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

Emanuele Alesci (1) , Carlo Rovelli (1)

1 CPT - Centre de Physique Théorique - UMR 6207

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.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Emanuele Alesci, Carlo Rovelli. Complete LQG propagator: I. Difficulties with the Barrett-Crane vertex. Physical Review D, 2007, 76 (10), pp.104012. ⟨10.1103/PhysRevD.76.104012⟩. ⟨hal-00166827⟩