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 -