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Article Dans Une Revue Classical and Quantum Gravity Année : 2015

A note on the secondary simplicity constraints in loop quantum gravity

Résumé

A debate has appeared in the literature on loop quantum gravity and spin foams, over whether secondary simplicity constraints should imply the shape matching conditions reducing twisted geometries to Regge geometries. We address the question using a model in which secondary simplicity constraints arise from a dynamical preservation of the primary ones, and answer it in the affirmative. The origin of the extra condition is to be found in the different graph localisations of the various constraints. Our results are consistent with previous claims by Dittrich and Ryan, and extend their validity to Lorentzian signature and a priori arbitrary cellular decompositions. Finally, we show how the (gauge-invariant version of the) twist angle {\xi} featuring in twisted geometries equals on-shell the Regge dihedral angle multiplied by the Immirzi parameter, thus recovering the discrete extrinsic geometry from the Ashtekar-Barbero holonomy.

Dates et versions

hal-01114687 , version 1 (09-02-2015)

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Fabio Anzà, Simone Speziale. A note on the secondary simplicity constraints in loop quantum gravity. Classical and Quantum Gravity, 2015, 32 (19), pp.195015. ⟨10.1088/0264-9381/32/19/195015⟩. ⟨hal-01114687⟩
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