FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 6, PAGES 201-210

**Finslerian 3-spinors and the generalized Duffin--Kemmer equation**

A. V. Solov'yov

Abstract

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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.

Location: http://mech.math.msu.su/~fpm/eng/k09/k096/k09613h.htm

Last modified: October 13, 2010