Recursion operator in a noncommutative Minkowski phase space
Abstract
A recursion operator for a geodesic flow, in a noncommutative (NC) phase space endowed with a Minkowski metric, is constructed and discussed in this work. A NC Hamiltonian function describing the dynamics of a free particle system in such a phase space, equipped with a noncommutative symplectic form is defined. A related NC Poisson bracket is obtained. This permits to construct the NC Hamiltonian vector field, also called NC geodesic flow. Further, using a canonical transformation induced by a generating function from the Hamilton-Jacobi equation, we obtain a relationship between old and new coordinates, and their conjugate momenta. These new coordinates are used to re-write the NC recursion operator in a simpler form, and to deduce the corresponding constants of motion. Finally, all obtained physical quantities are re-expressed and analyzed in the initial NC canonical coordinates.
Cite
@article{arxiv.2109.03822,
title = {Recursion operator in a noncommutative Minkowski phase space},
author = {Mahouton Norbert Hounkonnou and Mahougnon Justin Landalidji and Ezinvi Baloitcha},
journal= {arXiv preprint arXiv:2109.03822},
year = {2021}
}