Towards Euclidean Theory of Infrared Singular Quantum Fields

TL;DR

This paper develops a Euclidean framework for quantum fields with severe infrared singularities, extending existing theories to include indefinite metrics and providing a generalized spectral condition and reconstruction theorem.

Contribution

It introduces a generalized spectral condition and extends the Euclidean formulation to infrared singular quantum fields with indefinite metrics, including a new reconstruction theorem.

Findings

Verified the generalized spectral condition for fields expressed as infinite series in Wick powers.

Extended Osterwalder-Schrader Euclidean QFT framework to infrared singular indefinite metric theories.

Provided a mathematical foundation for analyzing highly singular quantum fields.

Abstract

A new generalized formulation of the spectral condition is proposed for quantum fields with highly singular infrared behavior whose vacuum correlation functions are well defined only under smearing with analytic test functions in momentum space. The Euclidean formulation of QFT developed by Osterwalder and Schrader is extended to theories with infrared singular indefinite metric. The corresponding generalization of the reconstruction theorem is obtained. The fulfilment of the generalized spectral condition is verified for quantum fields representable by infinite series in the Wick powers of indefinite metric free fields.