Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics. I. General Theory
arXiv:hep-th/0003255 · doi:10.1006/aphy.2000.6092
Abstract
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.
28 pages. To appear in Annals of Physics
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