Cubic Matrix, Nambu Mechanics and Beyond

TL;DR

This paper introduces a generalized cubic matrix mechanics framework that extends Nambu mechanics, providing a potential 'quantum' version and exploring its foundational relations.

Contribution

It proposes a novel generalization of cubic matrix mechanics incorporating a canonical triplet, linking it to Nambu mechanics and suggesting a quantum extension.

Findings

Established a formal connection between generalized cubic matrix mechanics and Nambu mechanics

Proposed a 'quantum' generalization of Nambu mechanics

Provided a mathematical framework for future quantum mechanical models based on cubic matrices

Abstract

We propose a generalization of cubic matrix mechanics by introducing a canonical triplet and study its relation to Nambu mechanics. The generalized cubic matrix mechanics we consider can be interpreted as a 'quantum' generalization of Nambu mechanics.