The entanglement between momentum modes of a quantum field theory at different scales is not as well studied as its counterpart in real space, despite the natural connection with the Wilsonian idea of integrating out the high-momentum degrees of freedom. Here, we push such a connection further by developing a novel method to calculate the Rényi and entanglement entropies between slow and fast modes, which is based on the Wilsonian effective action at a given scale. This procedure is applied to the perturbative regime of some scalar theories, comparing the lowest-order results with those from the literature and interpreting them in terms of Feynman diagrams. This method is easily generalized to higher-order or nonperturbative calculations. It has the advantage of avoiding matrix diagonalizations of other techniques.

中文翻译：

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来自威尔逊有效作用的动量空间纠缠

尽管与整合高动​​量自由度的威尔逊思想有着自然的联系，但不同尺度的量子场论动量模式之间的纠缠并没有像现实空间中的对应物那样得到很好的研究。在这里，我们通过开发一种新方法来进一步推动这种联系，该方法基于给定尺度下的威尔逊有效作用来计算慢模和快模之间的 Rényi 和纠缠熵。该过程适用于一些标量理论的微扰机制，将最低阶结果与文献中的结果进行比较，并根据费曼图对其进行解释。这种方法很容易推广到高阶或非微扰计算。它的优点是避免了其他技术的矩阵对角化。