q-Deformation of Lorentzian spin foam models

TL;DR

This paper develops a quantum-deformed Lorentzian spin foam model based on the quantum Lorentz group, demonstrating its finiteness and analyzing its algebraic properties.

Contribution

It introduces a quantum deformation of the Lorentzian EPRL model using the quantum Lorentz group, including new intertwiners and amplitude constructions.

Findings

The quantum EPRL model is finite.

The model's intertwiners exhibit specific braiding properties.

The construction provides a consistent quantum deformation of the Lorentzian spin foam.

Abstract

We construct and analyse a quantum deformation of the Lorentzian EPRL model. The model is based on the representation theory of the quantum Lorentz group with real deformation parameter. We give a definition of the quantum EPRL intertwiner, study its convergence and braiding properties and construct an amplitude for the four-simplexes. We find that the resulting model is finite.