Wong's equations in Yang-Mills theory

2010/12/31 by S. N. Storchak, Storchak, S. N.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1101.0195

18 pages, v2; typos corrected; appendix and some references added

openalex publication_date 2010/12/31 · arxiv created 2011/09/28 · arxiv updated 2011/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive Wong's equations for the finite-dimensional dynamical system representing the motion of a scalar particle on a compact Riemannian manifold with a given free isometric smooth action of a compact semisimple Lie group. The obtained equations are written in terms of dependent coordinates which are typically used in an implicit description of the local dynamics given on the orbit space of the principal fiber bundle. Using these equations we obtain Wong's equations in a pure Yang--Mills gauge theory with the Coulomb gauge fixing. This result is based on the existing analogy between the reduction procedures carried out in our finite-dimensional dynamical system and in Yang-Mills gauge fields.

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