Charges from Dressed Matter: Physics and Renormalisation

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.1 email: bagan@quark.phy.bnl.gov; permanent address: IFAE, Univ.

Structure of screening in QED

“…This has been taken [1] to mean that one cannot describe charged particles in gauge theories. In a series of papers [2][3][4][5][6] we have shown that this conclusion is overly hasty: it is in fact possible to construct gauge invariant operators whose S-matrix elements are free of infra-red divergences. These fields have been shown to asymptotically recover a particle description of charges and to have a rich structure which is physically reflected in the cancellation of both soft and phase divergences.…”

Asymptotic dynamics in quantum field theory

“…(It is in fact clear from the start that the Lagrangian matter cannot hope to do this since it is not gauge invariant.) That such fields exist has been shown elsewhere [16] and that their Green's functions have a good pole structure has been amply demonstrated, see, e.g., [17][18][19]. These are the physical fields which should be identified with the charged particles seen in experiment.…”

“…The cubic term in the interaction Hamiltonian (19), which comes from the J µ 1 term in (20), is made up of two parts, J µ 11 and J µ 12 . These two terms are similar in their structure and both contribute to the problem of infra-red divergences.…”

Charged Particles: A Builder's Guide

“…It is thus natural to ask whether they can be used in practical work. The answer is yes, as we have shown in a detailed series of calculations [7,8]. For the purposes of showing the particle nature of our dressed fields the main point to note is that the on-shell Green's functions of these gauge invariant variables have a good pole structure.…”