Sum rule relating pair fluctuations and the superfluid mass density in helium four

We derive a relation between the pairing function χ_q, of which Ristig has recently made a variational calculation for ⁴He, and the contribution of pairing fluctuations to the superfluid mass density in a bose fluid. We have shown that the two fluid hydrodynamic equations are unchanged in the presence of a pair condensate, though the microscopic identification of ρ{variant}_s is changed.