Presently, lattice quantum chromodynamics is the only available tool that allows for calculations of hadron properties, incorporating the non-perturbative nature of the strong interaction in the low-energy regime. However, information about few-hadron dynamics is not directly accessible. Instead, the finite volume energy spectra, extracted from lattice calculations, have to be related to the infinite volume scattering- and decay-amplitudes. Recent years have witnessed rapidly growing theoretical development in formulating three-particle quantization conditions that establish such a connection. Non-relativistic effective field theories (NREFT) naturally provide a convenient framework for their derivation.
In this talk, I shall put the issue of the relativistic covariance of the NREFT formulation under scrutiny. The role of Lorentz invariance is crucial, as only in an explicitly covariant setup the interactions are frame-independent, such that data from moving frames can be analyzed. Within a modified version of NREFT a relation can be derived that allows for the extraction of weak decay matrix elements from lattice calculations, where data from different frames is required.