  Planar systems with a general linear spin-orbit interaction (SOI) that can be
cast in the form of a non-Abelian pure gauge field are investigated using the
language of non-Abelian gauge field theory. A special class of these fields
that, though a $2\times2$ matrix, are Abelian are seen to emerge and their
general form is given. It is shown that the unitary transformation that gauges
away these fields induces at the same time a rotation on the wavefunction about
a fixed axis but with a space-dependent angle, both of which being
characteristics of the SOI involved.The experimentally important case of
equal-strength Rashba and Dresselhaus SOI (R+D SOI) is shown to fall within
this special class of Abelian gauge fields, and the phenomenon of Persistent
Spin Helix (PSH) that emerges in the presence of this latter SOI in a plane is
shown to fit naturally within the general formalism developed. The general
formalism is also extended to the case of a particle confined to a ring. It is
shown that the Hamiltonian on a ring in the presence of equal-strength R+D SOI
is unitarily equivalent to that of a particle subject to only a
spin-independent but $\theta$-dependent potential with the unitary
transformation relating the two being again the space-dependent rotation
operator characteristic of R+D SOI.
