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

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 particul...

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Detalles Bibliográficos
Autores: Camblong, Horacio E., Epele, Luis Nicolás, Fanchiotti, Huner, García Canal, Carlos Alberto
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2001
País:Argentina
Institución:Universidad Nacional de La Plata
Repositorio:SEDICI (UNLP)
Idioma:inglés
OAI Identifier:oai:sedici.unlp.edu.ar:10915/129658
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/129658
Access Level:acceso abierto
Palabra clave:Física
Quantum Mechanics
Dimensional transmutation
Rotational invariance
Descripción
Sumario: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.