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

Biagio Cassano ^[3] ; Vladimir Lotoreichik ^[4] ; Albert Mas ^[1] ; Matej Tušek ^[2]
1. [1] Universitat Politècnica de Catalunya
  
  Universitat Politècnica de Catalunya
  
  Barcelona, España
2. [2] Czech Technical University in Prague
  
  Czech Technical University in Prague
  
  Chequia
3. [3] Università degli Studi di Bari “A. Moro”
4. [4] Nuclear Physics Institute, Czech Academy of Sciences
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Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 4, 2023, págs. 1443-1492
Idioma: inglés
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Resumen
- 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.