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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/129658
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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:UNLP2025-09-29T11:31:17Zoai: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:13292025-09-29 11:31:17.695SEDICI (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 |
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Universidad Nacional de La Plata |
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SEDICI (UNLP) - Universidad Nacional de La Plata |
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alira@sedici.unlp.edu.ar |
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