arXiv subjects

Robin W. Tucker

Publications and source records attributed to Robin W. Tucker.

At least 19 recordsLinked to original sources

arXiv2021

Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

We review a technique for solving a class of classical linear partial differential systems of relevance to physics in Minkowski spacetime. All the equations are amenable to analysis in terms of complex solutions in the kernel of the scalar Laplacian and a complexified Hertz potential. The complexification prescription ensures the existence of regular physical solutions with chirality and propagating, non-singular, pulse-like characteristics that are bounded in all three spatial dimensions. The technique is applied to the source-free Maxwell, Bopp-Landé-Podolsky and linearised Einstein field systems, and particular solutions are used for constructing classical models describing single-cycle laser pulses and a mechanism is discussed for initiating astrophysical jets. Our article concludes with a brief introduction to spacetime Clifford algebra ideals that we use to represent spinor fields. We employ these to demonstrate how the same technique used for tensor fields enables one to construct new propagating, chiral, non-singular, pulse-like spinor solutions to the massless Dirac equation in Minkowski spacetime.

gr-qc↗

arXiv2019

A new paradigm for the dynamics of the early Universe

This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current observational astronomy. Our approach is formulated as a classical Einstein-vector-scalar-Maxwell-fluid field theory on a spacetime with three-sphere spatial sections. Analytic cosmological solutions are found using local charts familiar from standard LFRW cosmological models. These solutions can be used to describe different types of evolution for the metric scale factor, the Hubble, jerk and de-acceleration functions, the scalar spacetime curvature and the Kretschmann invariant. The cosmological sector of the theory accommodates a particular single big-bang scenario followed by an eternal exponential acceleration of the scale factor. Such a solution does not require an externally prescribed fluid equation of state and leads to a number of new predictions including a current value of the "jerk" parameter, "Hopfian-like" source-free Maxwell field configurations with magnetic helicity and distributional "bi-polar" solutions exhibiting a new charge conjugation symmetry. An approximate scheme for field perturbations about this particular cosmology is explored and its consequences for a thermalisation process and a thermal history are derived, leading to a prediction of the time interval between the big-bang and the decoupling era. Finally it is shown that field couplings exist where both vector and scalar localised linearised perturbations exhibit dispersive wave-packet behaviours. The scalar perturbation may also give rise to Yukawa solutions associated with a massive Klein-Gordon particle. It is argued that the vector and scalar fields may offer candidates for "dark-energy" and "dark-matter" respectively.

gr-qc↗

arXiv2018

Chirality in Gravitational and Electromagnetic Interactions with Matter

It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. We discuss how these solutions are motivated by the analytic structure of spatially compact finite energy pulse solutions of the source-free Maxwell equations generated from complex chiral eigenmodes of a chirality operator. Complex gravitational pulse solutions to the linearised source-free Einstein equations are classified in terms of their chirality and generate a family of non-stationary real spacetime metrics. Particular members of these families are used as backgrounds in analysing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields.

gr-qc↗

arXiv2016

On Gravitational Chirality as the Genesis of Astrophysical Jets

It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of plane-fronted and pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. These solutions are classified in terms of their chirality and generate a family of non-stationary spacetime metrics. Particular members of these families are used as backgrounds in analysing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields.

gr-qc↗

arXiv2015

On the self-force in Bopp-Podolsky electrodynamics

In the classical vacuum Maxwell-Lorentz theory the self-force of a charged point particle is infinite. This makes classical mass renormalization necessary and, in the special relativistic domain, leads to the Abraham-Lorentz-Dirac equation of motion possessing unphysical run-away and pre-acceleration solutions. In this paper we investigate whether the higher-order modification of classical vacuum electrodynamics suggested by Bopp, Lande, Thomas and Podolsky in the 1940s, can provide a solution to this problem. Since the theory is linear, Green-function techniques enable one to write the field of a charged point particle on Minkowski spacetime as an integral over the particle's history. By introducing the notion of timelike worldlines that are "bounded away from the backward light-cone" we are able to prescribe criteria for the convergence of such integrals. We also exhibit a timelike worldline yielding singular fields on a lightlike hyperplane in spacetime. In this case the field is mildly singular at the event where the particle crosses the hyperplane. Even in the case when the Bopp-Podolsky field is bounded, it exhibits a directional discontinuity as one approaches the point particle. We describe a procedure for assigning a value to the field on the particle worldline which enables one to define a finite Lorentz self-force. This is explicitly derived leading to an integro-differential equation for the motion of the particle in an external electromagnetic field. We conclude that any worldline solutions to this equation belonging to the categories discussed in the paper have continuous 4-velocities.

