Effective field theory for non-relativistic hydrodynamics

Understand

We write down a Schwinger-Keldysh effective field theory for non-relativistic (Galilean) hydrodynamics.

• We use the null background construction to covariantly couple Galilean field theories to a set of background sources.
• In this language, Galilean hydrodynamics gets recast as relativistic hydrodynamics formulated on a one-dimension higher spacetime admitting a null Killing vector.
• This allows us to import the existing field-theoretic techniques for relativistic hydrodynamics into the Galilean setting, with minor modifications to include the additional background vector field.