Relational Approach to Spin Networks

TL;DR

This paper presents a relational framework for spin networks that derives fundamental symmetries, particle masses, interactions, and gravity from an underlying SO(3,2) symmetry, reproducing key features of the standard model.

Contribution

It introduces a covariant relational approach to spin networks, deriving the standard model interactions and gravity from an SO(3,2) symmetry group.

Findings

Reproduces the lepton spectrum from cluster masses.

Derives standard model interaction terms from SO(3,2) symmetry.

Calculates the fine-structure constant matching Wyler's formula.

Abstract

Individual spinors in a SU(2) spin network are described by their relations to the background spin network. A 'covariant' formulation of these relations yields the de Sitter group SO(3,2) as the fundamental symmetry group. Locally this symmetry group is approximated by the Poincare group, which leaves invariant (certain) clusters of spinors. The calculated masses of these clusters reproduce the lepton spectrum. Corrections to the approximate Poincare group, based on the exact SO(3,2) symmetry, deliver interaction terms, identical to those of the standard model. In addition, gravitation is obtained. The calculation of the fine-structure constant reproduces Wyler's formula.