Faddeev equations for the coupledNN−πNNsystem

We show that the two different formulations of the $\mathrm{NN}-\pi \mathrm{NN}$ system proposed by Afnan-Blankleider and Stingl-Stelbovics lead to a set of three linear coupled operator equations which are identical in form to the Faddeev equations. The resulting equations include the fact that both nucleons are identical and either can emit a pion. They also have dressing for the $\pi \mathrm{NN}$ vertex and $\mathrm{NN}$ and $\pi \mathrm{NN}$ propagators. The final equations are shown to satisfy two-and three-body unitarity.