arXiv subjects
Publications and source records attributed to David McMullan.
The standard approach to the infra-red problem is to use the Bloch-Nordsieck trick to handle soft divergences and the Lee-Nauenberg (LN) theorem for collinear singularities. We show that this is inconsistent in the presence of massless initial particles. Furthermore, we show that using the LN theorem with such initial states introduces a non-convergent infinite series of diagrams at any fixed order in perturbation theory.
We address the question of defining the second quantised monopole creation operator in the 3+1 dimensional Georgi-Glashow model, and calculating its expectation value in the confining phase. Our calculation is performed directly in the continuum theory within the framework of perturbation theory. We find that, although it is possible to define the "coherent state" operator M(x) that creates the Coulomb magnetic field, the dependence of this operator on the Dirac string does not disappear even in the nonabelian theory. This is due to the presence of the charged fields (W^{\pm}). We also set up the calculation of the expectation value of this operator in the confining phase and show that it is not singular along the Dirac string. We find that in the leading order of the perturbation theory the VEV vanishes as a power of the volume of the system. This is in accordance with our naive expectation. We expect that nonperturbative effects will introduce an effective infrared cutoff on the calculation making the VEV finite.
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.
We calculate the change in the ultraviolet behaviour of the vortex operator due to the presence of dynamical Higgs field in both 2+1 dimensional QED and the 2+1 dimensional Georgi-Glashow model. We find that in the QED case the presence of the Higgs field leads at the one loop level to power like correction to the propagator of the vortex operator. On the other hand, in the Georgi-Glashow model, the adjoint Higgs at one loop has no affect on the vortex propagator. Thus, as long as the mass of the Higgs field is much larger than the gauge coupling constant, the ultraviolet behaviour of the vortex operator in the Georgi-Glashow model is independent of the Higgs mass.
It is sometimes claimed that one cannot describe charged particles in gauge theories. We identify the root of the problem and present an explicit construction of charged particles. This is shown to have good perturbative properties and, asymptotically before and after scattering, to recover particle modes.
The possibility of constructing charged particles in gauge theories has long been the subject of debate. In the context of QED we have shown how to construct operators which have a particle description. In this paper we further support this programme by showing how the screening interactions arise between these charges. Unexpectedly we see that there are two different gauge invariant contributions with opposite signs. Their difference gives the expected result.
This talk will summarise the progress we have made in our programme to both characterise and construct charges in gauge theories. As an application of these ideas we will see how the dominant glue surrounding quarks, which is responsible for asymptotic freedom, emerges from a constituent description of the interquark potential.
The particle Fock space of the matter fields in QED can be constructed using the free creation and annihilation operators. However, these particle operators are not, even at asymptotically large times, the modes of the matter fields that enter the QED Lagrangian. In this letter we construct the fields which do recover such particle modes at large times. We are thus able to demonstrate for the first time that, contrary to statements found in the literature, a relativistic description of charged particles in QED exists.
Descriptions of the ground state in unbroken gauge theories with charged particles are discussed. In particular it is shown that the on-shell Green's functions and S-matrix elements corresponding to the scattering of these variables in QED are free of soft and phase infra red divergences and that these variables may be multiplicatively renormalised.
We discuss the approach to asymptotic dynamics due to Kulish and Faddeev. We show that there are problems in applying this method to theories with four point interactions. The source of the difficulties is identified and a more general method is constructed. This is then applied to various theories including some where the coupling does switch off at large times and some where it does not.
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.
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.
Descriptions of hadrons and glueballs can be constructed using strings to preserve gauge invariance. We show how this string dependence may be removed to all orders in perturbation 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.
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.
If constituent quarks are to emerge from QCD they must have well defined colour and be energetically favoured. After reviewing the general properties of charges in gauge theories, a method for constructing charges is presented and applied to the infra-red structure of the theory and to the interquark potential. Both of these applications supply a physical interpretation of the structures found in the construction of charges. We will see that constituent structures arise in QCD.
The quarks of quark models cannot be identified with the quarks of the QCD Lagrangian. We review the restrictions that gauge field theories place on any description of physical (colour) charges. A method to construct charged particles is presented. The solutions are applied to a variety of applications. Their Green's functions are shown to be free of infra-red divergences to all orders in perturbation theory. The interquark potential is analysed and it is shown that the interaction responsible for anti-screening results from the force between two separately gauge invariant constituent quarks. A fundamental limit on the applicability of quark models is identified.
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.