Derivation of the transverse force on a moving vortex in a superfluid
  We describe an exact derivation of the total nondissipative transverse force acting on a quantized vortex moving in a uniform background. The derivation is valid for neutral boson or fermion superfluids, provided the order parameter is a complex scalar quantity. The force is determined by the one-particle density matrix far away from the vortex core, and is found to be the Magnus force proportional to the superfluid density. 
D.J. Thouless, P. Ao, and Q. Niu