New Light on Infrared Problems: Sectors, Statistics, Symmetries and Spectrum

TL;DR

This paper introduces a new framework within local quantum physics to analyze the state space of theories with long-range forces, like QED, using charge classes to address infrared issues and explore charge structures, statistics, and particle aspects.

Contribution

It develops a systematic approach to study charge classes, including conjugates and statistics, in theories with long-range forces, extending the superselection sector concept.

Findings

Charge classes are either Bose or Fermi types.

Each simple charge class corresponds to an irreducible representation of a compact Abelian group.

Covariant charge classes define representations satisfying the relativistic spectrum condition.

Abstract

A new approach to the analysis of the physical state space of a theory is presented within the general setting of local quantum physics. It also covers theories with long range forces, such as Quantum Electrodynamics. Making use of the notion of charge class, an extension of the concept of superselection sector, infrared problems are avoided by restricting the states to observables localized in a light cone. The charge structure of a theory can be explored in a systematic manner. The present analysis focuses on simple charges, thus including the electric charge. It is shown that any such charge has a conjugate charge. There is a meaningful concept of statistics: the corresponding charge classes are either of Bose or of Fermi type. The family of simple charge classes is in one--to--one correspondence with the irreducible unitary representations of a compact Abelian group. Moreover, there is a meaningful definition of covariant charge classes. Any such class determines a continuous unitary representation of the Poincar\'e group or its covering group satisfying the relativistic spectrum condition. The resulting particle aspects are also briefly discussed.