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Communications in Mathematical Physics

, Volume 83, Issue 2, pp 171–191 | Cite as

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

I. Local existence and smoothness properties
  • Douglas M. Eardley
  • Vincent Moncrief
Article

Abstract

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Gauge Group 
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References

  1. 1.
    Eardley, D., Moncrief, V.: The global existence problem and cosmic censorship in general relativity. Yale preprint (1980) (to appear in GRG)Google Scholar
  2. 2.
    Moncrief, V.: Ann. Phys. (N.Y.)132, 87 (1981)Google Scholar
  3. 3.
    Segal, I.: Ann. Math.78, 339 (1963)Google Scholar
  4. 4.
    Segal, I.: J. Funct. Anal.33, 175 (1979). See also Ref. (5).Google Scholar
  5. 5.
    The choice of function spaces made in Ref. (4) was subsequently amended in an erratum (J. Funct. Anal.). The original choice suffers from the difficulty described in the introduction to this paper. A more complete treatment of the amended local existence argument has been given by Ginibre and Velo (see Ref. (11) below)Google Scholar
  6. 6.
    Nirenberg, L., Walker, H.: J. Math. Anal. Appl.42, 271 (1973)Google Scholar
  7. 7.
    Cantor, M.: Ind. U. Math. J.24, 897 (1975)Google Scholar
  8. 8.
    McOwen, R.: Commun. Pure Appl. Math.32, 783 (1979)Google Scholar
  9. 9.
    Christodoulou, D.: The boost problem for weakly coupled quasi-linear hyperbolic systems of the second order. Max-Planck-Institute preprint (1980)Google Scholar
  10. 10.
    Choquet-Bruhat, Y., Christodoulou, D.: Elliptic systems in Hilbert spaces on manifolds which are euclidean at infinity, preprint (1980). See also C R Acad. Sci. Paris,290, 781 (1980) for a version of this paper in FrenchGoogle Scholar
  11. 11.
    Ginibre, J., Velo, G.: The Cauchy problem for coupled Yang-Mills and scalar fields in the temporal gauge, Commun. Math. Phys.82, 1–28 (1981); See also Phys. Lett.99B, 405 (1981)Google Scholar
  12. 12.
    Moncrief, V.: J. Math. Phys.21, 2291 (1980)Google Scholar
  13. 13.
    Gribov, V. N.: Nucl. Phys.B139, 1 (1978)Google Scholar
  14. 14.
    See, for example Marsden, J.: Applications of global analysis in mathematical physics, Sect. 3, Boston: Publish or Perish 1974Google Scholar
  15. 15.
    Reed, M., Simon, B.: Methods of modern mathematical physics. II. Fourier analysis and self-adjointness. New York: Academic 1975Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Douglas M. Eardley
    • 1
  • Vincent Moncrief
    • 2
  1. 1.Harvard College ObservatoryHavard UniversityCambridgeUSA
  2. 2.Department of PhysicsYale UniversityNew HavenUSA

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