标题： 关于费曼测度的威尔逊重正化群流的UV极限的存在定理 显示英文标题

标题： Existence theorem on the UV limit of Wilsonian RG flows of Feynman measures

摘要： 在欧几里得签名量子场论（QFT）的非微扰表述中，真空态由费曼测度的威尔逊重整化群（RG）流刻画。 这样一个RG流是在超紫外（UV）正则化场的空间上的一族费曼测度，它们通过威尔逊重整化群方程相互关联。 本文证明了，在温和的条件下，扩展到任意正则化强度的费曼测度的威尔逊RG流具有因子化性质：存在一个最终的费曼测度（UV极限）在分布意义下的场空间上，使得流中的正则化实例可以通过对调节器取边缘测度从这个UV极限获得。 关于相应作用泛函的流和UV极限的存在性定理也被证明。 显示英文摘要

摘要： In nonperturbative formulation of Euclidean signature quantum field theory (QFT), the vacuum state is characterized by the Wilsonian renormalization group (RG) flow of Feynman measures. Such an RG flow is a family of Feynman measures on the space of ultraviolet (UV) regularized fields, linked by the Wilsonian renormalization group equation. In this paper we show that under mild conditions, a Wilsonian RG flow of Feynman measures extending to arbitrary regularization strenghts has a factorization property: there exists an ultimate Feynman measure (UV limit) on the distribution sense fields, such that the regularized instances in the flow are obtained from this UV limit via taking the marginal measure against the regulator. Existence theorems about the flow and UV limit of the corresponding action functional are also proved.