Vol. 11 (2008) > lrr-2008-5

doi: 10.12942/lrr-2008-5
Living Rev. Relativity 11 (2008), 5

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 describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler’s “spacetime foam” intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein–Hawking black-hole entropy. (v) Low-energy calculations, yielding n-point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

Keywords: Quantum gravity, Loop quantum gravity

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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 11,  (2008),  5. 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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