Camblong HE, Epele LN, Fanchiotti H. Renormalization of the inverse square potential.
PHYSICAL REVIEW LETTERS 2000;
85:1590-1593. [PMID:
10970565 DOI:
10.1103/physrevlett.85.1590]
[Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2000] [Indexed: 05/23/2023]
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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