Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism
Mathematical Physics
2015-01-27 v2 math.MP
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.
Cite
@article{arxiv.1501.04917,
title = {Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism},
author = {José F. Cariñena and Héctor Figueroa and Partha Guha},
journal= {arXiv preprint arXiv:1501.04917},
year = {2015}
}
Comments
30 pages, few references have been added