  The forces on the vortex, transverse to its velocity, are considered. In
addition to the superfluid Magnus force from the condensate (superfluid
component), there are transverse forces from thermal quasiparticles and
external fields violating the translational invariance. The forces between
quasiparticles and the vortex originate from interference of quasiparticles
with trajectories on the left and on the right from the vortex like similar
forces for electrons interacting with the thin magnetic-flux tube (the
Aharonov-Bohm effect). These forces are derived in the Born approximation for
phonons from the equations of superfluid hydrodynamics, and for BCS
quasiparticles from the Bogolyubov-de Gennes equations. The effect of external
fields violating translational invariance is analyzed for vortices in the
two-dimensional Josephson junction array. The symmetry analysis of the
classical equations for the array shows that the total transverse force on the
vortex vanishes. Therefore the Hall effect which is linear in the transverse
force is absent also. This means that the Magnus force from the superfluid
component exactly cancels with the transverse force from the external fields.
The results of other approaches are also brought together for discussion.
