Barrett-Crane spin foam model from generalized BF-type action for gravity

TL;DR

This paper derives the Barrett-Crane spin foam model for quantum gravity from a generalized BF-type action, connecting it with the Plebanski formulation and analyzing discretization and quantization in both Euclidean and Lorentzian cases.

Contribution

It introduces a generalized action framework that naturally leads to the Barrett-Crane spin foam model, enhancing understanding of quantum gravity formulations.

Findings

Derivation of Barrett-Crane model from a generalized BF action

Analysis of constraints discretization in spin foam quantization

Applicability to both Euclidean and Lorentzian signatures

Abstract

We study a generalized action for gravity as a constrained BF theory, and its relationship with the Plebanski action. We analyse the discretization of the constraints and the spin foam quantization of the theory, showing that it leads naturally to the Barrett-Crane spin foam model for quantum gravity. Our analysis holds true in both the Euclidean and Lorentzian formulation.