Generation of electric field by spin-currents in the U(1)×SU(2)U(1)×SU(2) gauge invariant Pauli–Schrödinger non-relativistic theory

The non-relativistic Pauli–Schrödinger theory has a richer gauge structure than usually expected, being invariant under the U(1)×SU(2)U(1)×SU(2) gauge group, which allows to define spin-current density vectors and obtains the relevant conserved quantities from Noether's theorem. The electromagnetic fields E and B play the role of the gauge potentials for the SU(2)SU(2) sector of the gauge group and can possibly contribute with a corresponding invariant curvature self-energy term in the Lagrangian density. From the dynamics of the U(1)U(1) and SU(2)SU(2) gauge fields we show that electric fields can be induced by spin-currents originated from the SU(2)SU(2) gauge symmetry.