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.
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Eardley, D., Moncrief, V.: The global existence problem and cosmic censorship in general relativity. Yale preprint (1980) (to appear in GRG)
Moncrief, V.: Ann. Phys. (N.Y.)132, 87 (1981)
Segal, I.: Ann. Math.78, 339 (1963)
Segal, I.: J. Funct. Anal.33, 175 (1979). See also Ref. (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)
Nirenberg, L., Walker, H.: J. Math. Anal. Appl.42, 271 (1973)
Cantor, M.: Ind. U. Math. J.24, 897 (1975)
McOwen, R.: Commun. Pure Appl. Math.32, 783 (1979)
Christodoulou, D.: The boost problem for weakly coupled quasi-linear hyperbolic systems of the second order. Max-Planck-Institute preprint (1980)
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 French
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)
Moncrief, V.: J. Math. Phys.21, 2291 (1980)
Gribov, V. N.: Nucl. Phys.B139, 1 (1978)
See, for example Marsden, J.: Applications of global analysis in mathematical physics, Sect. 3, Boston: Publish or Perish 1974
Reed, M., Simon, B.: Methods of modern mathematical physics. II. Fourier analysis and self-adjointness. New York: Academic 1975
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Communicated by A. Jaffe
Supported in part by the National Science Foundation (Grant No. PHY79-16482 at Yale)
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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, 171–191 (1982). https://doi.org/10.1007/BF01976040
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DOI: https://doi.org/10.1007/BF01976040