Space-time Schrödinger symmetries of a post-Galilean particle

Abstract

We study the space-time symmetries of the actions obtained by expanding the action for a massive free relativistic particle around the Galilean action [1]. We obtain all the point space-time symmetries of the post-Galilean actions by working in canonical space. We also construct an infinite collection of generalized Schrödinger algebras parameterized by an integer M , with M = 0 corresponding to the standard Schrödinger algebra. We discuss the Schrödinger equations associated to these algebras, their solutions and projective phases.