Hidden Nambu mechanics - A variant formulation of Hamiltonian systems -

TL;DR

This paper introduces a variant formulation of Hamiltonian systems using extended variables, leading to a description via Nambu equations and applicable to constrained systems, offering new perspectives on their dynamics.

Contribution

It presents a novel formulation of Hamiltonian systems with redundant variables, connecting them to Nambu mechanics and extending applicability to constrained systems.

Findings

Hamiltonian systems can be described by extended dynamics using Nambu equations.

Partition functions for systems with many degrees of freedom are derived.

The formulation applies to Hamiltonian systems with first class constraints.

Abstract

We propose a variant formulation of Hamiltonian systems by the use of variables including redundant degrees of freedom. We show that Hamiltonian systems can be described by extended dynamics whose master equation is the Nambu equation or its generalization. Partition functions associated with the extended dynamics in many degrees of freedom systems are given. Our formulation can also be applied to Hamiltonian systems with first class constraints.