  Spin and charge currents in systems with Rashba or Dresselhaus spin-orbit
couplings are formulated in a unified version of four-dimensional
SU(2)$\times$U(1) gauge theory, with U(1) the Maxwell field and SU(2) the
Yang-Mills field. While the bare spin current is non-conserved, it is
compensated by a contribution from the SU(2) gauge field, which gives rise to a
spin torque in the spin transport, consistent with the semi-classical theory of
Culcer et al. Orbit current is shown to be non-conserved in the presence of
electromagnetic fields. Similar to the Maxwell field inducing forces on charge
and charge current, we derive forces acting on spin and spin current induced by
the Yang Mills fields such as the Rashba and Dresselhaus fields and the sheer
strain field. The spin density and spin current may be considered as a source
generating Yang-Mills field in certain condensed matter systems.
