The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. I. Local existence and smoothness properties. (English) Zbl 0496.35061


35L70 Second-order nonlinear hyperbolic equations
81T08 Constructive quantum field theory
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35L45 Initial value problems for first-order hyperbolic systems
35L65 Hyperbolic conservation laws
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[1] Eardley, D., Moncrief, V.: The global existence problem and cosmic censorship in general relativity. Yale preprint (1980) (to appear in GRG)
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[3] Segal, I.: Ann. Math.78, 339 (1963) · Zbl 0204.16004
[4] Segal, I.: J. Funct. Anal.33, 175 (1979). See also Ref. (5). · Zbl 0416.58027
[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)
[6] Nirenberg, L., Walker, H.: J. Math. Anal. Appl.42, 271 (1973) · Zbl 0272.35029
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[9] Christodoulou, D.: The boost problem for weakly coupled quasi-linear hyperbolic systems of the second order. Max-Planck-Institute preprint (1980)
[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 French · Zbl 0484.58028
[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) · Zbl 0486.35048
[12] Moncrief, V.: J. Math. Phys.21, 2291 (1980)
[13] Gribov, V. N.: Nucl. Phys.B139, 1 (1978)
[14] See, for example Marsden, J.: Applications of global analysis in mathematical physics, Sect. 3, Boston: Publish or Perish 1974 · Zbl 0367.58001
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