David McMullan

Charges from Dressed Matter: Construction

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 incoming and outgoing plane waves and generate infrared 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 Greens functions of these fields have a good pole structure describing particle propagation.

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 infrared 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 Greens 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 infrared finite predictions of QED are not altered and it is speculated that the good infrared 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.

Charges in gauge theories

In this article we investigate charged particles in gauge theories. After reviewing the physical and theoretical problems, a method to construct charged particles is presented. Explicit solutions are found in the abelian theory and a physical interpretation is given. These solutions and our interpretation of these variables as the true degrees of freedom for charged particles, are then tested in the perturbative domain and are demonstrated to yield infra-red finite, on-shell Green’s functions at all orders of perturbation theory. The extension to collinear divergences is studied and it is shown that this method applies to the case of massless charged particles. The application of these constructions to the charged sectors of the standard model is reviewed and we conclude with a discussion of the successes achieved so far in this programme and a list of open questions.

Collinearity, convergence and cancelling infrared divergences

The Lee-Nauenberg theorem is a fundamental quantum mechanical result which provides the standard theoretical response to the problem of collinear and infrared divergences. Its argument, that the divergences due to massless charged particles can be removed by summing over degenerate states, has been successfully applied to systems with final state degeneracies such as LEP processes. If there are massless particles in both the initial and final states, as will be the case at the LHC, the theorem requires the incorporation of disconnected diagrams which produce connected interference effects at the level of the cross-section. However, this aspect of the theory has never been fully tested in the calculation of a cross-section. We show through explicit examples that in such cases the theorem introduces a divergent series of diagrams and hence fails to cancel the infrared divergences. It is also demonstrated that the widespread practice of treating soft infrared divergences by the Bloch-Nordsieck method and handling collinear divergences by the Lee-Nauenberg method is not consistent in such cases.

Symmetry breaking, conformal geometry and gauge invariance

When the electroweak action is rewritten in terms of SU(2) gauge-invariant variables, the Higgs can be interpreted as a conformal metric factor. We show that asymptotic flatness of the metric is required to avoid a Gribov problem: without it, the new variables fail to be nonperturbatively gauge invariant. We also clarify the relations between this approach and unitary gauge fixing, and the existence of similar transformations in other gauge theories.

Infrared finite electron propagator

We investigate the properties of a dressed electron which reduces, in a particular class of gauges, to the usual fermion. A one-loop calculation of the propagator is presented. We show explicitly that an infrared finite, multiplicative, mass shell renormalization is possible for this dressed electron, or, equivalently, for the usual fermion in the above-mentioned gauges. The results are in complete accord with previous conjectures. {copyright} {ital 1997} {ital The American Physical Society}

Asymptotic dynamics in quantum field theory

A crucial element of scattering theory and the LSZ reduction formula is the assumption that the coupling vanishes at large times. This is known not to hold for the theories of the Standard Model and in general such asymptotic dynamics is not well understood. We give a description of asymptotic dynamics in field theories which incorporates the important features of weak convergence and physical boundary conditions. Applications to theories with three and four point interactions are presented and the results are shown to be completely consistent with the results of perturbation theory.

COLOUR CHARGES AND THE ANTI-SCREENING CONTRIBUTION TO THE INTERQUARK POTENTIAL

Abstract Asymptotic freedom arises from the dominance of anti-screening over screening in non-abelian gauge theories. In this paper we will present a simple and physically appealing derivation of the anti-screening contribution to the interquark potential. Our method allows us to identify the dominant gluonic distribution around static quarks. Extensions are discussed.

Is the ground state of Yang-Mills theory Coulombic?

We study trial states modelling the heavy quark-antiquark ground state in SU(2) Yang-Mills theory. A state describing the flux tube between quarks as a thin string of glue is found to be a poor description of the continuum ground state; the infinitesimal thickness of the string leads to UV artifacts which suppress the overlap with the ground state. Contrastingly, a state which surrounds the quarks with non-Abelian Coulomb fields is found to have a good overlap with the ground state for all charge separations. In fact, the overlap increases as the lattice regulator is removed. This opens up the possibility that the Coulomb state is the true ground state in the continuum limit.

Probing the ground state in gauge theories

We consider two very different models of the flux tube linking two heavy quarks: a string linking the matter fields and a Coulombic description of two separately gauge invariant charges. We compare how close they are to the unknown true ground state in compact U(1) and the SU(2) Higgs model. Simulations in compact U(1) show that the string description is better in the confined phase but the Coulombic description is best in the deconfined phase; the last result is shown to agree with analytical calculations. Surprisingly in the nonabelian theory the Coulombic description is better in both the Higgs and confined phases. This indicates a significant difference in the width of the flux tubes in the two theories.