The magnetic fields and rotation generators of free space electromagnetism

The relation is developed between rotation generators of the Lorentz group and the magnetic fields of free-space electromagnetism. Using these classical relations, it is shown that in the quantum field theory there exists a longitudinal photomagneton, a quantized magnetic flux density operator which is directly proportional to the photon spin angular momentum. Commutation relations are given in the quantum field between the longitudinal photomagneton and the usual transverse magnetic components of quantized electromagnetism. The longitudinal component is phase free, but the transverse components are phase dependent. All three components can magnetize material in general, but only the transverse components contribute to Planck's law. The photon therefore has three, not two, relativistically invariant degrees of polarization, an axial, longitudinal, polarization, and the usual right and left circular transverse polarizations. Since the longitudinal polarization is axial, it is a phase- free magnetic field.     

Magnetic strings in f(R) gravity

We construct a new class of spinning magnetic string solutions in f(R) gravity with constant scalar curvature. These solutions which produce a longitudinal magnetic field have no curvature singularity and no horizon, but have a conic geometry with a deficit angle. We also generalize this class of solutions to the case of spinning magnetic solutions with one rotation parameter. We find that the spinning string has a net electric charge which is proportional to the rotation parameter. With choosing a suitable counterterm, we remove the divergences of the action. The conserved quantities of the solutions are also calculated by using the counterterm method.     

Electric Chern–Simons term, enlarged exotic Galilei symmetry and noncommutative plane

The extended exotic planar model for a charged particle is constructed. It includes a Chern–Simons-like term for a dynamical electric field, but produces usual equations of motion for the particle in background constant uniform electric and magnetic fields. The electric Chern–Simons term is responsible for the noncommutativity of the boost generators in the 10-dimensional enlarged exotic Galilei symmetry algebra of the extended system. The model admits two reduction schemes by the integrals of motion, one of which reproduces the usual formulation for the charged particle in external constant electric and magnetic fields with associated field-deformed Galilei symmetry, whose commuting boost generators are identified with the nonlocal in time Noether charges reduced on-shell. Another reduction scheme, in which electric field transmutes into the commuting space translation generators, extracts from the model a free particle on the noncommutative plane described by the twofold centrally extended Galilei group of the nonrelativistic anyons.     

Wormhole solutions in Gauss–Bonnet–Born–Infeld gravity

A new class of solutions which yields an (n + 1)-dimensional spacetime with a longitudinal nonlinear magnetic field is introduced. These spacetimes have no curvature singularity and no horizon, and the magnetic field is non singular in the whole spacetime. They may be interpreted as traversable wormholes which could be supported by matter not violating the weak energy conditions. We generalize this class of solutions to the case of rotating solutions and show that the rotating wormhole solutions have a net electric charge which is proportional to the magnitude of the rotation parameter, while the static wormhole has no net electric charge. Finally, we use the counterterm method and compute the conserved quantities of these spacetimes.     

On the Non-Lorentz-Invariance of <Emphasis Type="SmallCaps">M.W. Evans’</Emphasis><Emphasis Type="Italic">O</Emphasis>(3)-Symmetry Law

In 1992 M.W. Evans proposed the O(3) symmetry of electromagnetic fields by adding a constant longitudinal magnetic field to the well-known transverse electric and magnetic fields of circularly polarized plane waves, such that certain cyclic relations of a so-called O(3) symmetry are fulfilled. Since then M.W. Evans has elevated this O(3) symmetry to the status of a new law of electromagnetics. As a law of physics must be invariant under admissible coordinate transforms, namely Lorentz transforms, in 2000 he published a proof of the Lorentz invariance of O(3) symmetry of electromagnetic fields. As will be shown below this proof is incorrect; more, after simple correction it will turn out here that the O(3) symmetry cannot be Lorentz invariant.     

