A Modification of Nambu's Mechanics

Details A Modification of Nambu's Mechanics A Modification of Nambu's Mechanics

1997-01-04

arxiv.org/abs/quant-ph/9701006v2

Physics

Quantum Physics

revised version, 10 pages AMS-LaTeX

Scientific paper

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 diffeomorphism groups. We introduce a modification of the Nambu bracket, which defines an evolution equation generating the whole diffeomorphism group. The relation between the modified and usual Nambu brackets is similar to the relation between the Poisson and contact structures. We briefly discuss the problem of quantization of the modified bracket.

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