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

✍ Scribed by Horacio E. Camblong; Luis N. Epele; Huner Fanchiotti; Carlos A. Garcı́a Canal

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
260 KB
Volume
287
Category
Article
ISSN
0003-4916

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✦ Synopsis

dedicated to c. g. bollini and j. j. giambiagi 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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