett. A21 (2006) 1017-1028

Physics

High Energy Physics

High Energy Physics - Theory

Typos corrected, 12 pages, 8 figures, LaTeX, JHEP class

Scientific paper

10.1142/S0217732306020329

A dynamical fuzzy space might be described by a three-index variable C_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c among the functions f_a on the fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on f_a. I study equations for the three-index variable invariant under the general linear transformation, and show that the solutions can be generally constructed from the invariant tensors of Lie groups. As specific examples, I study SO(3) symmetric solutions, and discuss the construction of a scalar field theory on a fuzzy two-sphere within this framework.

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