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Charges from Dressed Matter: Construction

Emili Bagan, Martin Lavelle, David McMullan

TL;DR

This work demonstrates that a relativistic description of charged particles in QED is achievable by dressing the matter field with its electromagnetic cloud to satisfy Gauss' law and a dressing equation. By constructing gauge-invariant, velocity-dependent dressings, the authors show that the soft infrared distortions cancel on-shell, yielding physical moving-charge states and allowing standard LSZ reduction to recover S-matrix elements with dressed fields. The approach resolves long-standing IR issues in QED, preserving a particle interpretation and providing a framework extendable to non-abelian theories like QCD, where soft gluon dressings relate to anti-screening and confinement phenomena. Perturbative tests and detailed Green's function analyses are deferred to a companion paper, which is set to confirm the pole structure and renormalisation properties of dressed fields.

Abstract

There is a widespread belief in particle physics that there is no relativistic description of a charged particle. This is claimed to be due to persistent, long range interactions which distort the in and out going plane waves and generate infra-red divergences. In this paper we will show that this is not the case in QED. We construct locally gauge invariant charged fields which do create in and out Fock states. In a companion paper we demonstrate that the Green's functions of these fields have a good pole structure describing particle propagation.

Charges from Dressed Matter: Construction

TL;DR

This work demonstrates that a relativistic description of charged particles in QED is achievable by dressing the matter field with its electromagnetic cloud to satisfy Gauss' law and a dressing equation. By constructing gauge-invariant, velocity-dependent dressings, the authors show that the soft infrared distortions cancel on-shell, yielding physical moving-charge states and allowing standard LSZ reduction to recover S-matrix elements with dressed fields. The approach resolves long-standing IR issues in QED, preserving a particle interpretation and providing a framework extendable to non-abelian theories like QCD, where soft gluon dressings relate to anti-screening and confinement phenomena. Perturbative tests and detailed Green's function analyses are deferred to a companion paper, which is set to confirm the pole structure and renormalisation properties of dressed fields.

Abstract

There is a widespread belief in particle physics that there is no relativistic description of a charged particle. This is claimed to be due to persistent, long range interactions which distort the in and out going plane waves and generate infra-red divergences. In this paper we will show that this is not the case in QED. We construct locally gauge invariant charged fields which do create in and out Fock states. In a companion paper we demonstrate that the Green's functions of these fields have a good pole structure describing particle propagation.

Paper Structure

This paper contains 7 sections, 115 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Dynamics and Asymptotic Dynamics
  3. Static Charges
  4. Moving Charges
  5. From Dressed Matter to the $S$-Matrix
  6. Conclusions
  7. Appendix

Figures (2)

  • Figure 1: Penrose diagram of Minkowski space-time: the dashed lines are the worldlines of massive particles while the short arrows depict incoming and outgoing radiation. We may only demand that fields vanish at space-like infinity, $i_0$.
  • Figure 2: Sketch of a scattering process where the coupling is assumed to vanish for large times.