NN奇异相互作用的非微扰方法
Non-perturbative methods for NN singular interactions
摘要：
手征有效场论（$χ$ EFT）在过去的三十年中被广泛地用于研究$NN$相互作用。在有效场论（EFT）中，重整化是一阶接一阶地进行的，包括必要的计数器项。由于$NN$相互作用的强特性，需要非微扰的重新计算。在这项工作中，我们将审查一些方法，提出完全消除截断依赖。所涉及的方法是带边界条件的重整化，动量空间中带一个反项的重整化（或等价的减法重整化）和精确的$N/D$方法。在一个重整化条件下，将检查方法之间的等效性，以显示$NN$系统中的结果。精确的$N/D$方法允许超越别人，并使用一个玩具模型，它是如何可以重整奇异排斥相互作用。
英文摘要：
Chiral Effective Field Theory ($χ$EFT) has been extensively used to study the $NN$ interaction during the last three decades. In Effective Field Theories (EFTs) the renormalization is performed order by order including the necessary counter terms. Due to the strong character of the $NN$ interaction a non-perturbative resummation is needed. In this work we will review some of the methods proposed to completely remove cutoff dependencies. The methods covered are renormalization with boundary conditions, renormalization with one counter term in momentum space (or equivalently substractive renormalization) and the exact $N/D$ method. The equivalence between the methods up to one renormalization condition will be checked showing results in the $NN$ system. The exact $N/D$ method allows to go beyond the others, and using a toy model it is shown how it can renormalize singular repulsive interactions.
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