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Group field theory with non-commutative metric variables

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

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

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1002.4723
(Preprint), 164KB

PRL105_221302.pdf
(Any fulltext), 166KB

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Citation

Baratin, A., & Oriti, D. (2010). Group field theory with non-commutative metric variables. Physical Review Letters, 105(22): 221302. doi:10.1103/PhysRevLett.105.221302.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-69CA-0
Abstract
We introduce a dual formulation of group field theories, making them a type of non-commutative field theories. In this formulation, the variables of the field are Lie algebra variables with a clear interpretation in terms of simplicial geometry. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. This formulation suggests ways to impose the simplicity constraints involved in BF formulations of 4d gravity directly at the level of the group field theory action. We illustrate this by giving a new GFT definition of the Barrett-Crane model.