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

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##### Fulltext (public)

1108.1178

(Preprint), 368KB

NJP_13_12_125011.pdf

(Publisher version), 781KB

##### Supplementary Material (public)

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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.