On the Concept of Spin

TL;DR

This paper explores the geometric and group-theoretic foundations of spin, proposing a wave equation for spin-1/2 particles, and discusses the distinct nature of quark spin as a gauge field rather than a quantum number.

Contribution

It introduces a new perspective on spin as related to internal symmetry groups and proposes a wave equation for particles with spin one-half, offering insights into quark confinement.

Findings

Spin is linked to internal symmetry groups and spacetime geometry.

The Dirac equation describes electron spin as a quantum number.

Quark spin may originate from non-abelian gauge fields, not as a quantum number.

Abstract

It is substantiated that spin is a notion associated with the group of internal symmetry that is tightly connected with the geometrical structure of spacetime. The wave equation for the description of the particles with spin one half is proposed. On this ground it is shown that the spin of electron is exhibited through the quantum number and accordingly the Dirac equation describes properties of particles with the projection of spin equal plus or minus one half. On contrary, we put forward the conjecture that the spin of the quark cannot be considered as a quantum number, but only as an origin of a non-abelian gauge field. It is a deep reason for understanding quark-lepton symmetry and such important phenomena as quark confinement.