Hydrodynamic Relations in Superconductivity

We explore the consequences for macroscopic effective Lagrangians of assuming that the momentum density is proportional to the flow of a conserved current. Such a relation holds in models that microscopically contain only one type of charge carrier. We show that such a relation leads to certain universal corrections to the usual effective Lagrangians considered for the description of superfluids. A fully consistent derivation of the superconducting Hall effect predicted by London is given. Some related issues that arise in anyon superconductivity are discussed: the linear Hall effect is derived in a transparent way, and the vanishing of the b term (under appropriate assumptions) is demonstrated formally. Some other possible applications are sketched.