Generalized dual symmetry for non-Abelian Yang-Mills fields

It is shown that classical nonsupersymmetric Yang-Mills theory in four dimensions is symmetric under a generalized dual transform which reduces to the usual dual * operation for electromagnetism. The parallel phase transport (A) over tilde(mu)(x) constructed earlier for monopoles is seen to function also as a potential in giving a full description of the gauge field, playing thus an entirely dual symmetric role to the usual potential A(mu)(x). Sources of A are monopoles of (A) over tilde and vice versa, and the Wu-Yang criterion for monopoles is found to yield as equations of motion the standard Wong and Yang-Mills equations for the classical and Dirac point charge, respectively; this applies whether the charge is electric or magnetic, the two cases being related just by a dual transform. The dual transformation itself is explicit, though somewhat complicated, being given in terms of loop space variables of the Polyakov type.