Remarks on some new models of interacting quantum fields with indefinite metric

TL;DR

This paper explores quantum field models with indefinite metrics, introducing modified axioms and constructing concrete models via analytical continuation, while establishing spectral conditions for scattering theory development.

Contribution

It presents a general framework for indefinite metric QFT using modified Wightman axioms and constructs new interacting models from stochastic processes.

Findings

Established spectral condition for translation group in indefinite metric models

Constructed concrete interacting relativistic models from Euclidean invariant stochastic processes

Provided groundwork for scattering theory in indefinite metric quantum field theory

Abstract

We study quantum field models in indefinite metric. We introduce the modified Wightman axioms of Morchio and Strocchi as a general framework of indefinite metric quantum field theory (QFT) and present concrete interacting relativistic models obtained by analytical continuation from some stochastic processes with Euclidean invariance. As a first step towards scattering theory in indefinite metric QFT, we give a proof of the spectral condition on the translation group for the relativistic models.