Physics – Mathematical Physics
Scientific paper
2009-06-16
J.Math.Sci.172:894-900,2011
Physics
Mathematical Physics
LaTeX2e, 11 pages, no figures, will be published in "Fundamental and Applied Mathematics"
Scientific paper
10.1007/s10958-011-0231-z
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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