Non-perturbative on-shell multiplet structure of SU(N) Yang-Mills fields

TL;DR

This paper classifies on-shell color multiplets in SU(N) Yang-Mills theory using a non-perturbative approach based on the Weyl group, revealing a universal color structure and redefining fundamental particles beyond perturbation theory.

Contribution

It provides a rigorous non-perturbative classification of quark and gluon multiplets based on Weyl group representations, introducing new concepts of fundamental particles.

Findings

Weyl group reveals inherent color symmetry on mass shell.

Universal color multiplet structure for quarks and gluons.

Redefinition of fundamental particles in non-perturbative context.

Abstract

Color multiplets of the gauge fields and fermions on mass shell in SU(N) Yang-Mills theory are classified according to representations of the Weyl group W(SU(N)). The multiplet structure of quark and gluon multiplets has been studied in the framework of a non-perturbative approach by considering complete exact equations of motion of the SU(N) Yang-Mills theory with matter fields. An important case of singlet non-Abelian gluon solutions corresponding to one-dimensional singlet representations of the Weyl group is revised on a rigorous mathematical basis. We demonstrate that Weyl group as a finite color subgroup of SU(N) reveals an inherent color symmetry of quarks and gluons on mass shell which determines a universal color miltiplet structure of quark-gluon solutions in a pure SU(N) Yang-Mills theory and in Abelian projected Yang-Mills theories with quarks. The obtained results allow to introduce strict concepts of fundamental particles, quarks and gluons, which differ drastically from the particle definitions in the conventional perturbative Yang-Mills theory. Possible applications of our results in non-perturbative quantum chromodynamics and hadron physics are discussed.