Relativistic superfluid hydrodynamics from field theory

It is well known that the hydrodynamics of a zero-temperature superfluid can be formulated in field-theoretic terms, relating for example the superfluid four-velocity to the gradient of the phase of a Bose-condensed scalar field. At nonzero temperatures, where the phenomenology of a superfluid is usually described within a two-fluid picture, this relationship is less obvious. For the case of a uniform, dissipationless superfluid at small temperatures and weak coupling we discuss this relationship within a φ4 model. For instance, we compute the entrainment coefficient, which describes the interaction between the superfluid and the normal-fluid components, and the velocities of first and second sound in the presence of a superflow. Our study is very general, but can also be seen as a step towards understanding the superfluid properties of various phases of dense nuclear and quark matter in the interior of compact stars.