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 $\pi (x)\to \pi (x)+b_{\mu }{x}^{\mu }$—a symmetry recently postulated in the context of so-called Galileon theories.

Close

PrevNext

View figure in article