Investigation of gauge ambiguity by means of the theory of harmonic maps

For the non-abelian gauge field theory with the gauge group $G=SU(2)$, $SO(4)$, $SU(3)$ in $n=2$ or $n=4$ dimension some infinite-dimensional and (in the case of $G=SU(3)$) some finite-dimensional sets of potentials $A_{\mu}=g^{-1}\partial_{\mu}g$ satisfying the gauge condition $\partial_{\mu}A_{\mu}=0$ are found in an explicit form. The number of dimensions of the intersection of the orbit $A_{\mu}=g^{-1}\partial_{\mu}g$ with the surface $\partial_{\mu}A_{\mu}=0$ is discussed.