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Spinors in the Four-Dimensional Pseudo-Euclidean Space

  • Vladimir A. Zhelnorovich
Chapter

Abstract

Let us consider the four-dimensional pseudo-Euclidean vector space \( E_4^1 \) of index 1 referred to an orthonormal basis Open image in new window , i = 1, 2, 3, 4.

References

  1. 15.
    Crawford, J.P.: On the algebra of Dirac bispinor densities: factorization and inversion. J. Math. Phys. 26, 1439–1441 (1985)ADSMathSciNetCrossRefGoogle Scholar
  2. 18.
    Ebner, D.: Classification of relativistic particles according to the representation theory of the eight nonisomorphic simply connected covering groups of the full Lorenz group. Gen. Relativ. Gravit. 8, 15–28 (1977)ADSCrossRefGoogle Scholar
  3. 25.
    Gel’fand, I.M., Minlos, R.A., Shapiro, Z.J.: Representation of the rotation group and of the Lorentz group, and their applicatins. Fizmatgiz, Moscow (1958); English transl.: Macmillan (1963)Google Scholar
  4. 31.
    Griffiths, J.B., Newing, R.A.: Tetrad equations for the two-component neutrino field in general relativity. J. Phys. A: Gen. Phys. 3, 269–273 (1970)ADSMathSciNetCrossRefGoogle Scholar
  5. 32.
    Gürsey, F.: Relativistic kinematics of a classical point particle in spinor form. Nuovo Cimento. 5, 784–809 (1957)CrossRefGoogle Scholar
  6. 34.
    Hara, O.: Space-time approach to the grand unified theory of the quarks and the leptons. Nuovo Chimento. 75A, 17–38 (1983)ADSMathSciNetCrossRefGoogle Scholar
  7. 35.
    Kaempffer, F.A.: Spinor electrodynamics as a dynamics of currents. Phys. Rev. D. 23, 918–921 (1981)ADSMathSciNetCrossRefGoogle Scholar
  8. 37.
    Klauder, J.: Linear representation of spinor fields by antisimmetric tensors. J. Math. Phys. 5, 1204–1214 (1964)ADSCrossRefGoogle Scholar
  9. 46.
    Newman, E., Penrose, R.: An approach to gravitational radiation by a method of spin coefficients. J. Math. Phys. 3, 566–578 (1962)ADSMathSciNetCrossRefGoogle Scholar
  10. 50.
    Penrose, R., Rindler, W.: Spinors and Space-Time, vol. 1. Cambridge University Press, Cambridge (1986)CrossRefGoogle Scholar
  11. 54.
    Rashevskii, P.K.: The theory of spinors. Usp. Mat. Nauk. 10, 3–110 (1955) (in Russian)MathSciNetGoogle Scholar
  12. 57.
    Reifler, F.: A vector model for electroweak interactions. J. Math. Phys. 26, 542–550 (1985)ADSMathSciNetCrossRefGoogle Scholar
  13. 65.
    Takabayasi, T.: Relativistic hidrodynamics equalent to the Dirac equation. Prog. Theor. Phys. 13, 222–224 (1955)ADSCrossRefGoogle Scholar
  14. 66.
    Takabayasi, T.: Symmetrical structure and conservation relations of four-component neutrino field. Nucl. Phys. 6, 477–488 (1958)CrossRefGoogle Scholar
  15. 67.
    Takahashi, Y.: Reconstructions of a spinor via Fierz identities. Phys. Rev. D, 26, 2169–2171 (1982)ADSMathSciNetCrossRefGoogle Scholar
  16. 70.
    Takahashi, Y., Okuda, K.: A spinorization of a constrained vector system and a spinor reconstruction theorem. Fortschr. Phys. 31, 511–534 (1983)MathSciNetCrossRefGoogle Scholar
  17. 73.
    Whittaker, E.T.: On the Relations of the tensor-calculus to the Spinor-calculus. Proc. R. Soc. A 158, 38–46 (1937)Google Scholar
  18. 74.
    Zhelnorovich, V.A.: Spinor as an invariant. J. Appl. Math. Mech. 30, 1289–1300 (1966)CrossRefGoogle Scholar
  19. 75.
    Zhelnorovich, V.A.: Representation of spinors by real and complex tensor aggregates. Theor. Math. Phys. 2, 66–77 (1970)MathSciNetCrossRefGoogle Scholar
  20. 88.
    Zhelnorovich V.A.: Complex vector triads in the theory of spinors in Minkowski space. Sov. Phys. Dokl. 35, 245–247 (1990)ADSMathSciNetzbMATHGoogle Scholar
  21. 89.
    Zhelnorovich, V.A.: Invariant tensor description of massless spinor fields. Sov. Phys. Dokl. 37, 34–36 (1992)ADSMathSciNetzbMATHGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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