Renormalization of the Inverse Square Potential

2000/03/31 by Horacio E. Camblong, Luis N. Epele, Huner Fanchiotti +1 · 1 citation
Physics and Astronomy · #hep-th #quant-ph

paper · pdf · doi:10.1103/physrevlett.85.1590

published as Phys.Rev.Lett. 85 (2000) 1590-1593 · 5 pages

arxiv created 2000/09/05 · arxiv updated 2009/11/30

Abstract

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element.

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