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

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

2007-08-07

arxiv.org/abs/0708.0883v1

Phys.Rev.D76:104012,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 pages

Scientific paper

10.1103/PhysRevD.76.104012

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.

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