4-dimensional Spin-foam Model with Quantum Lorentz Group

TL;DR

This paper develops a quantum group-deformed Lorentzian spin-foam model that is finite and free of infra-red divergences, potentially representing a quantum gravity model with a cosmological constant.

Contribution

It introduces a quantum Lorentz group deformation of the EPRL spin-foam model, ensuring finiteness and divergence-free behavior in the quantum gravity framework.

Findings

The quantum group spin-foam model is free of infra-red divergence.

The model yields a finite partition function on fixed triangulations.

It is proposed as a quantization of discrete gravity with a cosmological constant.

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.