On the Current Carried by `Neutral' Quasiparticles

The current should be proportional to the momentum in a Galilean-invariant system of particles of fixed charge-to-mass ratio, such as an electron liquid in jellium. However, strongly-interacting electron systems can have phases characterized by broken symmetry or fractionalization. Such phases can have neutral excitations which can presumably carry momentum but not current. In this paper, we show that there is no contradiction: `neutral' excitations {\em do} carry current in a Galilean-invariant system of particles of fixed charge-to-mass ratio. This is explicitly demonstrated in the context of spin waves, the Bogoliubov-de Gennes quasiparticles of a superconductor, the one-dimensional electron gas, and spin-charge separated systems in 2+1 dimensions. We discuss the implications for more realistic systems, which are not Galilean-invariant.