Simplicity and closure constraints in spin foam models of gravity

Abstract

We revise imposition of various constraints in spin foam models of 4-dimensional general relativity. We argue that the usual simplicity constraint must be supplemented by a constraint on holonomies and together they must be inserted explicitly into the discretized path integral. At the same time, the closure constraint must be relaxed so that the new constraint expresses covariance of intertwiners assigned to tetrahedra by spin foam quantization. As a result, the spin foam boundary states are shown to be realized in terms of projected spin networks of the covariant loop approach to quantum gravity.

18 pages; references added, some clarifications in discussion

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Cited by in corpus (36)

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• Quantum cosmology: a review
• Homogeneous cosmologies as group field theory condensates
• Phase space descriptions for simplicial 4d geometries
• Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
• Edge modes of gravity. Part III. Corner simplicity constraints
• Spin Foams and Canonical Quantization
• Lorentz covariance of loop quantum gravity
• Simplicity in simplicial phase space
• Lifting SU(2) Spin Networks to Projected Spin Networks
• SU(2) graph invariants, Regge actions and polytopes
• Regularization and finiteness of the Lorentzian LQG vertices
• The twistorial structure of loop-gravity transition amplitudes
• The new vertices and canonical quantization
• Critical Overview of Loops and Foams
• Asymptotic analysis of the EPRL model with timelike tetrahedra
• A Lagrangian approach to the Barrett-Crane spin foam model
• Classical general relativity as BF-Plebanski theory with linear constraints
• The Holst Spin Foam Model via Cubulations
• Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
• First order gravity on the light front
• Testing the imposition of the Spin Foam Simplicity Constraints
• Null twisted geometries
• Spin-Foam Models and the Physical Scalar Product
• Twisted geometries, twistors and conformal transformations
• Group field theory and simplicial quantum gravity
• Spinfoams: Foundations
• A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
• The new spin foam models and quantum gravity
• Poincare-Plebanski formulation of GR and dual simplicity constraints
• Degenerate Plebanski Sector and Spin Foam Quantization
• Pure Lorentz spin connection theories and uniqueness of General Relativity
• Exploring the Tomlin-Varadarajan quantum constraints in $U(1{)}^3$ loop quantum gravity: solutions and the Minkowski theorem
• On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity