# Un-spectral dimension and quantum spacetime phases

In this Letter, we propose a new scenario emerging from the conjectured presence of a minimal length $\ell$ in the spacetime fabric, on the one side, and the existence of a new scale invariant, continuous mass spectrum, of un-particles on the other side. We introduce the concept of \textit{un-spectral dimension} $\mathbb{D} U$ of a $d$-dimensional, euclidean quantum spacetime, as the spectral dimension measured by an -un-particle- probe. We find a general expression for the un-spectral dimension $\mathbb{D} U$ labelling different spacetime phases: a semi-classical phase, where ordinary spectral dimension gets contribution from the scaling dimension $d U$ of the un-particle probe ; a critical -Planckian phase-, where four-dimensional spacetime can be effectively considered two-dimensional when $d U=1$; a -Trans-Planckian phase-, which is accessible to un-particle probes only, where spacetime as we currently understand it looses its physical meaning.

Author: Piero Nicolini; Euro Spallucci

Source: https://archive.org/