Anomalous plasma diffusion transverse to high magnetic fields in InSb

Investigations on the ambipolar diffusion of an electron-hole plasma transverse to a magnetic field have been carried out in InSb. A plasma layer, produced at the surface of the sample by a short laser pulse, was moved through the sample in crossed electric and magnetic fields by the Lorentz force. From the broadening of the plasma layer we found at 80K an enhanced diffusion coefficient which decreased proportional to 1/B for magnetic fields higher than 1T, constrary to the expected classical 1/B ² dependence. Furthermore, the diffusion coefficient was strongly dependent on the electric field. The ambipolar drift velocity, measured simultaneously showed a classical behaviour. Together with the enhanced diffusion we observed instabilites in the electric potential. The instability threshold decreased towards the cathode.     

Infinitesimal Lorentz Transformations and the States of Polarization of Free Photons

Applying the tangent dynamics technique as generated by infinitesimal Lorentz transformations, it is shown that the components of an electromagnetic field correspond to the Lie-Cartan parameters of the group SO(3,1). Thus the maximum number of non-null components of the magnetic field (i.e., the number of the states of polarization) is not decided by the number of group generators.     

An elementaryU(2) theory of radiation fields with spinJ

An elementary theory for a radiation field with any spinJ is presented. This is a natural extension of Maxwell's equations for the electromagnetic field. The idea is to use the generators for theU(2) group in a multidimensional representation. These generators are a linear combination of the ones for infinitesimal Lorentz transformations. The constants of the motion in this formalism are discussed. As an example, angular distributions of the Poynting vector are given.Supported in part by grants from the Research Corporation and the Mitsubishi Fund.Parts of this work were done in partial fulfilment of the requirements for the M.A. Degree at Western Michigan University.     

Synchrotron Radiation in a Circular Metallic Waveguide

We study theoretically the influence of a circular metallic waveguide with a longitudinal magnetic field on the synchrotron radiation of a point electric charge moving along a helical trajectory coaxial with the waveguide axis. The main attention is focused on the analysis of the energy characteristics of radiation of electromagnetic E and H waves. We derive the formulas for the radiation powers of E and H waves. It is shown that, under certain conditions, slowly moving electric charges do not radiate any of these electromagnetic waves in the circular waveguide.     

Thomas rotation and the parametrization of the Lorentz transformation group

Two successive pure Lorentz transformations are equivalent to a pure Lorentz transformation preceded by a 3×3 space rotation, called a Thomas rotation. When applied to the gyration of the rotation axis of a spinning mass, Thomas rotation gives rise to the well-knownThomas precession. A 3×3 parametric, unimodular, orthogonal matrix that represents the Thomas rotation is presented and studied. This matrix representation enables the Lorentz transformation group to be parametrized by two physical observables: the (3-dimensional) relative velocity and orientation between inertial frames. The resulting parametrization of the Lorentz group, in turn, enables the composition of successive Lorentz transformations to be given by parameter composition. This composition is continuously deformed into a corresponding, well-known Galilean transformation composition by letting the speed of light approach infinity. Finally, as an application the Lorentz transformation with given orientation parameter is uniquely expressed in terms of an initial and a final time-like 4-vector.     

Reflections on the evolution of physical theories

Conclusion Let me come back to the successes of the Poincaré group in particle physics. This is a group with ten generators. The translation generators are responsible for the energy-momentum conservation laws, the rotation generators of the conservation of angular momentum, and the boost generators of the conservation ofinitial position. If positions are slightly different from the ones described by Minkowski space, it means that we have to change slightly the notion of boosts. If we remember that boosts were questionable in Minkowski space (see Section 9), we are not surprised. We are naturally led to a deformation of the Poincaré group which would preserve translations and rotations [such a deformation has been proposed by Lukierskiet al. (n.d.)]. By duality, small changes at short distances must correspond to small changes in large momenta. The fact that cutoffs for momenta are involved in QED is perhaps related to a noncommutative structure for our space. With such a structure, making the size of an electron go to zero is meaningless and consequently the difficulty of an electron with infinite energy also becomes meaningless. A noncommutative space is probably a way to solve the difficulties mentioned in the epigraphs to this paper.     

