The octonionic eigenvalue problem

TL;DR

This paper introduces a new coupled eigenvalue problem for octonionic operators, addressing previous challenges in formulating a consistent octonionic Hilbert space and discussing potential quantum mechanics applications.

Contribution

It proposes a real matrix translation approach to define a coupled eigenvalue problem for octonionic operators, enabling a consistent Hilbert space formulation.

Findings

A new coupled eigenvalue problem for octonionic operators is formulated.

A suitable scalar product for probability amplitudes is introduced.

The hermiticity of octonionic operators is analyzed in the new framework.

Abstract

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in formulating a consistent octonionic Hilbert space are solved by using the new coupled eigenvalue problem and introducing an appropriate scalar product for the probability amplitudes.