Universality of Low-Energy Scattering in 2+1 Dimensions: The Non Symmetric Case

Details Universality of Low-Energy Scattering in 2+1 Dimensions: The Non Symmetric Case Universality of Low-Energy Scattering in 2+1 Dimensions: The Non Symmetric Case

2004-01-28

arxiv.org/abs/hep-th/0401222v2

J.Math.Phys. 46 (2005) 032103; Erratum-ibid. 46 (2005) 129901

Physics

High Energy Physics

High Energy Physics - Theory

65 pages, Latex, significant changes, new sections and appendices

Scientific paper

10.1063/1.1843274

For a very large class of potentials, $V(\vec{x})$, $\vec{x}\in R^2$, we prove the universality of the low energy scattering amplitude, $f(\vec{k}', \vec{k})$. The result is $f=\sqrt{\frac{\pi}{2}}\{1/log k)+O(1/(log k)^2)$. The only exceptions occur if $V$ happens to have a zero energy bound state. Our new result includes as a special subclass the case of rotationally symmetric potentials, $V(|\vec{x}|)$.

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