Advertisement

Advances in Applied Clifford Algebras

, Volume 27, Issue 4, pp 2901–2920 | Cite as

General Dynamics of Spinors

  • Luca Fabbri
Article
Part of the following topical collections:
  1. Homage to Prof. W.A. Rodrigues Jr

Abstract

In this paper, we consider a general twisted-curved space-time hosting Dirac spinors and we take into account the Lorentz covariant polar decomposition of the Dirac spinor field: the corresponding decomposition of the Dirac spinor field equation leads to a set of field equations that are real and where spinorial components have disappeared while still maintaining Lorentz covariance. We will see that the Dirac spinor will contain two real scalar degrees of freedom, the module and the so-called Yvon–Takabayashi angle, and we will display their field equations. This will permit us to study the coupling of curvature and torsion respectively to the module and the YT angle.

Keywords

Torsion-gravity Electrodynamics Spinors Zitterbewegung 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abłamowicz, R., Gonçalves, I., Rocha, R.: Bilinear covariants and spinor fields duality in quantum Clifford algebras. J. Math. Phys. 55, 103501 (2014)ADSCrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Campos, A.G., Cabrera, R., Rabitz, H.A., Bondar, D.I.: Analytic solutions to coherent control of the Dirac equation and beyond. arXiv:1705.02001 [quant-ph]
  3. 3.
    Cavalcanti, R.T., Hoff da Silva, J.M., da Rocha, R.: VSR symmetries in the DKP algebra: the interplay between Dirac and Elko spinor fields. Eur. Phys. J. Plus 129, 246 (2014)CrossRefGoogle Scholar
  4. 4.
    Coronado Villalobos, C.H., Hoff da Silva, J.M., da Rocha, R.: Questing mass dimension 1 spinor fields. Eur. Phys. J. C 75, 266 (2015)ADSCrossRefGoogle Scholar
  5. 5.
    Fabbri, L.: A generally-relativistic gauge classification of the Dirac fields. Int. J. Geom. Meth. Mod. Phys. 13, 1650078 (2016)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Fabbri, L.: Torsion gravity for Dirac fields. Int. J. Geom. Methods Mod. Phys. 14, 1750037 (2017)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Fabbri, L.: Torsion gravity for Dirac particles. Int. J. Geom. Methods Mod. Phys. 14, 1750127 (2017)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Hestenes, D.: Real spinor fields. J. Math. Phys. 8, 798 (1967)ADSCrossRefGoogle Scholar
  9. 9.
    Hestenes, D.: Local observables in the Dirac theory. J. Math. Phys. 14, 893 (1973)ADSCrossRefGoogle Scholar
  10. 10.
    Hestenes, D.: Observables, operators and complex numbers in the Dirac theory. J. Math. Phys. 16, 556 (1975)ADSCrossRefMathSciNetGoogle Scholar
  11. 11.
    Hestenes, D.: Quantum mechanics from self-interaction. Found. Phys. 15, 63 (1985)ADSCrossRefMathSciNetGoogle Scholar
  12. 12.
    Hestenes, D.: The Zitterbewegung interpretation of quantum mechanics. Found. Phys. 20, 1213 (1990)ADSCrossRefMathSciNetGoogle Scholar
  13. 13.
    Hiley, B.J., Callaghan, R.E.: The Clifford Algebra approach to quantum mechanics A: the Schroedinger and Pauli particles. arXiv:1011.4031 [math-ph]
  14. 14.
    Hiley, B.J., Callaghan, R.E.: The Clifford algebra approach to quantum mechanics B: the Dirac particle and its relation to the Bohm approach. arXiv:1011.4033 [math-ph]
  15. 15.
    Hiley, B.J., Callaghan, E.: Delayed-choice experiments and the Bohm approach. Phys Scr. 74, 336 (2006)ADSCrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Hoff da Silva, J.M., da Rocha, R.: Unfolding physics from the algebraic classification of spinor fields. Phys. Lett. B 718, 1519 (2013)ADSCrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Jakobi, G., Lochak, G.: Introduction des parametres relativistes de Cayley–Klein dans la representation hydrodynamique de l’equation de Dirac. Comptes Rendus Acad. Sci. 243, 234 (1956)Google Scholar
  18. 18.
    Krueger, H.: Classical limit of real Dirac theory: quantization of relativistic central field orbits. Found. Phys. 23, 1265 (1993)ADSCrossRefMathSciNetGoogle Scholar
  19. 19.
    MacKenzie, R.B., Paranjape, M.B.: From Q walls to Q balls. JHEP 0108, 003 (2001)ADSCrossRefMATHGoogle Scholar
  20. 20.
    Moya, A.M., Rodrigues, W.A., Wainer, S.A.: The Dirac–Hestenes equation and its relation with the relativistic de Broglie–Bohm theory. Adv. Appl. Clifford Algebras 27, 2639 (2017). arXiv:1610.09655 [math-ph]CrossRefMathSciNetGoogle Scholar
  21. 21.
    Recami, E., Salesi, G.: Kinematics and hydrodynamics of spinning particles. Phys. Rev. A 57, 98 (1998)ADSCrossRefMATHGoogle Scholar
  22. 22.
    Rocha, R., Cavalcanti, T.: Flag-dipole and flagpole spinor fluid flows in Kerr spacetimes. Phys. Atom. Nucl. 80, 329 (2017)ADSCrossRefGoogle Scholar
  23. 23.
    Rocha, R., Hoff da Silva, M.: ELKO, flagpole and flag-dipole spinor fields, and the instanton Hopf fibration. Adv. Appl. Clifford Algebras 20, 847 (2010)CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    Rocha, R., Fabbri, L., Hoff da Silva, J.M., Cavalcanti, R.T., Silva-Neto, A.: Flag-dipole spinor fields in ESK gravities. J. Math. Phys. 54, 102505 (2013)ADSCrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    Rodrigues, W.A., Wainer, S.A.: The relativistic Hamilton–Jacobi equation for a massive, charged and spinning particle, its equivalent Dirac equation and the de Broglie–Bohm theory. Adv. Appl. Clifford Algebras 27, 1779 (2017). arXiv:1610.03310 [math-ph]CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    Rodrigues, W.A., Souza, Q.A.G., Vaz, J., Lounesto, P.: Dirac–Hestenes spinor fields in Riemann–Cartan space-time. Int. J. Theor. Phys. 35, 1849 (1996)CrossRefMATHGoogle Scholar
  27. 27.
    Salesi, G., Recami, E.: About the kinematics of spinning particles. Adv. Appl. Clifford Algebras 7, S253 (1997)MATHGoogle Scholar
  28. 28.
    Takahashi, K.: Soliton solutions of nonlinear Dirac equations. J. Math. Phys. 20, 1232 (1979)ADSCrossRefMATHGoogle Scholar
  29. 29.
    Vignolo, S., Fabbri, L., Cianci, R.: Dirac spinors in Bianchi-I f(R)-cosmology with torsion. J. Math. Phys. 52, 112502 (2011)ADSCrossRefMATHMathSciNetGoogle Scholar
  30. 30.
    Welton, T.A.: Some observable effects of the quantum-mechanical fluctuations of the electromagnetic field. Phys. Rev. 74, 1157 (1948)ADSCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.DIME, Università di GenovaGenoaItaly

Personalised recommendations