gr-qc↗

arXiv2013

Covariant Hysteretic Constitutive Theory for Maxwell's equations: Application to Axially Rotating Media

This paper explores a class of non-linear constitutive relations for materials with memory in the framework of covariant macroscopic Maxwell theory. Based on earlier models for the response of hysteretic ferromagnetic materials to prescribed slowly varying magnetic background fields, generalized models are explored that are applicable to accelerating hysteretic magneto-electric substances coupled self-consistently to Maxwell fields. Using a parameterized model consistent with experimental data for a particular material that exhibits purely ferroelectric hysteresis when at rest in a slowly varying electric field, a constitutive model is constructed that permits a numerical analysis of its response to a driven harmonic electromagnetic field in a rectangular cavity. This response is then contrasted with its predicted response when set in uniform rotary motion in the cavity.

math-ph↗

arXiv2012

Conservation Laws and Stress-energy-momentum Tensors for Systems with Background Fields

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics in media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields.

physics.class-ph↗

arXiv2012

Symplectic integrator for $s$-dependent static magnetic fields based on mixed-variable generating functions

We describe a technique for constructing a symplectic transfer map for a charged particle moving through an accelerator component with arbitrary three-dimensional static magnetic field. The transfer map is constructed by symplectic integration; by representing the map at each step of the integration by a mixed-variable generating function, exact symplecticity is ensured. By using an appropriate integration algorithm, there is no necessity to make the paraxial approximation. The technique is illustrated by application (in one degree of freedom) to a quadrupole magnet with strong octupole component and fringe field.

physics.acc-ph↗

arXiv2012

Numerical Regularization of Electromagnetic Quantum Fluctuations in Inhomogeneous Dielectric Media

Electromagnetic Casimir stresses are of relevance to many technologies based on mesoscopic devices such as MEMS embedded in dielectric media, Casimir induced friction in nano-machinery, micro-fluidics and molecular electronics. Computation of such stresses based on cavity QED generally require numerical analysis based on a regularization process. A new scheme is described that has the potential for wide applicability to systems involving realistic inhomogeneous media. From a knowledge of the spectrum of the stationary modes of the electromagnetic field the scheme is illustrated by estimating numerically the Casimir stress on opposite faces of a pair of perfectly conducting planes separated by a vacuum and the change in this result when the region between the plates is filled with an incompressible inhomogeneous non-dispersive dielectric.

math-ph↗

arXiv2011

Quantum Electromagnetic Fluctuations in Inhomogeneous Dielectric Media

A new mathematical and computational technique for calculating quantum vacuum expectation values of energy and momentum densities associated with electromagnetic fields in bounded domains containing inhomogeneous media is discussed. This technique is illustrated by calculating the mode contributions to the difference in the vacuum force expectation between opposite ends of an inhomogeneous dielectric non-dispersive medium confined to a perfectly conducting rigid box.

quant-ph↗

arXiv2010

The Electrodynamics of Inhomogeneous Rotating Media and the Abraham and Minkowski Tensors I: General Theory

This is paper I of a series of two papers, offering a self-contained analysis of the role of electromagnetic stress-energy-momentum tensors in the classical description of continuous polarizable perfectly insulating media. While acknowledging the primary role played by the total stress-energy-momentum tensor we argue that it is meaningful and useful in the context of covariant constitutive theory to assign preferred status to particular parts of this total tensor, when defined with respect to a particular splitting. The relevance of tensors, associated with the electromagnetic fields that appear in Maxwell's equations for polarizable media, to the forces and torques that they induce has been a debated since Minkowski, Einstein and Abraham considered these issues over a century ago. Consistency with the laws of Newtonian continuum mechanics demands that the total force density on any element of a medium be proportional to the local linear acceleration field of that element in an inertial frame and must also arise as part of the divergence of the total stress-energy-momentum tensor. The fact that, unlike the tensor proposed by Minkowski, the divergence of the Abraham tensor depends explicitly on the local acceleration field of the medium as well as the electromagnetic field, sets it apart from many other terms in the total stress-energy-momentum tensor for a medium. We explore how electromagnetic forces or torques on moving media can be defined in terms of a particular 3-form on spacetimes that exhibit particular Killing symmetries. It is shown how the forms associated with translational Killing vector fields lead to explicit expressions for the electromagnetic force densities in stationary media subject to the Minkowski constitutive relations. These are compared with other models involving polarizable media in electromagnetic fields that have been considered in the recent literature.

