Spin-orbit coupling heavily influences the dynamics of charge carriers in a solid, where its effective strength can be enhanced by orders of magnitude as compared to the vacuum. Remarkable consequences are phenomena such as the spin Hall and inverse spin galvanic (or Edelstein) effects, where spin currents and polarizations are generated by purely electrical means. The complexities of spin-charge coupled dynamics can be described within a non-Abelian gauge theory approach, based on Keldysh non-equilibrium formalism. A symmetric treatment of spin and charge degrees of freedom removes ambiguities related to spin non-conservation in the presence of spin-orbit and exchange couplings and yields a physically transparent picture. Furthermore, the non-Abelian language treats on the same footing standard spin-orbit interaction in solid state systems and exotic forms of (pseudo) spin-orbit coupling which arise, or can be engineered, in different contexts.

]]>