Vol. 1 (1998) > lrr-1998-1

doi: 10.12942/lrr-1998-1
Living Rev. Relativity 1 (1998), 1

Loop Quantum Gravity

1 Centre de Physique Théorique de Luminy, Case 907, Luminy, F-13288 Marseille, France

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Article Abstract

The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a mathematically well-defined, non-perturbative and background independent quantization of general relativity, with its conventional matter couplings. Research in loop quantum gravity today forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained are: (i) The computation of the physical spectra of geometrical quantities such as area and volume, which yields quantitative predictions on Planck-scale physics. (ii) A derivation of the Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical picture of the microstructure of quantum physical space, characterized by a polymer-like Planck scale discreteness. This discreteness emerges naturally from the quantum theory and provides a mathematically well-defined realization of Wheeler's intuition of a spacetime ``foam''. Long standing open problems within the approach (lack of a scalar product, over-completeness of the loop basis, implementation of reality conditions) have been fully solved. The weak part of the approach is the treatment of the dynamics: at present there exist several proposals, which are intensely debated. Here, I provide a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.


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Article Citation

Since a Living Reviews in Relativity article may evolve over time, please cite the access <date>, which uniquely identifies the version of the article you are referring to:

Carlo Rovelli,
"Loop Quantum Gravity",
Living Rev. Relativity 1,  (1998),  1. URL (cited on <date>):

Article History

ORIGINAL http://www.livingreviews.org/lrr-1998-1
Title Loop Quantum Gravity
Author Carlo Rovelli
Date accepted 1 December 1997, published 26 January 1998
UPDATE http://www.livingreviews.org/lrr-2008-5
Title Loop Quantum Gravity
Author Carlo Rovelli
Date accepted 31 May 2008, published 15 July 2008
Changes Substantially rewritten version of the original article. Changes include figures and updated references (increased from 217 to 300).
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