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

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 $S^{\prime }({\mathbb{R}}^d)$.

The proof of the cluster property (E4) for the superposition is wrong. Yoh Tanimoto and Wojciech Dybalski gave a counterexample s.t. the statement of cluster property can't hold in its full generality