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

TL;DR

This paper extends classical equations of motion for topological charges in Yang-Mills fields to the quantum regime, revealing doubled gauge symmetry and similarities to Yang-Mills theory, with implications for quantized topological charges.

Contribution

It introduces a quantum framework for topological charges in Yang-Mills fields, showing doubled gauge symmetry and new equations akin to Yang-Mills theory.

Findings

Classical equations extended to quantum Dirac particles.

Gauge symmetry doubled from G to G×G.

System exhibits similarities to Yang-Mills theory.

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)