Quaternion-Octonion Analyticity for Abelian and Non-Abelian Gauge Theories of Dyons

TL;DR

This paper extends Einstein-Schroedinger theory using quaternion and octonion mathematics to describe Abelian and non-Abelian gauge theories of dyons, unifying gravitation, electromagnetism, and Yang-Mills fields.

Contribution

It introduces quaternion-octonion metric realization for gauge theories of dyons, extending unified field theories to include electric and magnetic charges within internal gauge groups.

Findings

Covariant derivatives in quaternion and octonion spaces yield consistent field equations.

Representation extends unified gravitation-electromagnetism theory to Yang-Mills fields.

Two SU(2) gauge theories emerge due to electric and magnetic charges on dyons.

Abstract

Einstein- Schroedinger (ES) non-symmetric theory has been extended to accommodate the Abelian and non-Abelian gauge theories of dyons in terms of the quaternion-octonion metric realization. Corresponding covariant derivatives for complex, quaternion and octonion spaces in internal gauge groups are shown to describe the consistent field equations and generalized Dirac equation of dyons. It is also shown that quaternion and octonion representations extend the so-called unified theory of gravitation and electromagnetism to the Yang-Mill's fields leading to two SU(2) gauge theories of internal spaces due to the presence of electric and magnetic charges on dyons.