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Euclidean Yang-Mills flows in the orbit space

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1045)

Abstract

We establish a global setting for the canonical formalism of the Euclidean Yang-Mills theory in the orbit space M. In this setting it is shown that the Euclidean Yang-Mills equations lead to an ordinary second order differential system of M and the (anti) self-dual solutions are in the flow of a densely defined vector field ±H of M. We also prove that, for the particular case of having T3 as space manifold the flows ±H are homotopic complete, i.e., in each class of π1(M) there exists a closed integral curve of ±H.

Keywords

  • Gauge Transformation
  • Integral Curve
  • Orbit Space
  • Principal Bundle
  • Principal Fibre Bundle

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© 1984 Springer-Verlag

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Asorey, M. (1984). Euclidean Yang-Mills flows in the orbit space. In: Naveira, A.M. (eds) Differential Geometry. Lecture Notes in Mathematics, vol 1045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072161

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  • DOI: https://doi.org/10.1007/BFb0072161

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12882-3

  • Online ISBN: 978-3-540-38766-4

  • eBook Packages: Springer Book Archive