Self-adjoint Operators and Conserved Currents

It is shown that there exists a conservedcurrent associated with any system of homogeneous linearpartial differential equations that can be written interms of a self-adjoint operator. By showing that the linearized Einstein-Maxwell,Einstein-Klein-Gordon and Einstein-Weyl equations can beexpressed in terms of self-adjoint operators, aconserved current is obtained in each case. Theconserved current associated with the perturbations of solutionsof the Einstein and the Einstein-Maxwell equationscoincides with the symplectic current found by otherauthors.     

Point-Form Hamiltonian Dynamics and Applications

This short review summarizes recent developments and results in connection with point-form dynamics of relativistic quantum systems. We discuss a Poincaré invariant multichannel formalism which describes particle production and annihilation via vertex interactions that are derived from field theoretical interaction densities. We sketch how this rather general formalism can be used to derive electromagnetic form factors of confined quark?Cantiquark systems. As a further application it is explained how the chiral constituent quark model leads to hadronic states that can be considered as bare hadrons dressed by meson loops. Within this approach hadron resonances acquire a finite (non-perturbative) decay width. We will also discuss the point-form dynamics of quantum fields. After recalling basic facts of the free-field case we will address some quantum field theoretical problems for which canonical quantization on a space?Ctime hyperboloid could be advantageous.     

Current Problems of Electrodynamics of a Thunderstorm Cloud

Electrodynamics of a thunderstorm cloud is considered with allowance for recirculation and multiflow motion of charged intracloud particles. In this simulation, the large-scale electric-field emerges due to the charge separation at the process of air convection and develops through the oscillation regime in the initial and final stages of the thunderstorm evolution. These oscillations qualitatively explain the observed behavior of the electric field of a thunderstorm. On the other hand, the multiflow convection is unstable and leads to generation of small-scale electrostatic waves (wavelength from 1 to 100 m) with amplitude reaching the conventional breakdown value. Such an instability can initiate microdischarge intracloud activity at the preliminary stage of the lightning discharge and between individual return strokes. We propose a three-dimensional cellular automata model which describes the main features of the preliminary stage of the lightning. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 9, pp. 810–822, September 2005.     

Constraints of Cluster Separability and Covariance on Current Operators

Realistic models of hadronic systems should be defined by a dynamical unitary representation of the Poincaré group that is also consistent with cluster properties and a spectral condition. All three of these requirements constrain the structure of the interactions. These conditions can be satisfied in light-front quantum mechanics, maintaining the advantage of having a kinematic subgroup of boosts and translations tangent to a light front. The most straightforward construction of dynamical unitary representations of the Poincaré group due to Bakamjian and Thomas fails to satisfy the cluster condition for more than two particles. Cluster properties can be restored, at significant computational expense, using a recursive method due to Sokolov. In this work we report on an investigation of the size of the corrections needed to restore cluster properties in Bakamjian–Thomas models with a light-front kinematic symmetry. Our results suggest that for models based on nucleon and meson degrees of freedom these corrections are too small to be experimentally observed.     

Electrodynamics and Radiation Reaction

The self force of electrodynamics is derived from a scalar field. The resulting equation of motion is free of all of the problems that plague the Lorentz Abraham Dirac equation. The age-old problem of a particle in a constant field is solved and the solution has intuitive appeal.     

Two-body Current Operators and Deuteron Form Factors Within the Light-Front Hamiltonian Dynamics

The deuteron electromagnetic properties are investigated within the Light-Front Hamiltonian dynamics using one-body and two-body currents. The dynamical nature of the latter is generated within a Yukawa model from an analysis of the Light-Front current that acts on the three-dimensional valence component and fulfills the Ward?CTakahashi identity. Preliminary results for the magnetic moment and the probability of the nonvalence component are shown.     

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.     

Massive Electrodynamics and Magnetic Monopoles

Including torsion in the geometric framework of the Weyl-Dirac theory we build up an action integral, and obtain from it a gauge covariant (in the Weyl sense) general relativistic massive electrodynamics. Photons having an arbitrary mass, electric, and magnetic currents (Dirac's monopole) coexist within this theory. Assuming that the space-time is torsionless, taking the photon mass zero, and turning to the Einstein gauge we obtain Maxwell's electrodynamics.     

Gravitational Radiation and Nonlocal Electrodynamics

A model of nonlocal response of a medium with an initially constant and homogeneous magnetic field acted upon by a planar gravitational wave is constructed on the basis of a covariant formulation of integral constitutive equations. The model is studied in detail and the problem of anomalous behavior of the response of the given electrodynamic system to a gravitational-wave action is discussed.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 27–33, April, 2005.     

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.     

Electrodynamics of moving particles

A consistent relativistic theory of the classical Maxwell field interacting with classical, charged, point-like particles is proposed. The theory is derived from a classical soliton-like model of an extended particle. An approximation procedure for such a model is developed, which leads to an already renormalized formula for the total four-momentum of the system composed of fields and particles. Conservation of this quantity leads to a theory which is universal (i.e. does not depend upon a specific model we start with) and which may be regarded as a simple and necessary completion of special relativity. The renormalization method proposed here may be considered as a realization of Einstein's idea of deriving equations of motion from field equations. It is shown that the Dirac's 3-dots equation does not describe a fundamental law of physics, but only a specific family of solutions of our theory, corresponding to a specific choice of the field initial data.     

Electrodynamics of microstretch and micropolar fluids

A R I - A continuum theory is developed for anisotropic microstretch and micropolar fluids subject to electormagnetic interactions. Balance laws and thermodynamically admissible constitutive...     

Development of the Sachs Theory of Electrodynamics

The most general form of electrodynamics has been derived by Sachs [1] from the irreducible representations of the Einstein group. In this paper the Sachs theory is developed as a gauge theory with a vacuum four-current i _j . The B Cyclic Theorem O(3) electrodynamics is derived from a consideration of four-vectors appearing in the Sachs theory, and electromagnetic helicity, expressed in terms of the B ⁽³⁾ field of O(3) electrodynamics, is derived from the more general Sachs theory.     

Electrodynamics from the standpoint of stationary ether

A methodology of electrodynamics presentation from the standpoint of stationary ether is suggested. The presentation is based on the four-dimensional formalism [5] that allows a number of fundamental physical phenomena to be examined from the unified standpoint. The methodology is useful for teachers, scientists, and engineers involved in different scientific fields and disciplines. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 8–18, October, 2006.     

Electrodynamics of Perfect Conductors

The most general electrodynamic equations of a perfect conducting state are obtained using a variational principle in a classical framework, following an approach by Pierre-Gilles de Gennes. London equations are derived as the time-independent case of these equations, corresponding to the magnetostatic minimal energy state of the perfect conducting system. For further confirmation, the same equations are also derived in the classical limit of the Coleman-Weinberg model, the most successful quantum macroscopic theory of superconductivity. The magnetic field expulsion is, therefore, a direct consequence of zero resistivity and not an exclusive property of superconductors.     

Electrodynamics of Balanced Charges

We introduce here a new “neoclassical” electromagnetic (EM) theory in which elementary charges are represented by wave functions and individual EM fields to account for their EM interactions. We call so defined charges balanced or “b-charges”. We construct the EM theory of b-charges (BEM) based on a relativistic field Lagrangian and show that: (i) the elementary EM fields satisfy the Maxwell equations; (ii) the Newton equations with the Lorentz forces hold approximately when b-charges are well separated and move with non-relativistic velocities. When the BEM theory is applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the Schrodinger model with desired accuracy. An important feature of the theory is a mechanism of elementary EM energy absorption established for retarded potentials.