Old and new research on the Absolute Parallelism theory

TL;DR

This thesis explores the Absolute Parallelism theory, addressing singularities, topological charges, and cosmological models, proposing a unique 5D equation free of singularities and offering insights into the Standard Model's topological structure.

Contribution

It introduces a covariant test for singularities in Absolute Parallelism, identifies a unique 5D compatible equation, and discusses topological classifications relevant to fundamental physics.

Findings

A covariant test for solution singularities in AP.

Identification of a unique 5D equation without singularities.

Topological classification of field configurations related to the Standard Model.

Abstract

Compatible equations, Singularities of solutions, Topological charges and quasi-charges. PhD thesis (translated frorm Russian). The book shows the sights of Absolute Parallelism (AP), and contains useful information on the problem of singularities, compatibility theory, homotopy groups (also relative and k-ad), topological quasi-charge groups and their morphisms. AP is a single (frame) field theory proposed by Einstein some 80 years ago; it embraces symmetries of both Special and General Relativity. The compatibility theory, if applied to the cases when the frame matrix degenerates, gives a covariant test on singularities of solutions. This gives a single variant (missed in Einstein-Mayer's list of compatible equations), the unique 5D equation (nothing, nor D, can be changed), which solutions are free of emerging singularities. SO4-symmetrical nonstationary solutions give rise to a cosmological model (relativistic surfing; anti-Milne model in FRW framework) with a specific reduction of the extra-dimension. Topological classification of localized field configurations, combinatorics of topological quasi-charges (quanta), is discussed in an attempt to imagine the Standard Model (and quantum theory itself; and, perhaps, to make some qualitative predictions, like the absence of spin zero elementary quanta).