Charges from Dressed Matter: Physics and Renormalisation

TL;DR

This paper develops a method to construct physical charges in QED that incorporate electromagnetic clouds, ensuring proper infra-red behavior and renormalization, with potential applications to QCD.

Contribution

It introduces a perturbative construction of physical charges in QED that include electromagnetic clouds, addressing infra-red issues while maintaining standard predictions.

Findings

Green's functions and S-matrix elements have correct pole structure.

Renormalization can be performed straightforwardly.

Infra-red finite predictions of QED are preserved.

Abstract

Gauge theories are characterised by long range interactions. Neglecting these interactions at large times, and identifying the Lagrangian matter fields with the asymptotic physical fields, leads to the infra-red problem. In this paper we study the perturbative applications of a construction of physical charges in QED, where the matter fields are combined with the associated electromagnetic clouds. This has been formally shown, in a companion paper, to include these asymptotic interactions. It is explicitly demonstrated that the on-shell Green's functions and S-matrix elements describing these charged fields have, to all orders in the coupling, the pole structure associated with particle propagation and scattering. We show in detail that the renormalisation procedure may be carried out straightforwardly. It is shown that standard infra-red finite predictions of QED are not altered and it is speculated that the good infra-red properties of our construction may open the way to the calculation of previously uncalculable properties. Finally extensions of this approach to QCD are briefly discussed.