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 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.
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Quantum deformation of two four-dimensional spin foam models
Fairbairn, Winston J.; Meusburger, Catherine
Follow Journal of Mathematical Physics
, Volume 53 (2)
American Institute of Physics – Feb 1, 2012
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