The dynamics of a spinning colored particle in a background non-Abelian Yang-Mills field is of broad interest in many areas of physics. A physically important application arises in relativistic heavy-ion collisions, where hard probes such as heavy quarks and jets propagate through the strong early-time classical color fields collectively referred to as the glasma. The standard framework for describing the classical dynamics of colored particles in a background Yang-Mills field is provided by the Wong equations, but it does not incorporate spin degrees of freedom. Although several extensions of the Wong equations have been proposed to include spin, they generally fail to satisfy all the necessary requirements simultaneously, such as Lorentz covariance, allowance for an arbitrary chromomagnetic moment, and preservation of the required physical constraints. In this work, we extend the framework of a relativistic classical spinning particle in an electromagnetic field to describe spin-$1/2$ quarks propagating in a generic background non-Abelian Yang-Mills field. By systematically applying the Dirac-Bergmann algorithm, we derive a self-consistent set of equations of motion for the particle’s coordinates, momenta, spin, and color charge that satisfies all these requirements. This formalism provides a more complete and physically consistent description of spinning colored particles in background Yang-Mills fields and offers a suitable framework for studying momentum diffusion and spin polarization phenomena of hard probes in heavy-ion collisions, particularly in the glasma.

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• Jets & heavy flavor physics
• Quark-gluon plasma
• Relativistic heavy-ion collisions