Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 27, Issue 14, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/27/14/145009
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Funding
- Agence Nationale de la Recherche [ANR-06-BLAN-0050]
- l'Institut Universitaire de France
- Agence Nationale de la Recherche (ANR) [ANR-06-BLAN-0050] Funding Source: Agence Nationale de la Recherche (ANR)
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We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three-dimensional (Riemannian) gravity with a positive cosmological constant (Lambda > 0). We show that the usual regularization techniques (successful in the Lambda = 0 case and widely applied in four-dimensional LQG) led to a deformation of the classical constraint algebra (or anomaly) proportional to the local strength of the curvature squared. We argue that this is an unavoidable consequence of the nonlocal nature of generalized connections.
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