Un-spectral dimension and quantum spacetime phases

Piero Nicolini, Euro Spallucci

Research output: Contribution to journalArticlepeer-review


In this Letter, we propose a new scenario emerging from the conjectured presence of a minimal length ℓ 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 un-spectral dimension DU 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 DU labelling different spacetime phases: a semi-classical phase, where ordinary spectral dimension gets contribution from the scaling dimension dU of the un-particle probe; a critical "Planckian phase", where four-dimensional spacetime can be effectively considered two-dimensional when dU=1; a "Trans-Planckian phase", which is accessible to un-particle probes only, where spacetime as we currently understand it looses its physical meaning.

Original languageEnglish (US)
Pages (from-to)290-293
Number of pages4
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Issue number1-4
StatePublished - Jan 10 2011


  • Fractal dimension
  • Un-particle physics

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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