Towards a construction of inclusive collision cross-sections in the massless Nelson model

TL;DR

This paper explores a non-perturbative approach to defining inclusive collision cross-sections in the massless Nelson model, addressing infrared issues in quantum field theory.

Contribution

It introduces a non-perturbative construction of inclusive cross-sections based on algebraic quantum field theory insights for the massless Nelson model.

Findings

Consistent with standard scattering theory without infrared problems

Addresses infrared-singular case challenges

Proposes a framework for non-perturbative inclusive cross-sections

Abstract

The conventional approach to the infrared problem in perturbative quantum electrodynamics relies on the concept of inclusive collision cross-sections. A non-perturbative variant of this notion was introduced in algebraic quantum field theory. Relying on these insights, we take first steps towards a non-perturbative construction of inclusive collision cross-sections in the massless Nelson model. We show that our proposal is consistent with the standard scattering theory in the absence of the infrared problem and discuss its status in the infrared-singular case.