Electronic properties of a Weyl semimetal in crossed magnetic and electric fields

The study of Weyl semimetals is one of the most challenging problems of condensed matter physics. These materials exhibit interesting properties in a magnetic field. In this work, we investigate the Landau bands and the density of states (DOS) oscillations in a Weyl semimetal in crossed magnetic and electric fields. An expression is obtained for the energy spectrum of the system using the following three different methods: an algebraic approach, a Lorentz shift-based approach, and a quasi-classical approach. It is interesting that the energy spectrum calculated in terms of the quasi-classical approach coincides with the spectrum obtained using the microscopic approaches. An electric field is shown to change the Landau bands radically. In addition, the classical motion of a three-dimensional Dirac fermion in crossed fields is studied. In the case of a Dirac spectrum, the longitudinal (with respect to magnetic field) component of momentum (p _z ∥ H) is shown to be an oscillating function of the magnetic field. When the electric field is v⊥H/c, the Landau levels collapse and the motion becomes fully linear in an unusual manner. In this case, the wavefunction of bulk states vanishes and only states with p _z = 0 are retained. An electric field affects the character of DOS oscillations. An analytical expression is obtained for the quantum capacitance in crossed fields in the cases of strong and weak electric fields. Thus, an electric field is an additional parameter for adjusting the diamagnetic properties of Weyl semimetals.     

Wigner rotations and little groups

Wigner’s little groups are the subgroups of the Poincaré group whose transformations leave the four-momentum of a given particle invariant. For a relativistic particle in motion the little group is a boosted rotation. On the other hand, the kinematical effect of two non-colinear Lorentz boosts is another boost preceded or follwed by a rotation, which is called the Wigner rotation. It is shown that there is always a Wigner rotation for a given little group rotation. The differences between those two rotations are clearly demonstrated and some interesting physical applications are presented.     

Magnetic dilaton strings in anti-de Sitter spaces

With an appropriate combination of three Liouville-type dilaton potentials, we construct a new class of spinning magnetic dilaton string solutions which produces a longitudinal magnetic field in the background of anti-de Sitter spacetime. These solutions have no curvature singularity and no horizon, but have a conic geometry. We find that the spinning string has a net electric charge which is proportional to the rotation parameter. We present the suitable counterterm which removes the divergences of the action in the presence of dilaton potential. We also calculate the conserved quantities of the solutions by using the counterterm method.     

X-ray dichroism in biaxial gyrotropic media: Differential absorption and fluorescence excitation spectra

The differential absorption and the differential change in the polarization state of an X-ray beam propagating inside a gyrotropic crystal are described using a Müller matrix, the 16 elements of which are related to the anisotropic components of the multipolar polarizability tensors at the absorbing site. Analytical expressions are given up to third order for X-ray linear and circular dichroism, X-ray optical rotation and X-ray circular polarimetry in transmission. The same formalism is extended to discuss Fluorescence detected dichroism spectra with or without polarization analysis of the fluorescence. Fluorescence detected dichroism is strictly proportional to dichroism measured in the transmission geometry only for uniaxial crystals. In biaxial crystals, the tiny effects of X-ray gyrotropy are swamped by large linear dichroism signals due to the imperfect polarization transfer function of Bragg monochromators. Second order effects should also be taken into consideration. Our general formulation of linear and circular dichroism includes terms of odd parity with respect to the action of the time reversal operator: such terms cannot contribute to natural dichroism but can be activated by a magnetic field. The terms responsible for X-ray magnetic circular dichroism are well known but non-reciprocal X-ray gyrotropy effects are also predicted in magnetic crystals of appropriate symmetry. Received 3 March 1999     

Wavelet multi-resolution analysis of initial condition effects on near-wake turbulent structures

The effects of initial conditions on turbulence structures of various scales in a near wake have been investigated for two wake generators with the same characteristic dimension, i.e., a circular cylinder and a screen of 50% solidity, based on the wavelet multi-resolution analysis. The experimental investigation used two orthogonal arrays of sixteen X-wires, eight in the (x, y)-plane, and eight in the (x, z)-plane. Measurements were made atx/h (x is the streamwise distance downstream of the cylinder andh is the height of the wake generator) = 20. The wavelet multi-resolution technique was applied to decomposing the velocity data, obtained in the wakes generated by the two generators, into a number of wavelet components based on the central frequencies. The instantaneous sectional streamlines and vorticity field were thus ‘visualized’ for each wavelet component or central frequency. It was found that the behavior of large- and intermediate-scale structures depend on the initial conditions and the small-scale structures are independent of the initial conditions. The contributions from the wavelet components to the time-averaged Reynolds stresses and vorticity were estimated. Both the large-scale and intermediate longitudinal structures make the most significant contributions to Reynolds stresses in the circular cylinder wake, but the contribution from the large-scale structures appears dominating in the screen wake. The relatively small scale structures of the circular cylinder wake contribute most to the total rms spanwise vorticity.     

