Quarks as a combinatorial puzzle: a new approach to quantum chromodynamics

Quarks cannot propagate outside the nucleons or mesons, but inside they seem to behave at high energies as almost free particles. An alternative approach to color dynamics is proposed. It is based on the observation that the $Z_2 \times Z_3 = Z_6$ cyclic group generated by the sixth root of unity can be put into one-to-one correspondence with three colors and three anti-colors.
If we identify 0 as "colorless", or "white", there are two ternary and three binary combinations of roots yielding zero. Combining spin with color, and including particle-antiparticle symmetry, we arrive at 12-component objects, satisfying generalized Dirac equation whose solutions cannot propagate alone due to the complex wave vectors, but can form propagating combinations via ternary or binary products.
Relativistic invariance implemented via non-standard complex realizations of the Lorentz group is also discussed.