Related papers: Nambu bracket and M-theory
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.
A Local Resolution of the Problem of Time has recently been given, alongside reformulation as A Local Theory of Background Independence. The classical part of this can be viewed as requiring just Lie's Mathematics, albeit entrenched in…
We consider how to take an orbifold reduction for the multiple M2-brane theory recently proposed by Bagger and Lambert, and discuss its relation to Chern-Simons theories. Starting from the infinite dimensional 3-algebra realized as the…
We show that there exists a cut-off version of Nambu-Poisson bracket which defines a finite dimensional Lie 3-algebra. The algebra still satisfies the fundamental identity and thus produces N=8 supersymmetric BLG type equation of motion for…
M-branes are related to theories on function spaces $\cal{A}$ involving M-linear non-commutative maps from $\cal{A} \times \cdots \times \cal{A}$ to $\cal{A}$. While the Lie-symmetry-algebra of volume preserving diffeomorphisms of $T^M$…
This review is a collection of various methods and observations relevant to structures in three-dimensional systems similar to those responsible for integrability of two-dimensional systems. Particular focus is given to Nambu structures and…
In this paper, we extend the principles of Nambu mechanics by incorporating fractal calculus. This extension introduces Hamiltonian and Lagrangian mechanics that incorporate fractal derivatives. By doing so, we broaden the scope of our…
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…
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 review some aspects of Nambu mechanics on the basis of the works previously published separately by the present author. Main focuses are on three themes, its various symmetry structures, their possible relevance to string/M theory, and a…
In this thesis, the emerging field of higher gauge theory will be discussed, particularly in relation to problems arising in M-theory, such as selfdual strings and the so-called (2,0) theory. This thesis will begin with a Nahm-like…
We construct an alternative form of the M5-brane action in which the six-dimensional worldvolume is subject to a covariant split into 3+3 directions by a triplet of auxiliary fields. We consider the relation of this action to the original…
We give a preliminary discussion of how the addition of extra coordinates in M-theory, which together with the original ones parametrise a U-fold, can serve as a tool for formulating brane dynamics with manifest U-duality. The redundant…
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…
In analogy to Nambu's generalization of mechanics, we present a generalization of Poisson sigma models to higher dimensional world volumes. We find corresponding generalizations of string sigma models and open-closed string relations for…
The Grassmann-odd Nambu bracket on the Grassmann algebra is proposed.
Starting from the type IIB Dirichlet 3-brane action, we obtain a Nambu-Goto action. It is interpreted as the world volume action of a fundamental 3-brane, and its target space theory as F-theory. The target space is twelve dimensional, with…
If a Hamiltonian dynamical system with $n$ degrees of freedom admits $m$ constants of motion more than $2n-1$, then there exist some functional relations between the constants of motion. Among these relations the number of functionally…
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.
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…