General -shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation
Biagio Cassano
Università degli Studi di Bari “A. Moro”, ItalyVladimir Lotoreichik
Nuclear Physics Institute, Řež, CzechiaAlbert Mas
Universitat Politècnica de Catalunya, Barcelona, SpainMatěj Tušek
Czech Technical University in Prague, Czechia
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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