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

Horacio E. Camblong·Luis N. Epele·Huner Fanchiotti·Carlos A. Garcia Canal
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Abstract

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 and 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.

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Horacio E. Camblong, Luis N. Epele, Huner Fanchiotti, Carlos A. Garcia Canal. 2001-01-04. Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics. II: Rotational Invariance. https://doi.org/10.1006/aphy.2000.6093

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