Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics; 2, 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 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-invariant transmuting potentials, in the strong-coupling regime: scale invariance is broken, the transmuting system acquires a unique bound state, the coupling gets renormalized to its critical value, and the scattering displays a logarithmic dependence with respect to the energy