Higgs algebraic symmetry in the two-dimensional Dirac equation

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.

4p, no fig, pubulished version

References in corpus (10)

• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Hidden supersymmetry in quantum bosonic systems
• Superintegrability of the Caged Anisotropic Oscillator
• The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles
• Hidden nonlinear supersymmetry of finite-gap Lame equation
• Dynamical symmetry of Dirac hydrogen atom with spin symmetry and its connection with Ginocchio's oscillator
• Dynamical symmetries of the Klein-Gordon equation
• Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics

Cited by in corpus (9)

• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• First experimental realization of the Dirac oscillator
• Pseudospin symmetry in single particle resonances in spherical square wells
• Virial Theorem and Hypervirial Theorem in a spherical geometry
• Kappa-deformed Dirac oscillator in an external magnetic field
• Quadratic Algebra Approach to Relativistic Quantum Smorodinsky-Winternitz Systems
• Dynamical Algebras in the 1+1 Dirac Oscillator and the Jaynes-Cummings Model
• The Analytic Eigenvalue Structure of the 1+1 Dirac Oscillator
• Higgs algebraic symmetry of screened system in a spherical geometry