Tensor Forms of Differential Spinor Equations

  • Vladimir A. Zhelnorovich


Let us consider the four-dimensional pseudo-Euclidean Minkowski space with the metric signature (+, +, +, −) referred to an Cartesian coordinate system with the variables xi and holonomic vector basis Open image in new window (i = 1, 2, 3, 4). The contravariant and covariant components of the metric tensor of the Minkowski space calculated in the coordinate system xi are defined by the matrix.


  1. 6.
    Bergman, P.G.: Two-component spinors in general relativity. Phys. Rev. 107, 624–629 (1957)ADSMathSciNetCrossRefGoogle Scholar
  2. 17.
    Dürr, H., Heisenberg, W., Mitter, H., Schlieder, S., Yamazaki K.: Zur Theorie der Elementarteilchen. Zeitschrift für Naturforschung. A14, 441–485 (1959)ADSMathSciNetzbMATHGoogle Scholar
  3. 30.
    Golubyatnikov, A.N.: Model of the neutrino in the general theory of relativity. Sov. Phys. Dokl. 15, 451–453 (1970)ADSMathSciNetGoogle Scholar
  4. 36.
    Kent, R.D., Szamosi, G.: Spinor equations of motion in curved space-time. Nuovo Cimento. 64 B, 67–80 (1981)MathSciNetCrossRefGoogle Scholar
  5. 39.
    Kurdgelaidze, D.F.: On the nonlinear theory of elementary particles. J. Exp. Theor. Phys. 11, 339–346 (1960)MathSciNetzbMATHGoogle Scholar
  6. 41.
    Lichnerowicz, A.: Spineurs harmonicues. Compt. Rend. Paris. 257, 7–28 (1963)zbMATHGoogle Scholar
  7. 42.
    Luer, C.P., Rosenbaum, M.: Spinor connections in general relativity. J. Math. Phys. 15, 1120–1137 (1974)ADSMathSciNetCrossRefGoogle Scholar
  8. 44.
    Mickelsson, J.: On a relation between Maxwell and Dirac theories. Lett. Math. Phys. 6, 221–230 (1982)ADSMathSciNetCrossRefGoogle Scholar
  9. 45.
    Mickelsson, J.: The vector form of the neutrino equation and the photon neutrino duality. J. Math. Phys. 26, 2346–2349 (1985)ADSMathSciNetCrossRefGoogle Scholar
  10. 47.
    Ogievetskii, V.I., Polubarinov, I.V.: Spinors in gravitation theory. J. Exp. Theor. Phys. 21, 1093–1100 (1965)ADSMathSciNetGoogle Scholar
  11. 50.
    Penrose, R., Rindler, W.: Spinors and Space-Time, vol. 1. Cambridge University Press, Cambridge (1986)CrossRefGoogle Scholar
  12. 56.
    Reifler, F.: A vector wave equation for neutrinos. J. Math. Phys. 25, 1088–1092 (1984)ADSMathSciNetCrossRefGoogle Scholar
  13. 57.
    Reifler, F.: A vector model for electroweak interactions. J. Math. Phys. 26, 542–550 (1985)ADSMathSciNetCrossRefGoogle Scholar
  14. 58.
    Reifler, F., Morris, R. Hestenes’ tetrad and spin connections. Int. J. Theor. Phys. 44, 1307–1324 (2005)MathSciNetCrossRefGoogle Scholar
  15. 68.
    Takahashi, Y.: A Spinorization of the Frenet-Serret equation. Prog. Theor. Phys. 70, 1466–1467 (1983)ADSMathSciNetCrossRefGoogle Scholar
  16. 74.
    Zhelnorovich, V.A.: Spinor as an invariant. J. Appl. Math. Mech. 30, 1289–1300 (1966)CrossRefGoogle Scholar
  17. 76.
    Zhelnorovich, V.A.: Spinor field as the fusion of tensor fields. Mosc. Univ. Phys. Bull. 13, 705–714 (1972)MathSciNetGoogle Scholar
  18. 80.
    Zhelnorovich, V.A.: A tensor description of fields with half-integer spin. Sov. Phys. Dokl. 24, 899–901 (1979)ADSGoogle Scholar
  19. 82.
    Zhelnorovich, V.A.: Theory of Spinors and Its Application in Physics and Mechanics. Moscow, Nauka (1982) (in Russian)zbMATHGoogle Scholar
  20. 86.
    Zhelnorovich, V.A.: Dirac equations in the general theory of relativity. Sov. Phys. Dokl. 32, 726–728 (1987)ADSMathSciNetGoogle Scholar
  21. 88.
    Zhelnorovich V.A.: Complex vector triads in the theory of spinors in Minkowski space. Sov. Phys. Dokl. 35, 245–247 (1990)ADSMathSciNetzbMATHGoogle Scholar
  22. 90.
    Zhelnorovich, V.A.: Derivatives for spinor fields in three-dimensional space and some applications. Sov. Phys. Dokl. 38, 490–492 (1993)MathSciNetzbMATHGoogle Scholar
  23. 93.
    Zhelnorovich, V.A.: On Dirac equations in the formalism of spin coefficients. Gravit. Cosmol. 3, 97–99 (1997)ADSzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vladimir A. Zhelnorovich
    • 1
  1. 1.Institute of MechanicsMoscow State UniversityMoscowRussia

Personalised recommendations