Some comments on rigorous quantum field path integrals in the analytical regularization scheme

TL;DR

This paper develops mathematically rigorous quantum field path integrals in Euclidean space using the Minlos theorem, focusing on Gaussian free measures and generalized Laplacian operators in finite volume settings.

Contribution

It introduces a systematic approach to construct rigorous path integrals in interacting Euclidean quantum fields via cylindrical measures and the Minlos theorem.

Findings

Established rigorous path integrals for interacting fields

Applied Minlos theorem to support cylindrical measures

Defined Gaussian measures with generalized Laplacian operators

Abstract

Trough the systematic use of the Minlos theorem on the support of cylindrical measures on R infinity, we produce several mathematically rigorous path integrals in interacting euclidean quantum fields with Gaussian free measures defined by generalizeds powers of the laplacean operator on finite volume space-times