Algebrodynamical Approach in Field Theory: Bisingular Solution and its Modifications

TL;DR

This paper develops an algebraic field theory based on quaternion differentiability, deriving Maxwell and Yang-Mills equations, and presents a bisingular solution with topological modifications related to known electromagnetic fields.

Contribution

It introduces a novel algebrodynamical approach using quaternion differentiability and provides explicit solutions with topological structures in electromagnetic fields.

Findings

Derived Maxwell and Yang-Mills equations from quaternion differentiability

Presented bisingular solutions with ring-like and toroidal topologies

Connected solutions to known electromagnetic configurations like Born fields

Abstract

The criterion of differentiability of functions of quaternion variable is used as the basis of some algebraic field theory. Its necessary consequences are free Maxwell and Yang-Mills equations. The differentiability equations may be integrated in twistor variables and are reduced to algebraic ones. In the article we present bisingular solution and its topological modifications. Related EM-fields appear to be just the well-known Born solution and its modifications with singular structure of ring-like and toroidal topology. General problems of the algebrodynamical approach are discussed.