Quaternionic Analysis and the Algebrodynamics

TL;DR

This paper introduces an algebrodynamical framework based on quaternionic analysis, leading to a Lorentz-invariant, gauge-structured theory with quantized charges and a novel Minkowski geometry, offering a new perspective on field-particle interactions.

Contribution

It develops a nonlinear quaternionic generalization of Cauchy-Riemann conditions, integrating gauge, twistor structures, and a new geometry to model particles as singularities.

Findings

Electric charge is self-quantized.

Lorentz invariance is maintained in the quaternionic framework.

A new causal Minkowski geometry with phase is proposed.

Abstract

We present the ``algebrodynamical'' approach to field-particle theory based on a nonlinear generalization of the Cauchy-Riemann conditions to non-commutative algebras of quaternion-like type. For complex quaternions the theory is Lorentz invariant and naturally carries some gauge and twistor structures. Point- and string-like singularities are considered as particle-like formations; their electric charge is ``self-quantized''. A novel ``causal Minkowski geometry with additional phase'' is presented that is induced by the structure of primordial biquaternion algebra. On this geometrical background a self-consistent algebraic dynamics of singularities (``ensemble of dublicons'') is briefly discussed.