Asymptotics of loop quantum gravity fusion coefficients

Emanuele Alesci (1, 2, 3, 4) , Eugenio Bianchi (1, 3, 4) , Elena Magliaro (1, 3, 5, 4) , Claudio Perini (1, 5, 4)

1 HCTLab - Human Computer Technology Laboratory
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
3 SNS - Scuola Normale Superiore di Pisa
4 Dipartimento di Matematica [Roma 3]
5 DF-Roma3 - Dipartimento de Fisica Roma Tre

The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into SU (2)L ×SU (2)R semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.

Mots clés: Physical Sciences

Emanuele Alesci, Eugenio Bianchi, Elena Magliaro, Claudio Perini. Asymptotics of loop quantum gravity fusion coefficients. Classical and Quantum Gravity, 2010, 27 (9), pp.95016. ⟨10.1088/0264-9381/27/9/095016⟩. ⟨hal-00591192⟩