Three mathematical faces of SU(2) - spin networks

TL;DR

This paper explores the mathematical structures of SU(2) spin networks, aiming to connect discrete combinatorial models with continuous geometric frameworks to advance quantum gravity research.

Contribution

It introduces a novel approach to relate discrete spin network structures to continuous geometry, bridging a gap between combinatorial and geometric methods in quantum gravity.

Findings

Established a mathematical correspondence between spin networks and geometric structures

Proposed a new framework for integrating discrete and continuous models

Facilitated potential advancements in finite quantum gravity theories

Abstract

Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural backgraund, we would like to change the tack: to relate discrete (combinatorial) objects to the standard "contineous" geometry.