Classical and Quantum Mechanics of Dirac-like Topological Charges in Yang-Mills Fields

Abstract

Most nonabelian gauge theories admit the existence of conserved and quantized topological charges as generalizations of the Dirac monopole. Their interactions are dictated by topology. In this paper, previous work in deriving classical equations of motion for these charges is extended to quantized particles described by Dirac wave functions. The resulting equations show intriguing similarities to the Yang-Mills theory. Further, although the system is not dual symmetric, its gauge symmetry is nevertheless doubled as in the abelian case from $G$ to $G \times G$, where the second $G$ has opposite parity to the first but is mediated instead by an antisymmetric second-rank tensor potential. (hep-th/yymmnnn)