Quantum deformation of two four-dimensional spin foam models

Understand

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.