Boundary terms in the Barrett-Crane spin foam model and consistent gluing

TL;DR

This paper explores boundary terms and gluing procedures in the Barrett-Crane spin foam model for quantum gravity, providing consistency checks and discussing potential variations to improve the model's formulation.

Contribution

It extends the derivation of the Barrett-Crane model to different boundary conditions and analyzes the effects on boundary terms and simplex gluing.

Findings

Different boundary conditions lead to varied boundary terms.

The gluing of 4-simplices can be consistently re-analyzed under new boundary conditions.

The study suggests possible modifications and their implications for the model.

Abstract

We extend the lattice gauge theory-type derivation of the Barrett-Crane spin foam model for quantum gravity to other choices of boundary conditions, resulting in different boundary terms, and re-analyze the gluing of 4-simplices in this context. This provides a consistency check of the previous derivation. Moreover we study and discuss some possible alternatives and variations that can be made to it and the resulting models.