Generating Functions for Coherent Intertwiners

Abstract

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. Furthermore, we generalize explicitly these Wheeler-DeWitt equations for SU(2) flatness on coherent spin networks for arbitrary graphs.

31 pages

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• Deformed Spinor Networks for Loop Gravity: Towards Hyperbolic Twisted Geometries
• Loop expansion and the bosonic representation of loop quantum gravity
• Bubble Networks: Framed Discrete Geometry for Quantum Gravity
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• Cosmological states in loop quantum gravity on homogeneous graphs
• 3D Quantum Gravity from Holomorphic Blocks
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