Classical Yang-Mills theory in condensed matter physics

TL;DR

This paper discusses how classical Yang-Mills theory, a non-Abelian gauge field framework, can be applied to condensed matter physics to analyze spin-orbit interactions, making complex concepts accessible for educational purposes.

Contribution

It introduces a classical SU(2)$\times$U(1) gauge theory approach to condensed matter physics, illustrating fundamental non-Abelian field concepts in tangible physical systems.

Findings

Provides a pedagogical example of non-Abelian gauge theories in condensed matter.

Connects gauge symmetry principles with spin-orbit interactions.

Facilitates understanding of Yang-Mills equations through physical phenomena.

Abstract

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.