New Light on Infrared Problems: Sectors, Statistics, Spectrum and All That

TL;DR

This paper introduces a new algebraic quantum field theory approach that uses charge classes to analyze the physical state space, effectively addressing infrared problems in theories with long-range forces like QED.

Contribution

It develops a systematic classification of charge content, statistics, and spectral properties using charge classes, avoiding infrared issues in algebraic QFT.

Findings

Charge classes generalize superselection sectors.

Infrared problems are circumvented using a geometric infrared cutoff.

Systematic classification of states' charge, statistics, and spectra.

Abstract

Within the general setting of algebraic quantum field theory, a new approach to the analysis of the physical state space of a theory is presented; it covers theories with long range forces, such as quantum electrodynamics. Making use of the notion of charge class, which generalizes the concept of superselection sector, infrared problems are avoided. In fact, on this basis one can determine and classify in a systematic manner the proper charge content of a theory, the statistics of the corresponding states and their spectral properties. A key ingredient in this approach is the fact that in real experiments the arrow of time gives rise to a Lorentz invariant infrared cutoff of a purely geometric nature.