Revisiting the simplicity constraints and coherent intertwiners

Abstract

In the context of loop quantum gravity and spinfoam models, the simplicity constraints are essential in that they allow one to write general relativity as a constrained topological BF theory. In this work, we apply the recently developed U(N) framework for SU(2) intertwiners to the issue of imposing the simplicity constraints to spin network states. More particularly, we focus on solving on individual intertwiners in the 4D Euclidean theory. We review the standard way of solving the simplicity constraints using coherent intertwiners and we explain how these fit within the U(N) framework. Then we show how these constraints can be written as a closed algebra and we propose a set of U(N) coherent states that solves all the simplicity constraints weakly for an arbitrary Immirzi parameter.