States in non-associative quantum mechanics: Uncertainty relations and semiclassical evolution

TL;DR

This paper explores non-associative quantum mechanics, deriving uncertainty relations and semiclassical equations using algebraic methods, highlighting the unique features and potential physical implications of non-associative algebras.

Contribution

It introduces algebraic techniques to analyze non-associative quantum systems, deriving fundamental uncertainty relations and semiclassical evolution equations.

Findings

Derived uncertainty relations for non-associative observables

Formulated semiclassical equations based on quantum moments

Highlighted physical contexts where non-associative algebras may appear

Abstract

A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and semiclassical equations, based on general properties of quantum moments.