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  Spin foam models and the Duflo map

Finocchiaro, M., & Oriti, D. (in preparation). Spin foam models and the Duflo map.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0002-B979-6 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-EBAD-3
Genre: Paper

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1812.03550.pdf (Preprint), 953KB
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 Creators:
Finocchiaro, M., Author
Oriti, Daniele1, Author              
Affiliations:
1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              

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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: We give a general definition of spin foam models, and then of models of 4d quantum gravity based on constraining BF theory. We highlight the construction and quantization ambiguities entering model building, among which the choice of quantization map applied to the B-variables carrying metric information after imposing simplicity constraints, and the different strategies for imposing the latter constraints. We then construct a new spin foam model for 4d quantum gravity, using the flux representation of states and amplitudes, based on the Duflo quantization map and the associated non-commutative Fourier transform for Lie groups. The advantages of the new model are the geometrically transparent way in which constraints are imposed, and the underlying mathematical properties of the Duflo map itself. Finally, we study some properties of the resulting spin foam amplitudes, in particular the relation with other models and a few limiting cases.

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 Dates: 2018-12-09
 Publication Status: Not specified
 Pages: 46 pages, 5 figures
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1812.03550
URI: http://arxiv.org/abs/1812.03550
 Degree: -

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