arXiv subjects

J. D. Jackson

Publications and source records attributed to J. D. Jackson.

6 recordsLinked to original sources

arXiv2008

Solvable Examples of Drift and Diffusion of Ions in Non-uniform Electric Fields

The drift and diffusion of a cloud of ions in a fluid are distorted by an inhomogeneous electric field. If the electric field carries the center of the distribution in a straight line and the field configuration is suitably symmetric, the distortion can be calculated analytically. We examine the specific examples of fields with cylindrical and spherical symmetry in detail assuming the ion distributions to be of a generally Gaussian form. The effects of differing diffusion coefficients in the transverse and longitudinal directions are included.

physics.ins-det↗

arXiv2007

Examples of the Zeroth Theorem of the History of Physics

The zeroth theorem of the history of science (enunciated by E. P. Fischer) and widely known in the mathematics community as Arnol'd's Principle (decreed by M. V. Berry), states that a discovery (rule, regularity, insight) named after someone (often) did not originate with that person. I present five examples from physics: the Lorentz condition defining the Lorentz gauge of the electromagnetic potentials; the Dirac delta function (x); the Schumann resonances of the earth-ionosphere cavity; the Weizsacker-Williams method of virtual quanta; the BMT equation of spin dynamics. I give illustrated thumbnail sketches of both the true and reputed discoverers and quote from their "discovery" publications.

physics.hist-ph↗

arXiv2002

From Lorenz to Coulomb and other explicit gauge transformations

The main purposes of this paper are (i) to illustrate explicitly by a number of examples the gauge functions chi(x, t) whose spatial and temporal derivatives transform one set of electromagnetic potentials into another equivalent set; and (ii) to show that, whatever propagation or non-propagation characteristics are exhibited by the potentials in a particular gauge, the electric and magnetic fields are always the same and display the experimentally verified properties of causality and propagation at the speed of light. The example of the transformation from the Lorenz gauge (retarded solutions for both scalar and vector potential) to the Coulomb gauge (instantaneous, action-at-a-distance, scalar potential) is treated in detail. A transparent expression is obtained for the vector potential in the Coulomb gauge, with a finite nonlocality in time replacing the expected spatial nonlocality of the transverse current. A class of gauges (v-gauge) is described in which the scalar potential propagates at an arbitrary speed v relative to the speed of light. The Lorenz and Coulomb gauges are special cases of the v-gauge. The last examples of gauges and explicit gauge transformation functions are the Hamiltonian or temporal gauge, the nonrelativistic Poincare or multipolar gauge, and the relativistic Fock-Schwinger gauge.

physics.class-ph↗

arXiv2002

Criticism of "Necessity of simultaneous co-existence of instantaneous and retarded interactions in classical electrodynamics" by Andrew E. Chubykalo and Stoyan J. Vlaev

The demonstration that the electromagnetic fields derived from the Lienard-Wiechert potentials do not satisfy the Maxwell equations is proved to be false. Errors were made in the computation of the derivatives of retarded quantities. The subsequent inference of the necessity of both instantaneous and retarded electromagnetic interactions cannot be made. Different choices of gauge can lead to a variety of forms for the scalar and vector potentials, always with the same retarded fields. Classical electromagnetic theory is complete as usually expressed. One may choose to work in the Lorenz gauge in which all quantities are retarded.

hep-ph↗

arXiv2002

Semi-classical calculation of the number of photons emitted by a relativistic neutrino with mass and magnetic moment passing through a transverse magnetic field

A classical calculation, modified by Compton-recoil kinematics, of the radiation emitted by a relativistic neutrino with mass and a magnetic moment passing through a transverse magnetic field. The calculation is performed in the neutrinos rest frame by the method of virtual quanta. The total number N of virtual quanta scattered by the neutrino is determined. The semi-classical result for the analog of the Klein-Nishina formula is compared with a QED calculation of the photon scattering cross section. The different angular distributions, both strongly peaked, lead to a factor of two difference between the QED and semi-classical results for N.

hep-ph↗

arXiv2001

Historical roots of gauge invariance

Gauge invariance is the basis of the modern theory of electroweak and strong interactions (the so called Standard Model). The roots of gauge invariance go back to the year 1820 when electromagnetism was discovered and the first electrodynamic theory was proposed. Subsequent developments led to the discovery that different forms of the vector potential result in the same observable forces. The partial arbitrariness of the vector potential A brought forth various restrictions on it. div A = 0 was proposed by J. C. Maxwell; 4-div A = 0 was proposed L. V. Lorenz in the middle of 1860's . In most of the modern texts the latter condition is attributed to H. A. Lorentz, who half a century later was one of the key figures in the final formulation of classical electrodynamics. In 1926 a relativistic quantum-mechanical equation for charged spinless particles was formulated by E. Schrodinger, O. Klein, and V. Fock. The latter discovered that this equation is invariant with respect to multiplication of the wave function by a phase factor exp(ieX/hc) with the accompanying additions to the scalar potential of -dX/cdt and to the vector potential of grad X. In 1929 H. Weyl proclaimed this invariance as a general principle and called it Eichinvarianz in German and gauge invariance in English. The present era of non-abelian gauge theories started in 1954 with the paper by C. N. Yang and R. L. Mills.

hep-ph↗