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The paper reassesses the old but still controversial problem of thetransverse force on a vortex and the vortex mass. The transverse force fromfree bulk quasiparticles on the vortex, both in the Bose and the Fermi liquid,originates from the Aharonov--Bohm effect. However, in the Fermi liquid oneshould take into account peculiarities of the Aharonov--Bohm effect for BCSquasiparticles described by two-component spinor wave functions. There is noconnection between the transverse force (either from free bulk quasiparticlesor from vortex-core bound quasiparticles) and the spectral flow in the vortexcore in superfluid Fermi liquid, in contrast to widely known claims. In fact,there is no steady spectral flow in the core of the moving vortex, and theanalogy with the Andreev bound states in the SNS junction, where the spectralflow is really possible, is not valid in this respect.  The role of the backflow on the vortex mass is clarified. The backflow is aninevitable consequence of a mismatch between the currents inside and outsidethe vortex core and restores the conservation of the particle number (charge)violated by this mismatch. In the Fermi liquid the backflow compensates thecurrent through the core bound states, which is a source of the vortex mass(the Kopnin mass). This results in renormalization of the Kopnin vortex mass bya numerical factor.

Transverse force on a vortex and vortex mass: effects of free bulk and vortex-core bound quasiparticles