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  Group field theories for all loop quantum gravity

Oriti, D., Ryan, J. P., & Thürigen, J. (2015). Group field theories for all loop quantum gravity. New Journal of Physics, 17(2): 023042. doi:10.1088/1367-2630/17/2/023042.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0023-CE76-6 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0025-7A22-2
Genre: Journal Article

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 Creators:
Oriti, Daniele1, Author              
Ryan, James P.2, Author              
Thürigen, Johannes, Author
Affiliations:
1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              
2Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_102878              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 Abstract: Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the GFT formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.

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 Dates: 2014-09-102015
 Publication Status: Published in print
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 Identifiers: arXiv: 1409.3150
DOI: 10.1088/1367-2630/17/2/023042
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Title: New Journal of Physics
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Pages: - Volume / Issue: 17 (2) Sequence Number: 023042 Start / End Page: - Identifier: -