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Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity

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)

1111.5842
(Preprint), 333KB

PRD85_044003.pdf
(Any fulltext), 277KB

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There is no public supplementary material available
Citation

Baratin, A., & Oriti, D. (2012). Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity. Physical Review D, 85: 044003. doi:10.1103/PhysRevD.85.044003.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-86F5-C
Abstract
In a recent work, a dual formulation of group field theories as non-commutative quantum field theories has been proposed, providing an exact duality between spin foam models and non-commutative simplicial path integrals for constrained BF theories. In light of this new framework, we define a model for 4d gravity which includes the Immirzi parameter gamma. It reproduces the Barrett-Crane amplitudes when gamma goes to infinity, but differs from existing models otherwise; in particular it does not require any rationality condition for gamma. We formulate the amplitudes both as BF simplicial path integrals with explicit non-commutative B variables, and in spin foam form in terms of Wigner 15j-symbols. Finally, we briefly discuss the correlation between neighboring simplices, often argued to be a problematic feature, for example, in the Barrett-Crane model.