ИСТИНА

We consider SL(3, C)-covariant wave equations for free Finslerian 3-spinor particles in the momentum representation. Such particles live in the 9-dimensional flat Finslerian space with the metric function defined by the homogeneous cubic form of coordinates. Wave equations for massless Finslerian 3-spinor particles split into two types. The first one is reduced to the Weyl equation in the 4-dimensional limit. The second one is reduced to the Klein–Gordon and Dirac equations in the same limit. The wave equation for massive Finslerian 3-spinor particle can be represented in the Dirac-like form. However, the corresponding gamma-matrices do not satisfy the Clifford-Dirac algebra. We show that these gamma-matrices lead to a Finslerian generalization of the Duffin-Kemmer algebra.