Revisiting the Simplicity Constraints and Coherent Intertwiners

Abstract

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.

28 pages

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Cited by in corpus (25)

• The Spin Foam Approach to Quantum Gravity
• Spinor Representation for Loop Quantum Gravity
• Edge modes of gravity. Part III. Corner simplicity constraints
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
• Holomorphic Lorentzian Simplicity Constraints
• Pachner moves in a 4d Riemannian holomorphic Spin Foam model
• Deformations of Polyhedra and Polygons by the Unitary Group
• Holonomy Operator and Quantization Ambiguities on Spinor Space
• Coherent intertwiner solution of simplicity constraint in all dimensional loop quantum gravity
• Deformed Spinor Networks for Loop Gravity: Towards Hyperbolic Twisted Geometries
• Loop expansion and the bosonic representation of loop quantum gravity
• Spinors and Voros star-product for Group Field Theory: First Contact
• Loop gravity in terms of spinors
• Twisted Geometries Coherent States for Loop Quantum Gravity
• Bulk amplitude and degree of divergence in 4d spin foams
• Perelomov type coherent states of SO(D + 1) in all dimensional loop quantum gravity
• Holomorphic Simplicity Constraints for 4d Riemannian Spinfoam Models
• Quantum Surface and Intertwiner Dynamics in Loop Quantum Gravity
• 3d Lorentzian loop quantum gravity and the spinor approach
• Twisted geometry coherent states in all dimensional loop quantum gravity: II. Ehrenfest Property
• Classical dynamics for Loop Gravity: The 2-vertex model
• Local Observables in ${\mathrm{SU}}_q(2)$ Lattice Gauge Theory
• Gravity with torsion as deformed $BF$ theory
• A simpler way of imposing simplicity constraints
• 3D Quantum Gravity from Holomorphic Blocks