Spin Foam Models of Quantum Gravity

TL;DR

This paper reviews spin foam models of quantum gravity, focusing on the Barrett-Crane model, its limitations, and introduces two new approaches involving 3D spin foam invariants and string scattering amplitudes.

Contribution

It provides a concise overview of existing models and proposes two innovative methods to address the shortcomings of the Barrett-Crane model.

Findings

Identified limitations of the Barrett-Crane model

Introduced 3D spin foam state sum invariants for embedded spin networks

Proposed representing string scattering amplitudes as 2D spin foam invariants

Abstract

We give a short review of the spin foam models of quantum gravity, with an emphasis on the Barret-Crane model. After explaining the shortcomings of the Barret-Crane model, we briefly discuss two new approaches, one based on the 3d spin foam state sum invariants for the embedded spin networks, and the other based on representing the string scattering amplitudes as 2d spin foam state sum invariants.