Dirac operators with Lorentz scalar shell interactions

Markus Holzmann, Thomas Ourmieres-Bonafos, Konstantin Pankrashkin

Research output: Contribution to journalArticlepeer-review


This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions along the surface. After showing the self-adjointness of the resulting operator, we switch to the investigation of its spectral properties, in particular, to the existence and non-existence of eigenvalues. In the case of an attractive coupling, we study the eigenvalue asymptotics as the mass becomes large and show that the behavior of the individual eigenvalues and their total number are governed by an effective Schrödinger operator on the boundary with an external Yang–Mills potential and a curvature-induced potential.
Original languageEnglish
Article number18500137
JournalReviews in Mathematical Physics
Issue number5
Publication statusPublished - 2018

ASJC Scopus subject areas

  • Mathematical Physics

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

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