Long range correlations in quantum gravity

TL;DR

This paper investigates the limitations of spin network formulations in quantum gravity for achieving classical long-range correlations, proposing modifications to the scalar constraint to improve correlation properties.

Contribution

It introduces a restriction on the scalar constraint's action based on Thiemann's length operator and analyzes the implications of this restriction on anomalies and correlations.

Findings

The proposed restriction prevents the creation of color unity edges.

The [scalar, scalar] commutator exhibits anomalies under the new restriction.

Achieving long-range correlations in quantum gravity spin networks remains challenging due to anomalies.

Abstract

Smolin has pointed out that the spin network formulation of quantum gravity will not necessarily possess the long range correlations needed for a proper classical limit; typically, the action of the scalar constraint is too local. Thiemann's length operator is used to argue for a further restriction on the action of the scalar constraint: it should not introduce new edges of color unity into a spin network, but should rather change preexisting edges by $\pm$ one unit of color. Smolin has proposed a specific ansatz for a correlated scalar constraint. This ansatz does not introduce color unity edges, but the [scalar, scalar] commutator is shown to be anomalous. In general, it will be hard to avoid anomalies, once correlation is introduced into the constraint; but it is argued that the scalar constraint may not need to be anomaly-free when acting on the kinematic basis.