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Covariant derivatives of a spinor in finsler geometry


The aim of the author in the present article is to introduce covariant derivatives of a spinor into Finsler geometry and to show that such an operation is not only interesting from the purely mathematical point of view but also from the physical one since it is thus possible to extend the spinor theory of Heisenberg [1] to the Finsler space [2] (and, in particular, to the Riemann space [3]). The covariant form of the spinor theory of matter is essentially a nonlinear theory.

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Literature cited

  1. 1.

    Nonlinear Quantum Field Theory (Collected translations), IL (1959).

  2. 2.

    E. Cartan, Les Espaces de Finsler, Actualités 79 (Hermann) (1934).

  3. 3.

    P. K. Rashevskii, Riemannian Geometry and Tensor Analysis, Nauka (1967).

  4. 4.

    R. Utiyama, Phs. Rev.,101, 1597 (1956).

  5. 5.

    T. W. Kibble, J. of Math. Phys.,2, 212 (1961).

  6. 6.

    V. G. Ogievetsky and I. V. Polubarinov, Preprint P-388, Dubna (1959).

  7. 7.

    V. P. Sevryuk, Material for the 8-th Inter-University Mathematics Conference of the Far East, Khabarovsk (1970).

  8. 8.

    H. Dürr, Contrib. to the 15-th Internat. Conference in High-Energy Physics, Kiev (1970).

  9. 9.

    H. Dürr and N. I. Winter, Contrib. to the 15-th Internat. Conference in High-Energy Physics, Kiev (1970).

  10. 10.

    Yu. B. Rumer, Introduction to 5-Optics, Moscow (1956).

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 2, pp. 43–49, February, 1973.

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Sevryuk, V.P. Covariant derivatives of a spinor in finsler geometry. Soviet Physics Journal 16, 171–176 (1973).

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  • Present Article
  • Covariant Derivative
  • Nonlinear Theory
  • Mathematical Point
  • Spinor Theory