2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/180575We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a $\star$-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner function. The properties of these quasi-distributions are discussed as well as their relation to the sets of ordinary Wigner functions and positive Liouville probability densities. Based on these notions we propose criteria for assessing whether a commutative regime has emerged in the realm of noncommutative quantum mechanics. To induce this noncommutative-commutative transition, we couple a particle to an external bath of oscillators. The master equation for the Brownian particle is deduced.7 pages, Latex file, Based on a talk presented by Joao Prata at D.I.C.E. 2006, Piombino, ItalyHigh Energy Physics - Theorytext