Spin superfluidity and spin-orbit gauge symmetry fixing

The Hamiltonian describing 2D electron gas, in a spin-orbit active medium, can be cast into a consistent non-Abelian gauge field theory leading to a proper definition of the spin current. The generally advocated gauge symmetric version of the theory results in current densities that are gauge covariant, a fact that poses severe concerns on their physical nature. We show that in fact the problem demands gauge fixing, leaving no room to ambiguity in the definition of physical spin currents. Gauge fixing also allows for polarized edge excitations not present in the gauge symmetric case. The scenario here is analogous to that of superconductivity gauge theory. We develop a variational formulation that accounts for the constraints between U(1) physical fields and SU(2) gauge fields, show that gauge fixing renders physical matter and radiation currents and derive the particular consequences for the Rashba SO interaction.