%0 Report %D 2017 %T Discrete spectra for critical Dirac-Coulomb Hamiltonians %A Matteo Gallone %A Alessandro Michelangeli %X The one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished physically most natural one. For the latter, Sommerfeld’s celebrated fine structure formula provides the well-known expression for the eigenvalues in the gap of the continuum spectrum. Exploiting our recent general classification of all other self-adjoint realisations, we generalise Sommerfeld’s formula so as to determine the discrete spectrum of all other self-adjoint versions of the Dirac-Coulomb Hamiltonian. Such discrete spectra display naturally a fibred structure, whose bundle covers the whole gap of the continuum spectrum. %G en %U http://preprints.sissa.it/handle/1963/35300 %1 35606 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-11-06T14:27:38Z No. of bitstreams: 1 SISSA_preprint_44-2017-MATE.pdf: 1573857 bytes, checksum: 728e94322471701d89ed5741cda85d99 (MD5)