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Revisiting the Simplicity Constraints and Coherent Intertwiners
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. Then we
show how these constraints can be written as a closed u(N) algebra and we
propose a set of U(N) coherent states that solves all the simplicity
constraints weakly for an arbitrary Immirzi parameter.Comment: 28 page