Dynamical Symmetries and Nambu Mechanics

TL;DR

This paper demonstrates how Hamiltonian systems with hidden symmetries can be described using Nambu's generalized mechanics, revealing new insights into their integrals of motion and non-uniqueness of generalized Hamiltonians.

Contribution

It shows that systems with dynamical symmetries can be embedded in Nambu mechanics, highlighting the role of generalized Hamiltonians and their non-uniqueness.

Findings

SU(n)-isotropic harmonic oscillator fits within Nambu mechanics

SO(4)-Kepler problem is realizable in Nambu framework

Generalized Hamiltonians are not uniquely defined in these systems

Abstract

It is shown that several Hamiltonian systems possessing dynamical or hidden symmetries can be realized within the framework of Nambu's generalized mechanics. Among such systems are the SU(n)-isotropic harmonic oscillator and the SO(4)-Kepler problem. As required by the formulation of Nambu dynamics, the integrals of motion for these systems necessarily become the so-called generalized Hamiltonians. Furthermore, in most of these problems, the definition of these generalized Hamiltonians is not unique.