Classical and quantum Nambu mechanics

  title={Classical and quantum Nambu mechanics},
  author={Thomas L. Curtright and C. Zachos},
  journal={Physical Review D},
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation, and illustrated with detailed specific cases. Quantization is carried out with standard Hilbert space methods. With the proper physical interpretation, obtained by allowing for different time scales on different invariant sectors of a theory, the resulting non… 

The Mathematical Structure of Quantum Nambu Mechanics and Neutrino Oscillations

Some Lie-algebraic structures of three-dimensional quantum Nambu mechanics are studied. From our result, we argue that the three-dimensional quantum Nambu mechanics is a natural extension of the

Quantization of Nambu Brackets from Operator Formalism in Classical Mechanics

The quantization of Nambu brackets is formulated using the approach of quantum mechanical formulation of classical mechanics. It is shown that the quantum-momentum operator is defined by the

Quantizing dirac and nambu brackets.

We relate classical and quantum Dirac and Nambu brackets. At the classical level, we use the relations between the two brackets to gain some insight into the Jacobi identity for Dirac brackets, among

Remarks on the formulation of quantum mechanics on noncommutative phase spaces

We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position

Hidden Nambu mechanics II: Quantum/semiclassical dynamics

Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. Theor. Exp. Phys. 2013, 073A01 (2013)] we

Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology

A key symmetry of classical p-branes is invariance under worldvolume diffeo- morphisms. Under the assumption that the worldvolume, at fixed values of the time, is a compact, quantisable Kahler

Quantized Nambu–Poisson manifolds and n-Lie algebras

We investigate the geometric interpretation of quantized Nambu–Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which


A general algebraic condition for the functional independence of 2n-1 constants of motion of an n-dimensional maximal superintegrable Hamiltonian system has been proved for an arbitrary finite n.



Nambu mechanics and its quantization.

  • SahooValsakumar
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1992
The algebra of observables inherent in the Nambu formalism [Phys. Rev. D 7, 2405 (1973)] for a generalization of classical Hamiltonian dynamics is investigated. A consistency requirement of time

Dynamical symmetries and Nambu mechanics

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

On the quantization of Nambu brackets

We present several non-trivial examples of the three-dimensional quantum Nambu bracket which involve square matrices or three-index objects. Our examples satisfy two fundamental properties of the

Deformation quantization of superintegrable systems and Nambu mechanics

Phase space is the framework best suited for quantizing superintegrable systems, naturally preserving the symmetry algebras of the respective Hamiltonian invariants. The power and simplicity of the

Deformation Quantization, Superintegrability and Nambu Mechanics

Phase Space is the framework best suited for quantizing superintegrable systems—systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of

Relation between Nambu and Hamiltonian mechanics

The connection between Nambu's generalization of classical dynamics and conventional Hamiltonian ideas is explored. In particular, the possibility of embedding the dynamics of a Nambu triplet in a

On an Algebraic generalization of the quantum mechanical formalism

One of us has shown that the statistical properties of the measurements of a quantum mechanical system assume their simplest form when expressed in terms of a certain hypercomplex algebra which is

Lagrange, Hamilton-Dirac, and Nambu mechanics

In light of a recent work on the subject, the Nambu mechanics for Nambu triplets is compared with Lagrange, Hamilton, and Hamilton-Dirac mechanics. In order to have the proper tool to deal with this,

Exact solvability of superintegrable systems

It is shown that all four superintegrable quantum systems on the Euclidean plane possess the same underlying hidden algebra sl(3). The gauge-rotated Hamiltonians, as well as their integrals of