Revisiting the Symmetries of Galilean Electrodynamics

Abstract: We determine the symmetries of four different theories: I) Galilean Electrodynamics (GED), II) GED coupled to 5 free static scalar fields, III) Galilean Yang-Mills (GYM), and IV) GYM coupled to 5 interacting scalar fields. We correct some old results in the literature, by finding that the symmetries of GED in a spacetime of generic dimension $d+1$ is always infinite dimensional, and in $3+1$ they correspond to the conformal Milne algebra extended by a spatial dilatation generator, which we call $D_x$. Finally, we comment on how these results fit into the framework of the non-relativistic AdS$_5$/CFT$_4$ correspondence.