Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Cartan mapping and spinors in affinely connected space-time

  • 19 Accesses

Abstract

It is shown that Cartan spinors with a pair of mutual spinor connections exist only in a Weyl-nonmetric, affinely connected space-time with a torsion tensor absolutely antisymmetric in an orthonormal frame.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    É. Cartan, Theory of Spinors [Russian translation], IL, Moscow (1947).

  2. 2.

    V. Fock and D. D. Ivanenko, Compt. Rend. (Paris) Acad. Sci.,188, 1470 (1929).

  3. 3.

    H. Ruse, Proc. R. Soc. Edinburgh,57, 97 (1937).

  4. 4.

    R. Penrose and V. Rindler, Spinors and Space-Time, Vol. 1: Two-Spinor Calculus and Relativistic Fields; Vol. 2: Spinor and Twistor Methods in Space-Time, Cambridge Univ. Press, New York (1984, 1986); paperback (1987, 1988).

  5. 5.

    D. D. Ivanenko, P. I. Pronin, and G. A. Sardanashvili, Gauge Theory of Gravitation [in Russian], Izd. MGU, Moscow (1984).

  6. 6.

    F. W. Hehl, P. von der Heyde, G. D. Kerlick, and J. E. Nester, Rev. Mod. Phys.,48, 393 (1976).

  7. 7.

    A. S. Mishchenko, Vector Bundles and Their Applications [in Russian], Nauka, Moscow (1984).

  8. 8.

    V. E. Stepanov, Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 82 (1985).

  9. 9.

    V. E. Stepanov, Izv. Vyssh. Uchebn. Zaved., Mat., No. 1 (1987).

  10. 10.

    A. P. Norden, Spaces with Affine Connection [in Russian], Nauka, Moscow (1976).

Download references

Author information

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 84–88, January, 1995.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Stepanov, V.E. Cartan mapping and spinors in affinely connected space-time. Russ Phys J 38, 72–75 (1995). https://doi.org/10.1007/BF00559518

Download citation

Keywords

  • Orthonormal Frame
  • Spinor Connection
  • Torsion Tensor
  • Mutual Spinor