@inbook{bedcd07ef1f54725971961c70083b17a,
title = "A Primer on Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism",
abstract = "We present a comprehensive survey on dynamics of the motion of particles with noncommutative Poisson structure. We use Souriau{\textquoteright}s method of orbit to study this exotic mechanics on the tangent bundle of the configuration space or velocity phase space. We consider Feynman-Dyson{\textquoteright}s proof of Maxwell{\textquoteright}s equations using Jacobi identity on the velocity phase space. In this review we generalize the Feynman-Dyson{\textquoteright}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{\textquoteright}s scheme. Moreover, using the Souriau form we show that these new classes of generalized systems are volume preserving mechanical systems.",
keywords = "Feynman-Dyson{\textquoteright}s method, Generalized Hamiltonian dynamics, Kostant-Kirillov two form, Noncommutativity, Poisson manifolds, Schouten-Nijenhuis bracket, Souriau form",
author = "Cari{\~n}ena, \{Jos{\'e} F.\} and H{\'e}ctor Figueroa and Partha Guha",
note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2023",
doi = "10.1007/978-3-031-39334-1\_12",
language = "British English",
series = "STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics and Health",
publisher = "Springer Nature",
pages = "533--568",
booktitle = "STEAM-H",
address = "United Kingdom",
}