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Dirac operators and shell interactions: a survey

Ourmières-Bonafos, Thomas; Pizzichillo, Fabio (2019), Dirac operators and shell interactions: a survey. https://basepub.dauphine.fr/handle/123456789/18665

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02016328
Date
2019
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
19
Metadata
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Author(s)
Ourmières-Bonafos, Thomas
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Pizzichillo, Fabio
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this survey we gather recent results on Dirac operators coupled with delta-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterward 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.
Subjects / Keywords
Dirac operators; shell interactions