The Physical Propagator of a Slowly Moving Charge

TL;DR

This paper investigates the propagator of a gauge-invariant, electromagnetically dressed electron moving slowly, demonstrating at one loop that it can be multiplicatively renormalized with finite infrared constants, confirming its physical relevance.

Contribution

It provides a detailed one-loop analysis of the dressed electron propagator, establishing its multiplicative renormalizability and physical consistency for slow velocities.

Findings

The dressed electron propagator is multiplicatively renormalizable at one loop.

Renormalization constants are finite in the infrared regime.

The dressing corresponds to a physically meaningful, slowly moving electron field.

Abstract

We consider an electron which is electromagnetically dressed in such a way that it is both gauge invariant and that it has the associated electric and magnetic fields expected of a moving charge. We study the propagator of this dressed electron and, for small velocities, show explicitly at one loop that at the natural (on-shell) renormalisation point, $p_0=m$, ${\bold p}= m{\bold v}$, one can renormalise the propagator multiplicatively. Furthermore the renormalisation constants are infra-red finite. This shows that the dressing we use corresponds to a slowly moving, physical asymptotic field.