Seminar “Quantum Field Theory”

Date and Time: Wednesday, 21 October 2020, at 11:00 AM

Venue: Online conference on Zoom, Bogoliubov Laboratory of Theoretical Physics

Seminar topic: «Method of the Foldy-Wouthuysen transformation for relativistic particles with any spin in external fields and its applications in quantum mechanics and to search for EDMs and other moments of particles and nuclei»

Speaker: A. J. Silenko

Abstract:

For particles with any spin, a transformation to the Foldy-Wouthuysen (FW) representation restores the Schrödinger-like picture of relativistic quantum mechanics and the probabilistic interpretation of wave functions and connects relativistic and nonrelativistic quantum mechanics. In the presented cycle of works, the method of the relativistic FW transformation for particles (nuclei) with any spin has been developed. The method does not need the weak-field approximation and cumbersome derivations and is the only known method which gives exact leading terms in the Hamiltonian obtained. A sufficient condition of the exact FW transformation has been determined and a number of new cases of such a transformation, including for an initial nonstationary Hamiltonian has been found. The exact nonexponential operator of the FW transformation for particles with any spin has been derived. The developed method has been used for a solution of the most important problems of relativistic quantum mechanics and practically important ones of physics of particles and nuclei. The special role of the FW representation in relativistic quantum mechanics has been confirmed by a demonstration of the fact that quantum-mechanical counterparts of the classical variables of the position (coordinates) and the spin are the corresponding operators in the FW representation but not in the Dirac one. The presence of Zitterbewegung of bosons has been proven but it has been shown that Zitterbewegung of bosons is a purely mathematical effect which is not observable either. Relativistic FW Hamiltonians for spin-1/2 and spin-1 particles with anomalous magnetic moments and EDMs interacting with arbitrary electric and magnetic fields, operator equations of motion for particles and spins and corresponding classical equations have been derived for the first time. The results obtained are used for preparation of experiments to search for EDMs of charged particles and nuclei in storage rings. The developed “frozen” spin method underlies a majority of prepared experiments and improves the sensitivity of search by several orders of magnitude. Dynamics of polarization of relativistic particles and nuclei in storage rings caused by the spin-tensor interactions has been calculated and parameters of high-precision experiments to measure tensor electric and magnetic polarizabilities of the deuteron have been determined.