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Title: Spectral dimension of a quantum universe

Abstract

In this paper, we calculate in a transparent way the spectral dimension of a quantum spacetime, considering a diffusion process propagating on a fluctuating manifold. To describe the erratic path of the diffusion, we implement a minimal length by averaging the graininess of the quantum manifold in the flat space case. As a result we obtain that, for large diffusion times, the quantum spacetime behaves like a smooth differential manifold of discrete dimension. On the other hand, for smaller diffusion times, the spacetime looks like a fractal surface with a reduced effective dimension. For the specific case in which the diffusion time has the size of the minimal length, the spacetime turns out to have a spectral dimension equal to 2, suggesting a possible renormalizable character of gravity in this regime. For smaller diffusion times, the spectral dimension approaches zero, making any physical interpretation less reliable in this extreme regime. We extend our result to the presence of a background field and curvature. We show that in this case the spectral dimension has a more complicated relation with the diffusion time, and conclusions about the renormalizable character of gravity become less straightforward with respect to what we found with themore » flat space analysis.« less

Authors:
;  [1]
  1. Perimeter Institute for Theoretical Physics, 31 Caroline Street, Waterloo, ON N2L 2Y5 (Canada)
Publication Date:
OSTI Identifier:
21409752
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 81; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.81.104040; (c) 2010 The American Physical Society; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMPUTERIZED SIMULATION; GRAVITATION; MATHEMATICAL MANIFOLDS; QUANTUM GRAVITY; SPACE; SPACE-TIME; SURFACES; UNIVERSE; FIELD THEORIES; QUANTUM FIELD THEORY; SIMULATION

Citation Formats

Modesto, Leonardo, Nicolini, Piero, and Frankfurt Institute for Advanced Studies. Spectral dimension of a quantum universe. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.81.104040.
Modesto, Leonardo, Nicolini, Piero, & Frankfurt Institute for Advanced Studies. Spectral dimension of a quantum universe. United States. https://doi.org/10.1103/PHYSREVD.81.104040
Modesto, Leonardo, Nicolini, Piero, and Frankfurt Institute for Advanced Studies. 2010. "Spectral dimension of a quantum universe". United States. https://doi.org/10.1103/PHYSREVD.81.104040.
@article{osti_21409752,
title = {Spectral dimension of a quantum universe},
author = {Modesto, Leonardo and Nicolini, Piero and Frankfurt Institute for Advanced Studies},
abstractNote = {In this paper, we calculate in a transparent way the spectral dimension of a quantum spacetime, considering a diffusion process propagating on a fluctuating manifold. To describe the erratic path of the diffusion, we implement a minimal length by averaging the graininess of the quantum manifold in the flat space case. As a result we obtain that, for large diffusion times, the quantum spacetime behaves like a smooth differential manifold of discrete dimension. On the other hand, for smaller diffusion times, the spacetime looks like a fractal surface with a reduced effective dimension. For the specific case in which the diffusion time has the size of the minimal length, the spacetime turns out to have a spectral dimension equal to 2, suggesting a possible renormalizable character of gravity in this regime. For smaller diffusion times, the spectral dimension approaches zero, making any physical interpretation less reliable in this extreme regime. We extend our result to the presence of a background field and curvature. We show that in this case the spectral dimension has a more complicated relation with the diffusion time, and conclusions about the renormalizable character of gravity become less straightforward with respect to what we found with the flat space analysis.},
doi = {10.1103/PHYSREVD.81.104040},
url = {https://www.osti.gov/biblio/21409752}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 10,
volume = 81,
place = {United States},
year = {Sat May 15 00:00:00 EDT 2010},
month = {Sat May 15 00:00:00 EDT 2010}
}