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Polar analysis of the Dirac equation through dimensions

  • Luca FabbriEmail author
Regular Article

Abstract.

We consider the polar form of the spinor field equation in an n -dimensional space-time, studying the way in which the space-time dimension influences the number of the independent field equations and the number of the degrees of freedom of the spinor field written in the polar form: we will find that this polar form is the clearest tool to make manifest the fact that the degrees of freedom of the spinor field and the independent field equations match in dimensions 4 and 8 alone while in all the other instances there will be problems of general under-determination or over-determination.

References

  1. 1.
    P. Lounesto, Clifford Algebras and Spinors (Cambridge University Press, 2001)Google Scholar
  2. 2.
    M. Budinich, Adv. Appl. Clifford Algebras 29, 18 (2019)CrossRefGoogle Scholar
  3. 3.
    C. Castro, Adv. Appl. Clifford Algebras 24, 55 (2014)MathSciNetCrossRefGoogle Scholar
  4. 4.
    M. Gogberashvili, Int. J. Mod. Phys. A 21, 3513 (2006)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    D.S. Shirokov, Adv. Appl. Clifford Algebras 20, 411 (2010)MathSciNetCrossRefGoogle Scholar
  6. 6.
    R. Lopes, R. da Rocha, JHEP 08, 084 (2018)ADSCrossRefGoogle Scholar
  7. 7.
    R. da Rocha, J. Vaz Jr., J. Algebra 301, 459 (2011)CrossRefGoogle Scholar
  8. 8.
    R.T. Cavalcanti, Int. J. Mod. Phys. D 23, 1444002 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    H.L. Carrion, M. Rojas, F. Toppan, JHEP 04, 040 (2003)CrossRefGoogle Scholar
  10. 10.
    F. Toppan, JHEP 09, 016 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    S. Okubo, J. Math. Phys. 32, 1657 (1991)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    S. Okubo, J. Math. Phys. 32, 1669 (1991)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    J.M. Hoff da Silva, R. da Rocha, Phys. Lett. B 718, 1519 (2013)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    L. Bonora, K.P.S. de Brito, R. da Rocha, JHEP 02, 069 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    L. Fabbri, R. da Rocha, Phys. Lett. B 780, 427 (2018)ADSCrossRefGoogle Scholar
  16. 16.
    L. Fabbri, Int. J. Geom. Methods Mod. Phys. 13, 1650078 (2016)MathSciNetCrossRefGoogle Scholar
  17. 17.
    W.A. Rodrigues, Q.A.G. de Souza, J. Vaz, P. Lounesto, Int. J. Theor. Phys. 35, 1849 (1996)CrossRefGoogle Scholar
  18. 18.
    D. Hestenes, J. Math. Phys. 8, 798 (1967)ADSCrossRefGoogle Scholar
  19. 19.
    H. Krueger, Found. Phys. 23, 1265 (1993)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    L. Fabbri, Int. J. Geom. Methods Mod. Phys. 14, 1750037 (2017)MathSciNetCrossRefGoogle Scholar
  21. 21.
    L. Fabbri, Eur. Phys. J. C 78, 783 (2018)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.DIME Sez. Metodi e Modelli MatematiciUniversità di GenovaGenovaItaly

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