Nonrelativistic conformal groups and their dynamical realizations

TL;DR

This paper classifies nonrelativistic conformal groups with a nonzero mass parameter, showing their dynamical realizations as higher-order equations of motion, including special cases like the Schrödinger group and Newtonian mechanics.

Contribution

It provides a classification of coadjoint orbits of nonrelativistic conformal groups and links them to higher-order dynamical systems within the Ostrogradski framework.

Findings

Coadjoint orbits are classified for nonrelativistic conformal groups.

Dynamical systems correspond to higher-order equations of motion.

Special cases recover Schrödinger group and Newtonian mechanics.

Abstract

Nonrelativistic conformal groups, indexed by l=N/2, are analyzed. Under the assumption that the "mass" parametrizing the central extension is nonvanishing the coadjoint orbits are classified and described in terms of convenient variables. It is shown that the corresponding dynamical system describes, within Ostrogradski framework, the nonrelativistic particle obeying (N+1)-th order equation of motion. As a special case, the Schroedinger group and the standard Newton equations are obtained for N=1 (l=1/2).