Galilean symmetry in generalized abelian Schr\"odinger-Higgs models with and without gauge field interaction

TL;DR

This paper generalizes the Schr"odinger-Higgs model with a nonstandard kinetic term, demonstrating Galilean invariance, conserved charges, and algebra, both with and without gauge fields, and explores related twin models.

Contribution

It introduces a generalized nonrelativistic Schr"odinger-Higgs model with nonstandard kinetics and establishes its Galilean invariance and algebraic structure, including gauge interactions.

Findings

Model is Galilean invariant with conserved charges

Constructed Galilean algebra for the model

Explored relations between twin models and solutions

Abstract

We consider a generalization of nonrelativistic Schr\"odinger-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 twin models and their solutions.