Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics. I. General Theory

Details Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics. I. General Theory Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics. I. General Theory

2000-03-28

arxiv.org/abs/hep-th/0003255v2

Annals Phys. 287 (2001) 14-56

Physics

High Energy Physics

High Energy Physics - Theory

28 pages. To appear in Annals of Physics

Scientific paper

10.1006/aphy.2000.6092

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.

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