On Infravacua and the Superselection Structure of Theories with Massless Particles

TL;DR

This paper explores how infravacuum states can improve the localization of charges in quantum field theories with massless particles, enabling the application of superselection sector analysis.

Contribution

It introduces a model-independent definition of infravacuum representations and examines their role in superselection theory, especially regarding translation invariance and covariance.

Findings

Infravacua can enhance charge localization in massless particle theories.

Infravacuum backgrounds can be interpreted as infrared radiation clouds.

The analysis of charged sectors includes their covariance and spectral properties.

Abstract

In quantum field theories with massless particles, states carrying a nontrivial superselection charge may have very poor localisation properties when compared to the vacuum. In this case, replacing the vacuum with a suitable ``infravacuum'' state can improve the localisability of the charges in such a way that the Doplicher-Haag-Roberts (DHR) theory of superselection sectors is applicable. As an explicit example for this phenomenon, we consider a certain class of sectors of the free massless scalar field. These sectors carry a charge of electric type, and the corresponding infravacuum background may be interpreted as a cloud of infrared radiation. Motivated by this situation, we propose a model-independent definition of infravacuum representations and derive some of their properties. We analyse in particular their role as reference representations for DHR theory and investigate to what an extent the absence of a translation invariant vector affects the results of the DHR analysis. Special emphasis is put on the functorial aspects of the theory and on the description of the covariance and the spectral properties of charged sectors in terms of so-called charge transporting cocycles.