arXiv subjects

David McMullan

Publications and source records attributed to David McMullan.

At least 19 recordsLinked to original sources

arXiv2020

The simplest description of charge propagation in a strong background

Exploiting the gauge freedom associated with the Volkov description of a charge propagating in a plane wave background, we identify a new type of gauge choice which significantly simplifies the theory. This allows us to develop a compact description of the propagator for both scalar and fermionic matter, in a circularly polarised background. It is shown that many of the usually observed structures are gauge artefacts. We then analyse the full ultraviolet behaviour of the one-loop corrections for such charges. This enables us to identify and contrast the different renormalisation prescriptions needed for both types of matter.

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arXiv2019

One loop Volkov propagator in the Lorentz class of gauges

We calculate the ultraviolet divergences in a weak field expansion of the Volkov propagator. This is done for the full Lorentz class of gauges. The expected gauge invariance of the vacuum mass shift in each sideband is recovered. However, the renormalisation of the background induced mass shift is shown to be gauge dependent. In particular, we show that it vanishes in Landau gauge. We find that only in that gauge does the vacuum renormalisation remove all ultraviolet divergences.

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arXiv2019

Renormalisation of the Volkov propagator

The perturbative description of an electron propagating in a plane wave background is developed and loop corrections analysed. The ultraviolet divergences and associated renormalisation are studied using the sideband framework within which the multiplicative form of the corrections becomes manifest. An additional renormalisation beyond that usually expected is identified and interpreted as a loop correction to the background induced mass term. Results for the strong field sector are conjectured.

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arXiv2018

Electrons in an eccentric background field

We present a description of electrons propagating in an elliptically polarised plane wave background which includes circular and linear polarisations as special cases. We calculate to all orders in the background field the two point function and relate it to various expressions found in the literature. The background field induced mass shift of the electron is shown to be polarisation independent in the full elliptic class. The matrix nature of this mass shift in the fermionic theory is discussed. The extent to which a momentum space description is possible for this system is clarified.

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arXiv2015

The Fermionic Propagator in an Intense Background

New results for the fermion propagator in a laser background are presented. We show that the all orders electron propagator can be written in a compact and appealing form as a sum of sideband poles with a matrix wave function renormalisation and a matrix valued mass shift. This last result is essential in the fermionic theory if we are to maintain that both the mass and its square pick up a correction only at order e^2. A perturbative verification of our results is carried out.

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arXiv2014

Sideband Mixing in Intense Laser Backgrounds

The electron propagator in a laser background has been shown to be made up of a series of sideband poles. In this paper we study this decomposition by analysing the impact of the residual gauge freedom in the Volkov solution on the sidebands. We show that the gauge transformations do not alter the location of the poles. The identification of the propagator from the two-point function is maintained but we show that the sideband structures mix under residual gauge transformations.

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arXiv2013

Propagation in an intense background

The canonical quantisation of a charged particle in an intense laser background is developed and the associated two-point function calculated. It is shown how the causal propagator can be extracted. We provide an interpretation of this propagator in terms of degenerate quantum processes. The spectral properties of the propagator are derived and we show how multi-pole structures emerge as a perturbative feature. We also calculate the associated multiple wave-function renormalisations to all orders in perturbation theory. Our calculations are for both circular and linearly polarised plane wave laser backgrounds.

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arXiv2011

The factorisation of glue and mass terms in SU(N) gauge theories

In this paper we investigate the structure of the glue in Zwanziger's gauge invariant expansion for the A^2-type mass term in Yang-Mills theory. We show how to derive this expansion, in terms of the inverse covariant Laplacian, and extend it to higher orders. In particular, we give an explicit expression, for the first time, for the next to next to leading order term. We further show that the expansion is not unique and give examples of the resulting ambiguity.

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arXiv2010

Soft Collinear Degeneracies in an Asymptotically Free Theory

In asymptotically free theories with collinear divergences it is sometimes claimed that these divergences cancel if one sums over initial and final state degenerate cross-sections and uses an off-shell renormalisation scheme. We show for scalar $ϕ^3$ theory in six dimensions that there are further classes of soft collinear divergences and that they do not cancel. Furthermore, they yield a non-convergent series of terms at a fixed order of perturbation theory. Similar effects in gauge theories are also summarised.

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arXiv2010

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.

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arXiv2009

Physical charges in QED and QCD

We show that the `dressing' approach, which describes physical charges as gauge invariant composites of matter and clouds of gauge bosons, arises naturally in gauge theories. We give perturbative examples of dressings for both asymptotic charges and for states in which the fields are confined to a compact volume as is required, for example, by causality in pair creation. In QCD, we use dressed states to demonstrate explicitly how Gribov copies obstruct the non-perturbative construction of colour charges.

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arXiv2009

Stability, creation and annihilation of charges in gauge theories

We show how to construct physical, minimal energy states for systems of static and moving charges. These states are manifestly gauge invariant. For charge-anticharge systems we also construct states in which the gauge fields are restricted to a finite volume around the location of the matter fields. Although this is an excited state, it is not singular, unlike all previous finite volume descriptions. We use our states to model the processes of pair creation and annihilation.

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arXiv2008

Solution of the Gribov problem from gauge invariance

A new approach to gauge fixed Yang-Mills theory is derived using the Polyakov-Susskind projection techniques to build gauge invariant states. In our approach, in contrast to the Faddeev-Popov method, the Gribov problem does not prevent the gauge group from being factored out of the partition function. Lattice gauge theory is used to illustrate the method via a calculation of the static quark-antiquark potential generated by the gauge fields in the fundamental modular region of Coulomb gauge.

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arXiv2008

The ice-limit of Coulomb gauge Yang-Mills theory

In this paper we describe gauge invariant multi-quark states generalising the path integral framework developed by Parrinello, Jona-Lasinio and Zwanziger to amend the Faddeev-Popov approach. This allows us to produce states such that, in a limit which we call the ice-limit, fermions are dressed with glue exclusively from the fundamental modular region associated with Coulomb gauge. The limit can be taken analytically without difficulties, avoiding the Gribov problem. This is llustrated by an unambiguous construction of gauge invariant mesonic states for which we simulate the static quark--antiquark potential.

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arXiv2008

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.

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arXiv2007

Coulomb gauge Gribov copies and the confining potential

We study the approach, initiated by Marinari et al., to the static inter-quark potential based on Polyakov lines of finite temporal extent, evaluated in Coulomb gauge. We show that, at small spatial separations, the potential can be understood as being between two separately gauge invariant colour charges. At larger separations Gribov copies obstruct the non-perturbative identification of individually gauge invariant colour states. We demonstrate, for the first time, how gauge invariance can be maintained quite generally by averaging over Gribov copies. This allows us to extend the analysis of the Polyakov lines and the corresponding, gauge invariant quark-antiquark state to all distance scales. Using large scale lattice simulations, we show that this interpolating state possesses a good overlap with the ground state in the quark-antiquark sector and yields the full static inter-quark potential at all distances. A visual representation of the Gribov copies on the lattice is also presented.

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arXiv2007

Colour, copies and confinement

In this paper we construct a wide class of Gribov copies in Coulomb gauge SU(2) gauge theory. Infinitesimal copies are studied in some detail and their non-perturbative nature is made manifest. As an application it is shown that the copies prevent a non-perturbative definition of colour charge.

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arXiv2007

Charges in Gauge Theories

Recent progress in the construction of both electric, coloured and magnetic charges in gauge theories will be presented. The topological properties of the charged sectors will be highlighted as well as the applications of this work to confinement and infrared dynamics.

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