Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity

TL;DR

This paper introduces spin foam models as a non-perturbative approach to quantum gravity, connecting various research areas and reviewing key models like Barrett-Crane for understanding quantum geometry.

Contribution

It provides a comprehensive overview of the formalism, ideas, and results of spin foam models, emphasizing their role in non-perturbative quantum gravity research.

Findings

Review of spin foam formalism and ideas

Discussion of quantum geometry emerging from models

Summary of results for Euclidean and Lorentzian cases

Abstract

This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity, topological quantum field theories, path integral quantum gravity, lattice field theory, matrix models, category theory, statistical mechanics. We describe the general formalism and ideas of spin foam models, the picture of quantum geometry emerging from them, and give a review of the results obtained so far, in both the Euclidean and Lorentzian case. We focus in particular on the Barrett-Crane model for 4-dimensional quantum gravity.