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The Faddeev-Reshetikhin model arises as a truncation of strings in AdS_5XS^5.Its two particle S-matrix should be obtained by diagonalizing its Hamiltonian.However this does not happen in a straightforward way. There is a Lorentzviolating term in the Hamiltonian which prevents its plain diagonalization. Wethen find out the most general quartic Hamiltonian that can be diagonalized. Itincludes the bosonic Thirring model as well as another model which shares thesame two particle S-matrix as the Faddeev-Reshetikhin model. We also find a oneparameter family of interactions which lead to non-Hermitian Hamiltonians whichhave unitary S-matrices and are PT symmetric.

On the S-Matrix of the Faddeev-Reshetikhin Model