Skip to main content

Solution globale des equations de Maxwell-Dirac-Klein-Gordon


We prove the global existence on Minkowski space time of a solution of the Cauchy problem for the non linear system of coupled Maxwell, Dirac and Klein-Gordon equations, for small data with appropriate decay at space-like infinity. The method uses the conformal mapping of Minkowski space time onto a bounded open set of the Einstein cylinder.

This is a preview of subscription content, access via your institution.


  1. Lichnerowicz A.,Champs spinoriels et propagateurs en relativité générale, Bull. Soc. Math. Fr.,92 (1964), 11–100.Champ de Dirac, champ de neutrino et transformations,C, P, T, sur un espace temps courbe, Ann. Inst. H. Poincaré, I, n. 3 (1964), 233–290.

    MATH  MathSciNet  Google Scholar 

  2. Lichnerowicz A.,Topics on space time, Battelle rencontres, C. De Witt and J. W. Wheeler ed., Benjamin 1967.

  3. Geroch R.,Local characterization of singularities in general relativity, J. Math. Phys.,9 (1968), 1739 etSpinor structure of Space-Times in general relativisty,11 (1970), 343.

    MATH  Article  MathSciNet  Google Scholar 

  4. Dimock J.,Algebras of Local observables on a Manifold, Comm. Maths. Phys. Vol.77, n. 3 (1980), 219.

    MATH  Article  MathSciNet  Google Scholar 

  5. Castagnino M.,The Quantum Equivalence Principle and Spin 1/2 massive particles, Ann. Inst. H. Poincaré, XXXV, n. 1 (1981), 55.

    MathSciNet  Google Scholar 

  6. Leray J.,Hyperbolic Partial Differential Equations, I.A.S., Princeton, 1952.

    Google Scholar 

  7. Hughes T., Kato T., Marsden J.,Well posed Quasilinear Second Order Hyperbolic Systems with Applications to Nonlinear Elastodynamics and Global Relativity, Arch. Rat. Mech. An. 63, n. 3 (1977), 273–294.

    MATH  MathSciNet  Google Scholar 

  8. Choquet-Bruhat Y., Christodoulou D., Francaviglia M.,Cauchy data on a manifold, Ann. Inst. H. Poincaré, XXIX,3 (1978), 241–255.

    MathSciNet  Google Scholar 

  9. Glassey R. T., Strauss W. A.,Conservation laws for the Classical Maxwell-Dirac and Klein Gordon-Dirac equations, J. Maths. Phys. 20, n. 3 (1979), 454–458.

    Article  MathSciNet  Google Scholar 

  10. Choquet-Bruhat Y.,The Cauchy Problem, Chap. IV of «Gravitation, and Introduction to Current Research», L. Witten ed., J. Wiley, 1962.

  11. Segal I. E.,The global Cauchy Problem for a Relativistic Scalar Field with power interaction, Bull. Soc. Math. Fr.,91 (1963), 129–135.

    MATH  Google Scholar 

  12. Reed M.,Abstract non linear wave equations, Springer lecture Notes, 1976.

  13. Moncrief V.,Global existence of Maxwell-Klein Gordon fields in (2+1)-dimensional space time, J. Maths. Phys.,21, 8 (1980), 2291–2296.

    Article  MathSciNet  Google Scholar 

  14. Orsted B.,A Note on the Conformal Quasi-Invariance of the Laplacian on a Pseudo Riemannian Manifold, Letters in Math. Phys.,1, 3 (1976), 183.

    MATH  Article  MathSciNet  Google Scholar 

  15. Branson T.,Conformally invariant equations on differential forms, J. Diff. Geometry (à paraître).

  16. Penrose R.,Structure of Space Time, in Battelle Rencontres, C. De Witt and J. Wheeler ed., Benjamin 1967.

  17. Chadam J.,Asymptotic behavior of equations for a relativistic scalar field with power interaction, Applicable Analysis,3 (1973), 377–402.

    Article  MathSciNet  Google Scholar 

  18. Christodoulou D.,Solutions globales des équations de Yang et Mills, C. R. Ac. Sc. Paris, t. 293 (1981).

Download references

Author information

Authors and Affiliations


Additional information

Ce travail a été complété et rédigé à l'Université de Californie, à Santa Barbara, grâce à l'hospitalitè stimulante de l'Institute for Theoretical Physics. Une version préliminaire avait été exposée le 26 novembre 1980 au séminaire J. Vaillant.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Choquet-bruhat, Y. Solution globale des equations de Maxwell-Dirac-Klein-Gordon. Rend. Circ. Mat. Palermo 31, 267–288 (1982).

Download citation

  • Received:

  • Issue Date:

  • DOI: