Asymptotic algebra for charged particles and radiation

TL;DR

This paper introduces a new C*-algebra framework for describing the infrared structure of quantum electrodynamics, incorporating asymptotic electromagnetic and charged matter fields, satisfying Gauss's law, and aligning with the Kulish-Faddeev approach.

Contribution

It proposes a novel algebraic structure capturing the infrared behavior of charged particles and radiation in QED, ensuring gauge invariance and Coulomb field inclusion.

Findings

The algebra properly encodes the infrared structure of QED.

Gauss' law is satisfied within the algebraic framework.

A class of representations aligns with the Kulish-Faddeev treatment.

Abstract

A C*-algebra of asymptotic fields which properly describes the infrared structure in quantum electrodynamics is proposed. The algebra is generated by the null asymptotic of electromagnetic field and the time asymptotic of charged matter fields which incorporate the corresponding Coulomb fields. As a consequence Gauss' law is satisfied in the algebraic setting. Within this algebra the observables can be identified by the principle of gauge invariance. A class of representations of the asymptotic algebra is constructed which resembles the Kulish-Faddeev treatment of electrically charged asymptotic fields.