2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201878Conformal Galilei algebra contains so(1,2) subalgebra which is the conformal algebra in one dimension. In this note we generalize methods previously developed for one-dimensional many-body systems and construct a unitary map relating a quantum mechanics invariant under the conformal Galilean transformations to a set of decoupled particles for which the same symmetry is realized in a nonlocal way. Possible applications of the map are discussed.5 pages,V3: minor modificationsHigh Energy Physics - Theorytext