00941nas a2200109   4500008004100000245006900041210006800110260001000178520057200188100002000760856005100780       2017                        en  d00aSelf-Adjoint Extensions of Dirac Operator with Coulomb Potential0 aSelfAdjoint Extensions of Dirac Operator with Coulomb Potential  bSISSA3 aIn this note we give a concise review of the present state-of-art for the
problem of self-adjoint realisations for the Dirac operator with a Coulomb-like singular
scalar potential V(x) = Ø(x)I4. We try to follow the historical and conceptual
path that leads to the present understanding of the problem and to highlight the
techniques employed and the main ideas. In the final part we outline a few major
open questions that concern the topical problem of the multiplicity of self-adjoint
realisations of the model, and which are worth addressing in the future.1 aGallone, Matteo  uhttp://urania.sissa.it/xmlui/handle/1963/3527301120nas a2200109   4500008004100000245008000041210006900121520072300190100002000913700002900933856004800962       2017                        en  d00aSelf-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei0 aSelfadjoint realisations of the DiracCoulomb Hamiltonian for hea3 aWe derive a classification of the self-adjoint extensions of the
three-dimensional Dirac-Coulomb operator in the critical regime of the
Coulomb coupling. Our approach is solely based upon the KreĬn-Višik-
Birman extension scheme, or also on Grubb's universal classification
theory, as opposite to previous works within the standard von Neu-
mann framework. This let the boundary condition of self-adjointness
emerge, neatly and intrinsically, as a multiplicative constraint between
regular and singular part of the functions in the domain of the exten-
sion, the multiplicative constant giving also immediate information on
the invertibility property and on the resolvent and spectral gap of the
extension.1 aGallone, Matteo1 aMichelangeli, Alessandro  uhttp://preprints.sissa.it/handle/1963/35287