Set-indexed random fields and algebraic Euclidean quantum field theory

TL;DR

This paper constructs non-Gaussian measures on continuous functions over Euclidean space balls, leading to operator algebra nets satisfying quantum field theory axioms, thus extending free scalar fields with nonlinear transformations.

Contribution

It introduces a novel method to build non-Gaussian measures that generate algebraic quantum field theories from free scalar fields.

Findings

Construction of non-Gaussian measures on function spaces.

Induction of nets of operator algebras satisfying Haag-Kastler axioms.

Interpretation as nonlinear transformations of free scalar fields.

Abstract

We present a construction of non-Gaussian Borel measures on the space of continuous functions defined on the space of all balls in Euclidean space of arbitrary dimension. These measures induce nets of operator algebras satisfying the Haag-Kastler axioms of algebraic quantum field theory and may be interpreted as (nonlinear) continuous transformations of the free scalar massive Euclidean quantum field.