Quantum deformation of two four-dimensional spin foam models

Details Quantum deformation of two four-dimensional spin foam models Quantum deformation of two four-dimensional spin foam models

2010-12-21

arxiv.org/abs/1012.4784v3

J. Math. Phys. 53 (2012) 022501

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

45 pages, 4 figures, typos corrected, references added, proofs and explanations extended for readability

Scientific paper

10.1063/1.3675898

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.

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