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Zbl 1023.83013
Rovelli, Carlo
Loop quantum gravity. (English)
[J] Living Rev. Relativ. 1, Article No.1998-1, 68 p., electronic only (1998). ISSN 1433-8351/e

Summary: 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, we 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.

MSC 2000:: *83C45 Quantization of the gravitational field
81V17 Gravitational interaction
83-02 Research monographs (relativity)
81-02 Research monographs (quantum theory)
83C57 Black holes

Keywords: non-perturbative and background independent quantization; physical spectra of geometrical quantities; Bekenstein-Hawking black hole entropy formula; microstructure of quantum physical space; spacetime foam

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Zentralblatt MATH Berlin [Germany]