标题： 基于平滑费什巴赫-舒尔映射的谱归一化流：半群性质的引入 显示英文标题

标题： The Spectral Renormalization Flow Based on the Smooth Feshbach--Schur Map: The Introduction of the Semi-Group Property

摘要： 谱归一化方法是一种强大的数学工具，在低能量子场论的谱理论中被广泛使用，其在[5, 6]中的首次引入是该领域的一个里程碑。 受物理学启发，这种方法通常被称为重整化群，尽管它既不是群也不是半群（或者更准确地说，是一个流）。 直到2015年，在[1]中首次引入了一个流（或半群）结构，这是通过一种创新的谱参数重整化定义实现的。 然而，在[1]中提出的谱归一化流与平滑的Feshbach--Schur映射不相容（这在[1]中被列为一个开放问题），这是一个令人遗憾的缺陷，因为其平滑性是一个关键特性，显著简化了证明，并使其成为大多数文献中的首选工具。 在本文中，我们通过基于平滑的Feshbach--Schur映射引入了一种谱归一化流来解决这个开放问题。 显示英文摘要

摘要： The spectral renormalization method is a powerful mathematical tool that is prominently used in spectral theory in the context of low-energy quantum field theory and its original introduction in [5, 6] constituted a milestone in the field. Inspired by physics, this method is usually called renormalization group, even though it is not a group nor a semigroup (or, more properly, a flow). It was only in 2015 in [1] when a flow (or semigroup) structure was first introduced using an innovative definition of the renormalization of spectral parameters. The spectral renormalization flow in [1], however, is not compatible with the smooth Feshbach--Schur map (this is stated as an open problem in [1]), which is a lamentable weakness because its smoothness is a key feature that significantly simplifies the proofs and makes it the preferred tool in most of the literature. In this paper we solve this open problem introducing a spectral renormalization flow based on the smooth Feshbach--Schur map.