Quark State Confinement as a Consequence of the Extension of the Bose--Fermi Recoupling to SU(3) Colour

TL;DR

This paper extends the concept of Bose--Fermi recoupling from SU(2) to SU(3) colour, showing that quark confinement naturally arises from the mathematical structure of triality-based gradings.

Contribution

It introduces a non-associative recoupling framework for SU(3) colour, linking triality gradings to quark confinement as a fundamental consequence.

Findings

Recouplings graded by triality enforce quark confinement.

Only triality zero ensembles are physically permissible.

The approach generalizes Pauli exclusion to non-Z2 gradings.

Abstract

The Bose--Fermi recoupling of particles arising from the $\bZ_{2}$--grading of the irreducible representations of SU(2) is responsible for the Pauli exclusion principle. We demonstrate from fundamental physical assumptions how to extend this to gradings, other than the $\bZ_{2}$ grading, arising from other groups. This requires non--associative recouplings where phase factors arise due to {\it rebracketing} of states. In particular, we consider recouplings for the $\bZ_{3}$--grading of SU(3) colour and demonstrate that all the recouplings graded by triality leading to the Pauli exclusion principle demand quark state confinement. Note that quark state confinement asserts that only ensembles of triality zero are possible, as distinct from spatial confinement where particles are confined to a small region of space by a {\it confining force} such as given by the dynamics of QCD.