On the exact evaluation of spin networks

Abstract

We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtained by the contraction of parametrized intertwiners a la Schwinger. We finally give the explicit evaluation of this generating functional for arbitrary graphs.

References in corpus (7)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• Polyhedra in loop quantum gravity
• The Ponzano-Regge model
• A Discrete and Coherent Basis of Intertwiners
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Cited by in corpus (17)

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• Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
• A Discrete and Coherent Basis of Intertwiners
• Holonomy Operator and Quantization Ambiguities on Spinor Space
• Duality between Spin networks and the 2D Ising model
• Bubble Networks: Framed Discrete Geometry for Quantum Gravity
• Bulk amplitude and degree of divergence in 4d spin foams
• SO*(2N) coherent states for loop quantum gravity
• Coherent 3j-symbol representation for the loop quantum gravity intertwiner space
• Spin Foams Without Spins
• A simpler way of imposing simplicity constraints
• Generating Functionals for Spin Foam Amplitudes
• Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
• 3D Quantum Gravity from Holomorphic Blocks