Maxwell equation for coupled spin-charge wave propagation

We show that the dissipationless spin current in the ground state of the Rashba model gives rise to a reactive coupling between the spin and charge propagation, which is formally identical to the coupling between the electric and the magnetic fields in the (2+1)-dimensional Maxwell equation. This analogy leads to a remarkable effect of fractionalization of spin packets (FSP) where a density packet can spontaneously split into two counterpropagation packets, each carrying the opposite spin. In a certain parameter regime, the coupled spin and charge wave propagates like a transverse "photon." We propose both optical and purely electronic experiments to detect the FSP effect.