Remark on quantum mechanics with conformal Galilean symmetry

TL;DR

This paper develops a method to relate quantum systems with conformal Galilean symmetry to simpler decoupled particles, potentially aiding in understanding such symmetries in many-body quantum mechanics.

Contribution

It generalizes previous methods to construct a unitary map connecting conformal Galilean invariant quantum mechanics with decoupled particles.

Findings

Constructed a unitary map for conformal Galilean invariant systems.

Discussed potential applications of the map in quantum mechanics.

Extended methods from one-dimensional systems to more general cases.

Abstract

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.