Towards discrete octonionic analysis

TL;DR

This paper introduces initial concepts for discrete octonionic analysis, extending classical tools to the octonionic setting and presenting discrete Stokes' formulae relevant for quantum mechanics applications.

Contribution

It proposes the first ideas on discretizing octonionic analysis and develops several discrete Stokes' formulae, advancing the mathematical framework for octonionic functions.

Findings

Presented approaches to discretize octonionic analysis

Developed discrete Stokes' formulae for octonions

Laid groundwork for applications in quantum mechanics

Abstract

In recent years, there is a growing interest in the studying octonions, which are 8-dimensional hypercomplex numbers forming the biggest normed division algebras over the real numbers. In particular, various tools of the classical complex function theory have been extended to the octonionic setting in recent years. However not so many results related to a discrete octonionic analysis, which is relevant for various applications in quantum mechanics, have been presented so far. Therefore, in this paper, we present first ideas towards discrete octonionic analysis. In particular, we discuss several approaches to a discretisation of octonionic analysis and present several discrete octonionic Stokes' formulae.