Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials

We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, for $\nu,\mu,\lambda \in \mathbb R$. We characterize the self-adjoint...

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Detalles Bibliográficos
Autores: Cassano, B., Pizzichillo, F.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/780
Acceso en línea:http://hdl.handle.net/20.500.11824/780
Access Level:acceso abierto
Palabra clave:Dirac operator
Coulomb potential
Hardy inequality
self-adjoint operator
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spelling Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric PotentialsCassano, B.Pizzichillo, F.Dirac operatorCoulomb potentialHardy inequalityself-adjoint operatorWe describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, for $\nu,\mu,\lambda \in \mathbb R$. We characterize the self-adjointness in terms of the behaviour of the functions of the domain in the origin, exploiting Hardy-type estimates and trace lemmas. Finally, we describe the distinguished extension.Istituto Italiano di Alta Matematica "F. Severi"201820182018info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/780reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Inglésinfo:eu-repo/grantAgreement/EC/H2020/669689info:eu-repo/grantAgreement/MINECO//SEV-2013-0323info:eu-repo/grantAgreement/MINECO//MTM2014-53850-Pinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2014-2017Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/7802026-06-19T12:47:47Z
dc.title.none.fl_str_mv Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
title Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
spellingShingle Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
Cassano, B.
Dirac operator
Coulomb potential
Hardy inequality
self-adjoint operator
title_short Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
title_full Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
title_fullStr Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
title_full_unstemmed Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
title_sort Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
dc.creator.none.fl_str_mv Cassano, B.
Pizzichillo, F.
author Cassano, B.
author_facet Cassano, B.
Pizzichillo, F.
author_role author
author2 Pizzichillo, F.
author2_role author
dc.subject.none.fl_str_mv Dirac operator
Coulomb potential
Hardy inequality
self-adjoint operator
topic Dirac operator
Coulomb potential
Hardy inequality
self-adjoint operator
description We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, for $\nu,\mu,\lambda \in \mathbb R$. We characterize the self-adjointness in terms of the behaviour of the functions of the domain in the origin, exploiting Hardy-type estimates and trace lemmas. Finally, we describe the distinguished extension.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018
2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/780
url http://hdl.handle.net/20.500.11824/780
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/EC/H2020/669689
info:eu-repo/grantAgreement/MINECO//SEV-2013-0323
info:eu-repo/grantAgreement/MINECO//MTM2014-53850-P
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2014-2017
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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repository.mail.fl_str_mv
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