Magnetization, spin current, and spin-transfer torque from SU(2) local gauge invariance of the nonrelativistic Pauli-Schrodinger theory

In this Brief Report, we consider local gauge symmetries of the nonrelativistic Pauli-Schrodinger theory. From the simplest free Lagrangian density for Pauli two-component spinors, we obtain the spin interaction with a magnetic field and define the spin-current vector without invoking relativistic theory. Applying U(1)xSU(2) local gauge symmetry, and proceeding via the Noether's theorem, we are able to construct a covariant conserved spin-current density in a natural way. Our approach allow us to understand the main features of spin transport properties and suggests that SU(2) is a fundamental symmetry of nonrelativistic quantum mechanics.