Fractal properties of quantum spacetime

Abstract

We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to quantum gravity. In particular we analyze the cases of a quantum sphere and of $\k$-Minkowski, the latter being relevant in the context of quantum gravity.

4 pages, 2 figures; some minor corrections; reference added

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