Interactions, Strings and Isotopies in Higher Order Anisotropic Superspaces

TL;DR

This work develops a geometric framework for higher order anisotropic superspaces, unifying concepts from Kaluza--Klein, Lagrange, and Finsler geometries to model complex physical interactions and processes.

Contribution

It introduces the concept of higher order anisotropic (super)spaces, integrating various geometric theories to analyze field interactions, strings, and diffusion in complex anisotropic superspaces.

Findings

Unified geometric approach to anisotropic superspaces.

Modeling of physical processes on higher order fiber (super)bundles.

Application to field interactions, strings, and diffusion processes.

Abstract

The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions, published in J. Math. Phys., Nucl. Phys. B, Ann. Phys. (NY), JHEP, Rep. Math. Phys., Int. J. Theor. Phys. and in some former Soviet Union and Romanian scientific journals. The main subjects are in the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces with higher order anisotropy and inhomogeneity. The approach proceeds by developing the concept of higher order anisotropic (super)space which unifies the logical and manthematical aspects of modern Kaluza--Klein theories and generalized Lagrange and Finsler geometry and leads to modeling of physical processes on higher order fiber (super)bundles provided with nonlinear and distinguished connections and metric structures. This book can be also considered as a pedagogical survey on the mentioned subjects.