Color Conservation, Color Rotations, and \(\textrm{SU}(N)\) Irreducible Representations

After defining color conservation, we discuss \(\textrm{SU}(N)\) transformations or “color rotations” and their action on quark, antiquark and gluon color indices, allowing to introduce the notion of \(\textrm{SU}(N)\) representation. Considering infinitesimal color rotations, we observe that color conservation is equivalent to the \(\textrm{SU}(N)\) invariance of color singlet parton systems. Finally, we show how the irreducible representations (irreps) of a multi-parton system emerge pictorially.