The Harari-Shupe preon model and nonrelativistic quantum phase space

TL;DR

This paper presents a novel algebraic approach to the Harari-Shupe preon model using phase space linearization, avoiding preon confinement issues and naturally linking quark color to rishon ordering.

Contribution

It introduces a Dirac-like linearization of phase space quadratic forms to derive the Harari-Shupe model's algebraic structure without preons.

Findings

Derives the model's algebra from phase space linearization

Links quark color to rishon ordering naturally

Proposes phase space rotations and reflections for quark-lepton transformations

Abstract

We propose that the whole algebraic structure of the Harari-Shupe rishon model originates via a Dirac-like linearization of quadratic form x^2+p^2, with position and momentum satisfying standard commutation relations. The scheme does not invoke the concept of preons as spin-1/2 subparticles, thus evading the problem of preon confinement, while fully explaining all symmetries emboded in the Harari-Shupe model. Furthermore, the concept of quark colour is naturally linked to the ordering of rishons. Our scheme leads to group U(1)xSU(3) combined with SU(2), with two of the SU(2) generators not commuting with reflections. An interpretation of intra-generation quark-lepton transformations in terms of genuine rotations and reflections in phase space is proposed.