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...

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Detalhes bibliográficos
Autores: Ourmières-Bonafos, T., Pizzichillo, F.
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
Descrição
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.