Galilean currents and charges

According to Noether's theorem, each symmetry of the dynamics comes with an associated conservation law. Despite the importance of relativity symmetries-i.e., invariances under Galileo or Lorentz boosts-their associated conservation laws are never emphasized. Here we clarify the physical interpretation of such conservation laws: there exists a collective coordinate-the center-of-mass position-that undergoes uniform motion. This does not happen for theories that do not obey a relativity principle. As an application, we derive the Noether currents and charges associated with an internal Galilean invariance pi(x) -> pi(x) + b(mu)x(mu)-a symmetry recently postulated in the context of so-called Galileon theories.