# NAMBU-TYPE GENERALIZATION OF THE DIRAC EQUATION

@article{Czachor1996NAMBUTYPEGO, title={NAMBU-TYPE GENERALIZATION OF THE DIRAC EQUATION}, author={Marek Czachor}, journal={Physics Letters A}, year={1996}, volume={225}, pages={1-12} }

Abstract A nonlinear generalization of the Dirac equation extending the standard paradigm of nonlinear Hamiltonians is discussed. “Faster-than-light telegraphs” are absent for all theories formulated within the new framework. A new metric for infinite-dimensional Lie algebras associated with Lie-Poisson dynamics is introduced.

## 14 Citations

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Abstract We propose a generalization of the standard Lax equation defined by means of an arbitrary action of a Lie algebra on a matrix differential manifold. We analyze properties of obtained…

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

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

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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.

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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

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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…

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