Generalized dual symmetry for non-Abelian Yang-Mills fields.

It is shown that classical nonsupersymmetric Yang-Mills theory in 4 dimensions is symmetric under a generalized dual transform which reduces to the usual dual *-operation for electromagnetism. The parallel phase transport Ãμ(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 Aμ(x). Sources of A are monopoles of à 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 respectively the classical and Dirac point charge; 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. ∗) Dedicated to the memory of Professor Sir Rudolf Peierls, 1907 1995.