相关论文: Elements of nonlinear quantum mechanics (Part II):…

An extension of the Liouville-von Neumann dynamics to a Nambu-type dynamics is proposed. The resulting theory is the first version of nonlinear QM which is free from internal inconsistencies.

General features of nonlinear quantum mechanics are discussed in the context of applications to two-level atoms.

It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…

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 classical Nambu bracket: they are…

Linear quantum mechanics can be regarded as a particular example of a nonlinear Nambu-type theory. Some elements of this approach are presented.

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,…

A geometric formulation of a generalization of Nambu mechanics is proposed. This formulation is carried out, wherever possible, in analogy with that of Hamiltonian systems. In this formulation, a strictly nondegenerate constant 3-form is…

We propose a generalization of cubic matrix mechanics by introducing a canonical triplet and study its relation to Nambu mechanics. The generalized cubic matrix mechanics we consider can be interpreted as a 'quantum' generalization of Nambu…

We present recent developments in the theory of Nambu mechanics, which include new examples of Nambu-Poisson manifolds with linear Nambu brackets and new representations of Nambu-Heisenberg commutation relations.

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 the standard exponential time evolution, a…

We outline the basic principles of canonical formalism for the Nambu mechanics---a generalization of Hamiltonian mechanics proposed by Yoichiro Nambu in 1973. It is based on the notion of Nambu bracket which generalizes the Poisson bracket…

This paper proposes a novel approach to quantizing Nambu brackets in classical mechanics using operator formalism. The approach employs the ``Planck derivative'' to represent Nambu brackets, from which we derive a commutation relation for…

Far-from-equilibrium thermodynamic systems dominated by strong nonlinearity are reformulated within a dynamical framework based on the Nambu bracket formalism. It is demonstrated that general complex nonlinear non-equilibrium systems can be…

It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…

The Nambu Bracket quantization of the Hydrogen atom is worked out as an illustration of the general method. The dynamics of topological open branes is controlled classically by Nambu Brackets. Such branes then may be quantized through the…

We outline an approach that streamlines considerably the construction and analysis of well-behaved nonlinear quantum dynamics, with completely positive extensions to entangled systems. A few notes are added on the issue of quantum…

Nambu proposed an extension of dynamical system through the introduction of a new bracket (Nambu bracket) in 1973. This article is a short review of the developments after his paper. Some emphasis are put on a viewpoint that the Nambu…

A general theory is presented of quantum mechanics of singular, non-autonomous, higher derivative systems. Within that general theory, $n$-th order and $m$-th order Lagrangians are shown to be quantum mechanically equivalent if their…

A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…

So far fluid mechanical Nambu brackets have mainly been given on an intuitive basis. Alternatively an algorithmic construction of such a bracket for the two-dimensional vorticity equation is presented here. Starting from the Lie--Poisson…