The Symmetry Reduction from Interactions to Particles

TL;DR

This paper explores how the complex non-Abelian symmetries of the standard model reduce to the simpler electromagnetic symmetry for particles, revealing the role of central correlations and symmetry breaking in particle interactions.

Contribution

It demonstrates that symmetry reduction results from central correlations in the internal group, leading to confinement or isospin breakdown, and clarifies the mathematical structure behind these phenomena.

Findings

Symmetry reduction from non-Abelian to Abelian groups for particles.

Central correlations determine hypercharge and isospin properties.

Symmetry breaking explains confinement and weak isospin breakdown.

Abstract

The hypercharge-isospin-color symmetry of the standard model interaction is drastically reduced to a remaining Abelian electromagnetic $\U(1)$-symmetry for the particles. It is shown that such a symmetry reduction comes as a consequence of the central correlation in the internal group as represented by the standard fields where the hypercharge properties are given by the central isospin-color properties. A maximal diagonalizable symmetry subgroup (Cartan torus) of the interaction group for the particles as eigenvectors has to discard either color (confinement) or isospin. An additional diagonalization for the external spin properties which come centrally correlated with the isospin properties enforces the weak isospin breakdown.