Spin dynamics with non-abelian Berry gauge fields as a semiclassical constrained hamiltonian system

摘要

The dynamics of observables which are matrices depending on \hbar and takingvalues in classical phase space is defined retaining the terms up to the firstorder in \hbar of the Moyal bracket. Within this semiclassical approach a firstorder lagrangian involving gauge fields is studied as a constrained hamiltoniansystem. This provides a systematic study of spin dynamics in the presence ofnon-abelian Berry gauge fields. We applied the method to various types ofdynamical spin systems and clarified some persisting discussions. In particularemploying the Berry gauge field which generates the Thomas precession, wecalculated the force exerted on an electron in the external electric andmagnetic fields. Moreover, a simple semiclassical formulation of the spin Halleffect is accomplished.