The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex

Abstract

Some components of the graviton two-point function have been recently computed in the context of loop quantum gravity, using the spinfoam Barrett-Crane vertex. We complete the calculation of the remaining components. We find that, under our assumptions, the Barrett-Crane vertex does not yield the correct long distance limit. We argue that the problem is general and can be traced to the intertwiner-independence of the Barrett-Crane vertex, and therefore to the well-known mismatch between the Barrett-Crane formalism and the standard canonical spin networks. In a companion paper we illustrate the asymptotic behavior of a vertex amplitude that can correct this difficulty.

31 pages

References in corpus (4)

• A new spinfoam vertex for quantum gravity
• The loop-quantum-gravity vertex-amplitude
• Linearized dynamics from the 4-simplex Regge action
• Spin foam model from canonical quantization

Cited by in corpus (17)

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• Stepping out of Homogeneity in Loop Quantum Cosmology
• Numerical evidence of regularized correlations in spin foam gravity
• Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model
• Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
• The perturbative Regge-calculus regime of Loop Quantum Gravity
• Coherent states, constraint classes, and area operators in the new spin-foam models
• Semiclassical regime of Regge calculus and spin foams
• Spin-Foam Models and the Physical Scalar Product
• Numerical indications on the semiclassical limit of the flipped vertex
• Intertwiner dynamics in the flipped vertex
• Tensorial Structure of the LQG graviton propagator