The equations of the self-dual SU(3) gauge fields in the $R$ gauge with a Euclidean metric in a complexified space may be derived from a Lagrangian. The Lagrangian displays 12 symmetries of these fields. To these symmetries correspond divergence-free vectors (14 of them). It is remarkable that all eight SU(3) field equations are equivalent to eight divergence-free vectors. The symmetries permit finite transformations of given solutions of the field equations into new solutions. The divergence-free vectors suggest the existence of Bäcklund-type transformations of given solutions into new solutions. A five-element group of such transformations is given—one element being algebraic in nature, the other four being the form of integrable differentials. The elements of this group do not commute with the finite transformations so that from any given solution of the field equations an infinite set may be derived.

• Received 24 August 1981

DOI:https://doi.org/10.1103/PhysRevD.24.3161