Constrained systems described by Nambu mechanics

TL;DR

This paper introduces a novel approach to constrained Hamiltonian systems using Nambu mechanics, expanding phase space with an additional degree of freedom and exploring quantisation challenges.

Contribution

It provides a new formulation of constrained dynamics within Nambu's framework, including the use of a world sheet for the action integral and addressing quantisation issues.

Findings

New description of constrained Hamiltonian dynamics

Introduction of an extra degree of freedom in phase space

Discussion on quantising Nambu mechanics

Abstract

Using the framework of Nambu's generalised mechanics, we obtain a new description of constrained Hamiltonian dynamics, involving the introduction of another degree of freedom in phase space, and the necessity of defining the action integral on a world sheet. We also discuss the problem of quantising Nambu mechanics.