Non-associativity, supersymmetry and hidden variables

TL;DR

This paper introduces an octonionic extension of supersymmetric quantum mechanics, highlighting how non-associative properties lead to unobservable elements that may correspond to observable particles formed from unobservable constituents.

Contribution

It presents the first octonionic generalization of supersymmetric quantum mechanics, linking non-associativity to unobservability and proposing a new perspective on observable particles.

Findings

Octonionic supersymmetric quantum mechanics is formulated.

Unobservable elements arise from non-associative properties.

A conceptual model of observable particles composed of unobservable parts is proposed.

Abstract

It is shown that the supersymmetric quantum mechanics has an octonionic generalization. The generalization is based on the inclusion of quaternions into octonions. The elements from the coset octonions/quaternions are unobservables bacause they cannot be considered as quantum operators as a consequence of their non-associative properties. The idea that the octonionic generalization of the supersymmetric quantum mechanics describes an observable particle formed with unobservable ``particles'' is presented.