From self-consistent covariant effective field theories to their Galilean-invariant counterparts

We discuss how to obtain the nonrelativistic limit of a self-consistent relativistic effective field theory for dynamic problems. It is shown that the standard v/c expansions yields Galilean invariance only to first order in v/c, whereas second order is required to obtain important contributions such as the spin-orbit force. We propose a modified procedure which is a mapping rather than a strict v/c expansion.