arXiv subjects
Publications and source records attributed to Alexander A. Chernitskii.
Electromagnetic particle is considered as appropriate particle solution of nonlinear electrodynamics. Mass, spin, charge, and dipole moment for the electromagnetic particle are defined. Classical motion equations for massive charged particle with spin and dipole moment are obtained from integral conservation laws for the field.
Space-time multivectors in Clifford algebra (space-time algebra) and their application to nonlinear electrodynamics are considered. Functional product and infinitesimal operators for translation and rotation groups are introduced, where unit pseudoscalar or hyperimaginary unit is used instead of imaginary unit. Basic systems of orthogonal functions (plane waves, cylindrical, and spherical) for space-time multivectors are built by using the introduced infinitesimal operators. Appropriate orthogonal decompositions for electromagnetic field are presented. These decompositions are applied to nonlinear electrodynamics. Appropriate first order equation systems for cylindrical and spherical radial functions are obtained. Plane waves, cylindrical, and spherical solutions to the linear electrodynamics are represented by using the introduced orthogonal functions. A decomposition of a plane wave in terms of the introduced spherical harmonics is obtained.
Clifford number representation for linear electrodynamics with dyon sources is considered. Source function for the appropriate system of the first order equations for electromagnetic field is obtained. The field of an arbitrary moving point dyon is derived.
A general model of nonlinear electrodynamics with dyon singularities is considered. We consider the field configuration having two dyon singularities with identical electric and opposite magnetic charges and we name it bidyon. We investigate the sum of two dyon solutions as an initial approximation to the bidyon solution. We consider the case when the velocities of the dyons have equal modules and opposite directions on a common line. It is shown that the associated field configuration has a constant full angular momentum which is independent of distance between the dyons and their speed. This property permits a consideration of this bidyon configuration as an electromagnetic model for charged particle with spin. We discuss the possible electrodynamic world with oscillating bidyons as particles.
The problems connected with a causality of space-time universe and with the paradox of Einstein, Podolsky, and Rosen are considered. A main philosophical problem and its possible solutions are briefly discussed. A concept of unified local field theory is considered. It is shown that in the framework of such theory there are nonlocal correlations between space separate events. These correlations are predicted by quantum mechanics and they are confirmed by Aspect type experiments for testing of Bell inequality. The presence of these nonlocal correlations in the framework of a local field theory is connected with the fact that its solution is nonlocal in character. Prospects for possible applications of an unified local field theory are considered.
The effect of induced Riemann geometry in nonlinear electrodynamics is considered. The possibility for description of real gravitation by this effect is discussed.
The concept of unified local field theory is considered. According to this concept the quantum description and the classical one must be the levels for investigation of some world solution of the unified field model. It is shown that in the framework of the unified local field theory there are nonlocal correlations between space separate events. Thus the experiments of Aspect type for testing of the Bell inequalities and for showing of the nonlocal correlations do not reject a possibility for description of matter with the unified local field theory. Advantages of such theory for new technologies are considered.
Clifford number formalism for Maxwell equations is considered. The Clifford imaginary unit for space-time is introduced as coordinate independent form of fully antisymmetric fourth-rank tensor. The representation of Maxwell equations in massless Dirac equation form is considered; we also consider two approaches to the invariance of Dirac equation in respect of the Lorentz transformations. According to the first approach, the unknown column is invariant and according to the second approach it has the transformation properties known as spinorial ones. Clifford number representation for nonlinear electrodynamics equations is obtained. From this representation, we obtain the nonlinear like Dirac equation which is the form of nonlinear electrodynamics equations. As a special case we have the appropriate representations for Born-Infeld nonlinear electrodynamics.
Born-Infeld nonlinear electrodynamics with point singularities having both electric and magnetic charges are considered. Problem of interaction between the associated soliton dyon solutions is investigated. For the case of long-range interaction at first order by a small field of distant solitons we obtain that the generalized Lorentz force is acted on a dyon under consideration. Short-range interaction between two dyons having identical electric and opposite magnetic charges is investigated for an initial approximation. We consider the case when the velocities of the dyons have equal modules and opposite directions on a common line. It is shown that the associated field configuration has a constant full angular momentum which is independent of the interdyonic distance and their speed. This property permits a consideration of this bidyon configuration as an electromagnetic model of charged particle with spin. We numerically investigate movement of the dyons in this configuration for the case when the full electric charge equals the electron charge and the full angular momentum equals the electron spin. It is shown that for this case the absolute value of relation between electric and magnetic charges of the dyons equals the fine structure constant. The calculation gives that the bidyon may behave as nonlinear oscillator. Associated dependence of frequency on the full energy is obtained for the initial approximation. In the limits of the electrodynamic model we obtain that the quick-oscillating wave packet may behave like massive gravitating particle when it move in high background field. We discuss the possible electrodynamic world with the oscillating bidyons as particles.
We obtain the characteristic equation for the nonlinear Born-Infeld electrodynamics. This equation has the form of the characteristic equation for the linear electrodynamics in some effective Riemann space. The effective metric include the energy-momentum tensor components of electromagnetic field. We study a distortion of light beams by the action of some distant solitons. This distortion corresponds to attraction with the solitons and looks like the gravitational distortion.
Born-Infeld nonlinear electrodynamics are considered. Main attention is given to existence of singular point at static field configuration that M.Born and L.Infeld are considered as a model of electron. It is shown that such singularities are forbidden within the framework of the Born-Infeld model. It is proposed a modernized action that make possible an existence of the singularities. It is obtained main relations in view of the singularities. In initial approximation this model gives the usual linear electrodynamics with point charged particles.
A direct method for obtaining the differential conservation laws in the field theory from the principle of stationary action is proposed. The method is based on a variation of field functions through small local transformation of a special kind. The action of general theory of relativity are considered.