Dirac Operators and Shell Interactions: A Survey
In this survey we gather recent results on Dirac operators coupled with δ-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterwards we switch to an approximation question: can these operators be recovered as limits of Dirac...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1449 |
| Acesso em linha: | http://hdl.handle.net/20.500.11824/1449 |
| Access Level: | acceso abierto |
| Palavra-chave: | Dirac operator Klein’s paradox Self-adjoint operator Spectral theory δ-shell interaction |
| Resumo: | In this survey we gather recent results on Dirac operators coupled with δ-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterwards we switch to an approximation question: can these operators be recovered as limits of Dirac operators coupled with squeezing potentials? We also discuss spectral features of these models. Namely, we recall the main spectral consequences of a resolvent formula and conclude the survey by commenting a result of asymptotic nature for the eigenvalues in the gap of a Dirac operator coupled with a Lorentz-scalar interaction. |
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