$$\require{cancel}$$
So why don’t we see fractional charges in nature? This is an important point! In so-called deep inelastic scattering we see pips inside the nucleon – these have been identified as the quarks. We do not see any direct signature of individual quarks. Furthermore, if quarks are fermions, as they are spin $$1/2$$ particles, what about antisymmetry of their wavefunction? Let us investigate the $$\Delta^{++}$$, see Fig. [fig:D++], which consists of three $$u$$ quarks with identical spin and flavour (isospin) and symmetric spatial wavefunction, $\psi_{\rm total} = \psi_{\rm space} \times \psi_{\rm spin} \times \psi_{\rm flavour}.$ This would be symmetric under interchange, which is unacceptable. Actually there is a simple solution. We “just” assume that there is an additional quantity called colour, and take the colour wave function to be antisymmetric: $\psi_{\rm total} = \psi_{\rm space} \times \psi_{\rm spin} \times \psi_{\rm flavour} \times \psi_{\rm colour}$ We assume that quarks come in three colours. This naturally leads to yet another $$SU(3)$$ symmetry, which is actually related to the gauge symmetry of strong interactions, QCD. So we have shifted the question to: why can’t we see coloured particles?