Generating Functions for Coherent Intertwiners

Understand

We study generating functions for the scalar products of SU(2) coherent intertwiners, which can be interpreted as coherent spin network evaluations on a 2-vertex graph.

• We show that these generating functions are exactly summable for different choices of combinatorial weights.
• Moreover, we identify one choice of weight distinguished thanks to its geometric interpretation.
• As an example of dynamics, we consider the simple case of SU(2) flatness and describe the corresponding Hamiltonian constraint whose quantization on coherent intertwiners leads to partial differential equations that we solve.