  We point out that the Rashba and Dresselhaus spin-orbit interactions in two
dimensions can be regarded as a Yang-Mills non-Abelian gauge field. The
physical field generated by the gauge field gives the electron wave function a
spin-dependent phase which is frequently called the Aharonov-Casher phase.
Applying on an AB ring this non-Abelian field together with the usual vector
potential, we can make the interference condition completely destructive for
one component of the spin while completely constructive for the other component
of the spin over the entire energy range. This enables us to construct a
perfect spin filter.
