Higgs algebraic symmetry of screened system in a spherical geometry

TL;DR

This paper explores the dynamical symmetries of screened Coulomb and harmonic oscillator systems in spherical geometry, revealing Higgs algebra as the underlying symmetry structure and identifying conserved vectors at orbital points.

Contribution

It demonstrates that these systems' symmetries are described by Higgs algebra and identifies conserved vectors at orbital turning points in spherical space.

Findings

Dynamical symmetries are described by Higgs algebra.

Existence of conserved aphelion and perihelion vectors.

Symmetry group generators include angular momentum and these vectors.

Abstract

The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z. B. Wu and J. Y. Zeng, Phys. Rev. A 62,032509 (2000)]. We find the similar properties in the responding systems in a spherical space, whose dynamical symmetries are described by Higgs Algebra. There exists a conserved aphelion and perihelion vector, which, together with angular momentum, constitute the generators of the geometrical symmetry group at the aphelia and perihelia points $(\dot{r}=0)$.