arXiv subjects

R. W. Tucker

Publications and source records attributed to R. W. Tucker.

At least 19 recordsLinked to original sources

arXiv2016

Extended Particles and the Exterior Calculus

These notes were delivered as a series of NIMROD lectures at the Rutherford Appleton Laboratory by the author in February 1976 (RL-76-022). The purpose of these lectures was primarily two-fold: to discuss the classical theory of free point particles, free strings and free membranes from a unified viewpoint; and to present in the process of doing this the rudiments of an intrinsic geometrical calculus that the author has found of immense value in investigating these systems. It is shown how the equations of motion for such classically extended relativistic systems arise in a very simple manner from a principle of stationary action and furthermore how the boundary conditions for finite systems may be derived in a gauge invariant way. Momenta are naturally introduced and the primary constraints that exist in a Hamiltonian description follow simply. Calculations may proceed in an index-free manner until components are required. It is at this stage that one can, if one desires, impose gauge conditions and remove non-independent degrees of freedom. Such methods can be applied in any spacetime of any dimension and metric, and examples are given throughout.

math-ph↗

arXiv2016

The Dynamics of Compact Laser Pulses

We discuss the use of a class of exact finite energy solutions to the vacuum source-free Maxwell equations as models for multi- and single cycle laser pulses in classical interaction with relativistic charged point particles. These compact solutions are classified in terms of their chiral content and their influence on particular charge configurations in space. The results of such classical interactions motivate a phenomenological quantum description of a propagating laser pulse in a medium in terms of an effective quantum Hamiltonian.

quant-ph↗

arXiv2015

Classical Dynamics of Free Electromagnetic Laser Pulses

We discuss a class of exact finite energy solutions to the vacuum source-free Maxwell field equations as models for multi- and single cycle laser pulses in classical interaction with relativistic charged test particles. These solutions are classified in terms of their chiral content based on their influence on particular charge configurations in space. Such solutions offer a computationally efficient parameterization of compact laser pulses used in laser-matter simulations and provide a potential means for experimentally bounding the fundamental length scale in the generalized electrodynamics of Bopp, Lande and Podolsky.

physics.optics↗

arXiv2014

Aspects of Quantum Energy and Stress in Inhomogeneous Unbounded Dielectric Continua

This article addresses a number of issues associated with the problem of calculating contributions from the electromagnetic quantum induced energy and stress in a stationary material with an inhomogeneous polarizability. After briefly reviewing the conventional approaches developed by Lifshitz el al and more recent attempts by others, we emphasize the need to accommodate the effects due to the classical constitutive properties of the material in any experimental attempt to detect such contributions. Attention is then concentrated on a particular system composed of an ENZ-type (epsilon-near-zero) meta-material, chosen to have an anisotropic and inhomogeneous permittivity confined in an infinitely long perfectly conducting open waveguide. This permits us to deduce from the source-free Maxwell's equations a complete set of harmonic electromagnetic evanescent eigen-modes and eigen-frequencies. Since these solutions prohibit the existence of asymptotic scattering states in the guide an alternative regularization scheme, based on the Euler-Maclaurin formula, enables us to prescribe precise criteria for the extraction of finite quantum expectation values from regularized mode sums together with error bounds on these values. This scheme is used to derive analytic results for regularized energy densities in the guide. The criteria are exploited to construct a numerical scheme that is bench-marked by comparing its output with the analytic results derived from the special properties of the inhomogeneous ENZ medium.

quant-ph↗

arXiv2011

Born-Infeld Axion-Dilaton Electrodynamics and Electromagnetic Confinement

A generalization of Born-Infeld non-linear vacuum electrodynamics involving axion and dilaton fields is constructed with couplings dictated by electromagnetic duality and SL(2,R) symmetries in the weak field limit. Besides the Newtonian gravitational constant the model contains a single fundamental coupling parameter b0. In the absence of axion and dilaton interactions it reduces, in the limit as b0 tends to infinity, to Maxwell's linear vacuum theory while for finite b0 it reduces to the original Born-Infeld model. The spherically symmetric static sector of the theory is explored in a background Minkowski spacetime where numerical evidence suggests the existence of axion-dilaton bound states possessing confined electric flux.

