  Recently, gauge field theory approaches were extensively used in order to
discuss the physical consequences of spin-orbit interactions in condensed
matter physics. An SU(2)$\times$U(1) gauge theory is very naturally borne out
and provides an illustrative example of a classical Yang-Mills field theory at
work. This approach may serve as an exemplification of non-Abelian field
theories for students in general physics curriculum. It allows to introduce
discussions on fundamental ideas like Noether currents, gauge symmetry
principle, gauge symmetry breaking and non linear Yang Mills equations in very
concrete physical situations that makes it accessible to a broad audience.
