Conformal 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.

• Received 22 August 2008

DOI:https://doi.org/10.1103/PhysRevD.78.087701