Singular mechanics and Landau two-fluid model of superfluidity

Abstract

We present a theoretical treatment of the Landau two-fluid model of superfluidity in liquid helium by means of the Dirac formalism. We introduce hydrodynamic considerations in a natural way by means of Lagrange multipliers. All constraints in phase space, in Dirac's sense, are second class and, as a consequence, the Dirac bracket differs strongly from the Poisson bracket. We calculate the Dirac bracket of the canonical variables, putting special interest on the density and the momentum density of the system. Our results generalize the results given by Dzyaloshinskii and Volovik and correct other published results.