In this work we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to 2 þ J → 2 transition amplitudes. We also give various details relevant for the implementation of this formalism in a realistic numerical lattice QCD calculation. Particular focus is given to the role of single-particle form factors in disentangling finite-volume effects from the triangle diagram that arise when J couples to one of the two hadrons. This also leads to a new finite-volume function, denoted G, the numerical evaluation of which is described in detail. As an example we discuss the determination of the ππ þ J → ππ amplitude in the ρ channel, for which the single-pion form factor, F π ðQ 2 Þ, as well as the scattering phase, δ ππ , are required to remove all power-law finite-volume effects. The formalism presented here holds for local currents with arbitrary Lorentz structure, and we give specific examples of insertions with up to two Lorentz indices.

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