Gallone, MatteoMichelangeli, Alessandro2017-06-052017-06-052017-06https://openscience.sissa.it/handle/1963/35287We 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.enDirac-Coulomb operatorself-adjoint extensionsKreĭn-Višik- Birman extension theoryGrubb's universal classificationPreprint26/2017/MATE