Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations
type: Item
instance of: scholarly article
title: Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations
zbMATH Open document ID: 0562.53062
DOI: 10.1007/BF00420042
author: Richard Montgomery
published in: Letters in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 81V25
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 3895861
zbMATH Keywords: equations of motion
zbMATH Keywords: spin zero particle
zbMATH Keywords: Yang-Mills field
zbMATH Keywords: Wong's equations
zbMATH Keywords: fibre bundles
MaRDI profile type: Publication
cites work: Q4174811
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description: scientific article; zbMATH DE number 3895861