Iordanskii and Lifshitz-Pitaevskii forces in the two-fluid model

It has been known since the pioneering work of Onsager and Feynman that the statistical mechanics and dynamics of vortices play an essential role in t he behavior of superfluid and superconductors. However, the theory of vorti ces in quantum fluids remains in a most unsatisfactory state, with many con flicting results in the literature. In this paper we review the theory of T houless, Ao and Niu, which gives an expression for the total transverse for ce acting on a quantized vortex that is in apparent disagreement with the w ork of Iordanskii and of Lifshitz and Pitaevskii. In particular, no transve rse force proportional to Me asymptotic normal fluid velocity was found. We else two-fluid hydrodynamics to study this discrepancy.