General spin and pseudospin symmetries of the Dirac equation

Abstract

In the 70's Smith and Tassie, and Bell and Ruegg independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and applied to several physical systems. Twenty years after, in 1997, the pseudospin symmetry has been revealed by Ginocchio as a relativistic symmetry of the atomic nuclei when it is described by relativistic mean field hadronic models. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrödinger-like equations, i.e, without a matrix structure. In this paper we propose a generalization of these SU(2) symmetries for potentials in the Dirac equation with several Lorentz structures, which also allow for the suppression of the matrix structure of second-order equation equation of either the upper or lower components of the Dirac spinor. We derive the general properties of those potentials and list some possible candidates, which include the usual spin-pseudospin potentials, and also 2- and 1-dimensional potentials. An application for a particular physical system in two dimensions, electrons in graphene, is suggested.

7 pages, uses RevTeX macros, accepted for publication in Phys. Rev. A

References in corpus (5)

• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• Chiral Gauge Theory for Graphene
• Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator
• Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles
• Vortex and gap generation in gauge models of graphene

Cited by in corpus (6)

• On the 2D Dirac oscillator in the presence of vector and scalar potentials in the cosmic string spacetime in the context of spin and pseudospin symmetries
• Relativistic Killingbeck Energy States Under an External Magnetic Fields
• Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential
• An Investigation of the Bound State Solutions of the Klein-Gordon Equation for the Generalized Woods-Saxon Potential in Spin Symmetry and Pseudo-spin Symmetry Limits
• Generalizing spin and pseudospin symmetries for relativistic spin 1/2 fermions
• Scattering, bound states, and resonances in the one-dimensional Dirac equation via supersymmetric quantum mechanics