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 redu ces to the usual dual operation for electromagnetism. The parallel p hase 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 th e usual potential A(mu)(x). Sources of A are monopoles of (A) over til de and vice versa, and the Wu-Yang criterion for monopoles is found to yield as equations of motion the standard Wong and Yang-Mills equatio ns for the classical and Dirac point charge, respectively; this applie s whether the charge is electric or magnetic, the two cases being rela ted just by a dual transform. The dual transformation itself is explic it, though somewhat complicated, being given in terms of loop space va riables of the Polyakov type.