Symmetries of quantum spacetime in three dimensions

Cianfrani F;Kowalski-Glikman J;Pranzetti D;Rosati G

2016-01-01

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Abstract

By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant Λ, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of soq⁢(4), with q =exp⁡(ih⁢√Λ/2⁢k). By means of an Inonu-Wigner contraction of the quantum group bi-algebra, keeping k finite, we obtain the kappa-Poincaré algebra of the flat quantum spacetime symmetries.