The Hilbert space of 3d gravity: Quantum group symmetries and observables
Meusburger C, Noui K (2010)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2010
Journal
Publisher: International Press
Book Volume: 14
Pages Range: 1651-1716
Journal Issue: 6
URI: https://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84858185698&origin=inward
Abstract
We relate three-dimensional loop quantum gravity to the combinatorial quantization formalism based on the Chern-Simons formulation for three-dimensional Lorentzian and Euclidean gravity with vanishing cosmological constant. We compare the construction of the kinematical Hilbert space and the implementation of the constraints. This leads to an explicit and very interesting relation between the associated operators in the two approaches and sheds light on their physical interpretation. We demonstrate that the quantum group symmetries arising in the combinatorial formalism, the quantum double of the three-dimensional Lorentz and rotation group are also present in the loop formalism. We derive explicit expressions for the action of these quantum groups on the space of cylindrical functions associated with graphs. This establishes a direct link between the two quantization approaches and clarifies the role of quantum group symmetries in three-dimensional gravity. © 2011 International Press.
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France (FR)How to cite
APA:
Meusburger, C., & Noui, K. (2010). The Hilbert space of 3d gravity: Quantum group symmetries and observables. Advances in Theoretical and Mathematical Physics, 14(6), 1651-1716.
MLA:
Meusburger, Cathérine, and Karim Noui. "The Hilbert space of 3d gravity: Quantum group symmetries and observables." Advances in Theoretical and Mathematical Physics 14.6 (2010): 1651-1716.
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