GENERAL-SOLUTION OF THE NON-ABELIAN GAUSS LAW AND NON-ABELIAN ANALOGSOF THE HODGE DECOMPOSITION - ART. NO. 067702

A general solution of the non-Abelian Gauss law in terms of covariant curls and gradients is presented. Also two non-Abelian analogues of th e Hedge decomposition in three dimensions are addressed: (i) A decompo sition of an isotriplet vector field V-i(a)(x) as the sum of a covaria nt curl and gradient with respect to an arbitrary background Yang-Mill s potential is obtained; (ii) a decomposition of the form V-i(a)=B-i(a )(C) + D-i(C) phi(a) which involves a non-Abelian magnetic field of a new Yang-Mills potential C is also presented. These results are releva nt for duality transformation for non-Abelian gauge fields. [S0556-282 1(98)07416-5].