Nambu mechanics

Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. In the present paper we show that the Nambu mechanical structure is also hidden in some quantum or semiclassical dynamics, nambu mechanics, that is, in some cases the quantum or semiclassical time evolution of expectation values of quantum mechanical operators, nambu mechanics composite operators, can be formulated as 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. As required by the formulation of Nambu dynamics, the integrals of motion for these systems necessarily become the so-called generalized Hamiltonians. Furthermore, in most of these problems, the definition of these generalized Hamiltonians is not unique. This is a preview of subscription content, log in via an institution to check access. Rent this article via DeepDyve. Institutional subscriptions. Google Scholar.

Nambu mechanics

In mathematics , Nambu mechanics is a generalization of Hamiltonian mechanics involving multiple Hamiltonians. Recall that Hamiltonian mechanics is based upon the flows generated by a smooth Hamiltonian over a symplectic manifold. The flows are symplectomorphisms and hence obey Liouville's theorem. This was soon generalized to flows generated by a Hamiltonian over a Poisson manifold. In , Yoichiro Nambu suggested a generalization involving Nambu—Poisson manifolds with more than one Hamiltonian. The generalized phase-space velocity is divergenceless, enabling Liouville's theorem. Conserved quantity characterizing a superintegrable system that evolves in N -dimensional phase space. Nambu mechanics can be extended to fluid dynamics, where the resulting Nambu brackets are non-canonical and the Hamiltonians are identified with the Casimir of the system, such as enstrophy or helicity. Quantizing Nambu dynamics leads to intriguing structures [5] that coincide with conventional quantization ones when superintegrable systems are involved—as they must. Contents move to sidebar hide. Article Talk. Read Edit View history.

A52 Transport of quantum systems.

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We outline basic principles of a canonical formalism for the Nambu mechanics—a generalization of Hamiltonian mechanics proposed by Yoichiro Nambu in We introduce the analog of the action form and the action principle for the Nambu mechanics. We emphasize the role ternary and higher order algebraic operations and mathematical structures related to them play in passing from Hamilton's to Nambu's dynamical picture. This is a preview of subscription content, log in via an institution to check access. Rent this article via DeepDyve. Institutional subscriptions. Nambu, Y. D7 , — Google Scholar.

Nambu mechanics

Nambu mechanics [ 1 ] provides a means to view, in perspective, a diversity of phenomena from micro- to macro- and to cosmic-scales, with ordered structures characterized by helicity and chirality, and to approach the secret of their formations. The helicity was discovered for elementary particles, but the same terminology is given to an invariant for motion of a fluid. These structures are ubiquitous, but their formation process remains puzzles. These structures are realizations in quantum or classical multi-body systems and are governed by Hamiltonian mechanical systems that are intrinsic to their hierarchies. Phenomena of meso- and macro-scales have infinite degrees of freedom and are described by partial differential equations. The Hamilton structure of many degrees of freedom is often degenerate. In case nonlinear terms are quadratic, the governing equation takes the form of the Lie-Poisson equation.

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G15 Accelerator theory. J33 Quantum chemistry, electronic states. The Nambu mechanical structure is hidden not only in one-degree-of-freedom systems. H51 Manufacturing. E42 Acceleration of particles. Lattice realization of the axial U 1 non-invertible symmetry. B0 Gauge field theories. I Condensed Matter Physics. E37 Gamma ray bursts. We derived the consistency condition to determine the induced constraints. F10 Instrumentation and technique. F31 Expectation and estimation of gravitational radiation.

In mathematics , Nambu mechanics is a generalization of Hamiltonian mechanics involving multiple Hamiltonians. Recall that Hamiltonian mechanics is based upon the flows generated by a smooth Hamiltonian over a symplectic manifold. The flows are symplectomorphisms and hence obey Liouville's theorem.

B0 Gauge field theories. However, by explicitly solving the constraints in Eqs. J21 Plasma astrophysics. D12 General properties of nuclei systematics and theoretical analysis. The Nambu equations of Eq. JPS Journals. A73 Other thermal processes. E45 Neutrinos. E04 Higher-dimensional theories. Copy to clipboard. I36 Other topics. G02 Ion accelerators. I79 Other topics. B1 Supersymmetry. J16 Waves nonlinear waves, sound waves, shock waves.