The hyperbolic field theory on the plane of double variable

TL;DR

This paper develops a hyperbolic field theory on the plane of double variables, introducing analogues of classical field sources and exploring their physical implications and higher-dimensional extensions.

Contribution

It introduces a novel hyperbolic field theory on the double variable plane, including hyperbolic analogues of classical sources and their multipole generalizations.

Findings

Constructed hyperbolic analogues of point vortices and sources

Analyzed physical aspects of hyperbolic fields

Explored extension to higher-dimensional polynumber spaces

Abstract

By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their higher-order multipole generalizations. We examine the physical aspects and the possibility of extension to the space of polynumbers of higher dimensions.