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… Expand
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Nambu mechanics and its quantization.
  • Sahoo, Valsakumar
  • Physics, Medicine
  • 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 timeExpand
Nambu quantum mechanics: A Nonlinear generalization of geometric quantum mechanics
We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of theExpand
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 theExpand
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 theExpand
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 theExpand
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 aExpand
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 ofExpand
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 isExpand
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,Expand
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 ofExpand