Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Matrix form and certain solutions of the Feynman-Gell-Mann type equations for a spin-3/2 particle

  • 22 Accesses

Abstract

We consider a P-odd variant of a spin-3/2 particle theory in the matrix formulation. We determine a matrix algebra of a first-order equation. We find solutions of the free equation for a massive particle in the form of projection matrices-dyads. We obtain exact solutions of the equation in the case of an external plane wave field with linear polarization and in the case of an axially symmetric magnetic field.

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

Literature cited

  1. 1.

    W. J. Hurley, Phys. Rev. D,4, No. 12, 3605 (1971).

  2. 2.

    A. A. Leonovich and A. B. Pestov, Yad. Fiz.,39, No. 2, 509 (1984).

  3. 3.

    F. I. Fedorov, Lorentz Group [in Russian], Nauka, Moscow (1979).

  4. 4.

    A. A. Bogush and L. G. Moroz, Introduction to the Theory of Classical Fields [in Russian], Nauka Tekh. Minsk (1968).

  5. 5.

    A. A. Bogush, Introduction to the Field Theory of Elementary Particles [in Russian], Nauka Tekh. Minsk (1981).

  6. 6.

    F. I. Fedorov, Izv. Vyssh. Uchebn. Zaved. Fiz., No. 2, 32 (1980).

  7. 7.

    L. G. Moroz and F. I. Fedorov, Tr. Inst. Fiz. Mat. AN BSSR,3, 154 (1959).

  8. 8.

    A. A. Bogush and F. I. Fedorov, Dokl. Akad. Nauk BSSR,12, No. 1, 21 (1968).

  9. 9.

    F. I. Fedorov, Zh. Eksp. Teor. Fiz.,35, 495 (1958).

  10. 10.

    F. I. Fedorov, Dokl. Akad. Nauk BSSR,18, 17 (1974).

  11. 11.

    A. A. Sokolov and I. M. Ternov, Relativistic Electron [in Russian], Nauka, Moscow (1983).

  12. 12.

    H. Bateman, Higher Transcendental Functions, Bateman Manuscript Project, A. Erdelyi, Dir., McGraw-Hill (1953).

  13. 13.

    W. H. Furry, Phys. Rev.,81, 115 (1951).

  14. 14.

    V. I. Ritus, Tr. FIAN SSSR, Vol. 111, Nauka, Moscow (1979).

Download references

Author information

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 3–8, October, 1987.

The authors wish to thank A. A. Bogush for his interest in this work and useful discussions.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kruglov, S.I., Radyuk, A.F. Matrix form and certain solutions of the Feynman-Gell-Mann type equations for a spin-3/2 particle. Soviet Physics Journal 30, 809–813 (1987). https://doi.org/10.1007/BF00897244

Download citation

Keywords

  • Magnetic Field
  • Exact Solution
  • Plane Wave
  • Matrix Form
  • Massive Particle