On the Construction of Euclidean Invariant and Reflection Positive Measures on the Cylindrical Compactification of Distributions

TL;DR

This paper presents a simplified method for constructing Euclidean invariant and reflection positive measures on the cylindrical compactification, extending previous results to theories with finitely many constraints.

Contribution

It introduces a weaker hypothesis for measure construction and extends the framework to constrained theories, advancing the mathematical foundation of Euclidean quantum field theory.

Findings

Constructed measures under weaker hypotheses

Extended results to theories with finitely many constraints

Simplified the mathematical framework for measure construction

Abstract

A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when the theory under consideration has finitely many constraints.