Particle dynamics in constant synthetic non-abelian fields -I. The classical treatment

Yang–Mills theory has evolved beyond its origins in the strong interaction to become an effective framework for condensed matter, ultracold atomic, and photonic systems, where synthetic non-Abelian gauge fields enable phenomena such as spin transport, the spin-Hall effect, and polarisation control. These systems provide access to gauge-field dynamics beyond the reach of high-energy experiments. In all the above mentioned cases, the state of the system evolves in an effective external Yang-Mills field. Here, we report the results of a classical study (as preparatory for a full quantum study) of particle dynamics in constant gauge fields produced by constant gauge potentials, by focussing on configurations that are experimentally relevant. We show that consequences such as unbounded trajectories in a constant color magnetic field and unusual correlation between charge and color dynamics have a direct bearing on the physical phenomena observed, especially in experiments involving charge and spin transports. More generally, this work also shows how the low energy systems can act as laboratories to probe quintessentially non-Abelian features such as the Wu-Yang ambiguity.