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].     

On the Thomas precession in the classical theory of relativistic radiation

It is demonstrated that the radiation of the angular momentum power of electromagnetic field is directly proportional to the Thomas precession frequency. Thereby the dynamical aspect of origin of this phenomenon is established for the first time.     

Some connections between the classical theory of fluctuations and quantum field theory

A number of authors have noticed that the ground state of the harmonic oscillator can be represented as the motion of a classical charged particle under the influence of a fluctuating electromagnetic field, provided the effect of radiative reaction is taken into account. Their work is reviewed and some new results are obtained which extend the treatment to excited states.     

A generalization of the method of enclosing surfaces in classical radiation theory

The method of enclosing surfaces in classical radiation theory is generalized to the case of a charged particle moving in a transparent isotropic dispersive medium. The synchrotron and ondulator radiation problems are discussed, and expressions are derived and analyzed for the angular-spectral distribution of the radiation power in these cases.     

Some problems of classical and quantum gravitational collapse

Various aspects of the statics and dynamics of spherical gravitational distributions of an ideal fluid with distributed sources of zero-mass and massive vector fields are investigated. Both unrestricted configurations and isolated configurations with the appropriate matching to the external geometry are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 57–62, February, 1978.In conclusion the author considers it his pleasant duty to thank his colleagues V. N. Ponomarev and V. A. Berezin for stimulating discussions and analysis of the results.     

Some problems in the generalized theory of finite Fermi systems

A realistic version of the generalization of the theory of finite Fermi systems to the case where some complex configurations involving phonons are explicitly taken into account is proposed. Secular equations describing the fragmentation of simple states in odd and even-even nuclei over complex configurations that belong to, respectively, the quasiparticle ? phonon + quasiparticle ? phonon ? phonon and the two quasiparticles ? phonon type and which are presently of greatest interest are derived on the basis of general relations for nuclei that involve pairing (nonmagic nuclei). These equations take into account effects associated with ground-state correlations due to complex configurations and with the additional quasiparticle-phonon mechanism of Cooper pairing in nuclei. The effects in question were disregarded previously, but they are of interest since they can be observed in present-day experiments.     

Optical tomography problems: Investigation by the methods of the radiation transport theory

The problems of the optical diagnostics of inhomogeneous layered media are numerically studied. The question of the optical clearing of media is considered. A method for determining relative refractive indices from tomographic transmission data is proposed.     

Some problems in the theory of chaotic porous media with random internal geometry

A new approach has been developed for studying transport processes in a chaotic porous medium filled with an electrolyte solution or a gaseous phase. A system of equations for diffusive transport of a component of the solution is formulated taking account of interphase processes at the pore walls. A statistical method for their averaging and solution has been developed. Russian University of Friendship for the People. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–51, September, 1996.     

Quantum problems nonlinear in the classical limit

We discuss the solutions of quantum problems which are nonlinear in the classical limit. It is shown that in this case it is necessary to solve the corresponding nonlinear classical problem and study its bifurcation properties.Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 104–107, July, 1992.