Spin Foam Models from the Tetrad Integration

TL;DR

This paper introduces a new class of spin foam models for four-dimensional quantum gravity derived from tetrad integration, extending the Barrett-Crane model and enabling fermionic matter coupling.

Contribution

It presents a novel spin foam model based on tetrad integration, allowing independent coloring of edges and faces for matter coupling in quantum gravity.

Findings

Model generalizes Barrett-Crane spin foam

Allows fermionic matter coupling via source terms

Provides a new framework for quantum gravity simulations

Abstract

We describe a class of spin foam models of four-dimensional quantum gravity which is based on the integration of the tetrad one-forms in the path integral for the Palatini action of General Relativity. In the Euclidian gravity case this class of models 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.