On the limit cycle for the 1/r^2 potential in momentum space

Details On the limit cycle for the 1/r^2 potential in momentum space On the limit cycle for the 1/r^2 potential in momentum space

2005-03-08

arxiv.org/abs/quant-ph/0503074v1

Annals Phys. 321 (2006) 306-317

Physics

Quantum Physics

12 pages, 6 ps figures, revtex4

Scientific paper

10.1016/j.aop.2005.04.017

The renormalization of the attractive 1/r^2 potential has recently been studied using a variety of regulators. In particular, it was shown that renormalization with a square well in position space allows multiple solutions for the depth of the square well, including, but not requiring a renormalization group limit cycle. Here, we consider the renormalization of the 1/r^2 potential in momentum space. We regulate the problem with a momentum cutoff and absorb the cutoff dependence using a momentum-independent counterterm potential. The strength of this counterterm is uniquely determined and runs on a limit cycle. We also calculate the bound state spectrum and scattering observables, emphasizing the manifestation of the limit cycle in these observables.

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