  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.
