Spinors and Field Interactions in Higher Order Anisotropic Spaces

TL;DR

This paper develops a geometric framework for field interactions in higher order anisotropic spaces, extending Finsler and Kaluza-Klein geometries, and explores their physical implications for various fundamental fields.

Contribution

It introduces a comprehensive geometric formulation of spinors and field interactions in higher order anisotropic spaces, unifying various geometric structures and physical theories.

Findings

Defined spinors within Clifford bundle geometry on ha-spaces

Constructed spinor differential geometry for ha-spaces

Discussed physical implications for gravitational and gauge fields

Abstract

We formulate the theory of field interactions with higher order anisotropy. The concepts of higher order anisotropic space and locally anisotropic space (in brief, ha-space and la-space) are introduced as general ones for various types of higher order extensions of Lagrange and Finsler geometry and higher dimension (Kaluza-Klein type) spaces. The spinors on ha-spaces are defined in the framework of the geometry of Clifford bundles provided with compatible nonlinear and distinguished connections and metric structures (d-connection and d-metric). The spinor differential geometry of ha-spaces is constructed. There are discussed some related issues connected with the physical aspects of higher order anisotropic interactions for gravitational, gauge, spinor, Dirac spinor and Proca fields. Motion equations in higher order generalizations of Finsler spaces, of the mentioned type of fields, are defined by using bundles of linear and affine frames locally adapted to the nonlinear connection structure.