On the ternary complex analysis and its applications

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.

LaTeX 28 pages

References in corpus (5)

• The cubic chessboard
• Universal differential calculus on ternary algebras
• Approximate Homomorphisms of Ternary Semigroups
• Extension of sine-Gordon field theory from generalized Clifford algebras
• Extended Complex Trigonometry in Relation to Integrable 2D-Quantum Field Theories and Duality

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