Spinors in Higher Dimensional and Locally Anisotropic Spaces

TL;DR

This paper develops a spinor theory for locally anisotropic spaces, extending differential geometry and formulating dynamical equations for gravitational and matter interactions in these complex geometric settings.

Contribution

It introduces a novel spinor differential geometry framework for la-spaces, including connections, curvatures, torsions, and field equations, expanding the mathematical tools for anisotropic space theories.

Findings

Derived la-spinor expressions for curvature and torsion

Analyzed conditions for torsion and nonmetricity from spinor connections

Formulated dynamical equations for gravitational and matter interactions

Abstract

The theory of spinors is developed for locally anisotropic (la) spaces, in brief la-spaces, which in general are modeled as vector bundles provided with nonlinear and distinguished connections and metric structures (such la-spaces contain as particular cases the Lagrange, Finsler and, for trivial nonlinear connections, Kaluza-Klein spaces). The la-spinor differential geometry is constructed. The distinguished spinor connections are studied and compared with similar ones on la-spaces. We derive the la-spinor expressions of curvatures and torsions and analyze the conditions when the distinguished torsion and nonmetricity tensors can be generated from distinguished spinor connections. The dynamical equations for gravitational and matter field la-interactions are formulated.