Solution of the non-Abelian Gauss law and duality transformation for 3+1-d Yang-Mills theory

The role played by the Gauss law in constructing a dual theory is emphasized. General solution of the non-Abelian Gauss law for 3+1-dimensional Yang-Mills theory is obtained. The problem of Gauge field copies is resolved. The important roles played by the operator epsilon(ijk) D[A](j) and the torsion-free condition for a dreibein are pointed out. Non- Abelian analogue of the Hodge decomposition is considered. Another natural decomposition of an arbitrary colour-triplet vector field using a new gauge potential and its field strength is addressed. This is important for a possible duality invariance. Duality transformation is obtained by using a generating function of a canonical transformation.