Related papers: Constrained systems described by Nambu mechanics
We give an overview of the two different methods that have been introduced in order to describe the dynamics of constrained quantum systems; the symplectic formulation and the metric formulation. The symplectic method extends the work of…
In this paper we introduce a system of nonlinear ordinary differential equations which in a particular case reduces to Volterra's system. We found in two simplest cases the complete sets of the integrals of motion using Nambu--Poisson…
Nambu dynamics is a generalized Hamiltonian dynamics of more than two variables, whose time evolutions are given by the Nambu bracket, a generalization of the canonical Poisson bracket. Nambu dynamics can always be represented in the form…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems.…
We start with an overview of the "generalized Hamiltonian dynamics" introduced in 1973 by Y. Nambu, its motivations, mathematical background and subsequent developments -- all of it on the classical level. This includes the notion (not…
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…
We review various connections between condensed matter systems with the Nambu-Jona Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
Nambu Quantum Mechanics, proposed in Phys. Lett. B536, 305 (2002), is a deformation of canonical Quantum Mechanics in which only the time-evolution of the "phases" of energy eigenstates is modified. We discuss the effect this theory will…
The concept of the quantized space-time of the formless finite fundamental elements is suggested. This space-time can be defined as a set of continual space-time coverings by simply connected non-overlapping regions of any form and…
Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system…
We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…
Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…
Quantum mechanical time operator is introduced following the parametric formulation of classical mechanics in the extended phase space. Quantum constraint on the extended quantum system is defined in analogy to the constraint of the…
The {\it {gauge - fixing} } and {\it gaugeless } methods for reducing the phase space in the generalized Hamiltonian dynamics are compared with the aim to define the class of admissible gauges . In the gaugeless approach, the reduced phase…
A new version of NLQM is formulated in terms of the generalized Nambu dynamics. The generalization is free from the difficulties of earlier approaches. The paper is a second part of "Elements of NLQM (I): NL Schrodinger equation and…
For the case of a first-class constrained system with an equivariant momentum map, we study the conditions under which the double process of reducing to the constraint surface and dividing out by the group of gauge transformations $G$ is…
Using Dirac's approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the…
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…