Particle Dynamics in Constant Synthetic Non-Abelian Fields
Yang-Mills theory has extended well beyond its original role in describing the strong force and now emerges as an effective theory in condensed matter, ultracold atomic, and photonic systems. In these systems, the theory has been successful in explaining phenomena such as the spin-Hall effect, spin transport, and controlling the polarisation of light. Moreover, the ability to engineer and control synthetic non-Abelian gauge fields in these systems enables us to explore aspects of gauge dynamics inaccessible to high-energy experiments. In all the above mentioned cases, the state of the system evolves in an effective external Yang-Mills field. Thus, the study of test particle dynamics in such background fields is interesting in both the classical and quantum mechanical regimes. The background non-Abelian (color) gauge fields considered in this study are constant, and they generate uniform color magnetic fields or combined color electric and magnetic fields -- which are relevant configurations. Despite the apparent simplicity of these backgrounds, the coupled evolution of real space motion and internal color degrees of freedom results in rich, nontrivial behaviour that is qualitatively distinct from the electrodynamic (Abelian) case, such as unbounded trajectories in a constant color magnetic field. In particular, particle trajectories encode signatures of the underlying gauge sources. Finally, the classical dynamics presented in this paper serves as a precursor to the complete quantum mechanical treatment to follow.