arXiv subjects

I. T. Drummond

Publications and source records attributed to I. T. Drummond.

At least 19 recordsLinked to original sources

arXiv2023

Supersymmetry with Lorentz Symmetry Violation

We study two (massless free field) models, a photon/photino model with a vector gauge field and a Majorana spinor field, and a Wess-Zumino model. They each exhibit Lorentz symmetry violation but retain, in an appropriate way, the supersymmetry correspondance between the particles of the two fields. In relation to the photon field the Lorentz symmetry violation is of a simple but non-trivial kind that implies birefringence. In relation to the spinor field the Lorentz violation is produced by a modification of the Majorana equation that is a simplified version of more general investigations of Lorentz symmetry violation of the Dirac equation. In the case of the Wess-Zumino model we retain the same violation of Lorentz symmetry for the Majorana field and adjust the propagation of the scalar particles so that they exhibit a corresponding birefringence. The advantages of the models are that they are straightforward to investigate completely and both retain the basic aspect of supersymmetry namely the one-to-one correspondance between bosons and fermions. As a result of this bottom-up approach it is then possible to construct conserved supersymmetry charges and investigate their algebraic properties. To some extent these are similar to those encountered in the case of Lorentz invariance. However there are differences and in particular non-local terms appear in the commutation relations of the supersymmetry charges and fields of the models. We examine carefully the rather intricate nature of the limit back to Lorentz invariance.

hep-th↗

arXiv2019

Lorentz Symmetry Violation in QCD and the Frustration of Asymptotic Freedom

We study the effect of Lorentz symmetry violation (LSV) on the behaviour at high energy of SU(N) gauge theory with quarks in the fundamental representation. The approach is similar to that for QED treated in a previous paper. In contrast to QED, standard Lorentz invariant QCD is asymptotically free. Our aim is to explore the structure of the renormalisation group at high energy and hence weak coupling without requiring the Lorentz symmetry breaking to be small. The simplest type of LSV leaves the theory invariant under a subgroup of the Lorentz group that preserves a (time-like) 4-vector. We examine this case in detail and find that asymptotic freedom is frustrated. That is, at sufficiently high energy the running coupling constant attains a minimum value before increasing again, while the LSV parameter increases without bound.

hep-th↗

arXiv2016

Bimetric QED

We study, as a model of Lorentz symmetry breaking, the quantisation and renormalisation of an extension of QED in a flat spacetime where the photons and electrons propagate differently and do not share the same lightcone. We will refer to this model as Bimetric QED (BIMQED). As a preliminary we discuss the formulation of electrodynamics in a pre-metric formalism showing nevertheless that there is, on the basis of a simple criteron, a preferred metric. Arising from this choice of metric is a Weyl-like tensor (WLT). The Petrov classification of the WLT gives rise to a corresponding classification of Lorentz symmetry breaking. We do not impose any constraint on the strength of the symmetry breaking and are able to obtain explicit dispersion relations for photon propagation in each of the Petrov classes. The associated birefringence appears in some cases as two distinct polarisation dependent lightcones and in other cases as a a more complicated structure that cannot be disentangled in a simple way. We show how in BIMQED the renormalisation procedure can, in addition to its effect on standard parameters such as charge and mass, force the renormalisation of the metrics and the WLT. Two particularly tractable cases are studied in detail for which we can obtain renormalisation group flows for the parameters of the model together with an analysis of fixed point structure. Of course these results are consistent with previous studies but we are not constrained to treat Lorentz symmetry breaking as necessarily weak. As we found in a previous study of a scalar field theory model an acceptable causal structure for the model imposes constraints on relationship between the various lightcones in BIMQED.

hep-th↗

arXiv2013

Quantum Field Theory in a Multi-Metric Background

By means of simple models in a flat spacetime manifold we examine some of the issues that arise when quantizing interacting quantum fields in multi-metric backgrounds. In particular we investigate the maintenance of a causal structure in the models. In this context we introduce and explain the relevance of an interpolating metric that is a superposition of the individual metrics in the models. We study the renormalisation of a model with quartic interactions and elucidate the structure of the renormalisation group and its implications for Lorentz symmetry breakdown.

