| dc.contributor.author | Esteban, Maria J. | * |
| dc.contributor.author | Lewin, Mathieu | * |
| dc.contributor.author | Séré, Eric | * |
| dc.date.accessioned | 2020-04-03T10:31:09Z | |
| dc.date.available | 2020-04-03T10:31:09Z | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/20608 | |
| dc.language.iso | en | en |
| dc.subject | Dirac-Coulomb operators | en |
| dc.subject.ddc | 520 | en |
| dc.title | Dirac-Coulomb operators with general charge distribution. I. Distinguished extension and min-max formulas | en |
| dc.type | Document de travail / Working paper | |
| dc.description.abstracten | This paper is the first of a series where we study the spectral properties of Dirac operators with the Coulomb potential generated by any finite signed charge distribution μ. We show here that the operator has a unique distinguished self-adjoint extension under the sole condition that μ has no atom of weight larger than or equal to one. Then we discuss the case of a positive measure and characterize the domain using a quadratic form associated with the upper spinor, following earlier works by Esteban and Loss. This allows us to provide min-max formulas for the eigenvalues in the gap. In the event that some eigenvalues have dived into the negative continuum, the min-max formulas remain valid for the remaining ones. At the end of the paper we also discuss the case of multi-center Dirac-Coulomb operators corresponding to μ being a finite sum of deltas. | en |
| dc.publisher.name | Cahier de recherche CEREMADE, Université Paris-Dauphine | en |
| dc.publisher.city | Paris | en |
| dc.identifier.citationpages | 33 | en |
| dc.identifier.urlsite | https://hal.archives-ouvertes.fr/hal-02503460 | en |
| dc.subject.ddclabel | Sciences connexes (physique, astrophysique) | en |
| dc.identifier.citationdate | 2020-03 | |
| dc.description.ssrncandidate | non | en |
| dc.description.halcandidate | non | en |
| dc.description.readership | recherche | en |
| dc.description.audience | International | en |
| dc.date.updated | 2020-04-03T10:28:03Z | |
| hal.person.labIds | 60 | * |
| hal.person.labIds | 60 | * |
| hal.person.labIds | 60 | * |
