Geometry of Vlasov kinetic moments: a bosonic Fock space for the symmetric Schouten bracket

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The dynamics of Vlasov kinetic moments is shown to be Lie-Poisson on the dual Lie algebra of symmetric contravariant tensor fields. The corresponding Lie bracket is identified with the symmetric Schouten bracket and the moment Lie algebra is related with a bundle of bosonic Fock spaces, where creation and annihilation operators are used to construct the cold plasma closure. Kinetic moments are also shown to define a momentum map, which is infinitesimally equivariant. This momentum map is the dual of a Lie algebra homomorphism, defined through the Schouten bracket. Finally the moment Lie-Poisson bracket is extended to anisotropic interactions.
19 pages, no figures. Submitted to Phys. Lett. A

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Chaotic Dynamics, Mathematical Physics, Plasma Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/159657

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0803.2667
 http://arxiv.org/abs/0803.2667
 doi:10.1016/j.physleta.2008.03.034

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arXiv