Second-order amplitudes in loop quantum gravity

Davide Mamone (1, 2) , Carlo Rovelli (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

We explore some second-order amplitudes in loop quantum gravity. In particular, we compute some second-order contributions to diagonal components of the graviton propagator in the large distance limit, using the old version of the Barrett-Crane vertex amplitude. We illustrate the geometry associated to these terms. We find some peculiar phenomena in the large distance behavior of these amplitudes, related with the geometry of the generalized triangulations dual to the Feynman graphs of the corresponding group field theory. In particular, we point out a possible further difficulty with the old Barrett-Crane vertex: it appears to lead to flatness instead of Ricci-flatness, at least in some situations. The observation raises the question whether this difficulty remains with the new version of the vertex.

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

Davide Mamone, Carlo Rovelli. Second-order amplitudes in loop quantum gravity. Classical and Quantum Gravity, 2009, 26 (24), pp.245013. ⟨10.1088/0264-9381/26/24/245013⟩. ⟨hal-00385712⟩