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Group field theory with non-commutative metric variables
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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.
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Cited by 1 Pith paper
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A state sum for four-dimensional Lorentzian quantum geometry in terms of edge vectors
A new state sum model for 4D Lorentzian quantum gravity is constructed from quantum edge vectors and related to the Barrett-Crane spin foam model.
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