Colour had been introduced as an internal degree of freedom to solve a conflict between the quark model for baryons and the Pauli exclusion principle.
The Δ++ state in the quark model without colour has the following decomposition in terms of space, flavour and spin, respectively:
The flavour state as well as the state are also symmetric under exchange of any pair of quarks. Hence, the state is symmetric resulting in a violation of the Pauli principle which requires an anti-symmetric state.
The Pauli principle can be rescued by introducing three colour charges 'red', 'blue' and 'green'. A state consisting of equal weights in the three different colour charges is a colour neutral state.
Free quarks have never been observed. As a consequence, there is the hypothesis that all hadrons consisting of quarks are always colour neutral states.
The corresponding colour state is the colour singlet
In the full quark model the full Δ++ is described by
