On the regularization of the constraint algebra of quantum gravity in 2 + 1 dimensions with a nonvanishing cosmological constant

Alejandro Perez (1) , Daniele Pranzetti (1)

1 CPT - Centre de Physique Théorique - UMR 7332

We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with 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) 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.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Alejandro Perez, Daniele Pranzetti. On the regularization of the constraint algebra of quantum gravity in 2 + 1 dimensions with a nonvanishing cosmological constant. Classical and Quantum Gravity, 2010, 27 (14), ⟨10.1088/0264-9381/27/14/145009⟩. ⟨hal-00448639⟩