Acceleration-extended Newton-Hooke symmetry and its dynamical realization

TL;DR

This paper explores an extended Newton-Hooke symmetry incorporating acceleration, develops a higher order Lagrangian invariant under this symmetry, and demonstrates the invariance of the resulting Schrödinger equation, also touching on exotic conformal symmetry in 2+1 dimensions.

Contribution

It introduces an acceleration-extended Newton-Hooke symmetry, constructs a quasi-invariant Lagrangian, and shows the Schrödinger equation's invariance under this extended symmetry.

Findings

The Schrödinger equation remains invariant under acceleration-extended Newton-Hooke transformations.

A higher order Lagrangian quasi-invariant under the extended symmetry is constructed.

Discussion of exotic conformal Newton-Hooke symmetry in 2+1 dimensions is included.

Abstract

Newton-Hooke group is the nonrelativistic limit of de Sitter (anti-de Sitter) group, which can be enlarged with transformations that describe constant acceleration, as well as central charges. We consider a higher order Lagrangian that is quasi-invariant under the acceleration-extended Newton-Hooke symmetry, and obtain the Schr\"{o}dinger equation quantizing the Hamiltonian corresponding to its first order form. We show that the Schr\"{o}dinger equation is invariant under the acceleration-extended Newton-Hooke transformations. We also discuss briefly the exotic conformal Newton-Hooke symmetry in 2+1 dimension.