hep-th↗

arXiv2011

Stochastic Processes, Slaves and Supersymmetry

We extend the work of Tanase-Nicola and Kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external disturbances of various kinds. We consider both the stochastic differential equations (SDEs) for the process and the associated diffusion equation. The influence of the disturbances can be understood by augmenting the original SDE with an equation for {\it slave variables}. The evolution of the slave variables describes the behaviour of line elements carried along in the stochastic flow. These line elements together with the associated surface and volume elements constructed from them provide the basis of the supersymmetry properties of the theory. For ease of visualisation, and in order to emphasise a helpful electromagnetic analogy, we work in three dimensions. The results are all generalisable to higher dimensions and can be specialised to one and two dimensions. The electromagnetic analogy is a useful starting point for calculating asymptotic results at low temperature that can be compared with direct numerical evaluations. We also examine the problems that arise in a direct numerical simulation of the stochastic equation together with the slave equations. We pay special attention to the dependence of the slave variable statistics on temperature. We identify in specific models the critical temperature below which the slave variable distribution ceases to have a variance and consider the effect on estimates of susceptibilities.

cond-mat.stat-mech↗

arXiv2004

Perturbation theory for the effective diffusion constant in a medium of random scatterer

We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $ρ$ uniformly distributed through out the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalisation group approach based on thinning out the scatterers, this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation.

cond-mat.dis-nn↗

arXiv2003

Effective diffusion constant in a two dimensional medium of charged point scatterers

We obtain exact results for the effective diffusion constant of a two dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer.

cond-mat.dis-nn↗

arXiv2003

The contribution of O(alpha) radiative corrections to the renormalised anisotropy and application to general tadpole improvement schemes: addendum to "One loop calculation of the renormalised anisotropy for improved anisotropic gluon actions on a lattice" [hep-lat/0208010]

General O(alpha) radiative corrections to lattice actions may be interpreted as counterterms that give additive contributions to the one-loop renormalisation of the anisotropy. The effect of changing the radiative coefficients is thus easily calculable. In particular, the results obtained in a previous paper for Landau mean link improved actions apply in any tadpole improvement scheme. We explain how this method can be exploited when tuning radiatively improved actions. Efficient methods for self-consistently tuning tadpole improvement factors are also discussed.

hep-lat↗

arXiv2002

One loop calculation of the renormalised anisotropy for improved anisotropic gluon actions on a lattice

Using the infrared dispersion relation of the on shell gluon, we calculate the renormalisation of the the anisotropy to one loop in perturbation theory for lattice Yang-Mills theories, including the Wilson action and actions with Symanzik and/or tadpole improvement. Using twisted boundary conditions as a gauge invariant infrared regulator, we show for an SU(3) gauge group in D=3+1 dimensions that the one loop anisotropy is accurate to O(3%) for a range of g^2 and chi covering current simulations. In doing so we also present Feynman rules for SU(N) gauge groups with generic anisotropy structure (including `3+1' and `2+2' cases).

hep-lat↗

arXiv2002

Lattice perturbation theory for gluonic and fermionic actions

We calculate the two loop Landau mean links and the one loop renormalisation of the anisotropy for Wilson and improved SU(3) gauge actions, using twisted boundary conditions as a gauge invariant infrared regulator. We show these accurately describe simulated results, and outline a method for generating Feynman rules for general lattice field theories, in a form suitable for efficient numerical calculation of perturbative loop diagrams.

hep-lat↗

arXiv2000

The Effect of Helicity on the Effective Diffusivity for Incompressible Random Flows

The advection of a passive scalar by a quenched (frozen) incompressible velocity field is studied by extensive high precision numerical simulation and various approximation schemes. We show that second order self consistent perturbation theory, in the absence of helicity, perfectly predicts the effective diffusivity of a tracer particle in such a field. In the presence of helicity in the flow simulations reveal an unexpectedly strong enhancement of the effective diffusivity which is highly nonperturbative and is most visible when the bare molecular diffusivity of the particle is small. We develop and analyse a series of approximation schemes which indicate that this enhancement of the diffusivity is due to a novel second order effect whereby the helical component of the field, which does not directly renormalize the effective diffusivity, enhances the strength of the non helical part of the flow, which in turn renormalizes the molecular diffusivity. We show that this renormalization is most important at low bare molecular diffusivity, in agreement with the numerical simulations.

cond-mat.dis-nn↗

arXiv2000

Bi-metric Gravity and "Dark Matter"

We present a bi-metric theory of gravity containing a length scale of galactic size. For distances less than this scale the theory satisfies the standard tests of General Relativity. For distances greater than this scale the theory yields an effective gravitational constant much larger than the locally observed value of Newton's constant. The transition from one regime to the other through the galactic scale can explain the observed rotation curves of galaxies and hence the effects normally attributed to the presence of dark matter. Phenomena on an extragalactic scale such as galactic clusters and the expansion of the universe are controlled by the enhanced gravitational coupling. This provides an explanation of the missing matter normally invoked to account for the observed value of Hubble's constant in relation to observed matter.

