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arXiv · 1606.03085

Symmetries of quantum space-time in 3 dimensions

Francesco Cianfrani·Jerzy Kowalski-Glikman·Daniele Pranzetti·Giacomo Rosati
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Abstract

By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant $\Lambda$, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of $so_q(4)$, with $ q = \exp{(i\hbar \sqrt{\Lambda}/2\kappa)}$. By means of an Inonu-Wigner contraction of the quantum group bi-algebra, keeping $\kappa$ finite, we obtain the kappa-Poincar\'e algebra of the flat quantum space-time symmetries.

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Francesco Cianfrani, Jerzy Kowalski-Glikman, Daniele Pranzetti, Giacomo Rosati. 2016-06-09. Symmetries of quantum space-time in 3 dimensions. https://doi.org/10.1103/physrevd.94.084044

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