Electric field and Lorentz force contribution to atmospheric vortex phenomena

The physics that initiate and sustain tornados and dust devils is still under investigation. Forces that operate throughout a wide range of scales and could contribute to atmospheric vortex phenomena are the Lorentz force and the force of electric fields. The Lorentz force results in a circular motion of charged particles in a magnetic field. An electric field will pull or repel a charged particle in the direction of the field. This paper will demonstrate that the Lorentz force and the force of electric fields, acting on charged particles that exist in atmospheric vortex phenomena, plausibly contribute to the set of physics that will explain tornados and other atmospheric vortex phenomena.     

Dynamics and instability of current-carrying microbeams in a longitudinal magnetic field

The dynamics and instability of current-carrying slender microbeams immersed in a longitudinal magnetic field is investigated by considering the material length scale effect of the microbeam. On the basis of modified couple stress theory, a theoretical model considering the effect of Lorentz forces is developed to analyze the free vibration and possible instability of the microbeam. Using the differential quadrature method, the governing equations of motion are solved and the lowest three natural frequencies are determined. The obtained results reveal that the electric current and the longitudinal magnetic field tend to reduce the microbeam's flexural stiffness. It is therefore shown that the lowest natural frequencies would decrease with increasing magnetic field parameter. The mode shapes of the microbeam are found to be generally three-dimensional spatial in the presence of the longitudinal magnetic field. It is interesting that buckling instability would concurrently occur in the first mode or in the higher-order modes when the magnetic field parameter becomes sufficiently large.     

On the problem of polarization characteristics of radio waves in a randomly inhomogeneous magnetoactive plasma

Expressions for the Stokes parameters when radio waves propagate in a turbulent magnetoactive plasma have been obtained using a refractive scattering method. The problem of the spatial coherence of polarized radiation is considered. Expressions for the correlation functions and fluctuation dispersions of the Stokes parameters are found in the case of saturated wave field fluctuation. It is shown that the fluctuation of the circular polarized component will be observed in the received radiation even if the circular polarization is absent in the radiation that is incident on the magnetoactive plasma slab. A method is proposed to define the preference orientation of the magnetic field in the inhomogeneous layer of space plasma, which is biased on the simultaneous measurement of the space correlation functions of the I, V Stokes parameter fluctuation and Faraday rotation of the radiation polarization plane from the source with known polarization characteristics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 8, pp. 1007–1013, August, 1996.This work was supported in part by the Russian Foundation for Fundamental Research under Project No. 96-02-18632.     

Lorentz violation constrained by triplicity of lepton families and neutrino oscillations

In this paper we postulate an algebraic model to relate the triplet characteristic of lepton families to Lorentz violation. Inspired by the two-to-one mapping between the group SL(2, C) and the Lorentz group via the Pauli grading (the elements of SL(2, C) expressed by direct sum of unit matrix and generators of SU (2) group), we grade the SL(3, C) group with the generators of SU(3), i. e. the Gell-Mann matrices, then express the SU(3) group in terms of three SU(2) subgroups, each of which stands for a lepton species and is mapped into the proper Lorentz group as in the case of the group SL(2,C). If the mapping from group SL(3,C) to the Lorentz group is constructed by choosing one SU(2) subgroup as basis, then the other two subgroups display their impact only by one more additional generator to that of the original Lorentz group. Applying the mapping result to the Dirac equation, it is found that only when the kinetic vertex γμξμ is extended to encompass γμξμ can the Dirac-equation-form be conserved. The generalized vertex is useful in producing neutrino oscillations and mass differences.