Toy models of a non-associative quantum mechanics

TL;DR

This paper introduces toy models for non-associative quantum mechanics, modifying the Heisenberg equation with a non-associative commutator, and explores potential physical applications and the role of non-associative algebra in non-perturbative quantum theories.

Contribution

It presents the first toy models of non-associative quantum mechanics and discusses their implications for non-perturbative quantum theories.

Findings

Modified Heisenberg equation using non-associative commutator

Potential physical applications of non-associative quantum mechanics

Proposal that non-associative algebra could describe non-perturbative quantum phenomena

Abstract

Toy models of a non-associative quantum mechanics are presented. The Heisenberg equation of motion is modified using a non-associative commutator. Possible physical applications of a non-associative quantum mechanics are considered. The idea is discussed that a non-associative algebra could be the operator language for the non-perturbative quantum theory. In such approach the non-perturbative quantum theory has observables and unobservables quantities.