  The question of gauge-covariance in the non-Abelian gauge-field formulation
of two space-dimensional systems with spin-orbit coupling relevant to
spintronics is investigated. Although, these are generally gauge-fixed models,
it is found that for the class of gauge fields that are space-time independent
and satisfy a U(1) algebra, thus having a vanishing field strength, there is a
residual gauge freedom in the Hamiltonian. The gauge transformations assume the
form of a space-dependent rotation of the transformed wave functions with
rotation angles and axes determined by the specific form of the gauge-field,
i.e., the spin-orbit coupling. The fields can be gauged away, reducing the
Hamiltonian to one which is isospectral to the free-particle Hamiltonian, and
giving rise to the phenomenon of persistent spin helix reported first by
B.~A.~Bernevig \emph{et al.} [Phys.~Rev.~Lett. \textbf{97}, 236601 (2006)]. The
investigation of the global gauge transformations leads to the derivation of a
continuity equation where the component of the spin-density along given
directions, again fixed by the specific form of the gauge field, is conserved.
