On the ternary complex analysis and its applications Available to Purchase

In previous works, a possible extension of the complex numbers together with its connected trigonometry was introduced. In the present paper, we focus on the simplest case of ternary complex numbers. Then, some types of holomorphy adapted to the ternary complex numbers and the corresponding results upon integration of differential forms are given. Several physical applications are discussed and, in particular, 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.