2017/06/30 by Matteo Gallone, Alessandro Michelangeli · 1 citation
Mathematics · Physics and Astronomy · #Computer science #Coulomb #Coupling constant #Dirac (video compression format) #Domain (mathematical analysis) #Extension (predicate logic) #Hamiltonian (control theory) #Hilbert space #Mathematical analysis #Mathematical physics #Mathematics #Multiplicative function #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Resolvent #Self-adjoint operator #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena #math-ph #math.MP #msc:47B25 #msc:47N20 #msc:47N50 #msc:81Q10
paper · pdf · doi:10.1007/s13324-018-0219-7
26 pages, corrected some typos and the values of some constants. Final version to appear in Analysis and Mathematical Physics (2018)
openalex created_date 2017/06/09 · openalex publication_date 2018/02/24 · arxiv created 2018/03/10 · arxiv updated 2018/03/13 · openalex updated_date 2026/08/05
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 Kre\uın-Višik-Birman extension scheme, or also on Grubb's universal classification theory, as opposite to previous works within the standard von Neumann 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 extension, the multiplicative constant giving also immediate information on the invertibility property and on the resolvent and spectral gap of the extension.