On Dirac operators with electrostatic -shell interactions of critical strength

  • Jussi Behrndt

    Technische Universität Graz, Austria
  • Markus Holzmann

    Technische Universität Graz, Austria
On Dirac operators with electrostatic $\delta$-shell interactions of critical strength cover

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Abstract

In this paper we prove that the Dirac operator with an electrostatic -shell interaction of critical strength supported on a -smooth compact surface is self-adjoint in , we describe the domain explicitly in terms of traces and jump conditions in , and we investigate the spectral properties of . While the non-critical interaction strengths have received a lot of attention in the recent past, the critical case remained open. Our approach is based on abstract techniques in extension theory of symmetric operators, in particular, boundary triples and their Weyl functions.

Cite this article

Jussi Behrndt, Markus Holzmann, On Dirac operators with electrostatic -shell interactions of critical strength. J. Spectr. Theory 10 (2020), no. 1, pp. 147–184

DOI 10.4171/JST/289