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

References in corpus (2)

• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• Quantum fields, non-locality and quantum group symmetries

Cited by in corpus (3)

• Cosmology of the Lifshitz universe
• Fractal Dimension in 3d Spin-Foams
• Fractal Quantum Space-Time