Finslerian 4-spinors as a generalization of twistors

TL;DR

This paper explores Finslerian 4-spinors as a generalization of twistors, establishing their geometric properties, connection to a 16-dimensional Finslerian space, and the isometry group, including dimensional reduction methods.

Contribution

It introduces Finslerian 4-spinors as a broader framework that encompasses twistors and details their geometric and symmetry properties.

Findings

Twistors are a special case of Finslerian 4-spinors.

A 16-dimensional Finslerian space geometry is developed.

The isometry group of this space is characterized.

Abstract

The main facts of the geometry of Finslerian 4-spinors are formulated. It is shown that twistors are a special case of Finslerian 4-spinors. The close connection between Finslerian 4-spinors and the geometry of a 16-dimensional vector Finslerian space is established. The isometry group of this space is described. The procedure of dimensional reduction to 4-dimensional quantities is formulated.