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Joachim Nzotungicimpaye

Publications and source records attributed to Joachim Nzotungicimpaye.

11 recordsLinked to original sources
arXiv2019

Kinematical versus Dynamical Contractions of the de Sitter Lie algebras

We explicit and clarify better the contraction method that Bacry and Levy-Leblond\cite{jmll} used to link all the kinematical Lie groups. Firstly, we use the kinematical parameters: the speed $c$ of light, the radius $r$ of the universe and the period $τ$ of the universe constrained by $r=cτ$. Secondly, we use the dynamical parameters that are mass $m$, energy $E_0$ and compliance $C$. The kinematical and the dynamical parameters are related by the three relations $c^2=\frac{E_0}{m}$, $τ^2=mC$ and $r^2=CE_0$. For each kinematical Lie algebra, we express the associated physical quantities in function of these dynamical parameters.

math-ph↗
arXiv2013

Group theoretical construction of planar Noncommutative Phase Spaces

Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.

math-ph↗
arXiv2013

Noncommutative Phase Spaces on Aristotle group

We realize noncommutative phase spaces as coadjoint orbits of extensions of the Aristotle group in a two-dimensional space. Through these constructions the momenta of the phase spaces do not commute due to the presence of a naturally introduced magnetic field. These cases correspond to the minimal coupling of the momentum with a magnetic potential.

math-ph↗
arXiv2012

Para-Galilean versus Galilean Noncommutative Phase spaces

The present paper deals with the construction of noncommutative phase spaces as coadjoint orbits of noncentral extensions of Galilei and Para-Galilei groups in two-dimensional space. The noncommutativity is due to the presence of a dual magnetic field B* in the Galilei case and of a magnetic field B in the Para-Galilei case.

math-ph↗
arXiv2011

Noncommutative Phase Spaces by Coadjoint Orbits Method

We introduce noncommutative phase spaces by minimal couplings (usual one, dual one and their mixing). We then realize some of them as coadjoint orbits of the anisotropic Newton-Hooke groups in two- and three-dimensional spaces. Through these constructions the positions and the momenta of the phase spaces do not commute due to the presence of a magnetic field and a dual magnetic field.

math-ph↗
arXiv2007

On a two-particles system associated to the one spatial dimensional Galilei group

In [8], M.Daumens and M.Perroud studied a two Galilean free particles system by realizing the three dimensional Galilei group on its maximal coadjoint orbit. In this paper we realize a similar study for the one spatial dimesnional Galilei group. As its maximal coadjoint orbit describes a non free massive particle [6], this gives us a two non free galilean partcles system. Use of the barycenter coordinates gives rise to the notions of a total force and a relative force similar to those of a total linaer momentum and a relative linear momentum ([]8),[9],[10]). We will distinguish the case of a non isolated system from that of an isolated one. We will show that the barycenter is accelerated in the first case while it moves with a constant velocity in the second one.

math-ph↗
arXiv2005

Mass, Impetus and Force by Symplectic Realizations of the Static Group

We show by symplectic realizations of the one dimensional Static group $G$ that the maximal $G$-elementary system is a a massive particle under an invariant force $f$ participating in the linear momentum and an invariant impetus $I$ participating in the change of position. Moreover the system is characterized by four physical quantities : a mass $m$, a boost $u=\frac{I}{m}$, an acceleration $a=\frac{f}{m}$ and an internal energy $U$. The hamiltonian of the system is a sum of the potential energy $V=-fq$ and a contribution $pu$ of the impetus.

math-ph↗
arXiv2005

Method LAC

This is a paper which present a mnemotechnical method that we call LAC for Lists, Arrangements and Combinations. It can help students or any one to recollect formulae from combinatorial theory ([1],[2],[3],[4]) without an a priori memorization of them.

math.CO↗
arXiv2003

On a Two-Dimensional Symplectic Space-Time

We realize the hamiltonian action of the one spatial Poincare group G, analogous to the projective unitary representation, on a coadjoint orbit of G whic we interpret as a symplectic space-time where the time is associated to a physical quantity of cohomological origine (the force f). This time is the time delay necessary tor the system under the force f to have momentum p.

math-ph↗
arXiv2002

Yank and Hooke's constant group theoretically

We study the second central extension of the (1+1) Aristotle Lie.We find that the first central extension admit four orbits on the dual of second central extension of the (1+1) Aristotle Lie group.The generic orbit is characterised by a Hooke's constant k and a yank y.If the physics of the orbit is studied with respect the evolution in time,it represents an elementary system with internal energy U in a posotion-momentum under the conjugation of a Hooke's force and a damping one proportional to the velocity as in particle mechanics.If the physics of the orbit is studied with respect the evolution in space, it represents an elementary system with an internal momentum P under the conjugation of a kind of Hooke's force and a damping one proportional to a slowness, slowness usually used in time travel waves.

math-ph↗