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Finslerian 3-spinors and the generalized Duffin–Kemmer equation

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Abstract

The main facts of the geometry of Finslerian 3-spinors are formulated. The close connection between Finslerian 3-spinors and vectors of the 9-dimensional linear Finslerian space is established. The isometry group of this space is described. The procedure of dimensional reduction to 4-dimensional quantities is formulated. The generalized Duffin–Kemmer equation for a Finslerian 3-spinor wave function of a free particle in the momentum representation is obtained. From the viewpoint of a 4-dimensional observer, this 9-dimensional equation splits into the standard Dirac and Klein–Gordon equations.

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Authors and Affiliations

  1. Division of Theoretical Physics, Faculty of Physics, Moscow State University, Moscow, Russia

    A. V. Solov’yov

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  1. A. V. Solov’yov
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Correspondence to A. V. Solov’yov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 6, pp. 201–210, 2009.

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Solov’yov, A.V. Finslerian 3-spinors and the generalized Duffin–Kemmer equation. J Math Sci 172, 894–900 (2011). https://doi.org/10.1007/s10958-011-0231-z

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  • DOI: https://doi.org/10.1007/s10958-011-0231-z

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