Two-dimensional Dirac operators with singular interactions supported on closed curves

Jussi Behrndt, Markus Holzmann*, Thomas Ourmieres-Bonafos, Konstantin Pankrashkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study the two-dimensional Dirac operator with a class of interface conditions along a smooth closed curve, which model the so-called electrostatic and Lorentz scalar interactions of constant strengths, and we provide a rigorous description of their self-adjoint realizations and their qualitative spectral properties. We are able to cover in a uniform way all so-called critical combinations of coupling constants, for which there is a loss of regularity in the operator domain. For the case of a non-zero mass term, this results in an additional point in the essential spectrum, which reflects the creation of an infinite number of eigenvalues in the central gap, and the position of this point can be made arbitrary by a suitable choice of the parameters. The analysis is based on a combination of the extension theory of symmetric operators with a detailed study of boundary integral operators viewed as periodic pseudodifferential operators.

Original languageEnglish
Article number108700
JournalJournal of Functional Analysis
Issue number8
Publication statusPublished - 1 Nov 2020


  • Boundary triple
  • Dirac operator with singular interaction
  • Periodic pseudodifferential operators
  • Self-adjoint extension

ASJC Scopus subject areas

  • Analysis


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