Quantum deformation of two four-dimensional spin foam models

  • We construct the q-deformed version of two four-dimensional spin foam models, the Euclidean and Lorentzian versions of the Engle, Pereira, Rovelli and Livine (EPRL) model. The q-deformed models are based on the representation theory of two copies of Uq(math(2)) at a root of unity and on the quantum Lorentz group with a real deformation parameter. For both models, we give a definition of the quantum EPRL intertwiners, study their convergence and braiding properties, and construct an amplitude for the four-simplexes. We find that both of the resulting models are convergent.

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Author:Winston J. Fairbairn, Catherine Meusburger
Title of the journal / compilation:Journal of Mathematical Physics 53.2 (2012): 06.11.2012 <http://jmp.aip.org/resource/1/jmapaq/v53/i2/p022501_s1>
Document Type:Article
Date of Publication (online):2012/11/07
Publishing Institution:Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Release Date:2012/11/07
Tag:SU(2) theory; foams; quantum theory
Original publication:Journal of Mathematical Physics 53.2 (2012): 06.11.2012 <http://jmp.aip.org/resource/1/jmapaq/v53/i2/p022501_s1>
Institutes:Naturwissenschaftliche Fakultät -ohne weitere Spezifikation-
Dewey Decimal Classification:510 Mathematik
PACS-Classification:02.20.Sv Lie algebras of Lie groups
03.65.Fd Algebraic methods (see also 02.20.-a Group theory)
03.65.Ta Foundations of quantum mechanics; measurement theory (for optical tests of quantum theory, see 42.50.Xa)
Collections:Allianzlizenzen 2012

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