arXiv subjects

David McMullan

Publications and source records attributed to David McMullan.

50 records · Page 3Linked to original sources

arXiv1998

Soft Dynamics and Gauge Theories

Infra-red divergences obscure the underlying soft dynamics in gauge theories. They remove the pole structures associated with particle propagation in the various Green's functions of gauge theories. Here we present a solution to this problem. We give two equations which describe how charged particles must be dressed by gauge degrees of freedom. One follows from gauge invariance, the other, which is new, from velocity superselection rules familiar from the heavy quark effective theory. The solution to these equations in the abelian theory is proven to lead to on-shell Green's functions that are free of soft divergences at all orders in perturbation theory.

hep-th↗

arXiv1997

Constituent Quarks from QCD

Starting from the observation that colour charge is only well defined on gauge invariant states, we construct perturbatively gauge invariant, dynamical dressings for individual quarks. Explicit calculations show that an infra-red finite mass-shell renormalisation of the gauge invariant, dressed propagator is possible and, further, that operator product effects, which generate a running mass, may be included in a gauge invariant way in the propagator. We explain how these fields may be combined to form hadrons and show how the interquark potential can now be directly calculated. The onset of confinement is identified with an obstruction to building a non-perturbative dressing. We propose several methods to extract the hadronic scale from the interquark potential. Various extensions are discussed.

hep-ph↗

arXiv1997

An Infra-Red 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 infra-red finite, multiplicative, mass shell renormalisation is possible for this dressed electron, or, equivalently, for the usual fermion in the abovementioned gauges. The results are in complete accord with previous conjectures.

hep-th↗

arXiv1997

Infra-Red Finite Charge Propagation

The Coulomb gauge has a long history and many uses. It is especially useful in bound state applications. An important feature of this gauge is that the matter fields have an infra-red finite propagator in an on-shell renormalisation scheme. This is, however, only the case if the renormalisation point is chosen to be the static point on the mass shell, p = (m, 0, 0, 0). In this letter we show how to extend this key property of the Coulomb gauge to an arbitrary relativistic renormalisation point. This is achieved through the introduction of a new class of gauges of which the Coulomb gauge is a limiting case. A physical explanation for this result is given.

hep-ph↗

arXiv1995

The Physical Propagator of a Slowly Moving Charge

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.

hep-th↗

arXiv1995

The Colour of Quarks

It is shown that colour can only be defined on gauge invariant states. Since the ability to associate colour with constituent quarks is an integral part of the constituent quark model, this means that, if we want to extract constituent quarks from QCD, we need to dress Lagrangian quarks with gluons so that the result is gauge invariant. We further prove that gauge fixings can be used to construct such dressings. Gauge invariant dressed quark states are presented and a direct approach to the interquark potential is discussed. Some further aspects of dressing quarks are briefly discussed.

hep-ph↗

arXiv1995

The canonical connection in quantum mechanics

In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry's phase, can also be found in systems which have slow variables taking values in such a coset space.

hep-th↗

arXiv1994

Observables and Gauge Fixing in Spontaneously Broken Gauge Theories

Gauge fixing and the observable fields for both abelian and non-abelian gauge theories with spontaneous breaking of gauge symmetry are studied. We explicitly show that it is possible to globally fix the gauge in the broken sector and hence construct physical fields even in the non-abelian theory. We predict that any high temperature restoration of gauge symmetry will be accompanied by a confining transition.

hep-th↗

arXiv1994

Perturbative and Non-Perturbative Quarks and Gluons

BRST invariance supplies a sufficient condition for the observability of fields. We show that there is a global obstruction to the observability of quarks and gluons and argue that they will not become observables at finite temperature. We give expressions for quarks and gluons that are, however, {\it perturbatively\/} BRST invariant, and hence locally observable, up to order~$g^2$ and~$g$ respectively.

hep-th↗

arXiv1993

BPST instanton and Spin from inequivalent quantizations

We present a simple alternative to Mackey's account of the (infinite) inequivalent quantizations possible on a coset space G/H. Our reformulation is based on the reduction ${\rm G \rightarrow G/H}$ and employs a generalized form of Dirac's approach to the quantization of constrained systems. When applied to the four-sphere $S^4 \simeq {\rm Spin(5)/Spin(4)}$, the inequivalent quantizations induce relativistic spin and a background BPST instanton; thus they might provide a natural account of both of these physical entities.

hep-th↗

arXiv1993

On the emergence of gauge structures and generalized spin when quantizing on a coset space

It has been known for some time that there are many inequivalent quantizations possible when the configuration space of a system is a coset space G/H. Viewing this classical system as a constrained system on the group G, we show that these inequivalent quantizations can be recovered from a generalization of Dirac's approach to the quantization of such a constrained system within which the classical first class constraints (generating the H-action on G) are allowed to become anomalous (second class) when quantizing. The resulting quantum theories are characterized by the emergence of a Yang-Mills connection, with quantized couplings, and new 'spin' degrees of {}freedom. Various applications of this procedure are presented in detail: including a new account of how spin can be described within a path-integral formalism, and how on S^4 chiral spin degrees of {}freedom emerge, coupled to a BPST instanton.

hep-th↗

arXiv1993

On Quark Confinement

A sufficient condition for the confinement of quarks is presented. Quarks are shown to be unobservable. Colour singlets are however, observables. The results of deep inelastic scattering are discussed. We argue that QCD does not exhibit a deconfining transition.

hep-ph↗

arXiv1993

On the Physical Propagators of QED

The true variables in QED are the transverse photon components and Dirac's physical electron, constructed out of the fermionic field and the longitudinal components of the photon. We calculate the propagators in terms of these variables to one loop and demonstrate their gauge invariance. The physical electron propagator is shown not to suffer from infrared divergences in any gauge. In general, all physical Green's functions are gauge invariant and infrared-finite.

hep-th↗

arXiv1993

A New Symmetry for QED

We demonstrate that QED exhibits a previously unobserved symmetry. Some consequences are discussed.

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