dorsal/arxiv
View SchemaOn the limit cycle for the 1/r^2 potential in momentum space
| Authors | H. -W. Hammer, Brian G. Swingle |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503074 |
| URL | https://arxiv.org/abs/quant-ph/0503074 |
| DOI | 10.1016/j.aop.2005.04.017 |
| Journal | Annals Phys. 321 (2006) 306-317 |
Abstract
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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"abstract": "The renormalization of the attractive 1/r^2 potential has recently been\nstudied using a variety of regulators. In particular, it was shown that\nrenormalization with a square well in position space allows multiple solutions\nfor the depth of the square well, including, but not requiring a\nrenormalization group limit cycle. Here, we consider the renormalization of the\n1/r^2 potential in momentum space. We regulate the problem with a momentum\ncutoff and absorb the cutoff dependence using a momentum-independent\ncounterterm potential. The strength of this counterterm is uniquely determined\nand runs on a limit cycle. We also calculate the bound state spectrum and\nscattering observables, emphasizing the manifestation of the limit cycle in\nthese observables.",
"arxiv_id": "quant-ph/0503074",
"authors": [
"H. -W. Hammer",
"Brian G. Swingle"
],
"categories": [
"quant-ph",
"hep-th",
"nucl-th"
],
"doi": "10.1016/j.aop.2005.04.017",
"journal_ref": "Annals Phys. 321 (2006) 306-317",
"title": "On the limit cycle for the 1/r^2 potential in momentum space",
"url": "https://arxiv.org/abs/quant-ph/0503074"
},
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