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${\mathrm{̃}}_{\mathrm{\mu }}$(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 ${\mathit{A}}_{\mathrm{\mu }}$(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 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. © 1996 The American Physical Society.

• Received 15 December 1995

DOI:https://doi.org/10.1103/PhysRevD.53.7293