  We investigate how fields transform under the Poincar\'e group in
nonrelativistic effective field theories of QCD. In constructing these
transformations, we rely only on symmetries and field redefinitions to limit
the number of allowed terms. By requiring invariance of the action under these
transformations, nontrivial relations between Wilson coefficients for both
nonrelativistic QCD and potential nonrelativistic QCD are derived. We show
explicitly how the Poincar\'e algebra is satisfied, and how this gives
complementary information on the Wilson coefficients. We also briefly discuss
the implications of our results, as well as the possibility of applying this
method to other types of effective field theories.
