Tetrade Spin Foam Model

TL;DR

This paper introduces a new four-dimensional quantum gravity spin foam model derived from the Palatini action, extending the Barrett-Crane model and allowing fermionic matter coupling through a novel coloring scheme.

Contribution

It presents a tetrad-based spin foam model that modifies existing models and incorporates fermionic matter coupling via independent coloring of edges and faces.

Findings

Model reduces to a modified Barrett-Crane model in Euclidean case

Fermionic matter can be coupled using sources for tetrads and spin connection

Edges and faces are independently colored with irreducible representations

Abstract

We propose a spin foam model of four-dimensional quantum gravity which is based on the integration of the tetrads in the path integral for the Palatini action of General Relativity. In the Euclidian gravity case we show that the model can be understood as a modification of the Barrett-Crane spin foam model. Fermionic matter can be coupled by using the path integral with sources for the tetrads and the spin connection, and the corresponding state sum is based on a spin foam where both the edges and the faces are colored independently with the irreducible representations of the spacetime rotations group.