Quantized vortices in superfluids and superconductors

We give a general review of recent developments in the theory of Vortices i n superfluids and superconductors, discussing why the dynamics of vortices is important, and why some key results are still controversial. We discuss work that we have done on the dynamics of quantized vortices in a superflui d. Despite the fact that this problem has been recognized as important for forty years, there is still a lot of controversy about the forces on and ma sses of quantized vortices. We think that one can get unambiguous answers b y considering a broken symmetry state that consists of one vortex in an inf inite ideal system. We argue for a Magnus force that is proportional to the superfluid density, and we find that the effective mass density of a vorte x in a neutral superfluid is divergent at low frequencies. We have generali zed some of the results for a neutral superfluid to a charged system.