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/2k). 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.
Symmetries of quantum spacetime in three dimensions
Rosati G
2016-01-01
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/2k). 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.
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