Galilean symmetry in generalized Abelian Schrödinger–Higgs models with and without gauge field interaction

Abstract

We consider a generalization of non-relativistic Schrödinger–Higgs Lagrangian by introducing a nonstandard kinetic term. We show that this model is Galilean invariant, we construct the conserved charges associated to the symmetries and realize the algebra of the Galilean group. In addition, we study the model in the presence of a gauge field. We also show that the gauged model is Galilean invariant. Finally, we explore relations between the twin models and their solutions.