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Linear and nonlinear Dirac equation

  • Part III. Invited Papers Dedicated To David Hestenes
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Abstract

Using the usual matrix representation of Clifford algebra of spacetime, quantities independent of the choice of a representation in the Dirac theory are examined, relativistic invariance of the theory is discussed, and a nonlinear equation is proposed. The equation presents no negative energy waves and gives the same results as the linear theory for hydrogen atom.

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References

  1. P. A. M. Dirac,Proc. R. Soc. (London) 117, 610 (1928).

    Google Scholar 

  2. D. Hestenes,Space-Time Algebra (Gordon & Breach, New York, 1966, 1987, 1992).

    Google Scholar 

  3. D. Hestenes, “Real spinor fields,”J. Math. Phys. 8, 728–808 (1967).

    Google Scholar 

  4. D. Hestenes, “Local observables in the Dirac theory,”J. Math. Phys. 14, 893–905 (1973).

    Google Scholar 

  5. D. Hestenes, “Proper particle mechanics,”J. Math. Phys. 15, 1768–1777 (1974).

    Google Scholar 

  6. D. Hestenes, “Proper dynamics of a rigid point particle,”J. Math. Phys. 15, 1778–1786 (1974).

    Google Scholar 

  7. D. Hestenes, “Observables, operators and complex numbers in the Dirac theory,”J. Math. Phys. 16, 556–572 (1975).

    Google Scholar 

  8. C. Daviau, “Electromagnétisme, monopôles magnétiques et ondes de matière dans l'algèbre d'espace-temps,”Ann. Fond. Louis de Broglie 14(3 and 4) (1989).

  9. C. Daviau and G. Lochak, “Sur un modèle d'équation spinorielle non linéaire,”Ann. Fond. Louis de Broglie 16(1) (1991).

  10. C. Daviau, “Pourquoi il faut lire Hestenes,”Ann. Fond. Louis de Broglie 16, 391–403 (1991).

    Google Scholar 

  11. C. Daviau, Equation de Dirac non linéaire (Thesis, University of Nantes), 1993.

  12. R. Boudet, “Conservation laws in the Dirac theory,”J. Math. Phys. 26, 718–724 (1985).

    Google Scholar 

  13. G. Jakobi and G. Lochak, “Introduction des paramètres relativistes de Cayley-Klein dans la représentation hydrodynamique de l'équation de Dirac,”C. R. Acad. Sci. 234, 234–237 (1956).

    Google Scholar 

  14. Louis de Broglie,La réinterprétation de la mécanique ondulatoire (Gauthier-Villars, Paris, 1971).

    Google Scholar 

  15. D. Hestenes, “Clifford algebra and the interpretation of quantum mechanics,”Clifford algebras and Their Applications in Mathematical Physics, J. S. R. Chisholm and A. K. Common, eds. (Reidel, Dordrecht, 1986).

    Google Scholar 

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Daviau, C. Linear and nonlinear Dirac equation. Found Phys 23, 1431–1443 (1993). https://doi.org/10.1007/BF01243940

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  • DOI: https://doi.org/10.1007/BF01243940

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