Spinors and Space-Time Anisotropy

TL;DR

This paper explores the geometry of anisotropic spinor spaces and their applications in gravity and gauge theories, focusing on off-diagonal metrics, anholonomic frames, and higher order anisotropy.

Contribution

It provides a comprehensive monograph on the algebra, geometry, and physical applications of anisotropic spinor spaces, extending existing theories to higher order anisotropy.

Findings

Development of the theory of gravity and matter fields in anisotropic spaces

Extension of Clifford and spinor spaces to higher order anisotropy

Application of anisotropic spinor geometry to gauge theories

Abstract

This is the first monograph on the geometry of anisotropic spinor spaces and its applications in modern physics. The main subjects are the theory of gravity and matter fields in spaces provided with off--diagonal metrics and associated anholonomic frames and nonlinear connection structures, the algebra and geometry of distinguished anisotropic Clifford and spinor spaces, their extension to spaces of higher order anisotropy and the geometry of gravity and gauge theories with anisotropic spinor variables. The book summarizes the authors' results and can be also considered as a pedagogical survey on the mentioned subjects.