Renormalization group and the epsilon expansion of the He II superfluid density

The functional-steepest-descent method is applied to evaluate the Landau-Ginzburg-Wilson, homogeneous and isotropic functional integral describing the partition function of He II near the lambda point, by considering coordinate-dependent mean-field configurations, corresponding to flowing superfluid metastable states with velocity ν, and developing the loop expansion about it. The free-energy density is obtained to the one-loop approximation and this result is then combined with the renormalization-group equations and the epsilon expansion to obtain an expression for the superfluid density, which has the general scaling form rho/sub s/ = t/sup 2beta-nueta/f(ν2/t/sup 2nu/) in which t = T/sub c/-T and where the function f(ν2/t/sup 2nu/) is computed to order epsilon. In the limit of small superfluid velocities ν the Josephson relation is recovered