astro-ph↗

arXiv2000

Measuring the aspect ratio renormalization of anisotropic-lattice gluons

Using tadpole inproved actions we investigate the consistency between different methods of measuring the aspect ratio renormalization of anisotropic-lattice gluons for bare aspect ratios χ_0=4,6,10 and inverse lattice spacing in the range a_s^{-1}=660-840 MeV. The tadpole corrections to the action, which are established self-consistently, are defined for two cases, mean link tadpoles in Landau gauge and gauge invariant mean plaquette tadpoles. Parameters in the latter case exhibited no dependence on the spatial lattice size, L, while in the former, parameters showed only a weak dependence on L easily extrapolated to L=\infty. The renormalized anisotropy χ_R was measured using both the torelon dispersion relation and the sideways potential method. We found good agreement between these different approaches. Any discrepancy was at worst 3-4% which is consistent with the effect of lattice artifacts that for the torelon we estimate as O(\a_Sa_s^2/R^2) where R is the flux-tube radius. We also present some new data that suggests that rotational invariance is established more accurately for the mean-link action than the plaquette action.

hep-lat↗

arXiv1999

Spin Effects in Heavy Hybrid Mesons on an Anisotropic Lattice

We present a quenched calculation of lowest bottomonium hybrid states on an anisotropic lattice with Landau mean-link tadpole improvement, using the improved NRQCD Hamiltonian. We investigate the quark-spin s=0,1 sectors, which contain both the non-exotic 1-- and the exotic 1-+, and demonstrate their degeneracy in the case of the lowest order Hamiltonian. Both states are found at around 1.6 GeV above the Upsilon ground state. We examine the spin-splitting for several hybrid states that is due to the magnetic moment term in the NRQCD Hamiltonian, all other terms having negligible effect. The spin splittings are well resolved outside errors and are surprisingly large, and we investigate their dependence on the strength of the magnetic term. We calculate one contribution to these splittings using the Born-Oppenheimer picture for hybrids and show that the observed size of the effect is plausibly explained by mixing with hybrid states with more than one constituent gluon.

hep-lat↗

arXiv1999

Variable Light-Cone Theory of Gravity

We show how to reformulate Variable Speed of Light Theories (VSLT) in a covariant fashion as Variable Light-Cone Theories (VLCT) by introducing two vierbein bundles each associated with a distinct metric. The basic gravitational action relates to one bundle while matter propagates relative to the other in a conventional way. The variability of the speed of light is represented by the variability of the matter light-cone relative to the gravitational light-cone. The two bundles are related locally by an element M, of SL(4,R). The dynamics of the field M is that of a SL(4,R)-sigma model gauged with respect to local (orthochronous) Lorentz transformations on each of the bundles. Only the ``massless'' version of the model with a single new coupling, F, that has the same dimensions as Newton's constant $G_N$, is considered in this paper. When F vanishes the theory reduces to standard General Relativity. We verify that the modified Bianchi identities of the model are consistent with the standard conservation law for the matter energy-momentum tensor in its own background metric. The implications of the model for some simple applications are examined, the Newtonian limit, the flat FRW universe and the spherically symmetric static solution.

gr-qc↗

arXiv1998

NRQCD on an anisotropic lattice

We present preliminary results for the Upsilon spectrum on an anisotropic lattice using the improved O(mv^6) NRQCD Hamiltonian. We find accurate results can be obtained in moderate computer times and that they agree with earlier results on an isotropic lattice.

hep-lat↗

arXiv1997

Heavy Hybrids from NRQCD

We present a quenched lattice calculation for the lowest lying $b \bar b g$-hybrid states in the framework of NRQCD using the leading order Hamiltonian up to ${\cal O}(mv^2)$. We demonstrate the existence of a nearly degenerate rotational band of states with an excitation energy approximately 1.6 GeV above the $Υ$ ground state. This lies around the $B \bar B_J^*$-threshold but well above the $B \bar B$-threshold. Therefore a heavy hybrid signal may well be detected if the centre-of-mass energy in B-factories is raised a few hundred MeV to coincide with other resonances above the 4S state. Our prediction is consistent with most phenomenological models and lattice calculations carried out in the static limit.

hep-lat↗

arXiv1997

Hybrid Quarkonia with High Statistics from NRQCD

We have studied the O(mv^6) effects in NRQCD on the spectrum of heavy quarkonia and compare our results for different lattices (quenched and dynamical). We also report on an investigation into hybrid states within the framework of NRQCD. This suggests that the lowest lying hybrid is around the B^* \bar B threshold and 3 standard deviations above the B \bar B.

hep-lat↗