Classical Yang-Mills theory in condensed matter physics

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