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  Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model

Baratin, A., & Oriti, D. (2011). Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model. New Journal of Physics, 13: 125011. doi:10.1088/1367-2630/13/12/125011.

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1108.1178 (Preprint), 368KB
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 Urheber:
Baratin, Aristide1, Autor           
Oriti, Daniele2, Autor           
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              
2Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              

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Schlagwörter: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
 Zusammenfassung: A dual formulation of group field theories, obtained by a Fourier transform mapping functions on a group to functions on its Lie algebra, has been proposed recently. In the case of the Ooguri model for SO(4) BF theory, the variables of the dual field variables are thus so(4) bivectors, which have a direct interpretation as the discrete B variables. Here we study a modification of the model by means of a constraint operator implementing the simplicity of the bivectors, in such a way that projected fields describe metric tetrahedra. This involves a extension of the usual GFT framework, where boundary operators are labelled by projected spin network states. By construction, the Feynman amplitudes are simplicial path integrals for constrained BF theory. We show that the spin foam formulation of these amplitudes corresponds to a variant of the Barrett-Crane model for quantum gravity. We then re-examin the arguments against the Barrett-Crane model(s), in light of our construction.

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 Datum: 2011-08-042011-11-062011
 Publikationsstatus: Erschienen
 Seiten: revtex, 24 pages
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 Identifikatoren: arXiv: 1108.1178
DOI: 10.1088/1367-2630/13/12/125011
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Titel: New Journal of Physics
  Andere : New J. Phys.
Genre der Quelle: Zeitschrift
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Ort, Verlag, Ausgabe: Bristol, UK : Institute of Physics Pub.
Seiten: - Band / Heft: 13 Artikelnummer: 125011 Start- / Endseite: - Identifikator: ISSN: 1367-2630
CoNE: https://pure.mpg.de/cone/journals/resource/954926913666