Spin Oscillations in Storage Rings

The dependence of the particle rotation frequency on the particle orbit perturbations is found. The exact equation of spin motion in the cylindrical coordinate system is derived. The calculated formula for the frequency of g-2 precession is in the best agreement with previous results. Nevertheless, this formula contains the additional oscillatory term that can be used for fitting. The influence of spin oscillations on the spin dynamics in the EDM experiment is negligible.Comment: 5 pages. To appear in the proceedings of 16th International Spin Physics Symposium (SPIN 2004), Trieste, Italy, 10-16 Oct 200

Classical Limit of Relativistic Quantum Mechanical Equations in the Foldy-Wouthuysen Representation

It is shown that, under the Wentzel-Kramers-Brillouin approximation conditions, using the Foldy-Wouthuysen representation allows the problem of finding a classical limit of relativistic quantum mechanical equations to be reduced to the replacement of operators in the Hamiltonian and quantum mechanical equations of motion by the respective classical quantities.Comment: 6 page

Foldy-Wouthyusen Transformation and Semiclassical Limit for Relativistic Particles in Strong External Fields

A general method of the Foldy-Wouthyusen (FW) transformation for relativistic particles of arbitrary spin in strong external fields has been developed. The use of the found transformation operator is not restricted by any definite commutation relations between even and odd operators. The final FW Hamiltonian can be expanded into a power series in the Planck constant which characterizes the order of magnitude of quantum corrections. Exact expressions for low-order terms in the Planck constant can be derived. Finding these expressions allows to perform a simple transition to the semiclassical approximation which defines a classical limit of the relativistic quantum mechanics. As an example, interactions of spin-1/2 and scalar particles with a strong electromagnetic field have been considered. Quantum and semiclassical equations of motion of particles and their spins have been deduced. Full agreement between quantum and classical theories has been established.Comment: 10 page

Connection Between Wave Functions in the Dirac and Foldy-Wouthuysen Representations

The connection between wave functions in the Dirac and Foldy-Wouthuysen representations is found. When the Foldy-Wouthuysen transformation is exact, upper spinors in two representations differ only by constant factors, and lower spinors in the Foldy-Wouthuysen representation are equal to zero.Comment: 7 page