TY - JOUR

T1 - Un-spectral dimension and quantum spacetime phases

AU - Nicolini, Piero

AU - Spallucci, Euro

N1 - Funding Information:
P.N. is supported by the Helmholtz International Center for FAIR within the framework of the LOEWE program (Landesoffensive zur Entwicklung Wissenschaftlich-Ökonomischer Exzellenz) launched by the State of Hesse.

PY - 2011/1/10

Y1 - 2011/1/10

N2 - 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.

AB - 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.

KW - Fractal dimension

KW - Un-particle physics

UR - http://www.scopus.com/inward/record.url?scp=78650303591&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650303591&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2010.10.041

DO - 10.1016/j.physletb.2010.10.041

M3 - Article

AN - SCOPUS:78650303591

SN - 0370-2693

VL - 695

SP - 290

EP - 293

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 1-4

ER -