On the exact evaluation of spin networks

TL;DR

This paper introduces a coherent spin network amplitude that generates all SU(2) spin networks for a given graph and provides explicit evaluations for arbitrary graphs, advancing the mathematical tools in quantum gravity.

Contribution

It presents a new coherent amplitude for spin networks and derives explicit evaluations for any graph, enhancing computational methods in quantum gravity research.

Findings

Explicit evaluation of the coherent amplitude for arbitrary graphs

Derivation of a generating functional from parametrized intertwiners

Unified framework for spin network evaluation

Abstract

We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtained by the contraction of parametrized intertwiners a la Schwinger. We finally give the explicit evaluation of this generating functional for arbitrary graphs.