Schrödinger equations for higher order nonrelativistic particles and N-Galilean conformal symmetry

Abstract

We consider Schrödinger equations for a nonrelativistic particle obeying an N + 1 -th order higher derivative classical equation of motion. These equations are invariant under N (odd)-extended Galilean conformal algebras in general d + 1 dimensions. In 2 + 1 dimensions, the exotic Schrödinger equations are invariant under N (even)-Galilean conformal algebras.