# Asymptotic morphisms and superselection theory in the scaling limit II: analysis of some models

## TL;DR

This paper applies the concept of asymptotic morphisms to analyze superselection sectors in the scaling limit of quantum field models, including the Schwinger model and a massive scalar field, revealing observable confined charges and addressing infrared issues.

## Contribution

It extends the framework of asymptotic morphisms to specific models, explicitly constructing them for the Schwinger model and a massive scalar field, highlighting their physical implications.

## Key findings

- Confined charges in the Schwinger model are observable via asymptotic morphisms.
- Infrared singularities hinder full construction in the massless case.
- No infrared problems in the massive scalar field in four dimensions.

## Abstract

We introduced in a previous paper a general notion of asymptotic morphism of a given local net of observables, which allows to describe the sectors of a corresponding scaling limit net. Here, as an application, we illustrate the general framework by analyzing the Schwinger model, which features confined charges. In particular, we explicitly construct asymptotic morphisms for these sectors in restriction to the subnet generated by the derivatives of the field and momentum at time zero. As a consequence, the confined charges of the Schwinger model are in principle accessible to observation. We also study the obstructions, that can be traced back to the infrared singular nature of the massless free field in d=2, to perform the same construction for the complete Schwinger model net. Finally, we exhibit asymptotic morphisms for the net generated by the massive free charged scalar field in four dimensions, where no infrared problems appear in the scaling limit.