关于动量空间中1/r^2势的极限环
On the limit cycle for the 1/r^2 potential in momentum space
摘要：
最近，人们利用各种调节器研究了1/r^2引力势的重整化。特别是，它表明，重整化与位置空间中的方井允许多个解决方案的深度的方井，包括，但不需要一个重整化群极限环。在这里，我们考虑动量空间中1/r^2势的重整化。我们规范的问题与动量截止和吸收的截止依赖使用动量独立的counterterm潜在的。这个反项的强度是唯一确定的，并且在极限环上运行。我们还计算了束缚态谱和散射观测量，强调极限环在这些观测量中的表现。
英文摘要：
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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