The new vertices and canonical quantization

TL;DR

This paper analyzes recent spin foam models, showing how modifications relate to loop quantum gravity and critiquing the quantization method used, highlighting both connections and inconsistencies.

Contribution

It demonstrates a modified restriction on representations that introduces the Ashtekar-Barbero connection and critiques the quantization procedure of the new models.

Findings

Modified restriction yields Ashtekar-Barbero connection

Quantization procedure is inconsistent due to reliance on unconstraint BF theory

Bridges between spin foam models and LQG are clarified

Abstract

We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the EPRL model leads to the appearance of the Ashtekar-Barbero connection, thus bringing this model even closer to LQG. 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 unconstraint BF theory.