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arXiv · 0803.2667

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

John Gibbons·Darryl D Holm·Cesare Tronci
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Abstract

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.

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John Gibbons, Darryl D Holm, Cesare Tronci. 2008-03-18. Geometry of Vlasov kinetic moments: a bosonic Fock space for the symmetric Schouten bracket. https://doi.org/10.1016/j.physleta.2008.03.034

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