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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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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-86FC-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-86FF-7
Genre: Journal Article

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1108.1178 (Preprint), 368KB
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 Creators:
Baratin, Aristide1, Author              
Oriti, Daniele2, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              
2Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:67201              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
 Abstract: 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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 Dates: 2011-08-042011-11-062011
 Publication Status: Published in print
 Pages: revtex, 24 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1108.1178
DOI: 10.1088/1367-2630/13/12/125011
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Title: New Journal of Physics
  Other : New J. Phys.
Source Genre: Journal
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Publ. Info: Bristol, UK : Institute of Physics Pub.
Pages: - Volume / Issue: 13 Sequence Number: 125011 Start / End Page: - Identifier: ISSN: 1367-2630
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/954926913666