Bulg. J. Phys. vol.33 no.4 (2006), pp. 273-286

An invariant Approach to Dynamical Fuzzy Spaces with a Three-Index Variable

N. Sasakura
Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
Abstract. A dynamical fuzzy space might be described in terms of a dynamical three-index variable Cabc, which determines the algebraic relations fafb = Cabcfc of the functions fa on a fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on fa. The solutions to the invariant equations of motion of Cabc 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 S2/Z2.

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