Consistency in Formulation of Spin Current and Torque Associated with a Variance of Angular Momentum

Stimulated generally by recent interest in the novel spin Hall effect, the nonrelativistic quantum mechanical conserved currents, taken into account of spin-orbit coupling, are rigorously formulated based on the symmetries of system and Noether' theorem. The quantum mechanical force on the spin as well as the torque associated with the variance of angular momentum are obtained. Consequently, the kinetic interpretation of the variances of spin and orbit angular momentum currents implies a torque on the "electric dipole" associated with the moving spin. The bearing of the force and the torque on the properties of spin current in a two-dimensional electron gas with the Rashba spin-orbit interaction is discussed.