Noncommutative and Dynamical Analysis in a Curved Phase-space

In this work, we have analyzed the dynamics of the model of a free particle over a 2-sphere in a noncommutative (NC) phase-space. Besides, we have shown that the solution of the equations of motion allows one to show the equivalence between the movement of the particle upon a 2-sphere and the one described by a central field. We have considered the eective force felt by the particle as being caused by the curvature of the space. We have analyzed the NC Poisson algebra of classical observables in order to obtain the NC corrections to Newton’s second law analogous to the one caused by a central field. We have also discussed the relation between ane connection and Dirac brackets, as they describe the proper evolution of the model over the surface of constraints in the Lagrangian and Hamiltonian formalisms, respectively. As an application, we have treated the so-called Zitterbewegung of the Dirac electron. Since it is assumed to be an observable eect, then we have traced its physical origin by assuming that the electron has an internal structure.