Related papers: Classical Nambu brackets in higher dimensions

We present some new Poisson bivectors that are invariants by the flow of the nonholonomic Suslov problem. Two rank four invariant Poisson bivectors have globally defined Casimir functions and, therefore, define cubic Poisson brackets on the…

The phase diagram of the two-dimensional Nambu--Jona-Lasinio model with isospin is explored in the large Nc limit with semiclassical methods. We consider finite temperature and include chemical potentials for all conserved charges. In the…

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 the SU(n)-isotropic harmonic oscillator and the…

We present an explicit matrix algebra quantization of the algebra of volume-preserving diffeomorphisms of the $n$-torus. That is, we approximate the corresponding classical Nambu brackets using…

We present the results of further analysis of the integrability properties of the $N=4$ supersymmetric KdV equation deduced earlier by two of us (F.D. \& E.I.) as a hamiltonian flow on $N=4$ $SU(2)$ superconformal algebra in the harmonic…

We calculate the ground state energies of closed k-strings in (2+1)-dimensional SU(N) gauge theories, for N=4,5,6,8 and k=2,3,4. From the dependence of the ground state energy on the string length, we infer that such k-strings are described…

In this paper we continue our analysis of the stationary flows of $M$ component, coupled KdV (cKdV) hierarchies and their modifications. We describe the general structure of the $t_1$ and $t_2$ flows, using the case $M=3$ as our main…

Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide applications in modern physics and connection to many domains in…

We develop a Hamilton-Jacobi-like formulation of Nambu mechanics. The Nambu mechanics, originally proposed by Nambu more than four decades ago, provides a remarkable extension of the standard Hamilton equations of motion in even dimensional…

Using the framework of Nambu's generalised mechanics, we obtain a new description of constrained Hamiltonian dynamics, involving the introduction of another degree of freedom in phase space, and the necessity of defining the action integral…

The presentation of the algebra of classical observables of the closed bosonic Nambu-Goto-String in 3+1 dimensions is given for the massless case $P^2=0,P\neq0$ in the relevant standard frame up to and including the second stratum. The…

We consider the dynamics of 2+1 dimensional $SU(N)$ gauge theory with Chern-Simons level $k$ and $N_f$ fundamental fermions. By requiring consistency with previously suggested dualities for $N_f\leq 2k$ as well as the dynamics at $k=0$ we…

We discuss deformation quantization of the covariant, light-cone and conformal gauge-fixed p-brane actions (p>1) which are closely related to the structure of the classical and quantum Nambu brackets. It is known that deformation…

Given an n-dimensional natural Hamiltonian L on a Riemannian or pseudo-Riemannian manifold, we call "extension" of L the n+1 dimensional Hamiltonian $H=\frac 12 p_u^2+\alpha(u)L+\beta(u)$ with new canonically conjugated coordinates…

We investigate the super high-order Virasoro 3-algebra. By applying the appropriate scaling limits on the generators, we obtain the super $w_{\infty}$ 3-algebra which satisfies the generalized fundamental identity condition. We also define…

We consider D1-string in a constant R-R 3-form flux background and analyze its low energy limit. The leading order low energy theory has reparametrization symmetry and is a generalization of an earlier work by Takhtajan. We show that the…

We elaborate on a novel model of N=4 supersymmetric mechanics with extra spin variables. A dynamical linear (1,4,3) multiplet is coupled to a "semi-dynamical" linear (3,4,1) multiplet representing spin degrees of freedom in a Wess-Zumino…

In this paper we develop a straightforward procedure to construct higher dimensional isochronous Hamiltonian systems. We first show that a class of singular Hamiltonian systems obtained through the $\Omega$-modified procedure is equivalent…

We present two dimensional sigma model by using the Nambu structure on a manifold in general, and on a Lie group as a special case. Then, we consider model constructed from Nambu structure of order three and obtain conditions under which…

We define a super Nambu-Poisson algebra over a super manifold. A super Nambu bracket does not satisfy the usual skew-symmetric property, and we propose another skew-symmetric property. We show that the divergence of super Nambu-Hamiltonian…