Hamiltonian formulation for relativistic superfluids

We give a Hamiltonian formulation of relativistic superfluids free of any constraints, starting from an action principle based on four scalar fields. The main physical objects are two conserved currents---one associated with the flow of particles and the other with the flow of entropy, or heat. The superfluid state is characterized by the condition that the fluid flow be irrotational. There are three implicit relations which must be solved in order to pass from the Lagrangian to the Hamiltonian form of the equations of motion. We consider the weak coupling limit where, the particle and heat components of the fluid behave independently, to find explicit solutions of these implicit relations. We also examine the gauge invariance of the theory.