Galilei-invariant equations for massive fields

Galilei-invariant equations for massive fields with various spins have been found and classified. They have been derived directly, i.e., by using requirement of the Galilei invariance and various facts on representations of the Galilei group deduced in the paper written by de Montigny, Niederle and Nikitin (2006 J. Phys. A: Math. Gen. 39 1-21). A completed list of non-equivalent Galilei-invariant wave equations for vector and scalar fields is presented. It shows two things. First that the collection of such equations is very broad and describes many physically consistent systems. In particular it is possible to describe spin-orbit and Darwin couplings in frames of a Galilei-invariant approach. Second, these Galilei-invariant equations can be obtained either via contraction of known relativistic equations or via contractions of quite new relativistic wave equations.