Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics : II. Rotational Invariance

Autores
Camblong, Horacio E.; Epele, Luis Nicolás; Fanchiotti, Huner; García Canal, Carlos Alberto
Año de publicación
2001
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A thorough analysis is presented of the class of central fields of force that exhibit: (i) dimensional transmutation and (ii) rotational invariance. Using dimensional regularization, the two-dimensional delta-function potential an d the D-dimensional inverse square potential are studied. In particular, the following features are analyzed: the existence of a critical coupling, the boundary condition at the origin, the relationship between the bound-state and scattering sectors, and the similarities displayed by both potentials. It is found that, for rotationally symmetric scale-invariant potentials, there is a strong-coupling regime, for which quantum-mechanical breaking of symmetry takes place, with the appearance of a unique bound state as well as of a logarithmic energy dependence of the scattering with respect to the energy.
Facultad de Ciencias Exactas
Materia
Física
Quantum Mechanics
Dimensional transmutation
Rotational invariance
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/129658
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/129658
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics : II. Rotational InvarianceCamblong, Horacio E.Epele, Luis NicolásFanchiotti, HunerGarcía Canal, Carlos AlbertoFísicaQuantum MechanicsDimensional transmutationRotational invarianceA thorough analysis is presented of the class of central fields of force that exhibit: (i) dimensional transmutation and (ii) rotational invariance. Using dimensional regularization, the two-dimensional delta-function potential an d the D-dimensional inverse square potential are studied. In particular, the following features are analyzed: the existence of a critical coupling, the boundary condition at the origin, the relationship between the bound-state and scattering sectors, and the similarities displayed by both potentials. It is found that, for rotationally symmetric scale-invariant potentials, there is a strong-coupling regime, for which quantum-mechanical breaking of symmetry takes place, with the appearance of a unique bound state as well as of a logarithmic energy dependence of the scattering with respect to the energy.Facultad de Ciencias Exactas2001info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf57-100http://sedici.unlp.edu.ar/handle/10915/129658enginfo:eu-repo/semantics/altIdentifier/issn/0003-4916info:eu-repo/semantics/altIdentifier/issn/1096-035Xinfo:eu-repo/semantics/altIdentifier/arxiv/hep-th/0003267info:eu-repo/semantics/altIdentifier/doi/10.1006/aphy.2000.6093info:eu-repo/semantics/reference/hdl/10915/131217info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-22T17:12:11Zoai:sedici.unlp.edu.ar:10915/129658Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 17:12:11.815SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics : II. Rotational Invariance
title Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics : II. Rotational Invariance
spellingShingle Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics : II. Rotational Invariance
Camblong, Horacio E.
Física
Quantum Mechanics
Dimensional transmutation
Rotational invariance
title_short Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics : II. Rotational Invariance
title_full Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics : II. Rotational Invariance
title_fullStr Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics : II. Rotational Invariance
title_full_unstemmed Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics : II. Rotational Invariance
title_sort Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics : II. Rotational Invariance
dc.creator.none.fl_str_mv Camblong, Horacio E.
Epele, Luis Nicolás
Fanchiotti, Huner
García Canal, Carlos Alberto
author Camblong, Horacio E.
author_facet Camblong, Horacio E.
Epele, Luis Nicolás
Fanchiotti, Huner
García Canal, Carlos Alberto
author_role author
author2 Epele, Luis Nicolás
Fanchiotti, Huner
García Canal, Carlos Alberto
author2_role author
author
author
dc.subject.none.fl_str_mv Física
Quantum Mechanics
Dimensional transmutation
Rotational invariance
topic Física
Quantum Mechanics
Dimensional transmutation
Rotational invariance
dc.description.none.fl_txt_mv A thorough analysis is presented of the class of central fields of force that exhibit: (i) dimensional transmutation and (ii) rotational invariance. Using dimensional regularization, the two-dimensional delta-function potential an d the D-dimensional inverse square potential are studied. In particular, the following features are analyzed: the existence of a critical coupling, the boundary condition at the origin, the relationship between the bound-state and scattering sectors, and the similarities displayed by both potentials. It is found that, for rotationally symmetric scale-invariant potentials, there is a strong-coupling regime, for which quantum-mechanical breaking of symmetry takes place, with the appearance of a unique bound state as well as of a logarithmic energy dependence of the scattering with respect to the energy.
Facultad de Ciencias Exactas
description A thorough analysis is presented of the class of central fields of force that exhibit: (i) dimensional transmutation and (ii) rotational invariance. Using dimensional regularization, the two-dimensional delta-function potential an d the D-dimensional inverse square potential are studied. In particular, the following features are analyzed: the existence of a critical coupling, the boundary condition at the origin, the relationship between the bound-state and scattering sectors, and the similarities displayed by both potentials. It is found that, for rotationally symmetric scale-invariant potentials, there is a strong-coupling regime, for which quantum-mechanical breaking of symmetry takes place, with the appearance of a unique bound state as well as of a logarithmic energy dependence of the scattering with respect to the energy.
publishDate 2001
dc.date.none.fl_str_mv 2001
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/129658
url http://sedici.unlp.edu.ar/handle/10915/129658
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0003-4916
info:eu-repo/semantics/altIdentifier/issn/1096-035X
info:eu-repo/semantics/altIdentifier/arxiv/hep-th/0003267
info:eu-repo/semantics/altIdentifier/doi/10.1006/aphy.2000.6093
info:eu-repo/semantics/reference/hdl/10915/131217
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv application/pdf
57-100
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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