Weak adiabatic limit in quantum field theories with massless particles

TL;DR

This paper establishes the existence of the weak adiabatic limit in a broad class of perturbative quantum field theories with massless particles, ensuring well-defined Green functions under certain normalization conditions.

Contribution

It generalizes the weak adiabatic limit proof to models with interaction vertices of canonical dimension 3 or 4, including QED and Yang-Mills theories, within the Epstein-Glaser framework.

Findings

Proves the existence of the weak adiabatic limit under specific normalization conditions.

Shows the normalization condition can be imposed in models with certain interaction vertices and massive fields.

Demonstrates compatibility with standard normalization conditions in quantum electrodynamics and Yang-Mills theories.

Abstract

We construct the Wightman and Green functions in a large class of models of perturbative QFT in the four-dimensional Minkowski space in the Epstein-Glaser framework. To this end we prove the existence of the weak adiabatic limit, generalizing the results due to Blanchard and Seneor. Our proof is valid under the assumption that the time-ordered products satisfy certain normalization condition. We show that this normalization condition may be imposed in all models with interaction vertices of canonical dimension 4 as well as in all models with interaction vertices of canonical dimension 3 provided each of them contains at least one massive field. Moreover, we prove that it is compatible with all the standard normalization conditions which are usually imposed on the time-ordered products. The result applies, for example, to quantum electrodynamics and non-abelian Yang-Mills theories.