ASYMPTOTICS OF RECENT SPIN FOAM MODELS

Abstract

ρ denote the unitary irreps and ι are the intertwining operators of some group G which are associated to the triangles and tetrahedra respectively. The Euclidean EPRL and FK models are spin foam models of quantum gravity based on G = Spin(4) = SU(2) × SU(2), where the irreps are labelled by two half integer spins (j, j−). The Lorentzian EPRL model is based on G = SL(2,C) with representations (k, p) labelled by a half integer k and a real number p. The models solve some of the problems of the models in Refs. 3 and 4. The asymptotic regime of a spin foam model is important to verify that general relativity is recovered in the low energy limit. We show in Refs. 5 and 6 that the 4-simplex amplitudes for these models contain the Regge action for a 4-simplex.