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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Metadaten
Author:Winston J. Fairbairn, Catherine Meusburger
URN:urn:nbn:de:bvb:29-opus-38121
Document Type:Article
Language:English
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
SWD-Keyword:-
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 / Naturwissenschaftliche Fakultät -ohne weitere Spezifikation-
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
PACS-Classification:00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.20.-a Group theory (for algebraic methods in quantum mechanics, see 03.65.Fd; for symmetries in elementary particle physics, see 11.30.-j) / 02.20.Sv Lie algebras of Lie groups
00.00.00 GENERAL / 03.00.00 Quantum mechanics, field theories, and special relativity (see also section 11 General theory of fields and particles) / 03.65.-w Quantum mechanics [see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics] / 03.65.Fd Algebraic methods (see also 02.20.-a Group theory)
00.00.00 GENERAL / 03.00.00 Quantum mechanics, field theories, and special relativity (see also section 11 General theory of fields and particles) / 03.65.-w Quantum mechanics [see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics] / 03.65.Ta Foundations of quantum mechanics; measurement theory (for optical tests of quantum theory, see 42.50.Xa)
Collections:Universität Erlangen-Nürnberg / Allianzlizenzen / Allianzlizenzen 2012

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