General -shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation

  • Biagio Cassano

    Università degli Studi di Bari “A. Moro”, Italy
  • Vladimir Lotoreichik

    Nuclear Physics Institute, Řež, Czechia
  • Albert Mas

    Universitat Politècnica de Catalunya, Barcelona, Spain
  • Matěj Tušek

    Czech Technical University in Prague, Czechia
General $\delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation cover
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Abstract

In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four elementary interactions: electrostatic, Lorentz scalar, magnetic, and a fourth one which can be absorbed by using unitary transformations. We address the self-adjointness and the spectral description of the underlying Dirac operator. In the non-critical case, we do so by providing a boundary triple, and in the critical purely magnetic case, by exploiting the phenomenon of confinement and super-symmetry. Moreover, we justify our model by showing that Dirac operators with singular interactions are limits in the strong resolvent sense of Dirac operators with regular potentials.

Cite this article

Biagio Cassano, Vladimir Lotoreichik, Albert Mas, Matěj Tušek, General -shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation. Rev. Mat. Iberoam. 39 (2023), no. 4, pp. 1443–1492

DOI 10.4171/RMI/1354