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

✍ Scribed by Horacio E. Camblong; Luis N. Epele; Huner Fanchiotti; Carlos A. Garcı́a Canal

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
261 KB
Volume
287
Category
Article
ISSN
0003-4916

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✦ Synopsis

dedicated to c. g. bollini and j. j. giambiagi 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 twodimensional 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 quantummechanical 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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