NON-ABELIAN YANG-MILLS ANALOG OF CLASSICAL ELECTROMAGNETIC DUALITY

The classic question of a non-Abelian Yang-Mills analogue to electromagnetic duality is examined here in a minimalist fashion at the strictly four-dimensional, classical field, and point charge level. A generalization of the Abelian Hedge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the Abelian theory. For example, there is a dual potential, but it is a two-indexed tensor T-mu nu of the Freedman-Townsend-type, Though not itself functioning as such, T-mu nu gives rise to a dual parallel transport <(A)over tilde (mu)> for the phase of the wave function of the color magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard color (electric) charge itself is found to be a monopole of <(A)over tilde (mu)>. At the same time, the gauge symmetry is found doubled from say SU(N) to SU(N) x SU(N). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a ''universal'' principle, namely, the Wu-Yang criterion for monopoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of Polyakov.