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In this note we give a concise review of the present state-of-art for theproblem of self-adjoint realisations for the Dirac operator with a Coulomb-likesingular scalar potential $V(\vec x)=\phi(\vec x) I_4$. We try to follow thehistorical and conceptual path that leads to the present understanding of theproblem and to highlight the techniques employed and the main ideas. In thefinal part we outline a few major open questions that concern the topicalproblem of the multiplicity of self-adjoint realisations of the model, andwhich are worth addressing in the future.

Self-Adjoint Extensions of Dirac Operator with Coulomb Potential