10
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator

      Preprint
      , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials \(\mathbf V\) of Coulomb type: we characterise its eigenvalues in terms of the Birman-Schwinger principle and we bound its discrete spectrum from below, showing that the \emph{ground-state energy} is reached if and only if \(\mathbf V\) verifies some {rigidity} conditions. In the particular case of an electrostatic potential, these imply that \(\mathbf V\) is the Coulomb potential.

          Related collections

          Most cited references15

          • Record: found
          • Abstract: not found
          • Article: not found

          Note on a theorem of Hilbert

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Self-adjointness and invariance of the essential spectrum for Dirac operators defined as quadratic forms

            G. Nenciu (1976)
              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Distinguished selfadjoint extensions of Dirac operators

                Bookmark

                Author and article information

                Journal
                02 October 2018
                Article
                1810.01309
                e65f4943-375c-44c0-bc96-9f8fd84d8282

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                81Q10(Primary), 47N20, 35P05, 47B25 (Secondary)
                math.AP math-ph math.MP math.SP

                Mathematical physics,Analysis,Functional analysis,Mathematical & Computational physics

                Comments

                Comment on this article