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

In this paper and its sequel we shall prove the local and then the global existence of solutions of the classical Yang-Mills-Higgs equations in the temporal gauge. This paper proves local existence uniqueness and smoothness properties and improves, by essentially one order of differentiability, previous local existence results. Our results apply to any compact gauge group and to any invariant Higgs self-coupling which is positive and of no higher than quartic degree.

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1. Harvard College Observatory, Havard University, 02138, Cambridge, MA, USA

   Douglas M. Eardley

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

   Vincent Moncrief

1. Douglas M. Eardley
2. Vincent Moncrief

Communicated by A. Jaffe

Supported in part by the National Science Foundation (Grant No. PHY79-16482 at Yale)

Eardley, D.M., Moncrief, V. The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. Commun.Math. Phys. 83, 171–191 (1982). https://doi.org/10.1007/BF01976040

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• Received: 20 April 1981

• Revised: 19 June 1981

• Issue Date: February 1982

• DOI: https://doi.org/10.1007/BF01976040

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