  Spin-currents and non-abelian gauge potentials in electronic systems can be
treated by spin-current-density functional theory, whose main input is the
exchange-correlation (xc) energy expressed as a functional of spin-currents.
Constructing a functional of spin currents that is invariant under
U(1)$\times$SU(2) transformations is a long-standing challenge. We solve the
problem by expressing the energy as a functional of a new variable we call
"invariant vorticity". As an illustration we construct the xc energy functional
for a two-dimensional electron gas with linear spin-orbit coupling and show
that it is proportional to the fourth power of the spin current.
