Magnus and Iordanskii forces in superfluids

The transverse force acting on a quantized vortex in a superfluid is a problem that has eluded a complete understanding for more than three decades. In this Letter I calculate the superfluid velocity part of the transverse force in a way closely related to Laughlin's argument for the quantization of conductance in the quantum Hall effect. A combination of this result, the vortex velocity part of the transverse force found by Thouless, Ao, and Niu [Phys. Rev. Lett. 76, 3758 (1996)], and Galilean invariance shows that there cannot be a transverse force proportional to the normal fluid velocity.