Complete LQG propagator: Difficulties with the Barrett-Crane vertex

Emanuele Alesci and Carlo Rovelli
Phys. Rev. D 76, 104012 – Published 9 November 2007

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 another paper we illustrate the asymptotic behavior of a vertex amplitude that can correct this difficulty.

  • Received 8 August 2007

DOI:https://doi.org/10.1103/PhysRevD.76.104012

©2007 American Physical Society

Authors & Affiliations

Emanuele Alesci1,2 and Carlo Rovelli2

  • 1Dipartimento di Fisica, Università di Roma Tre, I-00146 Roma, Italy, European Union
  • 2Centre de Physique Théorique de Luminy, Université de la Méditerranée, F-13288 Marseille, France, European Union*

  • *Unité mixte de recherche (UMR 6207) du CNRS et des Universités de Provence (Aix-Marseille I), de la Mediterranée (Aix-Marseille II) et du Sud (Toulon-Var); laboratoire affilié à la FRUMAM (FR 2291).

See Also

Complete LQG propagator. II. Asymptotic behavior of the vertex

Emanuele Alesci and Carlo Rovelli
Phys. Rev. D 77, 044024 (2008)

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Issue

Vol. 76, Iss. 10 — 15 November 2007

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