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

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons20702

Baratin,  Aristide
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons20698

Oriti,  Daniele
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1108.1178
(Preprint), 368KB

NJP_13_12_125011.pdf
(Publisher version), 781KB

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Citation

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.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-86FC-D
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.