General δ-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation
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Biagio Cassano [3] ; Vladimir Lotoreichik [4] ; Albert Mas [1] ; Matej Tušek [2]
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[1] Universitat Politècnica de Catalunya
Universitat Politècnica de Catalunya
Barcelona, España
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[2] Czech Technical University in Prague
Czech Technical University in Prague
Chequia
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[3] Università degli Studi di Bari “A. Moro”
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[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
- DOI: 10.4171/RMI/1354
- Enlaces
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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.
