Dimensional Transmutation and Dimensional Regularization in Quantum   Mechanics. I. General Theory
  This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their general properties are derived. A strategy for dimensional renormalization of these systems in the strong-coupling regime is presented, and the emergence of an energy scale is shown, both for the bound-state and scattering sectors. Finally, dimensional transmutation is explicitly illustrated for the two-dimensional delta-function potential. 
Horacio E. Camblong, Luis N. Epele, Huner Fanchiotti and Carlos A.   Garcia Canal