Generalised Hodge Decomposition for the SU(3) Gauss Law

The SU(3) Gauss law is solved using a non-Abelian generalisation of the Hodge decomposition. The behaviour of the solution is discussed near points where one component of the colour-magnetic field possesses coinciding eigenvalues. It turns out that the singularities in the solution formula can be removed, but three degrees of freedom are lost if the solution is assumed to be continuous everywhere.