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The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space

II. Completion of proof

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Abstract

In this paper we complete the proof of global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space by showing that an appropriate norm of the solutions cannot blow up in a finite time. A key step in the proof is the demonstration that theL∞ norm of the curvature is boundeda priori. Our results apply to any compact guage group and to any invariant Higgs self-coupling which is positive and of no higher than quartic degree.

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Author notes

  1. Douglas M. Eardley

    Present address: Harvard College Observatory, Harvard University, 02138, Cambridge, MA, USA

Authors and Affiliations

  1. Institute for Theoretical Physics, University of California at Santa Barbara, 93106, Santa Barbara, CA, USA

    Douglas M. Eardley

  2. Department of Physics, Yale University, 06520, New Haven, CT, USA

    Vincent Moncrief

Authors
  1. Douglas M. Eardley
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  2. Vincent Moncrief
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Additional information

Communicated by A. Jaffe

Supported in part by the National Science Foundation (Grant No. PHY79-16482 at Yale, Grant No. PHY77-27084 at Santa Barbara)

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Eardley, D.M., Moncrief, V. The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. Commun.Math. Phys. 83, 193–212 (1982). https://doi.org/10.1007/BF01976041

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  • DOI: https://doi.org/10.1007/BF01976041

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