This article is cited in 2 papers

Finsler $N$-spinors with real components

A. V. Solov'ev

Lomonosov Moscow State University, Moscow, Russia, Faculty of Physics

Abstract: We study the mathematical objects called Finsler $N$-spinors over the field $\mathbb{R}$ and construct the general algebraic theory of these objects. We show that the Finsler $N$-spinors over the field $\mathbb{R}$ generate two families of $N(N{+}1)/2$- and $N(N{-}1)/2$-dimensional flat pseudo-Finsler spaces. We generalize the epimorphism $SL(2,\mathbb{R})\to O^\uparrow_+(1,2)$ to the case of the group $SL(N,\mathbb{R})$. We consider the examples of Finsler $N$-spinors over the field $\mathbb{R}$ for $N=2,3$ in detail.

Keywords: hyperspinor, Finsler $N$-spinor, pseudo-Finsler space, group $SL(N,\mathbb R)$.

Received: 29.10.2014
Revised: 05.02.2015

DOI: 10.4213/tmf8812

 English version: Theoretical and Mathematical Physics, 2015, 183:3, 756–767

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