The hydrodynamic description of a superfluid at non-zero temperature is the two-fluid model, where the two fluids are the superfluid and a normal fluid. The superfluid is a Bose-Einstein condensate, and the normal fluid is a thermal gas of phonons.
I will show how one can translate between the macroscopic two-fluid model and a microscopic field theoretic description, using the simplest field theory that can show Bose-Einstein condensation, namely the complex scalar field.
Questions that will be answered include:
* How can one get two fluids from a single field?
* What is the relationship between the different formalisms that have been proposed for relativistic superfluids?
* What is the role of the Goldstone boson?