hep-th↗

arXiv2010

Charged relativistic fluids and non-linear electrodynamics

The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these modified theories are tenable. However with the advent of high-intensity lasers and powerful laboratory magnetic fields this situation may be changing. We argue that an approach involving the self-consistent relativistic motion of a smooth fluid-like distribution of matter (composed of a large number of charged or neutral particles) in an electromagnetic field offers a viable theoretical framework in which to explore the experimental consequences of non-linear electrodynamics. We construct such a model based on the theory of Born and Infeld and suggest that a simple laboratory experiment involving the propagation of light in a static magnetic field could be used to place bounds on the fundamental coupling in that theory. Such a framework has many applications including a new description of the motion of particles in modern accelerators and plasmas as well as phenomena in astrophysical contexts such as in the environment of magnetars, quasars and gamma-ray bursts.

math-ph↗

arXiv2009

Wake potentials and impedances of charged beams in gradually tapering structures

An analytical method is developed for calculating the geometric wakefield and impedances of an ultrarelativistic beam propagating on- and off-axis through an axially symmetric geometry with slowly varying circular cross-section, such as a transition. Unlike previous analytical methods, our approach considers a beam of arbitrary longitudinal profile and permits detailed perturbative investigation of impedance as a function of frequency. We compare the accuracy of the results of our approach with numerical simulations performed using the code ECHO and determine parameters in which there is good agreement with the asymptotic analysis.

physics.acc-ph↗

arXiv2009

An Intrinsic Approach to Forces in Magnetoelectric Media

This paper offers a conceptually straightforward method for the calculation of stresses in polarisable media based on the notion of a drive form and its property of being closed in spacetimes with symmetry. After an outline of the notation required to exploit the powerful exterior calculus of differential forms, a discussion of the relation between Killing isometries and conservation laws for smooth and distributional drive forms is given. Instantaneous forces on isolated spacetime domains and regions with interfaces are defined, based on manifestly covariant equations of motion. The remaining sections apply these notions to media that sustain electromagnetic stresses, with emphasis on homogeneous magnetoelectric material. An explicit calculation of the average pressure exerted by a monochromatic wave normally incident on a homogeneous, magnetoelectric slab in vacuo is presented and the concluding section summarizes how this pressure depends on the parameters in the magnetoelectric tensors for the medium.

physics.class-ph↗

arXiv2007

Spinning particles in scalar-tensor gravity

We develop a new model of a spinning particle in Brans-Dicke spacetime using a metric-compatible connection with torsion. The particle's spin vector is shown to be Fermi-parallel (by the Levi-Civita connection) along its worldline (an autoparallel of the metric-compatible connection) when neglecting spin-curvature coupling.

gr-qc↗

arXiv2006

New Perspectives On the Relevance of Gravitation for the Covariant Description of Electromagnetically Polarizable Media

Electromagnetic properties of a simple polarisable medium may be parameterised in terms of a constitutive tensor whose properties can in principle be determined by experiments in non-inertial (accelerating) frames and in the presence of weak but variable gravitational fields. After establishing some geometric notation, discussion is given to basic concepts of stress, energy and momentum in the vacuum where the useful notion of a drive form is introduced in order to associate the conservation of currents involving the flux of energy, momentum and angular momentum with spacetime isometries. The definition of the stress-energy-momentum tensor is discussed with particular reference to its symmetry based on its role as a source of relativistic gravitation. General constitutive properties of material continua are formulated in terms of spacetime tensors including those that describe magneto-electric phenomena in moving media. This leads to a formulation of a self-adjoint constitutive tensor describing, in general, inhomogeneous, anisotropic, magneto-electric bulk matter in arbitrary motion. The question of an invariant characterisation of intrinsically magneto-electric media is explored. An action principle is established to generate the phenomenological Maxwell system and the use of variational derivatives to calculate stress-energy-momentum tensors is discussed in some detail. The relation of this result to tensors proposed by Abraham and others is discussed in the concluding section where the relevance of the whole approach to experiments on matter in non-inertial environments with variable gravitational and electromagnetic fields is stressed.

math-ph↗

arXiv2006

The Covariant Description of Electromagnetically Polarizable Media

The form of the phenomenological stress-energy-momentum tensor for the electromagnetic field in a class of inhomogeneous, anisotropic magneto-electric media is calculated from first principles, leading to a coherent understanding of the phenomenological stresses and energy-momentum exchanges induced by electromagnetic interactions with such matter in terms of a fully relativistic covariant variational framework.

