New vertices and canonical quantization

We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the Engle-Pereira-Rovelli-Livine model leads to the appearance of the Ashtekar-Barbero connection, thus bringing this model even closer to loop quantum gravity. Second, we however argue that the quantization procedure used to derive the new models is inconsistent since it relies on the symplectic structure of the unconstrained BF theory.

Figure 1

Projected spin network and the structure of its intertwiners.