The Faddeev equations for the Heisenberg ferromagnet

The Faddeev equations for the three-magnon T-matrix of the Heisenberg ferromagnet with nearest neighbour interactions are derived for the cubic lattice in arbitrary dimensions. The extreme case of spin $\text{1}\text{2}$ is considered and the kinematical restriction, that only one spin deviation per site is possible, has been taken into account rigorously. Hence the T-matrix is unitary and suited for the study of bound state as well as scattering state properties. The analytic solution of the homogeneous Faddeev equations in one dimension is given.