From Clifford Algebra of Nonrelativistic Phase Space to Quarks and Leptons of the Standard Model

TL;DR

This paper presents a Clifford algebra framework for elementary particles, linking phase space symmetries to Standard Model quantum numbers, offering a subquark-less explanation of particle structure and hadron composition.

Contribution

It introduces a Clifford algebra approach to derive Standard Model quantum numbers from phase space symmetries, providing a novel perspective on particle classification and hadron structure.

Findings

Identifies internal quantum numbers from phase space symmetries.

Provides a subquark-less explanation of the Harari-Shupe model.

Suggests new ideas on hadron construction from quarks.

Abstract

We review a recently proposed Clifford-algebra approach to elementary particles. We start with: (1) a philosophical background that motivates a maximally symmetric treatment of position and momentum variables, and: (2) an analysis of the minimal conceptual assumptions needed in quark mass extraction procedures. With these points in mind, a variation on Born's reciprocity argument provides us with an unorthodox view on the problem of mass. The idea of space quantization suggests then the linearization of the nonrelativistic quadratic form ${\bf p}^2 +{\bf x}^2$ with position and momentum satisfying standard commutation relations. This leads to the 64-dimensional Clifford algebra ${Cl}_{6,0}$ of nonrelativistic phase space within which one identifies the internal quantum numbers of a single Standard Model generation of elementary particles (i.e. weak isospin, hypercharge, and color). The relevant quantum numbers are naturally linked to the symmetries of macroscopic phase space. It is shown that the obtained phase-space-based description of elementary particles gives a subquark-less explanation of the celebrated Harari-Shupe rishon model. Finally, the concept of additivity is used to form novel suggestions as to how hadrons are constructed out of quarks and how macroscopically motivated invariances may be restored at the hadron level.