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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.'
address: |
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author:
- and
title: |
    Hidden Nambu mechanics:\
    [A variant formulation of Hamiltonian systems ]{}
---

Introduction {#Introduction}
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In general, we have a choice of variables describing a physical system. In most cases, we choose a set of variables whose number is same as the total number of degrees of freedom of the system so as to minimize the number of equations of motion. However, in some cases, it is quite useful to formulate the system by the use of variables including redundant ones. A system with gauge symmetry offers a typical example. To describe such a system, keeping the gauge symmetry manifest, we should employ a formulation that includes redundant variables. Although such a formulation is somewhat complicated, thanks to the symmetry, we can clearly 