Nonassociatuve generalization of supersymmetry

TL;DR

This paper explores a nonassociative extension of supersymmetry, linking four-generator associators to angular momentum and discussing implications for hidden variables and alternative quantum theories.

Contribution

It introduces a nonassociative framework for supersymmetry and establishes a novel connection between four-generator associators and angular momentum.

Findings

Associators for three and four multipliers are defined.

Associator of four supersymmetry generators relates to angular momentum.

Discussion on implications for hidden variables and alternative quantum mechanics.

Abstract

A nonassociative generalization of supersymmetry is studied, where supersymmetry generators are considered to be the nonassociative ones. Associators for the product of three and four multipliers are defined. Using a special choice of the parameters, it is shown that the associator of the product of four supersymmetry generators is connected with the angular momentum operator. The connection of operator decomposition to the hidden variables theory and alternative quantum mechanics is discussed.