LQG propagator: III. The new vertex

Abstract

In the first article of this series, we pointed out a difficulty in the attempt to derive the low-energy behavior of the graviton two-point function, from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that this difficulty disappears when using the corrected vertex amplitude recently introduced in the literature. In particular, we show that the asymptotic analysis of the new vertex amplitude recently performed by Barrett, Fairbairn and others, implies that the vertex has precisely the asymptotic structure that, in the second article of this series, was indicated as the key necessary condition for overcoming the difficulty.

9 pages

References in corpus (12)

• The loop-quantum-gravity vertex-amplitude
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• LQG propagator from the new spin foams
• Area-angle variables for general relativity
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• Group Integral Techniques for the Spinfoam Graviton Propagator
• Path integral representation of spin foam models of 4d gravity
• Towards the graviton from spinfoams: higher order corrections in the 3d toy model
• A semiclassical tetrahedron
• The perturbative Regge-calculus regime of Loop Quantum Gravity
• Compatibility of radial, Lorenz and harmonic gauges
• Tensorial Structure of the LQG graviton propagator

Cited by in corpus (29)

• The Spin Foam Approach to Quantum Gravity
• Twisted geometries: A geometric parametrisation of SU(2) phase space
• Asymptotic analysis of the EPRL four-simplex amplitude
• Towards Spinfoam Cosmology
• Coherent spin-networks
• Quantum geometry from phase space reduction
• Spinning Loop Black Holes
• Lorentzian spinfoam propagator
• Holonomy spin foam models: Asymptotic geometry of the partition function
• Linking covariant and canonical LQG: new solutions to the Euclidean Scalar Constraint
• Generalized Spinfoams
• A new look at loop quantum gravity
• Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recoupling theory
• Quantum Reduced Loop Gravity: Semiclassical limit
• Gluing polyhedra with entanglement in loop quantum gravity
• Spinfoams in the holomorphic representation
• A regularization of the hamiltonian constraint compatible with the spinfoam dynamics
• Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations
• Euclidean three-point function in loop and perturbative gravity
• Entanglement entropy of Bell-network states in LQG: Analytical and numerical results
• Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory
• Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
• The Lorentzian proper vertex amplitude: Classical analysis and quantum derivation
• Observables in 3d spinfoam quantum gravity with fermions
• Emergent Braided Matter of Quantum Geometry
• Partial absence of cosine problem in 3d Lorentzian spin foams
• Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, $3j$ Symbols, and Character Localization
• Boundary State Stability under Spinfoam Evolution for the Quantum 4-Simplex
• Hessian in the spinfoam models with cosmological constant