Mathematics

We 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.