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 and the D-dimensional inverse square potential arc studied. In particular, the following features;are analyzed: the existent 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 thr;appearance of a unique bound state as well as of a logarithmic energy dependence of the scattering with respect to the energy. (C) 2001 Academic Press.