General spin and pseudospin symmetries of the Dirac equation

TL;DR

This paper generalizes the SU(2) spin and pseudospin symmetries of the Dirac equation to include potentials with multiple Lorentz structures, broadening the understanding of these symmetries and their applications.

Contribution

It introduces a generalized framework for spin and pseudospin symmetries in the Dirac equation with complex potentials, including new potential candidates and applications.

Findings

Derived properties of generalized potentials

Identified potential candidates including 2D and 1D cases

Suggested application to electrons in graphene

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 Schr\"odinger-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.