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This article is cited in 47 scientific papers (total in 47 papers)
Spin foams and canonical quantization
Sergei Alexandrovab, Marc Geillerc, Karim Nouidc a Université Montpellier 2, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France
b CNRS, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France
c Laboratoire APC, Université Paris Diderot Paris 7, 75013 Paris, France
d LMPT, Université François Rabelais, Parc de Grandmont, 37200 Tours, France
Abstract:
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev–Viro spin foam model, and how the Ponzano–Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.
Keywords:
spin foam models, loop quantum gravity, canonical quantization.
Received: January 30, 2012; in final form August 12, 2012; Published online August 19, 2012
Citation:
Sergei Alexandrov, Marc Geiller, Karim Noui, “Spin foams and canonical quantization”, SIGMA, 8 (2012), 055, 79 pp.
Linking options:
https://www.mathnet.ru/eng/sigma732 https://www.mathnet.ru/eng/sigma/v8/p55
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