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

TL;DR

This paper proves that under certain conditions, Wilsonian RG flows of Feynman measures in Euclidean QFT have a well-defined UV limit, characterized by a factorization property linking regularized measures to a universal measure.

Contribution

It establishes the existence of a UV limit for Wilsonian RG flows of Feynman measures and describes their factorization property in Euclidean QFT.

Findings

Existence of a UV limit measure for Wilsonian RG flows.

Factorization property linking regularized measures to the UV limit.

Discussion of existence theorems for the flow and action functional.

Abstract

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 strengths 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 on the flow and UV limit of the corresponding action functional are also discussed.