Holomorphic Simplicity Constraints for 4d Riemannian Spinfoam Models

Abstract

Starting from the reformulation of the classical phase space of Loop Quantum Gravity in terms of spinor variables and spinor networks, we build coherent spin network states and show how to use them to write the spinfoam path integral for topological BF theory in terms of Gaussian integrals in the spinors. Finally, we use this framework to revisit the simplicity constraints reducing topological BF theory to 4d Riemannian gravity. These holomorphic simplicity constraints lead us to a new spinfoam model for quantum gravity whose amplitudes are defined as the evaluation of the coherent spin networks.

4 pages. Proceedings of Loops'11, Madrid. To appear in Journal of Physics: Conference Series (JPCS)

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Cited by in corpus (12)

• Holonomy spin foam models: Asymptotic geometry of the partition function
• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• Deformation Operators of Spin Networks and Coarse-Graining
• Pachner moves in a 4d Riemannian holomorphic Spin Foam model
• Linking covariant and canonical LQG II: Spin foam projector
• Holonomy Operator and Quantization Ambiguities on Spinor Space
• Twisted geometries, twistors and conformal transformations
• The Construction of Spin Foam Vertex Amplitudes
• Hamiltonian spinfoam gravity
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• A simpler way of imposing simplicity constraints
• 3D Quantum Gravity from Holomorphic Blocks