Galilean equations for massless fields

Galilei-invariant equations for massless fields are obtained via contractions of relativistic wave equations. It is shown that the collection of non-equivalent Galilei-invariant wave equations for massless fields with spin equal to 1 and 0 is very rich and corresponds to various contractions of the representations of the Lorentz group to those of the Galilei ones. It describes many physically consistent systems, e.g., those of electromagnetic fields in various media or Galilean Chern-Simons models. Finally, classification of all linear and a big group of nonlinear Galilei-invariant equations for massless fields is presented