On the ternary complex analysis and its applications

TL;DR

This paper explores the mathematical structure of ternary complex numbers, develops associated holomorphic functions, and applies these concepts to model physical phenomena such as magnetic fields and monopole dynamics.

Contribution

It introduces a new framework for ternary complex analysis, including holomorphicity and integration, and demonstrates novel physical applications like stationary magnetic fields and monopole motion.

Findings

A new form of stationary magnetic field derived from ternary holomorphic functions

Monopole movement in the ternary magnetic field is shown to be integrable

Analysis of monopole scattering in the ternary field

Abstract

Previouly a possible extension of the complex number, together with its connected trigonometry was introduced. In this paper we focuss on the simplest case of ternary complex numbers. Then, some types of holomorphicity adapted to the ternary complex numbers and the corresponding results upon integration of differential forms are given. Several physical applications are given, and in particuler one type of holomorphic function gives rise to a new form of stationary magnetic field. The movement of a monopole type object in this field is then studied and shown to be integrable. The monopole scattering in the ternary field is finally studied.