## 6 Citations

### Generalized Heisenberg Dynamics

- Physics
- 2004

We formulate a dynamical system based on many-index objects. These objects yield a generalization of the Heisenberg equation. Systems describing harmonic oscillators are presented.

### Classical and quantum Nambu mechanics

- Physics
- 2003

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…

### n−ary star product: construction and integral representation

- Physics
- 2014

This paper addresses a construction of an n-ary star product. Relevant identities are given. Besides, the formalism is illustrated by a computation of eigenvalues and eigenfunctions for a physical…

### Nambu-Lie 3-algebras on fuzzy 3-manifolds

- Mathematics
- 2009

We consider Nambu-Poisson 3-algebras on three dimensional manifolds 3, such as the Euclidean 3-space R3, the 3-sphere S3 as well as the 3-torus T3. We demonstrate that in the Clebsch-Monge gauge, the…

### A toy model of open membrane field theory in constant 3-form flux

- Physics
- 2007

Based on an explicit computation of the scattering amplitude of four open membranes in a constant 3-form background, we construct a toy model of the field theory for open membranes in the large C…

### n-ary algebras: a review with applications

- Mathematics
- 2010

This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the…

## 13 References

### Generalized Hamiltonian dynamics

- Mathematics
- 1973

Taking the Liouville theorem as a guiding principle, we propose a possible generalization of classical Hamiltonian dynamics to a three-dimensional phase space. The equation of motion involves two…

### Nambu mechanics , based on the deformation theory , path integral formulation and on

- Physics
- 2008

We outline 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,…

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- Phys. Rev
- 1973

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- Math. Phys.160
- 1994

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### ) 2405 . [ 2 ] L . Takhtajan

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