  We develop a gauge theory for diffusive and precessional spin dynamics in
two-dimensional electron gas with disorder. Our approach reveals a direct
connections between the absence of the equilibrium spin current and strong
anisotropy in the spin relaxation: both effects arise if the spin-orbit
coupling is reduced to a pure gauge SU(2) field. In this case, by a gauge
transformation in the form of a local SU(2) rotation in the spin subspace the
spin-orbit coupling can be removed. The resulting spin dynamics is exactly
described in terms of two kinetic coefficients: the spin diffusion and electron
mobility. After the inverse transformation, full diffusive and precessional
spin density dynamics, including the anisotropic spin relaxation, formation of
stable spin structures, and spin precession induced by a macroscopic current,
is restored. Explicit solutions of the spin evolution equations are found for
the initially uniform spin density and for stable nonuniform structures. Our
analysis demonstrates a universal relation between the spin relaxation rate and
spin diffusion coefficient.

Other Condensed Matter;Disordered Systems and Neural Networks