2015/01/20 by José F. Cariñena, Cariñena, José F., Héctor Figueroa +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #math-ph #math.MP #msc:53Dxx #msc:70Hxx
paper · pdf · doi:10.48550/arxiv.1501.04917
30 pages, few references have been added
arxiv created 2015/01/24 · arxiv updated 2015/01/27
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.