Abstract
In this paper we revise the main features of pseudospin and spin symmetries of the Dirac equation with scalar and vector potentials and mention several of its applications to physical systems. These symmetries have been extensively researched in the last 15 years, especially pseudospin symmetry, mainly in its application in understanding certain nuclear structure features of heavy nuclei. The realization of both symmetries has also been studied using several mean-field scalar and vector potentials. For many classes of potentials, these symmetries allow to have analytical solutions of the Dirac equation which otherwise would not have been possible. We report here some recent results related to anti-fermions, Coulomb and confining potentials.
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