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 Engle-Pereira-Rovelli-Livine 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.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)