physics.class-ph↗

arXiv2010

The Electrodynamics of Inhomogeneous Rotating Media and the Abraham and Minkowski Tensors II: Applications

Applications of the covariant theory of drive-forms are considered for a class of perfectly insulating media. The distinction between the notions of "classical photons" in homogeneous bounded and unbounded stationary media and in stationary unbounded magneto-electric media is pointed out in the context of the Abraham, Minkowski and symmetrized Minkowski electromagnetic stress-energy-momentum tensors. Such notions have led to intense debate about the role of these (and other) tensors in describing electromagnetic interactions in moving media. In order to address some of these issues for material subject to the Minkowski constitutive relations, the propagation of harmonic waves through homogeneous and inhomogeneous, isotropic plane-faced slabs at rest is first considered. To motivate the subsequent analysis on accelerating media two classes of electromagnetic modes that solve Maxwell's equations for uniformly rotating homogeneous polarizable media are enumerated. Finally it is shown that, under the influence of an incident monochromatic, circularly polarized, plane electromagnetic wave, the Abraham and symmetrized Minkowski tensors induce different time-averaged torques on a uniformly rotating materially inhomogeneous dielectric cylinder. We suggest that this observation may offer new avenues to explore experimentally the covariant electrodynamics of more general accelerating media.

physics.class-ph↗

arXiv2006

Asymptotic analysis of ultra-relativistic charge

This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneous linear equations for the self-consistent Maxwell field, charge current and time-like velocity field of the charged fluid and is defined as an ultra-relativistic configuration. To facilitate comparisons with existing accounts of beam dynamics an appendix translates the tensor formulation of the perturbation scheme into the language involving electric and magnetic fields observed in a laboratory (inertial) frame.

physics.acc-ph↗

arXiv2004

Twisted Electromagnetic Modes and Sagnac Ring-Lasers

A new approximation scheme, designed to solve the covariant Maxwell equations inside a rotating hollow slender conducting cavity (modelling a ring-laser), is constructed. It is shown that for well-defined conditions there exist TE and TM modes with respect to the longitudinal axis of the cavity. A twisted mode spectrum is found to depend on the integrated Frenet torsion of the cavity and this in turn may affect the Sagnac beat frequency induced by a non-zero rotation of the cavity. The analysis is motivated by attempts to use ring-lasers to measure terrestrial gravito-magnetism or the Lense-Thirring effect produced by the rotation of the Earth.

gr-qc↗

arXiv2003

Field-Particle Dynamics in Spacetime Geometries

With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin, electric charge and a magnetic moment,interacting with background electromagnetic fields and gravitation described by non-Riemannian geometries. A natural generalisation to relativistic Cosserat media is immediate.

gr-qc↗

arXiv2000

Gauge Symmetry and Gravito-Electromagnetism

A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to emulate electromagnetic gauge transformations under substitutions belonging to the gauge symmetry group of perturbative gravitation. These definitions have the advantage that on a flat background, with the aid of a covariantly constant timelike vector field, a subset of the linearised gravitational field equations can be written in a form that is fully analogous to Maxwell's equations (without awkward factors of 4 and extraneous tensor fields). It is shown how the remaining equations in the perturbed gravitational system restrict the time dependence of solutions to these equations and thereby prohibit the existence of propagating vector fields. The induced gravito-electromagnetic Lorentz force on a test particle is evaluated in terms of these fields together with the torque on a small gyroscope. It is concluded that the analogy of perturbative gravity to Maxwell's description of electromagnetism can be valuable for (quasi-)stationary gravitational phenomena but that the analogy has its limitations.

gr-qc↗

arXiv1998

String Fields and the Standard Model

The Cremmer-Scherk mechanism is generalised in a non-Abelian context. In the presence of the Higgs scalars of the standard model it is argued that fields arising from the low energy effective string action may contribute to the mass generation of the observed vector bosons that mediate the electroweak interactions and that future analyses of experimental data should consider the possibility of string induced radiative corrections to the Weinberg angle coming from physics beyond the standard model.

hep-th↗

arXiv1997

Tensor distributions on signature-changing space-times

Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and examine to what extent rigorous meaning can be given to field equations in the presence of signature-change, in particular those involving covariant derivatives. We find that, for both continuous and discontinuous signature-change, covariant differentiation can be defined on a class of tensor distributions wide enough to be physically interesting.

gr-qc↗