Complete LQG propagator: Difficulties with the Barrett-Crane vertex (original) (raw)
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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.
Publication:
Physical Review D
Pub Date:
November 2007
DOI:
arXiv:
Bibcode:
Keywords:
- 04.60.Pp;
- Loop quantum gravity quantum geometry spin foams;
- General Relativity and Quantum Cosmology
E-Print:
31 pages