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, but for the bound-state and scattering sectors. Finally, dimensional transmutation is explicitly illustrated for the two-dimensional delta-function potential. (C) 2001 Academic Press.