math-ph↗

arXiv2006

Multiple currents in charged beams

It is argued that continuum realisations of distributions of collisionless charged particles should accommodate a dynamically evolving number of electric currents even if the continuum is composed of only one species of particle, such as electrons. A model is proposed that self-consistently describes the interaction of such a continuum and its electromagnetic field. It is formulated using a Lagrangian approach and employs a "folded" flow map to describe the bulk particle motion. An asymptotic perturbation scheme is developed to analyse ultra-relativistic multi-component current configurations. The model is fully relativistic and is formulated over Minkowski spacetime using intrinsic tensor field theory.

physics.plasm-ph↗

arXiv2005

Relativistic Anelasticity

A formulation of Continuum Mechanics within the context of General Relativity is presented that allows for the incorporation of certain types of anelastic material behaviour, such as viscoelasticity and plasticity. The approach is based on the concept of a four-dimensional body-time complex structured as a principal bundle. The anelastic response is regarded as the result of a continuous distribution of inhomogeneities, whose evolution is dictated by a suggested relativistic version of the Eshelby tensor. The role played by various groups is emphasized throughout the presentation and illustrated by means of the example of an anelastic fluid.

gr-qc↗

arXiv2004

On the Energy-Momentum Density of Gravitational Plane Waves

By embedding Einstein's original formulation of GR into a broader context we show that a dynamic covariant description of gravitational stress-energy emerges naturally from a variational principle. A tensor $T^G$ is constructed from a contraction of the Bel tensor with a symmetric covariant second degree tensor field $Φ$ and has a form analogous to the stress-energy tensor of the Maxwell field in an arbitrary space-time. For plane-fronted gravitational waves helicity-2 polarised (graviton) states can be identified carrying non-zero energy and momentum.

hep-th↗

arXiv2003

Autoparallel orbits in Kerr Brans-Dicke spacetimes

The bounded orbital motion of a massive spinless test particle in the background of a Kerr Brans-Dicke geometry is analysed in terms of worldlines that are auto-parallels of different metric compatible spacetime connections. In one case the connection is that of Levi-Civita with zero-torsion. In the second case the connection has torsion determined by the gradient of the Brans-Dicke background scalar field. The calculations permit in principle to discriminate between these possibilities.

gr-qc↗

arXiv2001

A Broken Gauge Approach to Gravitational Mass and Charge

We argue that a spontaneous breakdown of local Weyl invariance offers a mechanism in which gravitational interactions contribute to the generation of particle masses and their electric charge. The theory is formulated in terms of a spacetime geometry whose natural connection has both dynamic torsion and non-metricity. Its structure illuminates the role of dynamic scales used to determine measurable aspects of particle interactions and it predicts an additional neutral vector boson with electroweak properties.

hep-th↗

arXiv2001

On the Motion of Matter in Spacetime

We argue that the geodesic hypothesis based on auto-parallels of the Levi-Civita connection may need refinement in theories of gravity with additional scalar fields. This argument is illustrated with a re-formulation of the Brans-Dicke theory in terms of a spacetime connection with torsion determined dynamically in terms of the gradient of the Brans-Dicke scalar field. The perihelion shift in the orbit of Mercury is calculated on the alternative hypothesis that its world-line is an auto-parallel of such a connection. If scalar fields couple significantly to matter and spinless test particles move on such world-lines, current time keeping methods based on the conventional geodesic hypothesis may need refinement.

gr-qc↗

arXiv2001

On the Detection of Scalar Field Induced Spacetime Torsion

We argue that the geodesic hypothesis based on the autoparalllels of the Levi-Civita connection may need refinement in the scalar- tensor theories of gravity. Based on a reformulation of the Brans- Dicke theory in terms of a connection with torsion determined dynamically in terms of the gradient of the Brans-Dicke scalar field, we compute the perihelion shift in the orbit of Mercury on the alternative hypothesis that its worldline is an autoparallel of a connection with torsion. If the Brans-Dicke scalar field couples significantly to matter and test particles move on such worldlines, the current time keeping methods based on the conventional geodesic hypothesis may need refinement.

gr-qc↗