Time asymmetry in classical electrodynamics

Source-free Maxwell equations are recast in a form that incorporates manifest time reversal invariance. It is argued that potentials are fundamental quantities. The basis of a formulation in which the source and fields are unified is also outlined.     

A time-symmetric classical electrodynamics

In this theory, both the advanced and retarded Liénard-Wiechert potentials are used to compute the fields of a charged point particle. The incoming radiation from the advanced fields balances the outgoing radiation of the retarded fields, and we assume that there are no radiation reaction terms in the equations of motion of the particles. We further assume that only retarded fields act on particles through the Lorentz force, and that advanced fields act on antiparticles. This is a theory that is symmetric under time reflection (reversal of the direction of motion plus charge conjugation).     

Spin flip effects in classical electrodynamics

It is shown that in the dipole approximation radiation accompanied by a spin flip in a homogeneous magnetic field can be described by the precession of the transverse component of the classical spin vector. The effect of Thomas precession on radiation by particles possessing spin and intrinsic magnetic moment is discussed. The correspondence principle for the theory of radiation by a relativistic magnetic moment is formulated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 43–45, February, 1986.The author takes the opporstunity to thank Prof. V. G. Bagrov for a useful discussion of the results in the study.     

Canonical transformation method in classical electrodynamics

The solutions of Maxwell's equations in the parabolic equation approximation is obtained on the basis of the canonical transformation method. The Hamiltonian form of the equations for the field in an anisotropic stratified medium is also examined. The perturbation theory for the calculation of the wave reflection and transmission coefficients is developed.     

Green's function method in classical electrodynamics

A perturbation theory for solution of the Vlasov and Klimontovich equations is formulated on the basis of the method of Green's functions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 85–89, February, 1991.     

Some problems of classical electrodynamics

In this lecture, I discuss issues that usually escape attention of students in electrodynamics. These are the questions of (1) what the photon observed in nature “looks like,” (2) how an interference pattern arises from a source containing a lot of incoherently emitting atoms, and (3) how light “slows down” in a medium. Answers to these questions, if discussed at all, are scattered over various textbooks. Here, I follow our textbook [1].     

Symmetries and asymmetries in classical and relativistic electrodynamics

By a comparison between Maxwell's electrodynamics classically interpreted (MT) and relativistic electrodynamics (RED), this paper discusses whether the asymmetries in MT mentioned by A. Einstein in his 1905 relativity paper are only of a conceptual nature or rather involve specific empirical claims. It is shown that in fact MT predicts strongly asymmetric behaviour for very simple interactions, and an analysis is made of the extent of the symmetry achieved by means of relativistic postulates. A low velocity experiment is suggested which could provide another test of the accuracy of RED with respect to MT.     

Electric strings and light-like lumps in classical electrodynamics

Soliton-like solutions of classical spinor electrodynamics with the symmetry of a cylinder of finite or infinite length are described. The solutions have non-vanishing total charge and, contrary to ordinary strings, an azimuthal magnetic and a radial electric field. For finite length, these lumps move with the velocity of light in the direction of the symmetry axis and the total four momentum is light-like. The crucial mechanism is a subtle compensation which prevents the matterfield from recoupling to its own electromagnetic field.     

Lie algebras of classical and stochastic electrodynamics

The Lie algebras associated with infinitesimal symmetry transformations of third-order differential equations of interest to classical electrodynamics and stochastic electrodynamics have been obtained. The structure constants for a general case are presented and the Lie algebra for each particular application is easily achieved. By the method used here it is not necessary to know the explicit expressions of the infinitesimal generators in order to determine the structure constants of the Lie algebra.     

Self-interaction and regularization of classical electrodynamics in higher dimensions

The classical electrodynamic system of a field and a single point-like source is considered in even-dimensional spacetime. The problem of self-interaction is discussed. It is manifestly shown that all singular terms appearing in these equations can be regularized. Relations between formulas for radiation and radiation friction are discussed. The text was submitted by the author in English.     

关于电磁学与电动力学打通的设想

从教材可行性、教材体系结构和教材内容三方面着手,提出了打通适合师范类教学的电磁学与电动力学教材的设想     

Galilean symmetry of Maxwell's equations in classical electrodynamics

It is shown that the Galilean group, like the Lorentz group, is a group of exact symmetry of Maxwell's equation. The Galilean group differs in that, while the field transformations are linear and global in the relativistic case, they are nonlinear in the Galilean and, generally speaking, depend on the coordinates of the event through some weight functions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 78–83, August, 1985.The author thanks D. P. Grechukhin, V. I. Man'ko, and V. I. Fushchich for discussion of the work and valuable comments.     

Synchrotron radiation of a magnetic moment in classical electrodynamics

It is established that the quantum correction (8/3) ₀ ² to the synchrotron radiation power has a classical origin and is related to the radiation of the intrinsic magnetic moment. The properties of the synchrotron radiation of the intrinsic magnetic moment are considered. It is shown that the spin relaxation time in classical electrodynamics practically coincides with the corresponding expression in quantum theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 3–7, February, 1982.     

An approach to introducing fractional integro-differentiation in classical electrodynamics

Analogs for Maxwell’s equations with fractional derivatives are obtained using the concepts of an effective current and the velocity of a charged particle in a medium. The calibration invariance is considered and a diffusion-wave equation is found and analyzed for scalar and vector potentials. It is shown that the stochastic nature of charged particle motion in a medium influences the dynamics of an electromagnetic field.     

Radiative corrections for extended charged particles in classical electrodynamics

Radiative effects on classical nonrelativistic charged particles are discussed in complete analogy with those arising in quantum electrodynamics. The effects originate in the interaction of the particle with its own electromagnetic fields. In particular, we derive an expression for the anomalous magnetic moment which provides both an intuitively appealing explanation of its origin and a reasonable relation to experimental values.     

Radiative damping of a relativistic electron in classical electrodynamics

An exact solution of the problem of the reaction of the field generated by a relativistic classical electron is derived. It is found that the solution differs dramatically from the known formulas by the presence of a component that is even under time reversal. It is also shown that the component of the generalized radiative damping force that is odd under time reversal coincides with the well-known relativistic damping force obtained from the approximate nonrelativistic formula via a Lorentz transformation. Zh. éksp. Teor. Fiz. 114, 1661–1671 (November 1998)     

“Minus c” symmetry in classical electrodynamics and quantum theory

A symmetry associated with the inversion of the speed of light is considered.     

New perspective on the reciprocity theorem of classical electrodynamics

We provide a simple physical proof of the reciprocity theorem of classical electrodynamics in the general case of material media that contain linearly polarizable as well as linearly magnetizable substances. The excitation source is taken to be a point-dipole, either electric or magnetic, and the monitored field at the observation point can be electric or magnetic, regardless of the nature of the source dipole. The electric and magnetic susceptibility tensors of the material system may vary from point to point in space, but they cannot be functions of time. In the case of spatially non-dispersive media, the only other constraint on the local susceptibility tensors is that they be symmetric at each and every point. The proof is readily extended to media that exhibit spatial dispersion: For reciprocity to hold, the electric susceptibility tensor χ_{E_mn} that relates the complex-valued magnitude of the electric dipole at location r_m to the strength of the electric field at r_n must be the transpose of χ_{E_nm}. Similarly, the necessary and sufficient condition for the magnetic susceptibility tensor is χ_{M_mn} = χ^T_{M_nm}.