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 $v/c$ expansion 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.