Simplicity and closure constraints in spin foam models of gravity

TL;DR

This paper revises the implementation of simplicity and closure constraints in 4D spin foam models of gravity, proposing a new approach that incorporates holonomy constraints and covariance of intertwiners, linking to covariant loop quantum gravity.

Contribution

It introduces a modified set of constraints in spin foam models, emphasizing the explicit inclusion of holonomy constraints and the covariance of intertwiners, enhancing the connection to covariant loop quantum gravity.

Findings

Boundary states are realized as projected spin networks.

The usual simplicity constraint must be supplemented by a holonomy constraint.

Closure constraints are relaxed to express covariance of intertwiners.

Abstract

We revise imposition of various constraints in spin foam models of 4-dimensional general relativity. We argue that the usual simplicity constraint must be supplemented by a constraint on holonomies and together they must be inserted explicitly into the discretized path integral. At the same time, the closure constraint must be relaxed so that the new constraint expresses covariance of intertwiners assigned to tetrahedra by spin foam quantization. As a result, the spin foam boundary states are shown to be realized in terms of projected spin networks of the covariant loop approach to quantum gravity.