Quantum deformation of two four-dimensional spin foam models
General Relativity and Quantum Cosmology
2012-02-07 v3 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We construct the q-deformed version of two four-dimensional spin foam models, the Euclidean and Lorentzian versions of the EPRL model. The q-deformed models are based on the representation theory of two copies of U_q(su(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.
Keywords
Cite
@article{arxiv.1012.4784,
title = {Quantum deformation of two four-dimensional spin foam models},
author = {Winston J. Fairbairn and Catherine Meusburger},
journal= {arXiv preprint arXiv:1012.4784},
year = {2012}
}
Comments
45 pages, 4 figures, typos corrected, references added, proofs and explanations extended for readability