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

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Abstract

Wong [14] introduced equations of motion for a spin 0 particle in a Yang-Mills field which was widely accepted among physicists. It is shown that these are equivalent to the various mathematical formulations for the motion of such particles as given by the Kaluza-Klein formulation of Kerner [4], and those of Sternberg [11], and Weinstein [12]. In doing this, we show that Sternberg's space is, in a natural way, a symplectic leaf of a reduced Poisson manifold and relations to a construction of Kummer's [5] for dynamics on the cotangent bundle of a principle bundle are clarified.

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Authors and Affiliations

  1. Department of Mathematics, University of Berkeley, 94720, Berkeley, CA, USA

    Richard Montgomery

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  1. Richard Montgomery
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Montgomery, R. Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations. Lett Math Phys 8, 59–67 (1984). https://doi.org/10.1007/BF00420042

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  • DOI: https://doi.org/10.1007/BF00420042

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