General spin and pseudospin symmetries of the Dirac equation

P. Alberto, M. Malheiro, T. Frederico, and A. de Castro
Phys. Rev. A 92, 062137 – Published 31 December 2015

Abstract

In the 1970s Smith and Tassie [G. B. Smith and L. J. Tassie, Ann. Phys. (NY) 65, 352 (1971)] and Bell and Ruegg [J. S. Bell and H. Ruegg, Nucl. Phys. B 98, 151 (1975); J. S. Bell and H. Ruegg, Nucl. Phys. B 104, 546 (1976)] 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 was revealed by Ginocchio [J. N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997)] 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 the second-order 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 two- and one-dimensional potentials. An application for a particular physical system in two dimensions, electrons in graphene, is suggested.

  • Received 19 October 2015

DOI:https://doi.org/10.1103/PhysRevA.92.062137

©2015 American Physical Society

Authors & Affiliations

P. Alberto

  • CFisUC, Physics Department, University of Coimbra, P-3004-516 Coimbra, Portugal

M. Malheiro and T. Frederico

  • Instituto Tecnológico de Aeronáutica, DCTA, 12228-900 São José dos Campos, São Paulo, Brazil

A. de Castro

  • Departamento de Física e Química, Universidade Estadual Paulista, 12516-410 Guaratinguetá, São Paulo, Brazil

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Issue

Vol. 92, Iss. 6 — December 2015

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