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arXiv · 1501.04917

Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism

José F. Cariñena·Héctor Figueroa·Partha Guha
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Abstract

We consider Feynman-Dyson's proof of Maxwell's equations using the Jacobi identities on the velocity phase space. In this paper we generalize the Feynman-Dyson's scheme by incorporating the non-commutativity between various spatial coordinates along with the velocity coordinates. This allows us to study a generalized class of Hamiltonian systems. We explore various dynamical flows associated to the Souriau form associated to this generalized Feynman-Dyson's scheme. Moreover, using the Souriau form we show that these new classes of generalized systems are volume preserving mechanical systems.

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José F. Cariñena, Héctor Figueroa, Partha Guha. 2015-01-24. Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism. https://arxiv.org/abs/1501.04917

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