Nambu Dynamics, Deformation Quantization, and Superintegrability

TL;DR

This paper explores the use of phase space and deformation quantization to analyze superintegrable systems, introducing new methods for non-Abelian quantization of Nambu brackets with applications to particles in de Sitter space.

Contribution

It presents novel approaches for non-Abelian quantization of Nambu brackets within phase space, advancing the understanding of superintegrable systems.

Findings

Application to de Sitter and chiral particles demonstrates the method's effectiveness.

New results on non-Abelian quantization of Nambu brackets.

Enhanced incorporation of quantum invariants in superintegrable models.

Abstract

Phase space is a framework ideally suited for quantizing superintegrable systems through the use of deformation methods, as illustrated here by applications to de Sitter and chiral particles. Within this framework, Nambu brackets elegantly incorporate the additional quantum invariants of such models. New results are presented for the non-Abelian quantization of these brackets.