Higgs algebraic symmetry in the two-dimensional Dirac equation

TL;DR

This paper constructs the Higgs algebra as the dynamical symmetry algebra of a specific two-dimensional Dirac Hamiltonian with particular potentials, allowing algebraic derivation of energy levels.

Contribution

It introduces the Higgs algebra as the symmetry algebra for this Dirac system, extending the understanding of algebraic structures in quantum mechanics.

Findings

Higgs algebra identified as the symmetry algebra

Energy levels derived algebraically using Casimir operators

Extension of algebraic methods to Dirac systems with specific potentials

Abstract

The dynamical symmetry algebra of the two-dimensional Dirac Hamiltonian with equal scalar and vector Smorodinsky-Winternitz potentials is constructed. It is the Higgs algebra, a cubic polynomial generalization of SU(2). With the help of the Casimir operators, the energy levels are derived algebraically.