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arXiv · 2102.09988

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

Biagio Cassano·Vladimir Lotoreichik·Albert Mas·Matěj Tušek
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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, and moreover we describe its approximation by Dirac operators with regular potentials.

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Biagio Cassano, Vladimir Lotoreichik, Albert Mas, Matěj Tušek. 2021-02-19. General $\delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation. https://doi.org/10.4171/rmi%2F1354

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