# Relativistic superfluids, and the connection between finite density and spontaneous symmetry breaking for interacting scalar fields

We study the low-energy effective action for relativistic superfluids obtained by integrating out the heavy fields of a UV theory. A careful renormalization procedure is required if one is interested in deriving the effective theory to all orders in the light fields (but still to fixed order in the derivative expansion). The result suggests a general relation between finite density and spontaneous symmetry breaking for QFTs of interacting scalars with an internal global symmetry.