Related papers: Classical Nambu brackets in higher dimensions
Kontsevich's graphs allow encoding multi-vectors whose coefficients are differential-polynomial in the coefficients of a given Poisson bracket on an affine real manifold. Encoding formulas by directed graphs adapts to the class of…
The Poisson, contact and Nambu brackets define algebraic structures on $C^{\infty}(M)$ satisfying the Jacobi identity or its generalization. The automorphism groups of these brackets are the symplectic, contact and volume preserving…
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 calculate energies and tensions of closed k-strings in (2+1)-dimensional SU(N) gauge theories with N=4,5,6,8. When we study the dependence of the ground state energy on the string length, we find that it is well described by a Nambu-Goto…
This is a pedagogical digest of results reported in Phys Lett B405 (1997) 37, and an explicit implementation of Euler's construction for the solution of the Poisson Bracket dual Nahm equation. But it does not cover 9 and 10-dimensional…
We investigate the nonlinear realization of spontaneously broken N=2 superconformal symmetry in 4 dimensions. We particularly study Nambu-Goldstone degrees of freedom for the partial breaking of N=2 superconformal symmetry down to N=1…
We give an explicit realization of quantum Nambu bracket via matrix of multi-index, which reduces in the continunm limit to the classical Nambu bracket.
We investigate the compositeness condition in four dimensions at the non-trivial order (next-to-leading order in $1/N$ with the number $N$ of the colors), taking the Nambu-Jona-Lasinio model as an example. In spite of its…
This paper offers an adaptation to the convenient setting of finite dimensional Nambu-Poisson structures. In particular, for partial Nambu structures, we look for those whose classical geometrical results in finite dimension can be extended…
We review an approach towards a covariant formulation of Matrix theory based on a discretization of the 11d membrane. Higher dimensional algebraic structures, such as the quantum triple Nambu bracket, naturally appear in this approach. We…
We construct $N=4$ supersymmetric KdV equation as a hamiltonian flow on the $N=4\;SU(2)$ super Virasoro algebra. The $N=4$ KdV superfield, the hamiltonian and the related Poisson structure are concisely formulated in $1D \;N=4$ harmonic…
In this paper, we describe the dynamical symmetries of classical supersymmetric oscillators in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket which is defined as a suitable classical…
The possibility of neutral, brane-like solutions in a higher dimensional setting is discussed. In particular, we describe a supersymmetric solution in six dimensions which can be interpreted as a "three-brane" with a non-compact transverse…
This lecture consists of three parts. In part I, an overview is given on the so-called Matrix theory in the light-front gauge as a proposal for a concrete and non-perturbative formulation of M-theory. I emphasize motivations towards its…
A few generalizations of a Poisson algebra to field theory canonically formulated in terms of the polymomentum variables are discussed. A graded Poisson bracket on differential forms and an $(n+1)$-ary bracket on functions are considered.…
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…
Central D-dimensional Hamiltonians $H = p^2 + a |\vec{r}|^2 + b |\vec{r}|^4 + >... + z |\vec{r}|^{4q+2}$ (where z=1) are considered in the limit $D \to \infty$ where numerical experiments revealed recently a new class of q-parametric…
We extend the Nambu bracket to 1-forms. Following the Poisson-Lie case, we define Nambu-Lie groups as Lie groups endowed with a multiplicative Nambu structure. A Lie group G with a Nambu structure P is a Nambu-Lie group iff P=0 at the unit…
The Nambu--Jona-Lasinio model is investigated in the $1/N_c$ expansion with the dimensional regularization. At the four-dimensional limit the meson propagators have simple forms in the leading order of the $1/N_c$ expansion. Thus the next…
Nambu-Goto action in classical bosonic string model for hadrons predicts quark-antiquark potential to be\cite{Nambu-Goto} $V(r)=-\frac{\gamma}{r}+\sigma r +\mu_0$. In this report we present studies of masses of heavy flavour mesons in…