On the regularization of the constraint algebra of quantum gravity in 2 + 1 dimensions with a nonvanishing cosmological constant
Résumé
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Λ > 0). We show that the usual regularization techniques (successful in the Λ = 0 case and widely applied in four dimensional LQG) lead 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 non-local nature of generalized connections.
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PEER_stage2_10.1088%2F0264-9381%2F27%2F14%2F145009.pdf (246.53 Ko)
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