Vortex Dynamics and the Problem of the Transverse Force in Clean Superconductors and Fermi Superfluids

We review the basic ideas and results on the vortex dynamics in clean superfluid Fermi systems. The forces acting on moving vortices are discussed including the problem of the transverse force which was a matter of confusion for quite a time. Finally, we formulate the equations of the vortex dynamics which include all the forces and the inertial term associated with excitations bound to the moving vortex.