Fractal properties of quantum spacetime

TL;DR

This paper demonstrates that quantum group symmetries induce a scale-dependent fractal dimension in spacetime, deviating from classical values at small scales, aligning with phenomena observed in quantum gravity research.

Contribution

It introduces the concept that quantum group symmetries lead to fractal spacetime structures with scale-dependent dimensions, specifically analyzing quantum sphere and κ-Minkowski cases.

Findings

Quantum group symmetries cause scale-dependent fractal dimensions.

Deviations from classical dimensions occur at short scales.

Analysis of quantum sphere and κ-Minkowski spacetime supports this phenomenon.

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.