## 14 Citations

Lie-Nambu and Beyond

- Physics
- 1999

Linear quantum mechanics can be regarded as aparticular example of a nonlinear Nambu-type theory.Some elements of this approach are presented.

Investigation of the time-dependent Schroedinger-Newton equation

- Physics
- 2005

The Schrödinger-Newton equation is a highly non-linear integro-partial differential equation that arises from both the theory of semiclassical gravity of Møller and Rosenfeld and as a possible…

Quantum morphogenesis: a variation on Thom's catastrophe theory.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

Noncommutative propositions are characteristic of both quantum and nonquantum (sociological, biological, and psychological) situations. In a Hilbert space model, states, understood as correlations…

Informal Resource Letter - Nonlinear quantum mechanics on arXiv up to August 2004

- Physics
- 2004

I compiled a list of articles on arXiv that deal with possible fundamental quantum nonlinearities or examine the origins of its linearity. The list extends til August 2004.

Abstract DNA-type systems

- Physics
- 2006

It is explained why non-Kolmogorovian probability models occurring in soliton kinetics are naturally associated with chemical reactions and why fluctuations based on Darboux transformations will not destroy the dynamics but only switch between a finite number of helical structures.

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…

## References

SHOWING 1-10 OF 63 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…

Relation between Nambu and Hamiltonian mechanics

- Physics
- 1976

The connection between Nambu's generalization of classical dynamics and conventional Hamiltonian ideas is explored. In particular, the possibility of embedding the dynamics of a Nambu triplet in a…

Quantum mechanics as a generalization of Nambu dynamics to the Weyl-Wigner formalism

- Physics, Mathematics
- 1991

Relativistic models of nonlinear quantum mechanics

- Physics
- 1978

I present and discuss a class of nonlinear quantum-theory models, based on simple relativistic field theories, in which the parameters depend on the state of the system via expectation values of…

On a general nonlinear Schrödinger equation admitting diffusion currents

- Mathematics, Physics
- 1992

Geometrization of quantum mechanics

- Physics
- 1979

Quantum mechanics is cast into a classical Hamiltonian form in terms of a symplectic structure, not on the Hilbert space of state-vectors but on the more physically relevant infinite-dimensional…

Classical Trajectories and Quantum Spectra

- Physics
- 1996

A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but…

Dynamical symmetries and Nambu mechanics

- Physics
- 1995

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…

Realization of Nambu mechanics: A particle interacting with an SU(2) monopole

- Physics
- 1977

We study the system of a particle bearing isospin degrees of freedom interacting with an SU(2) 't Hooft-Polyakov monopole. We show that its equation of motion can be cast into the form of Nambu's…