General $\delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation
Analysis of PDEs
2023-10-04 v1 Mathematical Physics
math.MP
Spectral Theory
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.
Keywords
Cite
@article{arxiv.2102.09988,
title = {General $\delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation},
author = {Biagio Cassano and Vladimir Lotoreichik and Albert Mas and Matěj Tušek},
journal= {arXiv preprint arXiv:2102.09988},
year = {2023}
}