An algebraic method for solving the SU(3) Gauss law

Abstract

A generalisation of existing SU(2) results is obtained. In particular, the source-free Gauss law for SU(3)-valued gauge fields is solved using a non-Abelian analogue of the Poincare lemma. When sources are present, the colour-electric field is divided into two parts in a way similar to the Hodge decomposition. Singularities due to coinciding eigenvalues of the colour-magnetic field are also analysed.Comment: 20 pages, LaTeX2e; references added, other changes minor; to appear in J. Math. Phy