Nontrivial models with indefinite metric

TL;DR

This paper reviews how quantum field models with indefinite metrics facilitate nonperturbative construction of models with nontrivial scattering in various dimensions, including solutions in 4D where positive metric models are unknown.

Contribution

It highlights the advantages of indefinite metric frameworks for constructing quantum field models and discusses solutions derived from analytic continuation of Euclidean SPDEs driven by non-Gaussian noise.

Findings

Existence of solutions in 4D quantum field models with indefinite metric.

Simplification of nonperturbative construction in indefinite metric frameworks.

Connection between Euclidean SPDE solutions and Minkowski space models.

Abstract

The non perturbative construction of quantum field models with nontrivial scattering in arbitrary dimension $d$ of the underlying Minkowski space-time is much more simple in the framework of quantum field theory with indefinite metric than in the positive metric case. In particular, there exist a number of solutions in the physical dimension $d=4$, where up to now no positive metric solutions are known. Here we review, why this is so, and we discuss some examples obtained by analytic continuation from the solutions of Euclidean covariant stochastic partial differential equations (SPDEs) driven by non-Gaussian white noise.