Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations (Q1056934)

\textit{S. K. Wong}'s equations of motions for a spin zero particle in a classical Yang-Mills field [see Nuovo Cimento, Ser. X, A 65, 689-694 (1970)] are shown to be equivalent to the formulations of the same problem in a Kaluza-Klein type picture by \textit{B. Kerner} [see Ann. Inst. Henri Poincaré 9, 143-152 (1968)] in a symplectic geometrical picture by \textit{S. Sternberg} [Proc. Natl. Acad. Sci. USA 74, 5253-5254 (1977)], and in terms of a reduction by \textit{A. Weinstein} [see Lett. Math. Phys. 2, 417-420 (1978; Zbl 0388.58010)]. The equivalence of the last three formulations was established by showing that all predict the same world lines for the particles. The fact that Wong's equations are equivalent to the other three is shown here in a geometrical manner, by using the language of fibre bundles.