Electrodynamics of moving media and the force on a current loop

The development of the Chu formulation of the electrodynamics of moving media is reviewed. The force on a current loop and/or magnetic dipole is developed for three different models and all three are shown to be identical, as already shown in previous publications. The electromagnetic momentum associated with the three different models is derived and the equality of the force expressions is confirmed on the basis of the momentum conservation theorem of electrodynamics. The paper is based on a lecture delivered at Technion at the occasion of Professor Franz Ollendorff's 80th birthday.     

Variational principle for electrodynamics of moving particles

A consistent relativistic theory of the classical Maxwell field interacting with classical, charged, point-like particles, proposed in [1], is now derived from a variational principle. For this purpose a new electrodynamical Lagrangian based on fluxes is constructed. As a result, we obtain the action principle where i) field degrees of freedom and particle degrees of freedom are kept at the same footing, ii) contrary to the standard formulation, no infinities arise, iii) energy (Hamiltonian) is obtained from the Lagrangian via the Legendre transformation, without any need of adding a complete divergence.     

Pre-Maxwell Electrodynamics

In the context of a covariant mechanics with Poincaré-invariant evolution parameter , Sa'ad, Horwitz, and Arshansky have argued that for the electromagnetic interaction to be well posed, the local gauge function of the field should include dependence on , as well as on the spacetime coordinates. This requirement of full gauge covariance leads to a theory of five -dependent gauge compensation fields, which differs in significant aspects from conventional electrodynamics, but whose zero modes coincide with the Maxwell theory. The pre-Maxwell fields may exchange mass with charged particles, permitting pair annihilation even at the classical level. The total mass-energy-momentum tensor of the fields and particles is conserved. The Green's functions for the fields provide spacelike and timelike support for correlations, as well as lightlike propagation. A -integration of the fields—singling out the massless photons—recovers the standard Maxwell theory, which then has the character of an equilibrium limit of the underlying microscopic dynamics. The pre-Maxwell theory also turns out to be the solution of the inverse problem in variational mechanics: it is shown to be the most general local gauge theory consistent with unconstrained commutation relations in four dimensions. Posed in this framework, the extension to n-dimensions, curved background space, and non-abelian gauge symmetry becomes straightforward.     

Radiation of ultrarelativistic particles moving near crystalline axes

The total radiation intensity of ultrarelativistic electrons and positrons moving near crystalline axes in thin crystals is considered. The approach avoids cumbersome analysis of the radiation from concrete trajectories. A general expression for the intensity is derived which is valid for any axial symmetric potential.     

Generalized Split-Octonion Electrodynamics

Starting with the usual definitions of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the consistent form of generalized Maxwell’s equations in presence of electric and magnetic charges (dyons). We have thus written the generalized potential, generalized field, and generalized current of dyons in terms of split octonions and accordingly the split octonion forms of generalized Dirac Maxwell’s equations are obtained in compact and consistent manner. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges.     

Proper-Time Classical Electrodynamics

We construct a generalization of Maxwell's equations associated with the proper-time of the source which accounts for radiation reaction without any assumptions concerning the nature of the source. The theory leads to a new invariance group, related to the Lorentz group, which leaves the proper-time of the source fixed for all observers.     

Non-Locality in Electrodynamics

We investigate the applicability of Hegerfeldts arguments on Quantum nonlocality in Quantum Electrodynamics following the work of Prigogine, Pronko, Petrosky, Ordonez and Karpov. We demonstrate the appearance of nonlocal effects at the level of quantum states. We show, however that the expectation values of some observables spread causally. Therefore the measurement of the nonlocality is questionable. We investigate an approach to classical measurement and conclude that the classical measurement cannot detect the acausal effects of the non-locality.     

Electrodynamics of effective charge

A portion of the charge induced in an isotropic plasma by an injected charged particle is shown to combine with the particle to form a charged quasi-particle, the effective charge, that is different from the conventional “dressed” charge. The remainder of the induced charge is found in a wake behind the effective charge. Properties of effective charge are described, and the application of this concept to coherent ion acceleration and stopping power is discussed.     

洛伦兹破缺的电动力学模型

由于宇宙常数的存在, 时空为渐近de Sitter(dS)的时空. 文中将静态dS度规作为时空的近似刻画, 研究了在此度规下的一个洛伦兹破缺的电动力学模型. 通过张量的标架场分解的方法, 得到了静态dS时空中的电磁场方程. 另外, 分别研究了静态dS时空中点电荷的静电场和圈电流的静磁场, 并且同时讨论了在此模型下的洛伦兹破缺效应.     

Pre-Maxwell Quantum Electrodynamics

In the framework of off-shell quantum electrodynamics—the quantum field theory of a covariant symplectic mechanics, in which events evolve according to a Poincaré-invariant parameter —we study the low-energy scattering of identical scalar particles. It is shown that exchange of mass is permitted in the formalism, and we calculate scattering cross-sections for this case. In these cross-sections, the usual forward pole of the standard scalar QED splits into two poles and a zero, slightly offset from the forward direction. As mass exchange vanishes, a pole-zero pair cancel, the remaining pole moves to = 0, and the standard cross-section is recovered.     

Electrodynamics of multilayer media

Using an exact solution of the Maxwell equations, two classes of electromagnetic fields are found, generated by currents in media consisting of plane-parallel layers with given electrodynamical characteristics.Institute for Strong Current Electronics, Russian Academy of Sciences, Siberian Branch. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 89–96, December, 1992.     

Torsional Weyl-Dirac Electrodynamics

Issuing from a geometry with nonmetricity and torsion we build up a generalized classical electrodynamics. This geometrically founded theory is coordinate covariant, as well as gauge covariant in the Weyl sense. Photons having arbitrary mass, intrinsic magnetic currents, (magnetic monopoles), and electric currents exist in this framework. The field equations, and the equations of motion of charged (either electrically or magnetically) particles are derived from an action principle. It is shown that the interaction between magnetic monopoles is transmitted by massive photons. On the other hand, the photon is massive only in the presence of magnetic currents. We obtained a static spherically symmetric solution, describing either the Reissner-Nordstrom metric of an electric monopole, or the metric and field of a magnetic monopole. The latter must be massive. In the absence of torsion and in the Einstein gauge one obtains the Einstein-Maxwell theory.     

Stationary shapes of deformable particles moving at low Reynolds numbers

We introduce an iterative solution scheme in order to calculate stationary shapes of deformable elastic capsules which are steadily moving through a viscous fluid at low Reynolds numbers. The iterative solution scheme couples hydrodynamic boundary integral methods and elastic shape equations to find the stationary axisymmetric shape and the velocity of an elastic capsule moving in a viscous fluid governed by the Stokes equation. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical resting shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Kármán number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Kármán number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical Föppl-von-Kármán numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force.