Relational Approach to Spin Networks

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.