Finslerian 3-spinors and the generalized Duffin-Kemmer equation
A. V. Solov'yov
TL;DR
This paper explores the geometry of Finslerian 3-spinors, establishing their connection to 9-dimensional Finslerian space, and derives a generalized Duffin-Kemmer equation that reduces to standard equations in 4D.
Contribution
It introduces the geometry of Finslerian 3-spinors and derives a generalized Duffin-Kemmer equation linking 9D Finslerian space to familiar 4D physics.
Findings
Finslerian 3-spinors are connected to vectors in 9D Finslerian space.
The isometry group of this space is characterized.
A dimensional reduction procedure to 4D is formulated.
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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