We describe an exact derivation of tile total nondissipative transvers
e force acting on a quantized vortex moving in a uniform background. T
ile derivation is valid for neutral boson or fermion superfluids, prov
ided the order parameter is a complex scalar quantity. The force is de
termined by the one-particle density matrix far away from the vortex c
ore, and is found to be the Magnus force proportional to the superflui
d density.