Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-03-29
Ann.Phys.287:57-100,2001
Physics
High Energy Physics
High Energy Physics - Theory
29 pages. To appear in Annals of Physics
Scientific paper
10.1006/aphy.2000.6093
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.
Camblong Horacio E.
Epele Luis N.
Fanchiotti Huner
Garcia Canal Carlos A.
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