Construction of non-trivial relativistic quantum fields in arbitrary space-time dimension via superposition of free fields

TL;DR

This paper presents a method to construct non-trivial relativistic quantum fields in any space-time dimension by superposing free fields, satisfying all Osterwalder-Schrader axioms, and defining moments of a non-Gaussian measure.

Contribution

It introduces a dimension-independent construction of interacting quantum fields through superposition of free fields, fulfilling all axioms of quantum field theory.

Findings

Construction satisfies Osterwalder-Schrader axioms

Works in arbitrary space-time dimensions

Defines non-Gaussian measures on distribution space

Abstract

We construct Schwinger functions as the superposition of Schwinger functions which correspond to those of free fields with sharp masses $ m $. We prove that all axioms of Osterwalder and Schrader are satisfied. This construction works independently of the space-time dimension $ d $. The Schwinger functions under consideration are the moments of a non-Gaussian measure on the space of tempered distributions $ S'(\mathbb R^d) $.