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The question of gauge-covariance in the non-Abelian gauge-field formulationof two space-dimensional systems with spin-orbit coupling relevant tospintronics is investigated. Although, these are generally gauge-fixed models,it is found that for the class of gauge fields that are space-time independentand satisfy a U(1) algebra, thus having a vanishing field strength, there is aresidual gauge freedom in the Hamiltonian. The gauge transformations assume theform of a space-dependent rotation of the transformed wave functions withrotation 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 theHamiltonian to one which is isospectral to the free-particle Hamiltonian, andgiving rise to the phenomenon of persistent spin helix reported first byB.~A.~Bernevig \emph{et al.} [Phys.~Rev.~Lett. \textbf{97}, 236601 (2006)]. Theinvestigation of the global gauge transformations leads to the derivation of acontinuity equation where the component of the spin-density along givendirections, again fixed by the specific form of the gauge field, is conserved.

Gauge Covariance and Spin Current Conservation in the Gauge Field Formulation of Systems with Spin-Orbit Coupling