Immirzi parameter in the Barrett-Crane model?

TL;DR

This paper investigates how the Immirzi parameter influences the Barrett-Crane spin foam model, finding it does not alter the fundamental representations but may affect the area spectrum, thus refining understanding of quantum geometry.

Contribution

It demonstrates that the Immirzi parameter can be incorporated into the Barrett-Crane model without changing its core representations, acting as a deformation that influences the area spectrum.

Findings

Immirzi parameter does not alter the simple representations used

The model remains based on a deformation of the Barrett-Crane model

The Immirzi parameter may appear as a factor in the area spectrum

Abstract

We study the generalised constrained BF theory described in gr-qc/0102073 in order to introduce the Immirzi parameter in spin foam models. We show that the resulting spin foam model is still based on simple representations and that the generalised BF action is simply a deformation of the Barrett-Crane model. The Immirzi parameter doesn't change the representations used in the spin foam model, so it doesn't affect the geometry of the model. However we show how it may still appear as a factor in the area spectrum.