Revisiting the Simplicity Constraints and Coherent Intertwiners

Understand

In the context of loop quantum gravity and spinfoam models, the simplicity constraints are essential in that they allow 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 them 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.