4-dimensional spin-foam model with quantum Lorentz group

Abstract

We study the quantum group deformation of the Lorentzian EPRL spin-foam model. The construction uses the harmonic analysis on the quantum Lorentz group. We show that the quantum group spin-foam model so defined is free of the infra-red divergence, thus gives a finite partition function on a fixed triangulation. We expect this quantum group spin-foam model is a spin-foam quantization of discrete gravity with a cosmological constant.