The Spin Foam Approach to Quantum Gravity

TL;DR

This paper reviews the current state of the spin foam approach to quantum gravity, focusing on new models for four-dimensional quantum gravity and their foundations in path integral quantization.

Contribution

It provides a pedagogical overview of recent spin foam models for 4D quantum gravity and discusses their motivation from the Plebanski formulation and simplicial regularization.

Findings

Introduction of new spin foam models for 4D quantum gravity

Analysis of 2+1 gravity as a simpler case for conceptual insights

Discussion of open issues in the spin foam approach to quantum gravity

Abstract

This article reviews the present status of the spin foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently introduced new models for four dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self-contained treatment of the 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.