A Construction of Euclidean Invariant, Reflection Positive Measures on a Compactification of Distributions

TL;DR

This paper presents a straightforward method to construct Euclidean invariant, reflection positive measures on a compactified space of distributions, highlighting that the employed regularizations are not reflection positive.

Contribution

It introduces a novel construction of reflection positive measures with non-reflection positive regularizations on a compactified distribution space.

Findings

Measures are Euclidean invariant and reflection positive.

Regularizations used are not reflection positive.

Construction applies to a compactification of distributions.

Abstract

A simple construction is given of a class of Euclidean invariant, reflection positive measures on a compactification of the space of distributions. An unusual feature is that the regularizations used are not reflection positive.