Fractal Structure of Loop Quantum Gravity

Details Fractal Structure of Loop Quantum Gravity Fractal Structure of Loop Quantum Gravity

2008-12-11

arxiv.org/abs/0812.2214v1

Class.Quant.Grav.26:242002,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages, 5 figures

Scientific paper

10.1088/0264-9381/26/24/242002

In this paper we have calculated the spectral dimension of loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We have obtained that the spectral dimension of the spatial section runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar field decrees from high to low energy. We have calculated the spectral dimension of the space-time also using results from spin-foam models, obtaining a 2-dimensional effective manifold at hight energy. Our result is consistent with other two approach to non perturbative quantum gravity: causal dynamical triangulation and asymptotic safety quantum gravity.

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