Lyubchenko M. Polarization and Electromagnetic Properties of relativistic spin particles

The thesis represents an attempt to systematize different methods of solution of problems about spin in electromagnetic field, and the focus attention was given to spin 1 and 1/2. We have investigated relations between various formalities for spin 1 particle, due to it corrective additions to Bargman-Wigner equations were found. The question about items corresponding to an anomalous magnetic moment in Proca equations was discussed. Nonrelativistic approximations for spin 1 particle have shown essential difference with the same for spin 1/2. They are: absence of spin-orbit coupling item and that of particle size. Quasi-classical approximation reveal possibility of anomalies in strong fields: in electrical field it is conical refraction for spin 1/2 and spin 1 particles (for ±1 spin projections on the magnetic field in rest system of the particle); at definite field invariant values it is possible the causality violation for spin 1 particle. To simplify the calculations of squared matrix elements for spin 1/2 processes the mathematical study of six-dimensional spin ? particle description was made. This allowed for succeed in solution of one-photon Vavilov-Cherenkov radiation problem. Stockes parameters for radiated photon were calculated too, and the relation between initial and final electron polarization 4-vectors were found. The Chebyshov polynomials and form factors in matrix element for Bargman-Wigner particle radiation have been used and in this way a problem about Vavilov-Cherenkov radiation by arbitrary spin has been solved. Key words: spin, relativistic wave equations, Vavilov-Cherenkov radiation, one-photon process, matrix element, form factor.