2009/11/02 by Elena Magliaro, Magliaro, Elena, Claudio Perini +3 · 22 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Computer science #FOS: Physical sciences #Fractal #General Relativity and Quantum Cosmology (gr-qc) #Geometry #Mathematical analysis #Mathematics #Physics #Space (punctuation) #Spin (aerodynamics) #Thermodynamics #gr-qc
paper · pdf · doi:10.48550/arxiv.0911.0437
published in arXiv (Cornell University) (Cornell University) · 5 pages, 2 figures
arxiv created 2009/11/02 · openalex publication_date 2009/11/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we perform the calculation of the spectral dimension of spacetime in 4d quantum gravity using the Barrett-Crane (BC) spinfoam model. We realize this considering a very simple decomposition of the 4d spacetime already used in the graviton propagator calculation and we introduce a boundary state which selects a classical geometry on the boundary. We obtain that the spectral dimension of the spacetime runs from ≈ 2 to 4, across a ≈ 1.5 phase, when the energy of a probe scalar field decreases from high E \lesssim EP/25 to low energy. The spectral dimension at the Planck scale E ≈ EP depends on the areas spectrum used in the calculation. For three different spectra lP2 √(j(j+1)), lP2 (2 j+1) and lP2 j we find respectively dimension ≈ 2.31, 2.45 and 2.08.