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

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.