标题： 量子场论中的有限熵和 显示英文标题

标题： Finite entropy sums in quantum field theory

摘要： 与传统局部量子场论中空间子系统相关的熵通常在空间区域具有边界时发散。 然而，在各种子系统的熵的某些线性组合中，这些发散可能相互抵消，从而得到提供关于底层状态的信息理论数据的有限量。 在本说明中，我们表明所有此类量都可以写成三种基本类型量的线性组合：i) 一个空间子系统的熵减去其补子系统的熵，ii) 非相邻子系统之间的互信息，以及iii) 不相交子系统三元组的三重信息。 对于空间切片的一个固定区域分解，我们描述了一组熵的和的基，这些和的熵对于这些区域的集合而言，所有与区域边界以及区域更高余维交叉相关的发散都会被抵消。 本工作中使用的关键数学技术（布尔立方体上的傅里叶变换和偏序集上函数的莫比乌斯变换）以及几个主要的证明思路是由AI（ChatGPT5）提出的。 我们根据我们的经验，对AI在物理学和数学中的使用提出了一些评论。 显示英文摘要

摘要： Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems, these divergences may cancel, giving finite quantities that provide information-theoretic data about the underlying state. In this note, we show that all such quantities can be written as linear combinations of three basic types of quantities: i) the entropy of a spatial subsystem minus the entropy of its complementary subsystem, ii) the mutual information between non-adjacent subsystems, and iii) the tripartite information for triples of disjoint sub-systems. For a fixed decomposition of a spatial slice into regions, we describe a basis of sums of entropies for collections of for these regions for which all divergences related to both region boundaries and higher-codimension intersections of regions cancel. Key mathematical technology used in this work (Fourier transforms on the Boolean cube and M\"obius transformations of functions on partially ordered sets) and several of the main proof ideas were suggested by AI (ChatGPT5). We offer a few comments on the use of AI in physics and mathematics, based on our experience.