The complete LQG propagator: II. Asymptotic behavior of the vertex

Abstract

In a previous article we have show that there are difficulties in obtaining the correct graviton propagator from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude that depends nontrivially on the intertwiners can yield the correct propagator. We give an explicit example of asymptotic behavior of a vertex amplitude that gives the correct full graviton propagator in the large distance limit.

16 pages

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• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• A Lagrangian approach to the Barrett-Crane spin foam model
• An elementary introduction to loop quantum gravity
• Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model
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• Intertwiner dynamics in the flipped vertex
• Tensorial Structure of the LQG graviton propagator
• Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity