Charged States In A Semiclassical Model Of Infrared Gupta-Bleuler Quantum Electrodynamics

TL;DR

This paper develops a semiclassical model of infrared quantum electrodynamics to identify and characterize charged states, demonstrating their localization properties and defining an infrared-minimal charge class.

Contribution

It introduces a novel semiclassical approach to charged states in infrared QED within the Gupta-Bleuler framework, utilizing the GNS construction and automorphisms of the observable algebra.

Findings

Charged states with Lie9nard-Wiechert asymptotics are constructed.

The model identifies an infrared-minimal charge class.

Localization properties of electromagnetic fields are analyzed.

Abstract

We address the problem of the identification and characterization of charged states within local and covariant quantizations of abelian gauge theories, focusing on a semiclassical model of infrared Gupta-Bleuler Quantum Electrodynamics, based on the Bloch-Nordsieck approximation and formulated in Feynman's gauge. The GNS construction over suitable functionals yields positive subspaces of the indefinite-metric space of the model; charged states with Li\'enard-Wiechert space-like asymptotics can then be constructed via an automorphism of the algebra of observables implementing Gauss' law. Finally, by an analysis of the localization properties of the corresponding expectations over the asymptotic electromagnetic fields, it is shown that such states identify an infrared-minimal charge class in the sense of Buchholz.