# Classical and quantum Nambu mechanics

@article{Curtright2003ClassicalAQ, title={Classical and quantum Nambu mechanics}, author={Thomas L. Curtright and C. Zachos}, journal={Physical Review D}, year={2003}, volume={68}, pages={085001} }

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… Expand

#### 115 Citations

The Mathematical Structure of Quantum Nambu Mechanics and Neutrino Oscillations

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- 2015

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… Expand

Quantizing dirac and nambu brackets.

- Physics
- 2003

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… Expand

Remarks on the formulation of quantum mechanics on noncommutative phase spaces

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- 2007

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… Expand

Hidden Nambu mechanics II: Quantum/semiclassical dynamics

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- 2019

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 revealed… Expand

Membranes and consistent quantization of Nambu dynamics

- Physics
- 2003

The dynamics of even topological open membranes relies on Nambu brackets. Consequently, such 2p-branes can be quantized through the consistent quantization of the underlying Nambu dynamical… Expand

Massive super-Yang–Mills quantum mechanics: Classification and the relation to supermembrane

- Physics
- 2006

Abstract We classify the supersymmetric mass deformations of all the super-Yang–Mills quantum mechanics, which are obtained by dimensional reductions of minimal super-Yang–Mills in spacetime… Expand

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

- Physics, Mathematics
- 2008

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… Expand

Quantized Nambu–Poisson manifolds and n-Lie algebras

- Mathematics, Physics
- 2010

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… Expand

SUPERINTEGRABLE SYSTEMS, MULTI-HAMILTONIAN STRUCTURES AND NAMBU MECHANICS IN AN ARBITRARY DIMENSION

- Physics, Mathematics
- 2004

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.… Expand

Classical and quantal ternary algebras

- Physics, Mathematics
- 2009

We consider several ternary algebras relevant to physics. We compare and contrast the quantal versions of the algebras, as realized through associative products of operators, with their classical… Expand

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