Classical Yang–Mills theory in condensed matter physics

Abstract

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.