Renormalization-group limit cycle for the 1/r{sup 2} potential

Journal Article · Mon Nov 01 04:00:00 EST 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.052111· OSTI ID:20646169

Braaten, Eric; Phillips, Demian ^[1]

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1. Department of Physics, The Ohio State University, Columbus, Ohio 43210 (United States)

Previous work has shown that if an attractive 1/r{sup 2} potential is regularized at short distances by a spherical square-well potential, renormalization allows multiple solutions for the depth of the square well. The depth can be chosen to be a continuous function of the short-distance cutoff R, but it can also be a log-periodic function of R with finite discontinuities, corresponding to a renormalization-group (RG) limit cycle. We consider the regularization with a {delta}-shell potential. In this case, the coupling constant is uniquely determined to be a log-periodic function of R with infinite discontinuities, and an RG limit cycle is unavoidable. In general, a regularization with an RG limit cycle is selected as the correct renormalization of the 1/r{sup 2} potential by the conditions that the cutoff radius R can be made arbitrarily small and that physical observables are reproduced accurately at all energies much less than ({Dirac_h}/2{pi}){sup 2}/mR{sup 2}.

• OSTI ID: 20646169
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
BOUND STATE
COUPLING CONSTANTS
DISTANCE
LIMIT CYCLE
MATHEMATICAL SOLUTIONS
PERIODICITY
QUANTUM MECHANICS
RENORMALIZATION
SPHERICAL CONFIGURATION
SQUARE-WELL POTENTIAL