Particle and spin motion in polarized media.pdf

a r X i v : h e p - p h / 0 4 0 3 1 0 7 v 1 1 0 M a r 2 0 0 4 Particle and spin motion in polarized media A.J. Silenko Institute of Nuclear Problems, Belarusian State University, Minsk, Belarus E-mail: silenko@inp.minsk.by Abstract Quantum mechanical equations of motion are obtained for particles and spin in media with polarized electrons in the presence of external fields. The motion of elec- trons and their spins is governed by the exchange interaction, while the motion of positrons and their spins is governed by the annihilation interaction. The equations obtained describe the motion of particles and spin in both magnetic and nonmag- netic media. The evolution of positronium spin in polarized media is investigated. Media with polarized electrons can be used for polarization of positronium beams. 1 1 Introduction The quantum mechanical description of the motion of particles and spin in matter is a very important problem. The classical theory of motion of particles and spin has been developed in great detail (see [1, 2])). A quantum mechanical equation of motion of relativistic particles in an electromagnetic field was derived by Derbenev and Kondratenko [3]. The motion of the spin of relativistic particles in an electromagnetic field is described by the Bargmann–Michel–Telegdi (BMT) equation [4]. The Lagrangian with an allowance for terms quadratic in spin was obtained in [5, 6]. The corresponding equation of spin motion was presented in [7]. The interaction between polarized particles and polarized matter was analyzed in [8, 9]. In the present paper, we find quantum mechanical equations of motion of particles and spin for relativistic particles with arbitrary spin that move in media with polarized electrons in the presence of external fields. The system of units h? = c = 1 is used. 2 Hamiltonian for particles in polarized media For particles with arbitrary spin, the Hamiltonian can be derived with the use of the interaction Lagrangian L, obtained in [5, 6].